MSU LIBRARIES .—;_—_ RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES will be charged if book is returned after the date stamped below. GENETIC AND NULTIVARIATE STATISTICAL IEVALUATION OF A PHENOTYPIC RECURRENT SELECTION PROGRAM FOR RECOMBINING ERECT ARCHITECTURE AND LARGE SEED SIZE IN EHAEEQLQS EHLEABIS L. BY George Acquaah A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Interdepartmental Plant Breeding and Genetics Program 1987 DEDICATION To Theresa, my beloved wife, and our kids - Parry and Kwasi. ii ACKNOWLEDGEMENT I came to the Michigan State University because of Prof. n.w. Adams. His paper on "Plant architecture and yield breeding" formed the basis of the research proposal I submitted in partial fulfilment of the requirements of the fellowship which funded my studies. Naturally, MSU was my first choice of American universities at which to study. Even though Prof. Adams was 'no show' at the meeting of IAEA-contracted scientists in Seoul, South Korea, in 1983, for which his paper had been circulated for our considerat- ion, I am very glad I showed up at MSU. I have thoroughly enjoyed the opportunities and challenges the research of- ‘fered me and wish to express my sincere and heartfelt gratitude to Prof. Adams, my major adviser, for having me learn at his feet. The members of my committee deserve special mention, too. Dr. Jim Kelly made the research practically possible. Most of the materials for the recurrent selection were sup- plied by him. In addition, Jim assisted in planting the experiment and guided the selection in the field. Thank you very much, Jim. I liked statistics before coming to MSU but I am leaving here loving it. This is largely due to the effective teaching of Dr. C.E Cress who made the subject iii enjoyable. I also appreciate his help during the data analysis. Dr. Tom Islieb, in addition to making himself available for consultation on statistics and genetics, loaned me his complete set of SAS statistical and graphics manuals. These made my computing tasks a lot easier and I am most gratefull to him. A successful ideotype breeding program has its foundation on sound physiological-genetic knowledge. Dr. James Hanover of the Department of Forestry increased my understanding of the area and helped me appre- ciate the ideotype concept much better and for that I am deeply thankfull. The critical review of the draft of this dissertation by the members of my advisory committee, and especially by my major advisor, Prof. Adams, is very deeply appreciated. The assistance of the technical staff, namely, Mary Lauver and Jerry Taylor, is hereby acknowledged with much thanks. The general support of my colleagues in the bean fraternity cannot be overlooked. I hope we have made friends and established life-long ties for future research cooperation. The work in Guatamala was made possible through the cooperation of Dr. Wallace of Cornell University and Dr. Masaya of ICTA in Guatemala who planted the experiment and assisted in the data collection. The hospitality of espe- cially Dr Masaya and Mr. Fernando Aldano and all the staff iv of the bean group at ICTA extended to me during my stay in Guatamala is deeply appreciated. I am greatly indebted to the University of Cape Coast in Ghana, my employer, for granting me study leave with pay for the duration of my program. The program was made possi- ble principally through funding provided by the Fulbright Hayes Foundation and supplemented by the Hargoes Founda- tion, both of the USA. The research in Guatamala was made possible with travel grants from the Candice Thoman Founda- tion chaneled through MSU. I thank these distinguished educational funding bodies for the invaluable contribution to international education. The generous financial assist- ance provided by the Sage Foundation towards the prepara- tion of this dissertation is hereby acknowledged with much thanks. Finally, and most importantly, I thank God for the great things He has done 1 ABSTRACT GENETIC AND HULTIVARIATE STATISTICAL EVALUATION OF A PHENOTYPIC RECURRENT SELECTION PROGRAM FOR RECOHBINING ERECT ARCHITECTURE AND LARGE SEED SIZE IN BHAEEQLHfi EHLQABIS L- BY George Acquaah Genetic and multivariate procedures were employed to evaluate populations from five cycles of phenotypic recur- rent selection in a dry bean ideotype breeding program. The populations derived from crosses between representa- tives of two distinct germplasm pools, namely, the indeter- minate, small-seeded, narrow-profiled, erect architectural pool, and the indeterminate, decumbent, large-seeded pinto pool, both from the Mesa-American center of domestication. The populations were grown at Michigan State University, East Lansing and at Chimaltenango, Guatemala. Differences in traits at the two locations were due to scale. Multiple regression, corroborated by other multiva- riate procedures, selected hypocotyl diameter, plant height, branch angle, pods on the main stem and pods in the middle third of the plant as the most effective indicators of bean plant architecture. Genetic consequences due to divergence between the two germplasm pools were manifest in the lack of desirable recombinations and poor yield in the early cycles. The principal sources of divergence were seed size and number of seeds per pod. Architectural traits were recovered in 3939 in the original cycle while seed weight was accumulated gradually. Principal factor analysis was used to summarize architectural traits into a height (elon- gation) factor, a structural (skeletal) factor and a dis- tribution (number) of reproductive parts factor. Compensat- ory relationships were encountered among yield and archi- tectural components. Phenotypic recurrent selection was ultimately effective in recombining erect architecture and large seed size. TABLE OF CONTENTS LIST OF TABLES C O O O O O O O O O O O O O O O O 0 LIST OF FIGURES O O O O O O O O O O O O O O O O 0 Chapter I. INTRODUCTION . . . . . . . . . . . . . . . . II. LITERATURE REVIEWED............. 2.1 Botany and evolution of the bean crop and their implications in the breeding of the crop. . . . . . . . . . . . . 2.2 Ideotype breeding: The concept and its implication with special reference to dry bean . . . . . . . . . . . . . . 2.2.1 Anatomy of a bean ideotype 2.3 Multivariate statistics in crop breeding . . . . . . . . . . . . . . 2.3.1 Factor analysis .‘. . . . . . 2.3.2 Principal component analysis. 2.3.3 Discriminant analysis and Mahalanobis' D2 analysis. . . 2.3.4 Multiple regression analysis. 2.3.5 Canonical correlation analysis . . . . . . . . . . 2.4 Recombination analysis . . . . . . . 2.5 Genetic basis for recurrent selection and its implications in the breeding of self-pollinating crops . . . . . . 2.6 Phenotypic recurrent selection in vi Page xi xxiv 10 12 14 18 20 23 25 26 28 Chapter Page ideotype breeding of pinto beans at the Michigan State University. . . 31 2.7 Aspects of the quantitative genetics of architectural traits with special reference to beans. . . . . . . . . . 35 III GENERAL MATERIALS AND METHODS . . . . . . . . 38 3.1 Sources of germplasm . . . . . . . . 38 3.2 Experiment I . . . . . . . . . . . . 40 3.3 Experiment II . . . . . . . . . . . . 43 3.4 Data collection . . . . . . . . . . . 44 3.5 Statistical methodologies. . . . . . . 47 3.5.1 Multiple linear regression . . 48 3.5.2 Principal factor analysis . . 48 3.5.3 Canonical correlation analysis . . . . . . . . . . . 49 3.5.4 Principal component analysis . 50 3.5.5 Canonical correlation analysis. . . . . . . . . . . 51 3.5.6 Mahalanobis' D2 analysis . 51 3.5.7 Other statistical procedures . 52 3.6 Recombination spindle analysis . . . 53 3.7 Quantitative genetic analysis . . . . 54 IV} STABILITY OF BEAN TRAITS. . . . . . . . . . . 57 4.1 Introduction . . . . . . . . . . . . 57 4.2 Materials and methods . . . . . . . . 58 4.3 Results and discussion. . . . . . . . 59 4.3.1 Comparison of the locations. . 59 vii Chapter 4.3.2 Comparison of parents at the locations. . . . . . . . . . . 4.3.3 Changes in magnitude of expression of traits under recurrent selection. . . . . . 4.3.4 Comparison of means for traits from various cycles . . 4.3.5 Comparison of trait means at two locations. . . . . . . . . V. CHANGES IN THE FREQUENCY AND METRIC VALUE OF BEAN TRAITS UNDER RECURRENT SELECTION . . . 5.1 Introduction . . . . . . . . . . . . 5.2 Materials and methods . . . . . . . . 5.3 Results and discussions . . . . . . . 5.3.1 Architectural traits . . . . . 5.3.2 Seed-pod traits . . . . . . VI. IDENTIFICATION OF INDICATORS OF ERECT PLANT ARCHITECTUREOFBEANS.......... 6.1 Introduction. . . . . . . . . . . . . 6.2 Materials and methods . . . . . . . . 6.3 Results and discussion. . . . . . . . 6.3.1 Magnitude of R2. . . . . . . . 6.3.2 Frequency of including a trait in a model . . . . . . . . . . VII. PHENOTYPIC CHARACTER ASSOCIATION AND THE EFFECT OF RECURRENT SELECTION ON ASSOCIAT- IONS IN BEANS O O O O O O O O O O O O O O O 7 C 1 IntrOduction O I O O O O O O O O O O 7.2 Materials and methods . . . . . . . . 7.3 Results and discussion. . . . . . . . viii Page 60 63 82 85 87 87 88 88 88 96 103 103 104 105 105 106 111 111 113 114 Chapter Page 7.3.1 Comparison of correlations among traits at two locations. 114 7.3.2 Patterns of association at two locations . . . . . . . . 126 7.3.3 Canonical correlation analysis . . . . . . . . . . . 136 ‘VIII. ANALYSIS OF RECOMBINATION AMONG BEAN TRAITS 138 8.1 Introduction. . . . . . . . . . . . . 138 8.2 Materials and methods . . . . . . . . 139 8.3 Results and discussion. . . . . . . . 139 8.3.1 Recombination in F2 and F3 populations. . . . . . . . . . 139 8.3.2 Recombination in cycles. . . . 144 8.3.3 Recombination spindle. . . . . 152 IX. IDENTIFICATION OF FUNDAMENTAL AND FUNCTIONAL RELATIONSHIPS IN BEANS . . . . . . . . . . 157 9.1 Introduction . . . . . . . . . . . . 157 9.2 Materials and methods . . . . . . . . 158 9.3 Results and discussion. . . . . . . . 159 9.3.1 Seed-pod traits. . . . . . . . 159 9.3.2 Architectural traits . . . . . 169 9.3.3 All traits combined. . . . . . 185 X. GENETIC DIVERGENCE AMONG CYCLES OF RECURRENT SELECTION OF BEANS . . . . . . . . . . . . . 191 10.1 Introduction . . . . . . . . . . . . 191 10.2 Materials and methods. . . . . . . . 192 10.3 Results and discussion . . . . . . . 193 10.3.1 Divergence among parents . . 193 ix Chapter 10.3.2 Divergence among cycles. XI. HERITABILITY AND GENETIC CONTROL OF BEAN TRAITS. 11.1 11.2 11.3 XII. GENERAL Introduction . . . . . . . . . . Materials and methods. . . . . . Results and discussion . . . . . 11.3.1 Test of dominance and epistasis. . . . . . . . 11.3.2 Broad-sense heritability DISCUSSION . . . . . . . . . . . XIII. SUMMARY AND CONCLUSIONS. . . . . . . . . LITERAWRE CITED I O O O O O O O O O O O O O O APPENDICES . . Appendix Appendix Appendix Appendix Appendix Appendix Appendix Appendix m c: an to «a o m s. Page 199 215 215 216 218 218 218 222 232 237 244 244 257 266 273 278 281 308 311 LIST OF TABLES Table Page 1. 2. 5a. 5b. 5c. 5d. 5e. 6a. 6b. 6C. 6d. 6e. Number of various genetic materials utilized in phenotypic recurrent selection program at MSU. . 32 Location and weather information for the two sites at which the research was conducted. . . . 41 Frequency of selection of a trait by the stepwise multiple regression procedure with architype as dependent variable . . . . . . . . . . . . . . . 107 Architectural traits selected in the parent population by the stepwise multiple regression procedure with architype as dependent variable. 108 Phenotypic character association among bean traits at East Lansing . . . . . . . . . . . . 115 Phenotypic character association among bean traits at East Lansing . . . . . . . . . . . . 116 Phenotypic character association among bean traits at East Lansing . . . . . . . . . . . . 117 Phenotypic character association among bean traits at East Lansing . . . . . . . . . . . . 118 Phenotypic character association among bean traits at East Lansing . . . . . . . . . . . . 119 Phenotypic character association among bean traits at Chimaltenango. . . . . . . . . . . . 120 Phenotypic character association among bean traits at Chimaltenango. . . . . . . . . . . . 121 Phenotypic character association among bean traits at Chimaltenango. . . . . . . . . . . . 122 Phenotypic character association among bean traits at Chimaltenango. . . . . . . . . . . . 123 Phenotypic character association among bean traits at Chimaltenango. . . . . . . . . . . . 124 xi Table Page 7. Sign of correlations among grain yield compo- nents in the cycles . . . . . . . . . . . . . 132 8. Contributions to variance by the first three principal components in parents, F2 and F3. . 141 9. Loadings of the first six most important prin- cipal components in the parents . . . . . . 142 10. Loadings of the first six most important prin- cipal components in C0° . . . . . . . . . . 145 11. Loadings of the first six most important prin- Cipal aCOmpOnODtS in C10 0 e e e e e e e e e 146 12. Loadings of the first six most important prin- cipal components in C2. . . . . . . . . . . . 147 13. Loadings of the first six most important prin- cipal components in C3. . . . . . . . . . . 148 14. Loadings of the first six most important prin- cipal components in C4. . . . . . . . . . . 149 15. Length of PC2 axis in various bean populations. 156 16. Loadings of the first two most important prin- cipal factors in Co for seed-pod traits in East unaing O O O C O O O O O O O O O O O O O O O 161 17. Loadings of the first two most important prin- ciple factors in C1 for seed-pod traits in East Lansing. . . . . . . . . . . . . . . . . . . 161 18. Loadings of the first two most important prin- cipal factors in C2 for seed-pod traits in East lanai-n9. I O O O O O O O O O O O O O O O O O 162 Table Page 19. Loadings of the first two most important prin- cipal factors in C3 for seed-pod traits in East “n.1ng I O O O O O O O O O O O O O O O 0 O O 162 20. Loadings of the first two most important prin- cipal factors in C4 for seed-pod traits in East Lansing. . . . . . . . . . . . . . . . . . . 163 21. Loadings of the first two most important prin- cipal factors in Co for seed-pod traits in Chimaltenango. . . . . . . . . . . . . . . . 163 22. Loadings of the first two most important prin- cipal factors in C1 for seed-pod traits in ChmltanangO e e e e e e e e e e e e .' e e e 164 23. Loadings of the first two most important prin- cipal factors in C2 for seed-pod traits in amltenango . O O O O O O O O O I O O O O O 164 24. Loadings of the first two most important prin- cipal factors in C3 for seed-pod traits in Chimaltenango . . . . . . . . . . . . . . . . . 165 25. Loadings of the first two most important prin- cipal factors in C4 for seed-pod traits in Chimaltenango . . . . . . . . . . . . . . . . . 165 26. Loadings of the first two most important prin- cipal factors in the parents for seed-pod traits O O O O O O O O O O O O O O O 0 O O O O 166 27. Loadings of the first six most important prin- cipal factors in Co in Chimaltenango for architectural traits. . . . . . . . . . . . . . 170 28. Loadings of the first five most important prin- cipal factors in C1 in Chimaltenango for architectural traits. . . . . . . . . . . . . 171 xiii Table 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. Loadings of the first five most important prin- cipal factors in C2 in Chimaltenango for architectural traits. . . . . . . . . . . Loadings of the first five most important prin- cipal factors in C3 in Chimaltenango for architectural traits. . . . . . . . . . . . . . Loadings of the first five most important prin- cipal factors in C4 in Chimaltenango for architectural traits. . . . . . . . . . . . . . Loadings of the first six most important prin- cipal factors in Co in East Lansing for architectural traits. . . . . . . . . . . . . Loadings of the first six most important prin- cipal factors in C1 in East Lansing for architectural traits. . . . . . . . . . . . Loadings of the first six most important prin— cipal factors in C2 in East Lansing for architectural traits. . . . . . . . . . . . . Loadings of the first six most important prin- cipal factors in C3 in East Lansing for architectural traits. . . . . . . . . . . . . Loadings of the first six most important prin- cipal factors in C4 in East Lansing for architectural traits. . . . . . . . . . . . . Loadings of the first six most important prin- cipal factors in the parents for architectural Loadings of the first six most important prin- cipal factors in the parents for all traits . Mahalanobis' D2 distances between parents on the basis of architectural traits. . . . . . . . . xiv Page 172 173 174 176 177 178 179 180 186 187 196 Table Page 40. Mahalanobis' D2 distances between parents on the basis of seed-pod traits . . . . . . . . . . . 196 41. Standardized canonical coefficients for seed-pod traits in parents . . . . . . . . . . . . . . 197 42. Mahalanobis' D2 distances between cycles on the basis of architectural traits in East Lansing. 201 43. Mahalanobis' D2 distances between cycles on the basis of architectural traits in Chimaltenango. 201 44. Standardized canonical coefficients for architec- tural traits in East Lansing. . . . . . . . . . 204 45. Standardized canonical coefficients for architec- tural traits in Chimaltenango. . . . . . . . . 205 46. Standardized canonical coefficients for seed-pod traits at East Lansing . . . . . . . . . . . . 206 47. Standardized canonical coefficients for seed-pod traits at Chimaltenango. . . . . . . . . . . . 206 48. Mahalanobis' D2 distances between cycles on the basis of seedwt in East Lansing . . . . . . 211 49. Mahalanobis' D2 distances between cycles on the basis of seed-pod traits in Chimaltenango . 211 50. Mahalanobis' D2 distances between cycles on the basis of seed-pod traits in East Lansing . 212 51. Mahalanobis' D2 distances between cycles on the basis of all traits in East Lansing . . . . 212 52. Mahalanobis' D2 distances between cycles on the basis of all traits in Chimaltenango. . . . 213 53. Broad-sense heritability estimates for bean traits in six crosses. . . . . . . . . . . . . . 220 Appendix A: 1. 2. 10. 11. 12. 13. 14. 15. .16. 17. Means of traits measured on parents at two locations.. . . . . . . . Means of traits measured locations. . . . . . . . Means of traits measured locations. . . . . . . . Means of traits measured locations. . . . . . . . Means of traits measured locations. . . . . . . . Means of traits measured locations. . . . . . . . Means of traits measured locations. . . . . . . . Means of traits measured locations. . . . . . . . Means of traits measured locations. . . . . . . . Means of traits measured at two locations. . . . . on parents at on parents at on parents at on parents at on parents at on parents at on parents at on parents at on parents at Means of traits measured on parents at two locations. . . . . . . . Means of traits in various cycles at two locations. . . . . . . . Means of traits in various cycles at two locations. . . . . . . . Means of traits in various cycles at two locations. . . . . . . . Means of traits in various cycles at two locations. . . . . . . . Means of traits in various cycles at two locations. . . . . . . . Means of traits in various cycles at two locations. . . . . . . . xvi 245 245 246 246 247 247 248 248 249 249 250 251 251 252 252 253 253 Table Page 18. Means of traits in various cycles at two locations. . . . . . . . . . . . . . . . 254 19. Means of traits in various cycles at two locations. . . . . . . . . . . . . . . . 254 20. Means of traits in various cycles at two locations. . . . . . . . . . . . . . . . 255 21. Means of traits in various cycles at two locations. . . . . . . . . . . . . . . . 255 22. Means of traits in various cycles at two locations . . . . . . . . . . . . . . . 256 23. Means of traits in various cycles at two locations. . . . . . . . . . . . . . . . . . . 256 Appendix B: 1. Architectural traits selected from Co by the stepwise multiple regression procedure with architype as dependent variable . . . . . . . 258 2. Architectural traits selected from C1 by the stepwise multiple regression procedure with architype as dependent variable . . . . . . . . 259 3. Architectural traits selected from C2 by the stepwise multiple regression procedure with architype as dependent variable . . . . . . . . 260 4. Architectural traits selected from C3 by the stepwise multiple regression procedure with architype as dependent variable . . . . . . . 261 5. Architectural traits selected from C4 by the stepwise multiple regression procedure with architype as dependent variable . . . . . . . . 262 6. Architectural traits selected in two crosses by the stepwise multiple regression procedure with architype as dependent variable . . . . 263 xvii Table 7. Architectural traits selected in two crosses by the stepwise multiple regression procedure with architype as dependent variable . . . . . 8. Architectural traits selected in two crosses by the stepwise multiple regression procedure with architype as dependent variable . . . . . Appendix C: 1a. Phenotypic character association among bean traits in the parents. . . . . . . . . . . . . 1b. Phenotypic character association among bean traits in the parents. . . . . . . . . . . . . . 1c. Phenotypic character association among bean traits in the parents. . . . . . . . . . . . . . 2a. Phenotypic character association among bean traits in the F3 0 e e e e e e e e e 2b. Phenotypic character association among bean traits in th. P3 0 e e e e e e e e e e e e e 0 2c. Phenotypic character association among bean traits in the F3 e e e e e e e e e e e e e e 0 Appendix D: Canonical correlation between architectural traits and seed-pod traits in various selection cycles in East Lansing . . . . . . . . . . . . Canonical redundancy analysis . . . . . . . . . Canonical redundancy analysis . . . . . . . . . Squared multiple correlation between the archi- chitural variables and the canonical variables of the seed-pod traits. . . . . . . . . . . . . xviii Page 264 265 267 268 269 270 271 272 274 275 275 276 Table Page 5. Squared multiple correlation between seed-pod traits and the canonical variables of the archi- tectural traits. . . . . . . . . . . . . . . . 277 Appendix E: 1. Loadings of the first six most important prin- cipal components in the F2 . . . . . . . . . 279 2. Loadings of the first six most important prin- cipal components in F3 families . . . . . . . 280 Appendix F: 1. Correlation between principal factors extracted from data from the two locations for seed-pod traits. . . . . . . . . . . . . . . . . . . . 282 2a. Biological concepts associated with principal factors extracted from parents for seed-pod traits . . . . . . . . . . . . . . . . . . . . 283 2b. Biological concepts associated with principal factors in Co at two locations for seed-pod traits O O O O O O O O O O O O O O O O O O O O 2 8 3 2c. Biological factors associated with principal factors in C1 at two locations for seed-pod traits O O O O O O O O O O O O O O O O O O O O 2 8 4 2d. Biological concepts associated with principal factors in C2 at two locations for seed-pod traits O O O O O O O O O O O O O O O O O O O O 284 2e. Biological concepts associated with principal factors in C3 at two locations for seed-pod xix Table Page traits O O O O O O O O O O O O O O O O O O O O 285 2f. Biological concepts associated with principal factors in C4 at two locations for seed-pod traitSO O O O O O O O O O O O O O O O O O O O 285 3. Correlations among factor loadings in Co at two locations for architectural traits. . . . . 286 4. Correlations among factor loadings in C1 at two locations for architectural traits. . . . . 286 5. Correlations among factor loadings in C2 at two locations for architectural traits. . . . . 287 6. Correlations among factor loadings in C3 at two locations for architectural traits. . . . . 287 7. Correlations among factor loadings in C4 at two locations for architectural traits. . . . . 288 8. Biological concepts associated with principal factors in Co at two locations for archi- tectural traits. . . . . . . . . . . . . . . . 289 9. Biological concepts associated with principal factors in C1 at two locations for archi- tectural traits. . . . . . . . . . . . . . . . 289 10. Biological concepts associated with principal factors in C2 at two locations for archi- tectural traits. . . . . . . . . . . . . . . . 290 ll. Biological concepts associated with principal factors in C3 at two locations for archi- tectural traits. . . . . . . . . . . . . . . . 290 12. Biological concepts associated with principal factors in C4 at two locations for archi- XX Table Page tectural traits. . . . . . . . . . . . . . . . 291 13. Correlations among principal factors extracted at two locations in Co for all traits. . . . 292 14. Correlations among principal factors extracted at two locations in C1 for all traits. . . . 292 15. Correlations among principal factors extracted at two locations in C2 for all traits. . . . 293 16. Correlations among principal factors extracted at two locations in C3 for all traits. . . . 293 17. Correlations among principal factors extracted at two locations in C4 for all traits. . . . 294 18. Loadings of the first six most important prin- cipal factors in CO at Chimaltenango for all traitSO O O O O O O O O O O O O O O O O O O O 295 19. Loadings of the first six most important prin- cipal factors in C1 at Chimaltenango for all traitsO O O O O O O O O O O O O O O O O O O O 296 20. Loadings of the first six most important prin- cipal factors in C2 at Chimaltenango for all traits. O O O O O O O O O O O O O O O O O O O 297 21. Loadings of the first six most important prin- cipal factors in C3 at Chimaltenango for all traits O O O O O O O O O O O O O O O O O O O 2 98 xxi Table Page 22. Loadings of the first six most important prin- cipal factors in C4 at Chimaltenango for all traits. . . . . . . . . . . . . . . . . . . 299 23. Loadings of the first six most important prin- cipal factors in Co at East Lansing for all traits. . . . . . . . . . . . . .. . . . . . 300 24. Loadings of the first six most important prin- cipal factors in C1 at East Lansing for all traits . . . . . . . . . . . . . . . . . . . 301 25. Loadings of the first six most important prin- cipal factors in C2 at East Lansing for all traits . . . . . . . . . . . . . . . . . . 302 26. Loadings of the first six most important prin- cipal factors in C3 at East Lansing for all traits O O O O O O O O O O O O O O O O O O 3 o 3 27. Loadings of the first six most important prin- cipal factors in C4 at East Lansing for all traits . . . . . . . . . . . . . . . . . . 304 28. Biological concepts associated with principal factors on Co at two locations for all traits 305 29. Biological concepts associated with principal factors in C1 at two locations for all traits 305 30. Biological concepts associated with principal factors in C2 at two locations for all traits 306 31. Biological concepts associated with principal factors in C3 at two locations for all traits 306 xxii Table Page 32. Biological concepts associated with principal factors in C4 at two locations for all traits 307 Appendix G: 1. Standardized canonical coefficients for all traits at East Lansing. . . . . . . . . . 309 2. Standardized canonical coefficients for all traits at Chimaltenango . . . . . . . . . . . . 310 Appendix H: 1. Test of dominance and epistasis in cross 1. 312 2. Test of dominance and epistasis in cross 2. 313 3. Test of dominance and epistasis in cross 3. 314 4. Test of diminance and epistasis in cross 4. 315 5. Test of dominanec and epistasis in cross 5. 316 6. Test of dominance and epistasis in cross 6. 317 xxiii LIST OF FIGURES Figure 1. 2a. 2b. 10. 11. 12. 13. Comparison of the representative parents from the germplasm pools utilized: Midnight (left) represents the architectural germplasm pool while UI 114 represents the pinto pool. . . . . . . . Classification of multivariate procedures . . . Diagramatic presentations of various multivariate procedures. . . . . . . . . . . . . . . . . . . Model for recombination spindle analysis using raw trait scores. P1, P2 8 parents; X,Y,Z = traits in which parents exhibit most contrast. . . . . Average total number of nodes in the upper third of plants in different cycles at two locations. . Average total number of pods per plant in dif- ferent cycles at two locations. . . . . . . . . Average length of internodes in the upper third of plants in different cycles at two locations. Average length of internodes in the middle third of plants in different cycles at two locations. Average length of internodes in the lower third of plants in different cycles at two locations. Average yield of plants in different cycles at two locations. . . . . . . . . . . . . . . . . Average plant height in different cycles at two locations. . . . . . . . . . . . . . . . . . Average number of pods in the upper third of plants in different cycles at two locations. . Average height of the lowest pod of plants in different cycles at two locations . . . . . . Average branch angle of plants in different xxiv Page 11 13 16 27 65 65 66 66 67 67 68 68 70 Figure 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. cycles at two locations. . . . . . . . . . . . Average number of nodes in the middle third of plants in different cycles at two locations. . Average hypocotyl length of plants in different cycles at two locations. . . . . . . . . . . . Average pod length of plants in different cycles at two locations. . . . . . . . . . . . . . . Average pod width of plants in different cycles at two locations. . . . . . . . . . . . . . . Average loo-seedwt of plants in different cycles at two locations. . . . . . . . . . . . . . . . Average architype rating of plants in different cycles at two locations . . . . . . . . . . . . Average hypocotyl diameter of plants in different cycles at two locations. . . . . . . Average number of nodes in the lower third of plants in different cycles at two locations. . Average number of pods in the middle third of plants in different cycles at two locations. . Average number of seeds per pod of plants in different cycles at two locations. . . . . . . Average number of pods in the lower third of plants in different cycles at two locations. . Average number of pods on the main stem of plants in different cycles at two locations. . Average number of days to maturity of plants in different cycles at two locations. . . . . Comparison of parents from the two germplasm pools utilized and a recombinant selection from cycle three. Midnight (left) representing the architectural pool and UI 111 (left) repre- senting the pinto pool. The cycle three selection is in the center. . . . . . . . . . . Frequency of architype rating in five cycles of recurrent selection. . . . . . . . . . . . . . XXV Page 70 71 71 73 73 74 74 75 75 77 77 78 78 79 83 89 Figure 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. Frequency of hypocotyl diameter in five cycles of recurrent selection. . . . . . . . . . . . Frequency of branch angle in five cycles of recurrent selection. . . . . . . . . . . . . . Frequency of pods on the central axis of plants in five cycles of recurrent selection. . . . . Frequency of plant height in five cycles of recurrent selection. . . . . . . . . . . . . Frequency of pods in the lower third of plants in five cycles of recurrent selection. . . . . Frequency of pod width in five cycles of recurrent selection. . . . . . . . . . . . . Frequency of pod length in five cycles of recurrent selection. . . . . . . . . . . . . Frequency of number of seeds per pod in five cycles of recurrent selection. . . . . . . . . Frequency of loo-seedwt in five cycles of recurrent selection . . . . . . . . . . . . . . Recombination analysis in F2 and F3 generations of been crosses using principal components. . . . . . . . . . . . . . . . . . Recombination analysis in the cycles using principal components . . . . . . . . . . . . Plot of the first two canonical discriminant functions for parents using seed and pod traits for grouping. . . . . . . . . . . . . . . . . . Plot of the first two canonical discriminant functions using architectural traits for grouping. . . . . .'. . . . . . . . . . . . . Plot of the first two canonical discriminant functions using seed and pod traits for group ing O O O O O O O O O O O O O O O O O O O O Plot of the first two canonical discriminant functions using all traits for grouping. . . . . xxvi Page 89 92 92 95 95 97 97 99 99 153 154 200 202 207 210 CHAPTER ONE INTRODUCTION The plant breeder is in the business of nudging nature toward his or her specific breeding objectives, manipulat- ing the genetic text of his or her plants to varying de- grees depending on the special objectives, with the ulti- mate goal of optimizing economic production. Before the breeder sets out to develop a crop culti- var certain considerations must be understood, of which physiological-genetic, environmental and cultural are para- mount. The former has to do with the biological machinery of the plant which is fueled by the meteorological, abiotic and biotic environmental components, for harnessing by the farmer within cultural limits. The biological machinery may be made to work more efficiently through genetic manipulat- ion based on sound physiological principles, for optimal exploitation of the environment, the uncertainties of the latter notwithstanding. Agriculture and culture are bedfel- lows and thus crop cultivars must be amenable to particular cultural practices. Sometimes, the breeder may encounter a situation in which a combination of plant attributes and environmental 1 “I- u. p a .e em" a ‘4. OI. '\e I... 7‘. as. at 'O ' .IO 8. O" :‘~ .‘v. factors will "nick" and translate into optimal economic yield. This is the basis of the concept of ideotype breed- ing, the development of a ”designer cultivar" for a speci- fic cultural and environmental milieu. Such a breeding program has been embarked upon at the Michigan State University and has successfully produced commercial navy and black bean cultivars for mechanized farming under favourable conditions in the "Thumb" region of Michigan (Adams, 1982; Kelly e; 1]., 1984). In achieving this goal, the architecture of the navy bean was transform- ed from a low-growing, branching, determinate bush, into a sturdy, erect form. Induced mutagenesis played a signifi- cant role in producing basic germplasm for the subsequent development of the new cultivars (Adams, 1982). The success in navy and black beans prompted the application of the ideotype concept to the breeding of the pinto class of beans for upright architecture in order to facilitate di- rect combine harvesting. A phenotypic recurrent selection program was designed to achieve recombination between the erect plant architecture of the navy bean and the larger seed size and pattern of the pinto bean (Kelly and Adams, 1987) . This breeding program was initiated without the benefit of some basic genetic information. The program quickly encountered some problems of genetic origin. The genetic recombination between the two gene pools did not Al~' J... .g. e. ‘ I.‘ g: ~~I "40'. .N In‘ Os“ ll- 'es. ‘fl‘. '0 3": .Ol‘ ‘.~ Nu. AC ‘4 occur as freely. as was expected. Nonetheless, it appeared to have succeeded although several cycles of selection ‘were :required. Certain 'traits distinguish. a. plant 'with desirable architecture from plants with less desirable architecture. These traits include hypocotyl diameter, height, branch angle, number of branches, pod distribution and many more. When selecting plants on a phenotypic basis it is necessary to know which traits are effective predict- ors of the desired objective and how they are inherited. A knowledge of the associations among the characters along with their genetic control will help in adopting effective and efficient breeding procedures. The literature is defi- cient in such information as it pertains to dry beans. When quantitative traits such as those defining plant architecture are considered, numerous relationships, both favorable and adverse, are bound to be encountered. Study- ing the traits independently may not reveal the true nature of interrelated effects and there is the need, therefore, to consider them together. The latter objective is accom- plished by the elegant procedures of multivariate data analysis. In view of the foregoing, the research herein report- ed, using materials from the Michigan State University pinto been breeding program, sought to bridge the informa- tion gap by investigating the following: 1. Follow, through successive cycles of recurrent select- ion, the changes in frequency and metric value of plant traits as recombination coupled with selection occurred. 2. Determine the statistical associations among morpholo- gical traits . 3. Study the changes in the pattern of association of traits under selection. 4. Determine the stability of the traits in various envi- ronments. 5. Identify the pattern of recovery of plant architecture and the cycle in which recombination between the two di- verse gene pools took place. 6. To identify the traits which are good indicators of bean plant architecture. 7. To determine whether evidence exists for linkage be- tween plant architecture and seed size (or any association that could be attributed to genetic linkage). 8. To determine the genetic control of the plant traits under consideration. To this end, simple correlation and multivariate sta- tistical procedures, namely, principal component analysis, principal factor analysis, canonical correlation, canonical discriminant analysis, Mahalanobis' D2 analysis, and multi- ple regression were employed to evaluate selections from five cycles of phenotypic recurrent selection planted at two locations. Some information was also obtained from a second experiment comprising a 2 x 3 factorial cross among representative parents from the gene pools. CHAPTER TWO LITERATURE REVIEW 2.1 BOTANY AND EVOLUTION OF THE BEAN CROP AND THEIR IMPLICATONS IN THE BREEDING OF THE CROP. Dry bean (W W L.) has papilionaceous, hermaphroditic and cleistogamous flowers which are self- fertilizing (Singh and Gutierrez, 1984). This relatively closed breeding system suggests that the crop may be prone to genetic vulnerability and that breeders should make an effort to broaden the genetic base of cultivars to guard against adverse consequences. Singh and Gutierrez (1984) observed in Latin America, the primary center of bean diversity, that small-seeded bean types are predominant in the relatively warmer lowlands of Central America, Mexico and over most of Brazil and Venezuela. This region is also called the Meso-American region, Brazil and Venezuela not included. The medium and large-seeded bean forms, they observed, abound in the moderately cooler environments of Mexico, Colombia, Equador and Peru. This region is also termed the Andean region, Mexico not included. In addition to this geographical distribution of dry bean forms, genetically controlled incompatibility has been 6 found to occur in crosses between the two groups by va- rious workers, including Davis and Frazier (1964) and Coyne (1965) . Singh and Gutierrez (1984) proposed a two complementary dominant gene (0L1 , DLZ) system of control for this apparent incompatiblity. The small-seeded bean group carries the 0L1 allele while the medium- and large- seeded group carries the complementary DLZ allele, and in concert produce dysgenic effects called dwarf lethals. Gepts (1984) has further shown that two centers of domestication of dry beans exist which can be differentiat- ed electrophoretically on the basis of a major seed storage protein (phaseolin) type. The Mexican center of origin is characterized by a Sanilac (S-type) gel banding pattern while the Andean group possesses a Tendergreen (T-type) banding in gel electrophoresis. Incompatibility in hybridi- zation occurred when the parents in a cross exhibited the opposite phaseolin protein types described (Gepts, 1984). Singh and Gutierrez (1984) suggested that this genetic situation in dry beans may have had significant evolution- ary implications through the imposition of restricting genetic barriers to inter-group hybridization. They further suggested that should it become necessary to use parents from the two gene pools in a breeding program the problem may be circumvented by using a suitable parent as a bridge between the two pools. Kelly and Adams (1987) also suggest- ed that parents, to the extent possible, be selected from within the same center of domestication to minimize hin- drance to genetic recombination. The germplasm utilised in the present study is cha- racterised by the S-type phaseolin marker and derives from the Central American-Mexican center of origin, according to Kelly and Adams (1987). 2.2 IDEOTYPE BREEDING: THE CONCEPT AND ITS APPLICATION WITH SPECIAL REFERENCE TO DRY BEAN. Ideotype breeding may be viewed as the science of custom designing of crops. Donald (1968) was credited with the origin of the con- cept of breeding plants with model characteristics (ideo- type) known to influence photosynthesis, growth and econo- mic production. As Mock and Pearce (1975) further elabo- rated, ideotype breeding involves defining a crop product- ion environment, designing a plant model from morphological and physiological traits known to influence performance in that environment, and combining the traits in one plant type. On the subject of ideotype breeding Adams (1982) added that the strategy has to do with the number, size, shape, structure, arrangement and display of particular plant parts. The ideal plant architecture, he further stated, has no value on its own in terms of economic yield unless such a structure translates into accentuated physio- logical responses and eventually into productive superiori- ty. In other words, a crop ideotype should maximize both biomass and partition. In embarking upon the ideotype concept the breeder, as Adams (1982) pointed out, implicitly operates on the pre- mise that an agronomic situation is identifiable which will especially favor the genetic model characteristics and confer upon the "designer cultivar" superior fitness. In this respect, ideotype breeding should aim at the improve- ment of yield potential and stability of a crop (Adams, 1973)..A crop ideotype will exploit efficiently the envi- ronmental resources (Donald, 1968). Concepts such as this are not without their detractors. . Coyne (1980) , questioning the ideotype concept, stated that information on the relative merits and contribution of many of the morphological (architectural) and physiological genetic yield components is inadequate to contribute to the design of a model plant with superior yielding ability. Such objections notwithstanding, the ideotype strategy has been successfully employed to improve many crops, including wheat (Donald, 1968), rice (Jennings, 1964), maize (Mock and Pearce 1975), barley (Donald, 1979) and dry bean I; e . 1 8‘“ ll . I 'O" ‘Q' ‘ us.. 10 (Adams, 1973, 1982; Kelly g; 11: 1984). 2.2.1 Anatomy of a bean ideotype Adams (1973), in designing a bean ideotype for mech- anized agriculture in favourable environments in the mid- west region of the USA, enunciated certain plant morpholo- gical attributes. These were later revised (Adams, 1982) as follows: 1. Tall, with main stem nodes numbering 12-15. 2. Moderate number of basal branches, 3-5. 3. Indeterminate growth, large overall plant size, but not with extended vine growth. 4. ‘Upper' internodes longer and. more numerous than basal internodes. 5. Thick stem diameter. 6. Narrow plant profile. 7. High values of first-order yield components in keeping with commercial class requirement. 8. Leaf area index near four at flowering time. Some of the architectural attributes may be seen in Figure 1. This ideal plant design has subsequently been referred to as an "architype" (Adams, 1982). Singh (1982) described three distinct plant habits in beans as type I (bush), type 11 Figure 1. Comaparison of the representative parents of the germplasm used: Midnight (left) represents the architecture pool while UI 114 (right) represents the pinto pool. ' v 0' e.‘ .6 l 0“‘ IO‘S",‘ ..e we. I u“ . v" I I, ’gEeOeu' n ‘Eelly ‘P'.\ II ed" I q ‘ h‘ ‘4‘ Rivas et‘. v‘ers 'au“ . ‘~\.. 53:8 l 12 II (indeterminate, erect) and type III (indeterminate, prostrate). The type II plant habit has shown superior yielding stability across diverse locations, in dry beans (Kelly 33; 3]., 1987) and in soybeans (Beaver and Johnson, 1982). ‘ 2.3 MULTIVARIATE STATISTICS IN CROP BREEDING Multivariate analysis is the branch of statistics con- cerned with analyzing multiple measurements that have been made on one or several samples of individuals (Cooley and Lohnes, 1971). The variates are inter-dependent among them- selves so that we cannot split off one or more from the others and consider it by itself (Kendall, 1957). However, handling data with multicolinearity can be unwieldy and some meaningful summarization is required. Multivariate techniques have been classified by Cooley and Lohnes (1971) as presented in Figure 2a. Kendall (1957) further summed up the models in the figure as follows: A. Interdependence models - represented by models in qua- drat Ql (principal component, factor analysis). B. Dependence models - represented by models in quadrats 02, QB, and Q4 (include multivariate analysis of variance, classification functions, discriminant function, multiple correlation, canonical correlation). These models may be 13 POPULATION ONE POPULATION TWO OR MORE POPULATITIONS Principal component Multivariate analysis of variance ONE Factor analysis SET Discriminant functions V Classification functions A R I 01 02 A ------------------------ 1 .- ___________________________ B 03 Q4 L E S Polynomial fit Multivariate covariance Two Multiple correlation OR MORE SETS Canonical correlation Multiple partial cor- relation Figure 2a. Classification of multivariate procedures (Cooley and Lohnes, 1971). 14 summed under the general regression theory and differ from the other set of models in the sense that the researcher may specify predictor variables as well as criteria varia- bles. Various multivariate procedures have been used inde- pendently or along with others to effectively summarize and interprete data in plant breeding and genetics. Those used in this study will be briefly reviewed. 2.3.1 Factor analysis A variable is explained to the extent that its varian- ce can be attributed to an identifiable source (Geer, 1971). Factor analysis may be use to find ways of identi- fying fundamental and meaningful dimensions of a multiva- riate domain Cooley and Lohnes, 1971). Factor analysis is a decision-making model for ex- tracting subsets of covarying variables (Guertin and Bai- ley, 1970). This method entails reformulating a set of natural or observed inter-correlated variables into a new set (usually fewer in number) of independent variables such that the latter set has certain desired properties speci- fied by the analyst (Stopher and Meyburg, 1971). Factor analysis is frequently accomplished by first Performing a principal component analysis (PCA) and using 15 the resulting principal factors as a set of reference axes for determining the simplest structure of factors (Cooley and Lohnes, 1971). Factors are hypothetical constructs (Harman, 1976). In Figure 2b, the factor analysis model (b) assumes that a set of observed variables x can be inter- preted as dependent on a set of unobserved variables f (de Gear, 1971). The f variables are called factors and accord- ing to Guertin and Bailey (1970) are of three types: a. General - shows all variables have sizeable loadings on this factor. b. Group - this factor has 2, 3 or few variables with size- able loadings. c. Specific - one variable only gets loaded on this factor alone. From the factor patterns names may be assigned to each factor. Naming a factor is merely a mnemonic conve- nience (Guertin and .Bailey, 1970). The factor analysis should be conceptually interpretable, that is, the compo- nents or factors should be named sensibly such as to convey information to both the analyst and audience (Stopher and Meyburg, 1971). There is no test of significance of factor loadings so the selection of level of 'cut off' is arbitrary. Guer- ‘tin and Bailey, 1970) suggest that factors be cut off only until 95% of the complete principal axes variance is ac- counted for except with variables of 50 or more. Multiple correlation. CAIEWQQH- Figure 2b. Diagramatic presentations of various multivariate procedures (Geer, de 1971) . 35.35 a 1.. O‘Aui , ‘h‘ «.5 , 0". t...‘ ’8‘. . Ill A6 ‘6 17 Bramel it a]. (1984), while observing the scanty re- ports on the use of principal factor analysis (PFA) in plant research, used the procedure to identify plant cha- racters associated with seed yield (and, hence, have some predictive powers for yield) in three stem termination types of soybeans. The authors also reported that by using PFA they reduced the number of variables from 25 to eight. Further, they suggested that grouping of traits into con- cepts and then selecting traits for developing prediction equations from within the grouping would result in equat- ions that have measurements of different biological func- tions instead of repeated measurements of characters re- lated to the same func-tion in the plant. The last proce- dure has the effect of reducing bias due to multicolineari- ty (Bramel g; 31, 1984). Rao and Paroda (1982) used the centroid method of factor analysis to analyse the pattern of diversity in 40 genotypes of cluster bean (W W (L.) Taub) based on nine characters. They ob- served changes in factor loadings from one environment to another but none-the-less found that the compositions of the variables in the factors remained the same. The coeffi- cients of the residual matrix were negligible after the first three factors had been extracted, the three account- ing for 98.88% of the original variance. Walton (1971) used the maximum likelihood method of 25133 '3‘.e“ edu- W:ee nee... O .35 n‘ 4.26 A... vyH‘E l'n‘ , fit“ . 0‘) w o 18 estimating communalities in a factor analysis of wheat cha- racters to determine predictors for yield selection. He cautioned that information from factor analysis be taken to relate, in detail, to the range in genetic variability test-ed. In dry beans, Denis and Adams (1978) used image cova- riance matrix procedure to extract eigenroots and eigenvec- tors in PFA to search for and identify patterns of morpho- logical characteristics in a set of bean cultivars which are related to yield. A total of 22 morphological charac- ters and 16 cultivars were used. Only factor loadings of values above 0.72 were used in identifying and naming a conceptual factor. Three principal factors were retained and named weight (or size), number, and plant architectural factors, respectively. The plant architectural factor was loaded by variables including number of long internodes, average long internode length and total number of inter- nodes. Linear correlations among loading coefficients in principal factors from data at two locations were highly significant and mostly positive. 2.3.2 Principal component analysis The PCA is a common ordination numeric technique 19 which reduces the dimensions of multivariate data by remov- ing intercorrelations among the traits under study and thereby enables multidimensional relationships to be plot- ted on 2 or 3 principal axes (Harman, 1976). PCA is the same as the PFA analysis except the factors are not rotat- ed. If the only objective of a factor analysis is to pro- vide a reduction in the number of variables to be used for prediction or description, the PCA is appropriate (Guertin and Bailey, 1970). The number of factors extracted from a PCA is usual- 1y equal to the number of variables employed in the inter— correlations. Each principal component is a linear com- bination of the original variables. The first principal component (PC1) has the largest variance of any unit-length linear combination of the observed variables (Rao, 1964). Akoroda (1983) used PCA to identify the principal characters which account for the major variation among yellow yams (Diggggnga ggygngngig Lam). Data based on 20 accessions and 49 characters were analysed. The first three factors accounted for only 56.14% of the original variance and these were used to construct a three dimensional ordi- nation of the accessions. Using the magnitude of eigenva- lues of the first three principal axes, he was able to select six characters for a metroglyph from which he iden- tified clusters of accessions similar to what was observed 1Erom the PCA analysis. 20 Adams (1977) used a modification of the PCA (Adams and Wiersma, 1978) to estimate distances among dry bean culti- vars to serve as an index of genetic homogeneity for the crop in various regions of the USA. PCA was used in a more conventional way by Ghaderi gt 31 (1984) to reveal quality traits of navy and pinto beans. Loadings of 15 quality traits in 12 principal components were examined. The results indicated that quality traits, namely, dry characters, soaking characters and cooking characters were independent, having loaded in separate axes. This prompted the authors to suggest a tandem select- ion procedure to be followed by construction of selection indices for a breeding a program. 2.3.3 Discriminant analysis and Mahalanobis' 02 analysis This is a dimension-reduction techinique related to principal component analysis and canonical correlation (sas, 1935). According to Spoher and Meyburg (1971) , discriminant analysis has two assumptions: 1. A population is made up of two subpopulations 2. It is possible to find a linear function of certain mea- sures and attributes of the population that will allow an “5:1 ~- V3.31 a: .‘ d. H, ‘1 "1‘ , eu‘.' lars ?E:e' m.‘ I 21 observer to discriminate between the two subpopulations. They further pointed out that the procedures are not de— signed for seeking population groupings (as is the case in cluster analysis) because the population has already been grouped (for example into cycles as in the present study). The solution is nothing but a principal component solution applied after transformation to spherical variance (that is, the error variance is normalized to identical value in all directions) according to de Geer (1971). Mahalanobis' D2 statistic is often a part of the discriminant analysis procedure and is used in order to indicate the biological distance between separated groups. Lee and Kaltsikes (1973) used D2 estimates to discern divergence among durum wheat (m m L.) culti- vars, while Ghaderi g; a], (1984) used it to estimate the genetic distance between parents in dry beans (W5, We, L.) beans (2191; Lab; L.) as an indicator of the of the in- herent capacity of their hybrids for superior performance. To achieve the latter, the relationships be- tween 02 estimates for eight cultivars and heterosis for various traits in their F2 progenies were studied. Vairavan gt a]. (1973) used the canonical discriminant analysis along with D2 estimates to study the nature of divergence in rice (m m L.) germplasm. Just as With PCA, the first two canonical variables extracted re- 22 present, geometrically, the axes along which the separation of the groupings is greatest (Walters and Evans, 1978) . When the first canonical variables account for most of the total variation (about 90% or more) the grouping based on the first two vectors would amply serve this purpose (Vairavan g; 11, (1973). In dry beans, Walters and Evans (1978) used canonical variate analysis to evaluate beans from various countries, using eight characters. Plotting the first two canonical variates, they found it to be a reasonable reflection of the 'distance' between samples from the eight countries studied. Ghaderi gt a1 (1984) used a canonical discriminant function to indicate the effects of location on quality traits. The same cultivar grown in two locations was distinctly separated along the canonical discriminant function on a location basis. Ramagosa g; a], (1986) used canonical discriminant analysis to classify sugarbeet (B333 W L.) . plants within environments. Multivariate analyses are sometimes used to support each other. Narayan and Macefield (1976) used canonical factor and D2 analyses to evaluate 5477 chickpea (919g; m L.) lines on the basis of eight characters re- lated to firness and yield, for adaptive responses and genetic divergence. Plant type was found to be the most important character affecting genetic divergence between geographical groups. Ghaderi e; a; (1982) , in studying 23 environmental response patterns in commercial classes of common bean, used canonical analysis to support evidence from a cluster analysis. The first two canonical variates in the study accounted for 88.8% of the total variation. Navy and pinto bean classes fell into distinct groups with a significant D2 estimate of 8.20 between them. 2.3.4 Multiple regression analysis This is a model-developing procedure which allows the researcher to specify a dependent variable as well as a set of predictor variables (Figure 3). From the latter, variables which best indicate the former may be identified. There are four general procedures available for model- fitting: a. Forward selection:- The procedure begins with a zero- variable model and includes independent variables as their calculated F statistic satisfies the specified minimum significance level. Once selected, a variable cannot be dropped. b. Backward elimination:- This is the reverse of the for- ward process. An all-variable model is started with and systematically reduced through elimination of variables whose F-statistic fails to satisfy a specified level of significance, which was 0.10 in this study. 24 c. Stepwise:- This variation of the forward procedure does not guarantee a place for a variable in a model once selec- ted. A variable may be ejected from a model at any time when, upon evaluation, it fails to produce an F-statistic which is significant at a specified level due to the inclu- sion of new variables. d. Maximum R2:- This technique produces a series of models which eventually includes all variables in the model. The first, a one-variable model, will include the variable which produces the highest R2 (coefficient of determina- tion) and follows with a two variable model, the latter adding on the variable which produces the greatest increase in R2. The difference between this procedure and stepwise is that in the former, all switches are evaluated before any switch is made, while in the latter the 'worst' vari- able may be removed without considering what adding the 'best' remaining variable might accomplish (SAS,1985). These stepwise model selection methods were conduct- ed on a PRS cycle basis including architectural traits only. Variables selected by each procedure were further evaluated on the basis of the magnitude and significance of their F-statistic. Those retained were compared among the four iterations and pooled together to produce a list of architype-influencing variables for each cycle. The five lists were compared and summarized on the basis of frequen- cy of occurrence in the cycles to determine which variables 25 were important in all cycles and thus are major indicators of bean plant architecture. Multiple regression analysis may suffer from bias due to multicolinearity and thus preceding it with factor ana- lysis to group traits and then selecting from the groupings for prediction equations may be advisable (Bramel gt 91.1, 1984). Welton (1971) used factor’ analysis and. multiple stepwise regression in the suggested complementary way to determine dependence relationship between yield, its compo- nents and other morphological structures in wheat. Lee and Kaltsikes (1973) also employed stepwise regres sion and factor analysis to identify potent indicators of yield in F1 and F2 diallel populations of durum wheat (Initials mm L.) . 2.3.5 Canonical correlation analysis This analysis is a generalisation of the multiple correlation procedure (de Geer, 1971) . The technique was developed by Hotelling (1936) to analyse the relations be- tween two sets of variables drawn from the same subjects. An assumption is made that there are unobserved variables dependent on a known set of variables x, and determining another known set, y. The intermediating umobserved vari- ables are used to canalize the influence of set x on set y 26 (de Geer, 1971). Model c in Figure 3 illustrates this last point. A comparision of models b and c shows that factor analysi hidden in canonical analysis (de Geer, 1971) and may be used along with factor analysis (Cooley and Lohnes, 1971). 2.4 Recombination analysis Anderson (1939) first proposed the concept of the recombination spindle and presented a model for it. He pro- posed that in the absence of restriction to free recombina- tion among traits, all possible recombinants, according to the genic differences between parents for the traits, should, theoretically, be attained in the F2 such that the vortices of a correlation cube (a hyperspace) are occupied. In reality, however, there are usually restrictions to free recombination, as enunciated elsewhere in this disserta- tion, whose effects reduce the number of recombinants such that the cube is only partially filled, in an ellipsoidal fashion (a spindle shape), as shown in Figure 4. It must be pointed out that in any genetic system, extreme recombin- ants occur less frequently than the others and hence the density of the recombinants will be decreased at the mar- gins of the ellipsoid as compared to its center. 27 Figure 3. Model for recombination spindle analysis using raw trait scores. P and P - parents ; x, y, and z = traits in which parents e ibit e most contrasts. 28 2.5 GENETIC BASIS FOR RECURRENT SELECTION AND ITS IMPLICA- TIONS IN THE BREEDING OF SELF-POLLINATED CROPS. Recurrent selection is a cyclic breeding procedure of which phenotypic recurrent selection (PRS) is one and per- haps the simplest of the types. As a breeding procedure it has two main purposes (Briggs and Knowles, 1967) which are: 1. to increase the frequency of superior genes in the population, and 2. to increase the chances for genetic recombination to occur. Each cycle comprises two general steps: 1. evaluation and selection of parents, and 2. intermating of selected parents . Intermeting in each cycle coupled with selection en- ables the purposes of recurrent selection to be achieved. In PRS, evaluation is solely visual (or on a phenotypic basis without progeny testing) and hence is especially useful for traits of high heritability (Briggs and Know- les, 1967). Significant handicap in employing PRS (and for that matter all types of recurrent selection) is the diffi- culty of obtaining a sufficient number of successful cros- ses (Khadr and Frey, 1965). Recurrent selection has been successfully used to im- prove quantitative characters in self-pollinated crops 29 (Miller and Fehr, 1979: Kenworthy and Brim, 1979: Sullivan and Bliss, 1983). VandeLogt gt a]. (1984) observed that numerous agronomic traits in crop plants are influenced by genes segregating at many loci, causing the variation in segregating generations to be continuous or quantitative in nature. It would be useful adjunct information to know the degree of linkage and nature of the gene action involved in these traits. The breeding method adopted will be influenced by the presence or absence and type of linkage (Croissant gt a1, 1971). If coupling relationships predominate for a particu- lar character, the existing combinations are usually de- sired. Hansen (1959) observed that if parents are elite, significant linkages would be in coupling phase. A breeding method such as the backcross will keep favorable gene blocks intact. A preponderance of additive genetic varian- ce and coupling phase linkage suggests a different breeding approach from a preponderance of dominance variance with repulsion phase linkage (VanderLogt g; :1, 1984). New genic recombinations will be required when repulsion phase link- age predominates. Presumably, blocks of favorable alleles are present in the two sets of parents in the last situat- ion (Hansen, 1959). The need for intermating in breeding programs for self-pollinating crops has been quite widely discussed. 30 Jensen (1970) stated that the lack of intermating beyond the initial cross, as is the case in systems for breeding self-pollinated crops such as mass selection, pedigree and single seed descent, limits the recombination options to those that are residual in isolated lines of descent fol- lowing meiosis of the hybrid plant. Intermating has been shown to break up linkage groups. Miller and Rawlings (1967) reported dissipation of initial linkage disequilibrium upon intermating two divergent in- bred lines of cotton. Generalizing, Hanson (1959) concluded from a theoretical study of breaking of initial linkage blocks that at least four cycles of intermating will be required to accomplish substantial breakup of linkage blocks in self-pollinated crops. As to the generation in which intermating should start, Hanson (1959) favored an early generation, F2, while Pederson (1974) cautioned that from a two-locus theory study, intermating in the F2 will be effective only if close linkages are predominantly in the repulsion phase of a multi-locus character. Such intermating will result in increase in the relative frequency of desirable homozygotes after repeated self-fertilization. Kelly and Adams (1987) acknowledged the disadvantage of intermating in the 82 without selfing by stating that desired characters are not necessarily fixed by then so 31 that 82 parents may not serve efficiently as genetic do- nors. On the other hand, they found the procedure to quick- en the breeding program by enabling them, with the help of a winter nursery, to obtain one cycle per year, in addition to increasing the chance of genetic recombination between heterozygous parents. The actual selection process may be done visually or with the aid of a selection index, the latter being very laborious. Kelly and Adams (1987) suggested that when the desired traits are easily recognizable, selecting on a phenotypic basis has the advantage of allowing the breeder to evaluate large populations, thereby increasing the chance of finding desired recombinant types. 2.5 PHENOTYPIC RECURRENT SELECTION (PRS) IN IDEOTYPE BREEDING or PINTO BEANS AT THE MICHIGAN STATE UNIVERSITY (MSU). The above breeding program is the subject of evaluat- ion in this dissertation. The details of the program, whose objective was to recombine the large seed size of the pinto been with the desirable erect plant architecture of the navy/black, have been presented in a paper by Kelly and Adams (1987). A summary of the materials and methods, as 32 well as results, is presented herein to provide a basis for discussion. Table 1 summarizes this program. The base population (Co) was established by making 124 genetically different crosses between nine pinto parents, 16 architypes and six intermediate types. Forty four percent of these crosses were either three or four-way crosses. Table 1. Number of various genetic materials utilized in the PRS program at MSU. Year 1980- 1981- 1982- 1983- 1984- 1981 1982_ 1983 1984 1985 Parents 27 133 169 108 109 Crosses 124 267 136 344 600 $1 populations 55 351 399 bulk bulk 81 individuals # 13 277 338 94 57 $1 selections 271 1,272 524 1,064 402 #: figure shown x1000 - number of individuals planted Cn: where C a cycle and n - stage of recurrent selection. 33 By using a winter nursery, one cycle of recurrent selection was obtained per year. Selection was done in the $1 generation and the progeny from the selected individuals (82) crossed (large-seed selections with architypes) to generate the next cycle. To maintain adequate variability for traits from the two sources of germplasm, less desirable recombinants (good architecture with smaller than desired seed size and desir- able seed size with poor architecture) were chosen as pa rents. Plant selections were evaluated on the basis of maturity (early, medium, late), plant habit (type I, II, III), architecture (compressed, architype, ragged), height (short, medium, tall), pod number, and location of pods. The selection criteria were modified to include seed shape and disease resistance (rust) after C3. The results at the end of each recurrent selection cycle are presented below, where Cn designates the cycle and the stage of recurrent selection and Sn the level of selfing. C031: - No favourable recombinants found: plants showed predo- minantly parental characteristics. - Compromise selection made for certain architectural 34 types with smaller seeds and likewise for pinto, to main- tain the desired seed type in the population. - Seed size range for small-seeded selections was 22-25 gm/loo seeds. C181: - Progress made for highly heritable traits such as color of seed testa and architype. - Recombinants with good architype rating and small pinto-like seeds were found. - Seed size range was 23-25 gm/100 seeds. C281: - Architypes still had small seeds (30gm/100 seeds). - Suggested, based on the size of the population and the low frequency of desired recombinants, that a tight linkage would exist between genes for architype and small seed characteristics. - Considered advancing the selections through more re- current cycles since seed size is controlled by additive genes (Coyne, 1968) and also, according to Motto gt :1, (1978) is accounted for by at least 10 factors. 35 C351: - Selected 1064 recombinants with good architecture and large seed size (29-53gm/100 seeds) out of a population of 94,000 individuals. The pinto parents averaged 38gm/100seeds. - Further identified 280 individuals with good architype and superior seed size. Reflecting on this breeding program, Kelly and Adams (1987) observed that progress of recovery of the architype trait was not characterised by gradualism (or partial step- by-step recovery) but rather, the complex traits comprising architype were recovered in;;gtg. 2.7 ASPECTS OF THE QUANTITATIVE GENETICS OF ARCHITECTURAL TRAITS WITH SPECIAL REFERENCE TO BEANS. Adams (1982) remarked that little is known about the degree to which architectural traits in bean may be asso- ciated as linked effects in inheritance. Harmsen (1983) re- ported a very significant and positive correlation between hypocotyl diameter and yield in beans. Internode length on the main stem was not significantly associated with bean yield. She also observed significant heterosis in the F1 for nodes on the main stem, pods on the main stem and plant 36 height. Pod number was highly determined architecturally by number of nodes (or leaves) according to Adams (1982). He also reported that the main stem number of nodes correlated highly with plant height. By including some tropical culti- vars the number of main stem nodes correlated negatively and significantly with number of effective (fruit-bearing) branches. Ghaderi and Adams (1981) reported high broad-sense heritability for plant height (80%), pod length (97% ), number of branches (75%), hypocotyl diameter (84%), number of seeds per pod(74%), main stem nodes below 15cm (81%) in dry beans. Narrow-sense heritability of 75% was reported for seed weight in cowpea (yigng nngtigglata L.) by Drabo gt :1 (1984). Using generation means analysis, Ghaderi and Adams (1981) reported, preliminarily, that plant height and hypo- cotyl diameter were affected by both additive and dominant gene action. The results were not the same for all crosses. Dominance effects were present in number of nodes below 15cm while pod length and number of nodes above 15cm exhi- bited additive effects. Croissant and Torrie (1971) pre- sented evidence for repulsion phase linkage between height and yield and dominance effects for height and seed weight in soybean. Dickson (1967), working with snap beans, found addi- tive gene control of seed number per pod while Drabo gt g1 37 (1984) reported that seed weight in cowpea was predominant- ly under additive gene control but with significant domi- nance and additive x additive epistasis. Seed weight in cowpea was inherited quantitatively, small seed size being partially dominant to large seed size (Aryeetey and Laing, 1973: Drabo gt g1, 1984). Aryeetey and Laing (1973) report- ed also that seed size in cowpea was controlled by 10 pairs of genes. This conclusion was reached on the basis of an estimate of the number of effective factors (K) proposed by Mather (1973). CHAPTER THREE GENERAL MATERIALS AND METHODS 3.1 SOURCES OF GERMPLASM Two experiments were conducted utilizing germplasm drawn from two diverse gene pools whose charateristics were described by Kelly and Adams (1987) and are herein summa— rized as follows: A. Architecural germplasm source: - Small-seeded navy and black architectural types which range between 18 - 22 gm/100 seed. - Type II classified indeterminate plant habit. - A dominant main stem with an upright branching pattern. - 2 - 3 branches angled acutely upwards. - Tall (50 - 55 cm) and producing nodes vertically rather than laterally. - Pods not set predominantly in the lower nodes but 38 39 distributed throughout the plant canopy and sufficiently high off the ground to facilitate direct harvesting. - Thick hypocotyl. - Thick tap root. - 6 to 8 seeds per normal pod. B: Pinto germplasm source: - Large-seeded pinto cultivars averaging 40 gm/100 seeds. - Type I or III plant habit. - Flatter seed shape. - Pinto seed color: variegated dark brown on light tan seed color. In addition to genetic materials from these two germ— plasm pools, other lines or cultivars with characteristics not strictly allied with either source were incorporated. These included a small-seeded, single-stem, indeterminate line (791583) from Cornell University and a breeding line, A 35. In 1980, a phenotypic recurrent selection (PRS) breed- ing program was started at MSU with the objective of deve- loping a large-seeded erect pinto bean utilising materials from the two germplasm pools described above. Table 1 (adapted from Kelly and Adams, 1987) summarizes the 4O breeding program. I joined this program at the cycle three (C3) stage. The original cycle (Co) was reconstituted using 16 and nine parents from the achitectural and pinto source populations, respetively. Remnant sed lots for each succssive cycle were obtained from storage. The first three cycles (Co to C2) contained predominantly architectural types since desirable recombinants with large seed and the preferred architecture were not found in these cycles. To maintain the desirable pinto seed size in the population, plants with mediocre architecture but large seed size were also selected and advanced in these cycles. Selection pressure and target traits were changed from one cycle to another according to the progress made towards attaining the breeding goal. 3.2 EXPERIMENT I This experiment was conducted at two locations whose geographic and meteorological characteristics are presented in Table 2. A second location in Guatemala was excluded from the analysis because of very poor plant stand in the field. 41 Table 2. Location and weather information for the two sites at which research was conducted. Location East Lansing Chimaltenango (Michigan, USA) (Guatemala, CA) Longitude 84° 36'W 90° 48'W Latitude 42° 47'N, 14° 38'N Elevation 255 m asl 1793 m asl Temperature # l9.44° C 19.10° C Precipitation # 243.59 mm 232.60 mm # : monthly average during growing season In this experiment, selections from five cycles were evaluated in the field. The first four cycles were produced as described by Kelly and Adams (1987). The original cycle, Co, was reconstituted in the 1983/84 growing season in East Lansing because original remnant seed of that cycle was not available. The appropriate parent materials were planted in pots in the green house in October of 1983 followed by intermating between the two sets of germplasm in a factor- ial design. The F1 seeds were planted in the greenhouse in .1984 to produce 51 seed from field planting. 42 All the S1 phenotypic selections were threshed indi- vidually and kept in separate seed envelopes. One hundred envelopes were randomly selected from each cycle and four sets (replications) of single seed bulks created. The bulks were field planted in separate rows at a spacing of 20cm within rows and 50cm between rows. The rows were completely randomized and planting was done by a tractor drawn seed planter. There were four rows (replications) of each cycle, consisting of 100 selections randomized within each row and bodered on both ends by a standard variety. Each parent had only two rows. In effect, each plant was considered as a plot. The experiment in East Lansing was planted in summer of 1985 and harvested in fall, 1985. The Chimaltenango experiment was planted in May, 1986 and harvested in August 1986. For practical reasons, the Guatemala study comprised 50 81 lines randomly selected from the 100 planted at East Lansing. At maturity, the plants were pulled up and tied in bundles of about 10 plants each and hung on wires in a field laboratory until the time for data collection. All the listed traits were measured on each individual plant. A total of 1900 plants were measured at East Lansing and 800 at Chimaltenango. These included parents from each of the two gene pools. 43 3.3 EXPERIMENT II This experiment was conducted at East Lansing begin- ning in the Fall of 1983. Two cultivars (Olathe and UI 114) representing the pinto gene pool, and two varieties and a line (C-20, Midnight and X80149) representing the archi- tecture gene pool, were planted in the greenhouse and intermated in a factorial design. Sixteen F1 seeds of each of the six crosses were planted in the field in the summer of 1984. In the fall of 1984, 80 F2 seeds (five seeds per F1) were planted in the greenhouse to generate materials for planting F3 families in the following season. The final planting of this experiment in the field was made in the summer of 1983 at East Lansing, Michigan. Each set of six crosses comprised four sets of each parent, 16 F2 populations and 80 F3 families, giving a total of 104 entries per combination. The planting was done in a 25 x 25 simple lattice design. Each plot consisted of a single row of five plants spaced 20 cm apart in the row and 50cm between rows. There were a total of 625 rows per replicat- ion including one filler row. At maturity, the three inner plants in each row were uprooted and handled as described for Experiment I. 44 3.4 DATA COLLECTION The same kinds of data were collected for both experi- ments at both locations except for a few additional data at Chimaltenango. Only post-harvest data were taken, as fol- lows: 1. Plant height - Distance between the soil level and the top of the central axis excluding the vine. 2. Architype rating - A scale of 1 - 5 was employed based on an intuitively composed index. A rating of 1 was least representative, while a rating of 5 was most representative of the type which has been described previously as 'archi- type'. 3.Number of branches per plant - A count of primary bran- ches. 4. Branch angle - Angles were drawn on a board with the help of a protractor. Placing the central axis of a plant on the 90° line and the node with the branch to be measured on the 90° - 0° intersection, the inclination of the branch to the central axis was determined. The larger the value, the wider the plant profile. 5. Hypocotyl length- Measured as the distance between the soil level and the lowest branch position on the main stem. 6. Hypocotyl diameter- Determined by placing the portion 45 just below the cotyledonary node against a ruler. 7. Lowest pod height- Distance from soil level to the point of pod attachment of the lowest pedicel. 8. Pod distribution - Each plant was divided into three equal sections based on height and the pods in each sec- tion, namely, upper, middle and lower, were counted and recorded. 9. Number of pods on the main stem - Total number of pods after branches had been removed. 10. Node distribution on the central axis- The central axis was divided as in (8) and the nodes in each section counted 11. Length of internodes on the central axis - The average length of internodes in each of the three sections in (10) was determined. 12. Pod width - Six pods (two from each section) were picked and measured across a seed locule in the mid-section of each pod and averaged. 13. Pod length - The distance between the point of attach- ment to the pedicel and the base of the beak was measured for each pod and averaged over the six pods used in 12. 14. Number of seeds per pod - The number of seeds in each of the six pods used for the pod dimension measurements *were counted and averaged. 15. loo-seed weight - 50 seeds were randomly selected and weighed after equilibrating to 10% moisture content, and 46 expressed as loo-seed weight. 16. Plant yield - Total seed weight per plant at 10% moist- ure. 17. Maturity - The average days to physiological maturity averaged over all plants in the group. (Taken at Guatemala only). A list of abbreviated names for the variables des- cribed above. which are used in this dissertation is pre- sented below: 1. HEIGHT - plant height (cm) 2. ARCHITYPE - architype rating 3. NBRANCH - number of branches 4. ANGLE - branch angle 5. HYPOLEN - hypocotyl length (cm) 6. HYPODIAM - hypocotyl diameter (mm) 7. LOWPODHT - lowest pod height (cm) 8. Pod distribution: a. PODSUP - number of pods in the upper third of the plant b. PODSMID - number of pods in the middle third of the plant c. PODSLOW - number of pods in the lower third of the plant 47 9. PODSMAIN - number of pods on the central (main) axis 10. Node distribution: a. NODESUP - number of nodes in upper third of plant b. NODESMID number of nodes in middle third of plant c. NODESLOW - number of node in lower third of plant 11. Internode length (cm): a. INTNODUP - internode length in upper third of plant b. INTNODMID - internode length in middle third of plant c. INTNODLOW - internode length in lower third of plant 3.5 STATISTICAL HETHODOLOGIES The Statistical Analysis System (SAS) package instal- led on the MSU IBM 3090 180 VM mainframe computer was used for most of the analysis. In addition, the MSTAT statistic- al package developed at MSU in collaboration with the ‘University of Norway was used for data management prior to ‘the mainframe work as well as for basic statistical analy- Sis. 48 3.5.1 Multiple linear regression The SAS (1985) STEPWISE procedure was used. With the architype rating taken as the dependent variable and all architectural traits as independent variables, the object- ive of this analysis was to determine which of the inde- pendent variables (x's) have predictive value for plant architecture (y). A model was developed for each cycle separately as well as for parents and F3 populations. Traits that were included in a model were ranked according to the magnitude of the partial F estimate. The frequency of inclusion of a variable in a model in the five cycles was computed. 3.5.2. Principal Factor Analysis (PFA) The PFA technique of SAS (1985) was used. Prior commu- nalities (the amount of variance of a test shared with all others in a common-factor space) were estimated using squared multiple correlations of each variable with all other variables. Factors were extracted by the method of principal components using the mineigen criterion: all factors with eigenvalues of 1.0 or less were eliminated. The principal factors are called eigenvectors and an eigen- value or latent root is the sum of squared factor loadings. 49 The retained factors were then submitted to orthogonal rotation about their origin by the varimax method. The process has the effect of increasing the magnitude of the large variable loadings while diminishing the size of the small ones. Factors extracted later contain a higher pro- portion of error (Guertin and Bailey, 1970). The factor scores were standardized to unit variance. The rotated pattern (table showing linear composition of variables in terms of factors in the form of regression equations), factor structure (table of correlations between variables and factors), variance explained by each factor, and, the original and calculated communalities, were ob- tained for each cycle. The analysis was performed using all the selected variables together in one run and separately for two subsets of variables classified as architecture and seed-pod traits. 3.5.3 Canonical Correlation Analysis (CCA). Mathematically, the canonical correlation technique finds a linear compound of the x-variable set that has the maximum correlation with a linear compound of the y-varia- ble set (de Geer, 1971). This linear combination is called a canonical variable. The SAS (1985) procedure CANCORR was used to perform 50 that analysis. After identifying the first canonical variable, the procedure continues by finding a second set of canonical variables, uncorrelated with the first pair, that produces the second highest correlation, and so on. Canonical correlation may be conceived of as a stepwise procedure (Cooley and Lohnes, 1971) . The canonical corre- lation coefficients were standardized and a canonical re- dundancy analysis performed to examine how well the origin- al variables are predicted from the calculated canonical variables. The analysis was performed on each cycle inde- pendently using data from Experiment I only, and architect- ural traits and seed-pod traits as the two sets of varia- bles. 3.5.4 Principal Component Analysis (PCA). Each principal component is a linear combination of the original variables. The SAS (1985) PRINCOMP for PCA was used to compute principal components from a correlation matrix. A covariance matrix is not standardized and hence not invariant under scaling (de Geer, 1971). The analysis produces the eigenvalues of the correlation matrix (the discriminating power of the axes), the difference between successive eigenvalues, the proportion of variance explain- ed by each eigenvalue, as well as the cummulative propor- tion of variance explained, for interpreting the data. 51 3.5.5 Canonical Discriminant Analysis (CDA). Given a classification variable, cycles, and quantita- tive variables (architectural traits and seed-pod traits) the SAS (1985) CANDISC routine derives canonical variables (linear combinations of quantitative variables) that summa- rize between-class variation in much the same way that principal components summarize total variation. variation between the classification variable is maximized with res- pect to the variation within it. The canonical variables are derived in the same way as described for canonical correlation. The classification variable in this study was cycles. Three sets of variables were analysed, the first for seed- pod traits, the second for architectural traits and the third for a combination of the two. Aplot of the first two canonical variables was made in each case. Wilks' lambda test was performed to test the significance of the discri- minating power of the measurement battery for the grouping criterion. 3.5.6 Mahalanobis' Dz. In this study, the SAS (1985) MAR option was specified in the CANDISC procedure to obtain the generalized distanc- es among the various grouping criteria. The steps involved 52 according to Narayan and Macefield (1976) are: a. Uncorrelated linear combinations (y's) were obtained by pivotal condensation of the common dispersion matrix of correlated variables (x's). b. The mean values for all the traits specified were trans- formed into the mean values of a set of uncorrelated linear combinations (y's). c. The D2 between the ith and jth populations for k charac- ters was calculated as 2 2 0 ij ' E0111; " th> t 1 3.5.7 Other statistical procedures used. a. Simple correlations: Simple correlations among all traits were estimated by the Pearson procedure using the SAS (1985) CORR procedure. 53 b. Frequency analysis: The MSTAT statistical package was used to obtain fre- quency classes for all traits on a cycle basis. For each trait, the frequencies were plotted using the Plotit graph- ics package and the cubic spline procedure to obtain smooth curves . c. Mean separation: Trait means were computed on a cycle basis and compar- ed using the Duncans multiple range test (DMRT) as test criterion. 3.6 RECOHBINATION SPINDLE ANALYSIS. In this study, a modification of the model proposed by Anderson ( 1939) was used. Data from Experiment II were submitted to a PCA, analysing parents, Fz's and F3's sepa- rately. The first PC has the largest variance of any unit- length linear combination of the observed variables, ac- cording to Rao (1964). With PC 1 as a regression line, the variance contributed by the remaining PCs may be taken to represent deviations from the regression line. Plotting the 54 PC scores in multi-spacial configuration such that the vortices are occupied by parents displaying contrasting traits and the PC 1 as the principal axis or the regression line from which the other PC's project at right angles, their lengths being proportional to their contribution to variance, an ellipsoid is produced. Since the length of each PC in a hyperspace is equivalent to its eigenvalue, each successive PC axis is shorter than the preceeding one. If the first two PC's account for most of the variation, a two-dimensional plot would suffice, otherwise, a three dimensional model should be considered. The bulge of this ellipsoid indicates the extent of recombination that ocur- red in the population after intermating. A similar analysis was performed on data from Experi- ment I. 3.7 QUANTITATIVE GENETIC ANALYSIS Data from Experiment II were used in this analysis to obtain information on gene action and heritability. The data were first submitted to analysis of variance and then the variance due to the mean was partitioned into the contri- butions by the contrasts below which were tested by the t- test to indicate the significance of gene action, as fol- lows: 55 a. Test of dominance: Na—e b. Test of epistasis: F3 vs 2’ (F2 + MP) where P1 - navy parent P2 - pinto parent MP - mid-parent c. Broad sense heritability (H) H - ((VR'2 -2WP1 + VP2)) / (VFZ) = vg/vp 56 Where VFZ, VPl and VPZ a variance of F2, P1 and P2, res- pectively, and V9 and V? - genotypic and phenotypic varian— ce, respectively (Knowles and Briggs, 1967). CHAPTER FOUR STABILITY OF BEAN TRAITS 4.1 Introduction The observed phenotype for a trait is produced from an interaction between the genotype and the environment in which the trait is evaluated. Traits, to varying extents, are environmentally labile and may be expressed to varying degrees in different environments. Cultivar testing pro- grams evaluate materials at a number of locations and for several years within the same location to determine the stability of the cultivar and its performance for desired traits. An ideotype breeding program is, by definition, orga- nised for a specified environmental and cultural situation. However, for a specified objective such as architecture development, there may be certain fundamental and salient features of the design which would be applicable to a wide variety of situations. These features would have to be stable in different environments to be useful in this suggested manner. 57 58 The purpose of this study was to determine if changes in the magnitude of expression of traits in different environments was due to scale (expression of a trait con- sistently lower or higher at one location) or rank (expres- sion of a trait inconsistent - higher and lower values crisscrossing environments). 4.2 Materials and methods Data from Experiment II were utilized in this study. Representative parents from the two germplasm pools were compared within each location. These parents were: N1 - X80149 P1 = Olathe N2 - Midnight P2 = UI 114 N3 - C-20 P3 - Ouray where N and P represent navy/black and pinto, respectively. Only Midnight and UI 114 were tested in East Lansing. Owing to the large difference between locations, geno- type x environment interaction was not considered a useful estimate. The five recurrent cycles were also compared on the basis of average expression of each trait. In addition, the trend of change in the expression of traits were com- pared for the means of cycles at the two locations. 59 The Duncan's multiple range was the test statistic em— ployed to discriminate among trait means in this study. 4.3 Results and discussion 4.3.1 Comparison of the locations The two locations, East Lansing in Michigan and Chi— maltenango in Guatemala, differed mainly in latitude and elevation, the former being at a higher latitude while the latter was at a higher altitude (Table 2). East Lansing, located in the temperate midwestern USA, experienced humid and warm conditions during the growing season. The day length in this region was longer than in Guatemala during the period in question. Chimaltenango is located in the tropics. Despite the big difference in elevation of over 1000m, the difference in average temperature during the growing season was only very slight (less than one degree). The average precipitation differed only slightly. For both meteorological variables, higher values were recorded at East Lansing. The means of these variables do not indicate that the two environments were dissimilar. Any difference observed in this study may be due to differences in the diurnal temperatures as well as the conditions at critical 60 stages in the plant growth, including emergence, early growth and flowering. Day length differences would induce maturity differences, the plants in East Lansing being delayed in maturity, and, with prolonged growing season, growing to larger sizes. 4.3.2 Comparison of the parents at two locations Trends in response of been plant characters to differ- ent environments were similar in nearly all cases. Culti- vars in the navy class were generally taller than those from the pinto class at the Chimaltenango location (Append- ix A, Table 1). The two classes were of similar height at East Lansing. Plants at the East Lansing location were generally taller than those at Chimaltenango. Cooler tempe- ratures at Chimaltenango may have slowed down plant growth resulting in shorter plants, while plants at East Lansing displayed a more vigorous growth. The shorter day length also contributed to the shortness of plants by causing plants to mature early. Architype rating was higher for the navy group than for the pinto group at both locations (Appendix A, Table 1) . Further, the rating was higher at East Lansing for the navy group but lower for pinto as compared to the scores at Chimaltenango. The difference is 61 due largely to height effects. Tallness is one attribute of good architecture and it affects other traits such as lowest pod height and pod distribution in the plant profile which were all considered in the rating of architecture. Shorter plants tended to have pods bunched together and set lower on the plant and, thus, appeared less architectural- ly desirable. Plants branched considerably more at the East Lansing location than at Chimaltenango (Appendix A, Table 2). This is attributable to more vigorous plant growth at the former than at the latter location. The navy group, generally, had ' more branches than the pintos at Chimaltenango. With regard to hypocotyl length (measured as lowest branch height) there was variability in the groups even though, consider- ing the locations together, it appears the pinto group tended to branch nearer to the ground than the navy (Ap- pendix A, Table 2). Parents from the architectural germplasm source had larger hypocotyls (hypodiam) and set their pods higher above the ground (lowpodht) than the pinto parents (Append- ix A, Table 3). The larger value for lowpodht at Chimalte- nango than at East Lansing may be due to the fact that with more vigorous growth at the latter location, the plants got more viny and pulled branches farther down so that pods were nearer the ground. 62 The navy cultivar had a narrower plant profile than the pinto cultivar at East Lansing, whereas P2 had a profile narrower than all the navy varieties in Chimalte- nango (Appendix A,. Table 4). The pintos, it should be recalled, had fewer branches at that location and this may have contributed to the narrower plant profile than the navy parents. The long vines of the pintos caused them to produce fewer nodes in the upper third of the plant (Ap- pend-ix A, Table 4) . Shorter internodes and hence more nodes increases the erectness of a plant and may account for why parents from the architectural group had more nodes (Appendix A, Table 5). The trends in pod distribution were similar at the two locations. The architectural varieties bore more of their pods in the upper two-thirds of the plant while the pintos bore most of their pods in the lower two-thirds of the plant (Appendix A, Tables 6 and 7). It appears the pintos yielded poorly at Chimaltenango. Their pods set poorly as indicated by podslow in Appendix A, Tables 6 and 7. Generally, the navy group set more pods on the main stem (podsmain) as indicated by the results in Appendix A, Table 7. 63 Internode lengths were generally longer throughout the plant in the pinto group than the navy group (Appendix A, Tables 8 and 9). Some navy parents had long internodes, especially in the upper and middle parts of the plant. Parents from the pinto group, generally, had wider and longer pods but fewer seeds per pod than the parents from the navy group (Appendix A, Tables 9 and 10). The pintos also had higher seed weight (seedwt) and matured earlier than the navy parents (Appendix A, Tables 10 and 11). The late maturity is attributable to increased number of pods in the upper third of the architectural types. 4.3.3 Changes in magnitude of expression of traits under recurrent selection. Trends in the behavior of bean plant characters across cycles of recurrent selection were very similar at the two locations. On the basis of the patterns of change, the traits were assigned to four general groups as described bellow. Where the trends were not similar for the two locations, the East Lansing trend, which was based on a much larger sample, was chosen to represent the group. 64 a. Traits which decreased in magnitude of expression before subsequently increasing. Traits in this group generally decreased in magnitude of expression from C0 before eventually increasing in value in the advanced cycles. They included nodesup, totpods, intnodup, intnodmid, intnodlow, yield and height (Figures 4 to 10). These traits may be further reduced to two, namely, yield and height, since the others are components of these. Totpods is a component of yield while internode measure- ments reflect plant height. Yield decreased in the early cycles before increasing in the later ones because there was a lack of substantial recombination between large seed size and architecture in CO, with the result that plants selected for good architecture had small seeds. Further, the high-yielding pinto group was Characterised by pods predominantly set in the lower third of the plant and since this was one of the traits selected against, the early cycles were poor-yielding. In the advanced cycles, as deli- brate efforts were made to increase seedwt and number of pods in the top two-thirds of the plant, yield began to increase. This trend may also be explained with reference to the thoughts of Mather ( 1973) alluded to earlier, who hypothe- sized the existence of functionally-integrated or 'rela- tionally-balanced ' gene blocks. The lack of substantial 'l’otol number of pods/plant. 65 l‘.‘ Hush. rem Avg.no.nodeehwm.cm 0 I 2 4 flgm4.Av«ogenunberolnodeshUu uppertflrdolplmtslndlflerentcydee and at two locations. 35.0 e—e Len-lug e—e Chimaltenango 33.0 - 28.0 - 23.0 - l 8.0 o 0 l 2 I 4 t» O/de figure 5. Total number of pods per pleat in dilterent cycles and at two locotlone. 66 Avg. length at We h meet ”*4 (cm) -‘-1 .q L-t 2r 3 we. figureEAverogelengtnothternodee htheupperthirdoiplanteindlflemt cycleeandattwolocations. 9‘ 9‘ P ‘1 o c o 'o 1 1 -1 Avg. length oi Internodee in middle third (cm) 9‘ o H Lanehg e—e Chimaltenango A \_/ r fi 1 2 +1 I 3 Cycle c figute 7. Average length oi lnternodee in the middle third at plants in dliierent cycles and at two locations. ‘\ M-bngtheihternedeehleserthbd(un) Avg. plant yield (gm) 67 3.0 H testa e-e W 3,5. 2,04 1.5 o i 5 i 4 :5 (Nels Figure 8. Average length oi internodes intheloeerthirdolplontshdiflerent cycles and at two locations. e—e Lonelng 43.0 " CII " 9. 38.0- 33.0- 280-4 i 23.0.. 18.0 r I u i i 3 4 Li Cycle Figure 9. Average yield at plants in diilsrsnt cycles and at two locations. M- NO!“ Wt (an) Avg. no. pads in upper third oi plant Egg; 1 881:3 N lei-1 s.- -_-_ Hts-um l 0"! We ”9“" l0 Average plant height in “"0“"! cycles and at tea location. d . e—e Lansing e-e Chimaltenango 7 4 5 .1 5 .. 4 .4 ‘ _ 3 j 2 l l I r 0 l 2 3 4 Li Cycle Figure ll. Average number oi pads in the upper third oi plants in diiisrsnt cycles and at two locations. 69 recombination in the early cycles may in fact be due to what Kelly and Adams described as " a 'linkage-freeze' upon free and random recombination for effects regulated by genes in the integrated linkage segments". An effect of recurrent selection is to concentrate desirable genes in a population. With time, the adaptive gene complexes were regrouped in some of the advanced cycle selections, restor- ing them to peak functional status. At that stage, plant yield started to increase. b. Traits which increased in magnitude of expression from the original cycle before subsequently decreasing. Traits in this group included podsup, lowpodht, branch angle and nodesmid (Figures 11 to 14). This trend is attri- butable to the fact that a selection objective was to displace pods in the lower third of the plant to the upper parts while maintaining a narrow plant profile. As seedwt increased and the pods became longer, wider and heavier, the plants assumed the branch angle characteristic of the pinto parents, thereby decreasing lowpodht as well as branch angle. The number of pods in the upper-third of the plant (podsup) had to decrease in the advanced cycles because 70 v“ iO-i M°~Wflwfld(un) 3 a 5 i i 5 r s we. ”awakens-Worm,“ oi plants in alierent cycles aid at two locations. so H Lansing re maltenango i754 g l g 70- 55 r 0 ir 2 5 4 ‘J Qcie Figure l3. Average branch angle oi plants in dliisrcnt cycles and at two locations. 71 .5 .. Ht.“ 1 “W 34.0- 3““ “in 32.5 E 2.0 i i 5 5 i 5 Cycle Avg. hypocotyl length (cm) Figureu.~erogenurnberoinodeehthe mlddlethlrdoiplmtsindiierentcycles ondattwolacatlans. 5.5 H Lansing e-e Chimaltenango 5.0 -‘ 4.5 - 4.0- 3.5-1 3.04 2.5 2.0 us—I fi-n ‘- I 3 Cycle 0-1 00—! Figure 15. Average hypocotyl length oi plants in diiisrsnt cycles and at two locations. vi 72 with more pods in that region, maturity time was delayed. Late maturing plants were not selected or were discarded during evaluation in the field laboratory, after harvest- ing. c. Traits which increased in magnitude from the original cycle to the advanced cycles. These traits, generally, showed a progressive increase in mean value from Co to C4 and included hypolen, podlen, podwidth, seedwt, architype, nodeslow and hypodiam (Figures 15 to 21) . Architecture and large seedwt (size) were the principal selection objectives in the breeding program. The multiple regression analysis indicated hypodiam as one of the principal indicators of plant architecture. It was not surprising, therefore, that architype rating, hypodiam and seedwt showed a trend of general increase from Co to C4. Seed size was estimated as loo-seedwt. In addition to size, the shape that was desired was flatish and not- kidney-like. The drop in C2 may be a result of discarding large seeds which did not meet other qualities. From C2 onwards, the curves show a steady increase in seedwt (Fi- gure 18). Pod length had to increase progressiveLy to accommo- date the increase in seedwt. With longer pods, plant bran- Ches needed to be set well above the ground so that the Avenue-mush) 73 12.0- 11.5- 11.04 10.5-i 10.0 9.5 9.0 K Avg. pod width (cm) Figure d-w 5 5 Me On 9 16. hrsroge pod length oi plants in dliiererit cycles and at two locations. 15.0 14.5- 14.0: 13.54 13.0“ 12.5~ 12.0-1 11.54 11.0- e—eLonslng "We 10.5 che Figure 17. Average pod width oi plants in dilierent cycles and at two locations. 71+ [i as . _l .e . l .s . l .e tn L Aug. too-nu we.» (gm) '4 1 us . +1 (I “FT {S we. mummies-muons”:- indiierentcyclesandattwalocodons. Avg. architype rating Figure 19. Average O'ChllyfiO rating at plant: 4 “Lancing HChimaltenango 4‘1 37 /———‘ 31 4 2.4 2 l i T 0 l 2 3 . :5 CyCIe in ailierent cycles at two locations. Avg. no. nodes in lower third oi plant 75 p-i i 3 od- haliierentcyclesandattwolecotions. dd 0.0 H Lansing e—e Chimaltenango 7.0 + "N—d 6.0-1 5.0- 4.0 3'0 F 1 l 0 1 2 3 4 l1 cw. Flgurle. Average number oi nodes in the lower third oi plants In diiierent cycles and at two locations. cia ta ta 76 pods set on them would not touch the ground. The hypolen (height of the lowest branch) thus progressively increased in value. The closeness of curves for architype rating and espe- cially seedwt indicated that these traits were relatively more environmentally stable. Reports of heritability esti- mates for seedwt have frequently indicated high values but no reports are available for architype rating. The manner in which architecture was recovered in this breeding prog- ram seems to suggest that, complex as this trait may appear to be, it may have a simple mode of inheritance. The genes controlling architecture would have to be tightly linked to be inherited gn hlgg. Selecting for architecture and seed size in a breeding program will be effective, a proposition which is consistent with the outcome of the breeding prog- ram being evaluated. d_. Traits which decreased in magnitude from the original cycles to the advanced cycles. Traits in this group behave oppositely of those in the previous group. These traits, generally, decreased in mag- nitude of mean value from Co to C4 (Figures 22 to 26). The decrease was not systematic and trends were more erratic than those of the other traits. They comprised predominant- ly numeric traits and included podsmid, seednum, podslow, M-M-poahuueomum t - to 2 3 l l I O l - 5% (1°- Ifldamstsoq 77 i Hum us . l -‘-1 .e-I u i 5 Cycle F"TANK-ivAveragemunberoipodsin the midde third oi plants in dliie'ront cycles md at two locations. zo-r——-—~ - --- , o-e Lanshg e-eChlmdtenanga lad-1 *‘1 .v- F" ' " T ll 1 2 Cycle Figure 23. Average number oi seeds per pod oi plants in diiisrent cycles and at two locations. Avg. no. pads on main stem Avg. no. pads in lower third oi plant N “-1 78 ”- u... .- 5: CW“ figmuAveragenumberoipodsinthe lowerthirdoiplontsindiiierentcycies aid at two locations. 10.0 * H Lansing . e-e Chimdtsnmgo 9.0- 8.0“ 7.0- 5.0-< 5.0 i i F 0 l 2 3 4 l.) cw- Flgure 25. Average number oi pads on the main stem oi plants in dliierent cycles and at two locations. 79 Hm I at 0 —4-1 am I: i i We Figure 26. Average number of days to maturity oi plants in diierent cycles. 80 podsmain and maturity. The number of pods in the lower- third of the plant (podslow) was about the only trait in this group which showed a steady, less erratic decrease. This trait was readily observed in the field and could be selected for on a phenotypic basis without counting. Except for C3 in Chimaltenango , podsmain also showed a steady pattern. Unlike podslow, podsmain was not directly selected for from Co to C4 since it could be effectively scored only after the branches had been removed from the stem, as was done during data collection in this study. This notwith- standing, podsmain appears to have responded well to se- lection probably because of close association with one or more of the other traits which were directly selected for in the field by Kelly and Adams (1987). Considering espe- cially the curve for East Lansing, podsmain appears to have stabilized around 8 pods, after the initial drop between C0 and C1. A few pods may have been lost when the plant height was reduced due to selecting against vinyness of the central axis and for increased hypolen (higher first branch). It may also have been due to the reorganization of plant parts which moved some pods from the main stem to the branches. Number of pods in the middle-third (podsmid) was also easy to observe and in fact, was one of the traits directly selected for in the field. Its pattern was very similar to that for the total pods per plant (totpods). Except for a 81 sharp drop from C0 to CO, podsmid appeared to fluctuate around a line parallel to the x-axis (Figure 22). Maturity, which was scored only in Chimaltenango, showed a curve similar to podsup at that location (Figures 11 and 26). This indicated that as pods in the upper-third of the plant increased, plant maturity was delayed. Late- maturing plants were selected against, causing a decrease in maturity time in the next cycle. The fluctuations would have had some effect on the pod distribution in the plant profile, especially those in the upper two-thirds, and might have contributed to the fluctuations observed in trends for these traits. At this juncture, a general statement may be made to explain, partly, some of the erratic trends observed in this study. As was mentioned earlier, this practical breed- ing program being evaluated was not meant to supply data for theoretical purposes. Selection pressure was not uni- formly exerted from one cycle to another, changing as the breeders assessment of progress in a previous cycle dic- tated. It is not expected that for even the desirable traits which were directly selected for, that progress would be smooth and gradual since emphasis most realistic- ally shifted from one cycles to another. Traits in which progress was made early may have received less attention in the advanced cycles, with the results that they actually 82 retrogressed or were surpassed by others temporarily, until they were seriously reconsidered later. 4.3.4 Comparison of means for traits from various cycles The means of especially C0 and C4 were of interest. On the basis of comparison between these two cycles, two classes of traits were identified as follows: a. C4 mean greater than Co mean. This class included height, architype rating, hypolen, hypodiam, lowpodht, branch angle, nodesup, nodesmid, nodes- low, podlen, podwidth and seedwt. (Appendix A, Tables 12 to 19) . The principal architectural traits, namely, height, hypodiam, branch angle and seedwt were included in this class. These traits were also included in those proposed by Adams (1982) as the desired traits for a bean ideotype. This indicates the success of the breeding program. The phenotypic recurrent selection strategy employed was ef- fective in breaking any associations which might have ex- isted in the parental classes of beans and was also effect- ive in reorganising the variability into a new desired genetic combination. Figure 27 compares the representative 83 Figure 27. Comparison of representative parents from the two germplasm pools utilized in the phenotypic recurrent selection program at MSU and a recombinant selection from cycle three. Midnight (left) represents the atchitecture pool and UL 114 (right) represents the pinto pool. The selection is in the center. 84 parents from the two germplasm pools used in the breeding program with a selection from an advanced cycle. The se- lection carries genes for the desired excellent architect- ure of the navy/black and the seed-pod size of the pinto. b. C4 mean smaller than C0 mean. This group comprised nbranch, podsmain, seednum, yield intnodup, intnodmid, maturity, totpods, and the pod distribution traits (podsup, podsmid, podslow). The plant selections were spaced-planted in the experiment and this favoured the pinto traits whose frequency and thus genetic contribution was greatest in the Co. A denser population, similar to that used for planting commercial navy will make up for the descrepancy in performance and cause the type II pinto to improve in yield. The original type III pinto parents were earlier than the type II navy parents (Appendix A, Table 11). By select- ing against late maturity, the semi-determinate type II pintos became relatively earlier-maturing than the semi- determinate type II parents and the selections from the original cycle (Appendix A, Table 23). The new pinto mate- rial had a seednum average of 5.77 which was between the average for the parents at the East Lansing location (Ap- pendix A, Tables 10 and 18) . The same trend was true for 85 the Chimaltenango location. This indicates that high seed number was sacrificed for increased seed size. There may be a physiological genetic limitation on the number of seeds per pod. It is also possible that while pod length increas- ed, seed size also increased and with a negative develop- mental dependancy between seedwt and seednum, the two could not be increased simultaneously. 4.3.5 Comparison of trait means at the two locations. Because of the vast distance between the two locations used in this study, genotype x environment interaction was not considered a useful estimation and hence was not ex- tracted in the analysis of variance. Except in the case of branch angle (Figure 12), podwidth (Figure 17) and hypoco- tyl diameter (Figure 20), all other trait; means from the East Lansing data were larger in all cycles than those from Chimaltenango. The effect of environment (location) on these traits thus appears to have been predominantly one of scale and not rank. Any traits identified as significant indicators of plant architecture may be effectively select- ed irrespective of the environment. The need to design a cultivar for specific situations (ideotype) may be inferred from the results since nearly all traits were expressed to different extents at the two locations, the expression 86 being greater at East Lansing where the plants were origin- ally selected, and lower at Chimaltenango. Branch angle means were greater in Chimaltenango because the plants were shorter, smaller and more compact, Even though the pods were wider, the seedwt means were not larger than means from East Lansing (Figure 18). CHAPTER FIVE CHANGES IN FREQUENCY AND METRIC VALUE OF TRAITS UNDER RECURRENT SELECTION 5.1 Introduction Recurrent selection has the effect of breaking link- ages and coupled with selection is able to change associat- ions among characters and increase the frequency of desired genes in the population. It is expected that the modal class frequency of traits would shift from one cycle to another if steady selection pressure is exerted on these target. traits. Further; the advanced. cycles 'would. have narrower ranges of variation under this condition. In the absence of recombination between the two gene pools under consideration, tendencies to bimodality in the frequency curves may occur. The objective of this analysis was to study the chang- es in the modal class frequency of traits under recurrent selection. The results may shed some light on the actions of the breeders and the patterns of progress that was made from one cycle to another. 87 88 5.2 Materials and methods Data from Experiment II were used. The frequencies of plant selections in various classes were obtained as per- centages of the total number of selections included, for each trait. The frequencies were plotted against the class means using the cubic spline procedure of the Plotit graph- ics package. 5.3 Results and discussion The curves showed fairly normal distribution with slight skewing in some cases. Occasionally, some curves in the early cycles tended to show bimodal distribution. The high- est peaks for high-valued traits were usually recorded by the advanced cycles. The trends in selected traits are presented below. 5.3.1 Architectural traits a. Architype rating: The frequency curves separated into two distinct groups, the early cycles (Co and C1) in one and the rest in the the other (Figure 28) . The early cycle group had a 89 2222;; ‘ r i 2 3 4 5 0 7 8 Architype rating Figure 23- Froauoncy oi architype rating in live recurrent selection cylces. cycle 0 11111 Frequency CV0 h.) o l 15- 10~ 51 . s” 0 : Hypocotyl diameter (mm) Figure 29. Frequency oi branch angle in five recurrent selection cycces 90 modal class which peaked around a rating of 2 while the advanced cycles peaked around an architype rating of 3. The modal class frequencies for the advanced cycles shifted very slightly, staying around 45%. The ranges for all cycles were the same except that the advanced cycle group had the lowest frequencies (less than 5%) for the lowest rating and the highest frequencies (up to 10%) for the highest architype rating. The converse was true for the early cycle group. The frequency pattern suggests that architecture did not change gradually from one cylce to another but rather was established in the early cycles. However, it was not until C3 that architecture stabilized. Some major modifi- cations appear to have been made between C0 and C2. Failure by Kelly and Adams (1987) to observe desired recombinants in the early cycles caused them, in fact, to advance some compromise plants to maintain adequate variability for seed and plant architecture. Stronger selection pressure was possible in the later cycles and was probably responsible for the quantum leap from a modal class frequency of about 2 in the Co to 3 in the later cycles.- b . Hypodiam The modal classes for Co to C4 bunched together 91 between 7 and 8mm (Figure 29). It appeared the class fre- quencies for C3 and C4 lagged slightly behind those for Co and C2. The modal class frequencies for C3 and C4 were 30% while the rest had lower values. The range was similar for all cycles. From Figure 20, it is seen that the increase in hypo- cotyl diameter from Co to C4 was not systematic. This may be due to the effect of varying selection pressure on the trait from one cycle to another. Besides, hypocotyl diame- ter was not given priority attention in the field selection as were traits such as seedwt, maturity, plant habit, general architecture and height, which were the characters evaluated on $1 plant selections by Kelly and Adams (1987) for choosing individuals to be used as parents in subse- quent cycles. c. Branch angle: The frequency pattern was similar for Co to C3 (Fi- gure 30). The modal class for these was around 75° and the frequency in that class around 40%. The curve for Co was distinctly separated from the rest with a modal class peaking around 65°. It was also evident that the C4 modal class was lower than those for C1 to C3 (Figure 30). The range was widest for Co and C4 and spanned 50° (38° to 88°) . q “Gecko GO .Heydel recycle! (.0. HCydeJ "cycle. O :40-: e. g ”c. 3 201 immune)! a", 92 r F ' ‘ ‘0 30 60 7O 30 90 I 00 Branch angle 30 F igure ”frequency a! branch angle in live cycles at recurrent election 45 0-0 cycle 0 ‘0-1 H Cycle ' e-e cycle 2 35- . H cycle 3 ‘ I-e cycle 4 30- / \ :5. / .-‘0- '~ / ‘( IS~ / \ \ h" p .. . ’ \ .‘a ' ‘ .\_ o “" I I l l r l O 5 l0 l5 20 2: 33 Pod: on control 0439 Figure 3|, Frequent-y of pads on ccnlral an: at plonttin “V0 recurrent -.. lr :‘tinn CyPM. 93 The distinct separation of the Co from the rest indi- cates that, just as occurred in architecture, the desired branch angle was recovered after the first cycle. The subsequent cycles did not undergo major changes until C4 whose curve lags behind those of C2 and C3. This lag may be due to wider branch angles in C4, probably the result of the fact that at this stage, pinto seeds and pods were associated with a navy architecture. Wider branch angle is a characteristic of the pinto germplasm. d. Podsmain: The curves showed a general skewing to the right (Figure 31). The modal classes for the advanced cycles . peaked around a lower mean podsmain (six pods) than, and generally lagged behind those for the early cycles, which peaked around eight pods. Except for C1, the frequencies for the modal classes were between 35% and 40%. Pods on the main stem generally decreased from the original cycle to the advanced ones (Appendix A, Table 17) and so did the total number of pods (Appendix A, Table 20). The latter event influenced the former. As selection gains are made for larger pods and seeds, it is expected that there will be slightly fewer pods per plant (Adams, 1967). 94 e. Height: Cycle 1 showed a bimodal tendency, peaking around 35cm and 50cm (Figure 32). Cycle 0 peaked around 45cm with a modal class frequency of 30% while the other cycles peaked around 50cm, the frequency being highest for C4 (40%) and the same for the ramaining cycles (about 32%). Plant height was one of the criteria used for select- ing parents with which to initiate subsequent cycles. It appears height was improved in three steps; it was increas- ed from C0 to C1 and therafter stabilized (with minor fluctuations) around a mean for the next two cycles. Height was then increased in C4 with more of the population being taller. f. Podslow: The curves for this trait were the most skewed of all (Figure 33). The modal class peak frequencies were lowest for the advanced cycles (20% to 30%) and highest in the earlier cycles (31 to 39). Cycle 0 had the widest range of about 1 to 35 pods while C4 had the shortest range of between 1 and 16 pods. The other cycles ranged between 1 and 25 pods. It is clear that pads in the lower-third of the plant were effectively selected against in the breeding program, frequency 0/. Hayden 50-1 “W' recycle! so... recycle) H”; 5.0. a 2 i”' 20-. iO-i 0" T T I r“ ' ti 1525354555557555 95 Plant height (cm) Figure32. Frequency of plant height in live cycles at recurrent election o—e cycle 0 60- e-e cyclel H cycle 2 H cycle 3 50-1 H ”a. ‘ 0 3 1101'5202530354045 mar Pads in lower third of plant Figure 33. Frequency a! pad: in the lower third 0! planbin live recurrent selection cycles. 96 reducing progressively from C0 to C4. This trait was easy to observe and to select against. A breeding objective was to select plants with good pod distribution in the plant profile as against the tendency of pinto varieties to concentrate most of their pods in the lower region. 5.3.2 Seed and pod traits a. Podwidth: The curve for C1 showed a slight bimodality, with C0 and C2 peaking around the lower mode at about 11mm, while the advanced cycles peaked around the higher mode at about 13mm (Figure 34). The class ranges were different. Cycle 0 ranged between 8 to 14mm, C1 from 8 to 16mm, C2 from 9 to 15mm, C3 from 9 to 19mm, and C4 from 10 to 16mm. Pod width had to increase to accommodate the increase in seed size (seedwt) as the cycles advanced. Cycle 0 had some very large pods but these were not filled with large seeds. This observation may have also been caused by the fact that compromise plants were advanced, as mentioned earlier, to maintain the desired variablity in the program. b. Podlen: Pod length in cycle 0 ranged from 1 to 13cm while C4 97 50-1 50+ e > .0- fl 0 g i ”" 20-1 10-1 0 l 0 5 Podwidth (mm) Figure “frequency a! pad width in live cycles of recurrent sflectlon o—e cl 0 Isa-J " c’ ' 1 50- ‘E .0- Frequenc 8 l 4 Ve101214101020 Pad length (cm) Figure 35. Frequency al pad length in tile recurrent selection cycles 98 ranged from 8 to 20cm (Figure 35) . The extremes of the ranges, however, occurred at very low frequencies of about 1%. The modal classes for cycles C1 to C4 peaked around 11cm but differed in the frequency, C1 and C2 being around 35% while C3 and C4 were around 55% and 60%, respectively. The C0 modal class peaked around 9cm. This seem to indicate that a pod length of about 11cm was about ideal since the mode of the curve did not shift toward longer pods but instead the population, as the cycles advanced, moved, numerically, toward this 'ideal' length that was achieved already in the C1. The same is true of pod width (Figure 34). c. Seednum: The frequency curves showed very slight shifts in modal classes (Figure 36). The modal class frequencies were higher (about 55%) for the early cycles (except Cl) than for the advanced cycles (about 50). The modal class peak values were similar for Co and C4, being at about six seeds A per pod. With the exception of C1 (in which seednum of above eight was recorded as a very low frequency) all cycles recorded a maximum of 8 seeds per pod, the maximum being at a very low frequency of about 1% or 2%. Tables 10 and 22 (Appendix A) show that the average Frequency frequency 99 60 cycle 0 i" <13 i 11:11 N O l 10‘ "‘ l o 2 4 6 a 10 Number of seeds per pod figure 35. Frequency of number of seeds per pod In five recurrent cycles. o—e cycle 0 60° e—e cycle 1 H cycle 2 50.. . H cycle 3 111—111 cycle 4 401 50‘ 20+ 10-1 oJ i ; ' l T W ' 813182328333845485358 loo-seedwt (gm) figurc37. Frequency of loo-seedwt in flve cycles of recurrent clectlan 100 seed number per pod for C4 was between the parental ave- rages. It suggests that increase in seedwt was attained at the expense of seed number per pod. Since seednum of above eight was rarely found, it appears dry beans may not be abLe to optimally support more than eight seeds per pod. There may be a physiological genetic limitation on this trait. However, it may only reflect the fact that neither of the initial gene pools carried genes for high seednum. d . Seedwt: This trait showed the most separation among the fre— quency curves from the various cycles (Figure 37) . The parental gene pools showed more variation for this trait than for many others such as number of seeds per pod. The curves showed greater ranges. The C4 modal class peaked around 43gm while Co peaked around 259m. Co ranged between 18 and 43gm while C4 ranged between 25 and 50gm. There was approximately 89111 of change in modal value between succes- sive cycles, the change being slightly greater from Co to Cl. Unlike pod dimensions (length and width) in which there was basically one shift from early to advanced cy- cles, seedwt showed successive shifts at remarkably fairly even intervals. This suggests that seedwt (seed size) was 101 recovered by a gradual step-by-step process, as observed by Kelly and Adams (1987). The seedwt mean for the parent check (01 114) was 36.07gm which was attained, for most of the selections, first in the C3 (Figure 37). Though the curve indicates that this seed weight was attained much earlier, it must be pointed out that the desired combina- tion of large seed size and erect architecture was not achieved before C3. Further, as mentioned previously, com— promise plants were advanced in the early cycles, hence accounting for the presence of large seed in these cycles. Stringent selection pressure may account for the set back in progress in C2 as shown in Figure 37. Considering the fact that C2 showed a tendency to bimodality, it would have been expected that the preceding cycles would have shown a similar pattern and perhaps to a greater degree. From Table 1, it appears to be a problem with numbers. Cycle 0 (which was recreated) and C1 had large initial 31 populations (more than 1000) to select from as compared to about 500 for C2. The curves for the first two cycles showed fairly normal distribution, due perhaps to‘a large size and range of materials to select from for planting the experiments. One would also have expected the C4 and possibly C3 to have relatively smaller ranges than the previous cycles. As explained earlier, there were differences in selection pressure applied from one cycle to another. With 1064 $1 102 to choose from (Table 1), the C3 had a wider range than the C4. The lower value of the range for the C4, however, is distinctly higher than the rest. It appears stringent selection was not applied in the C4, the breeders having just observed the desired recombinants in the previous cycle. The selections retained included some small-seeded plants causing this wide range. CHAPTER SIX IDENTIFICATION OF INDICATORS OF ERECT PLANT ARCHITECTURE OF BEANS 6.1 Introduction Breeders frequently depend on target traits as indi- cators of complex traits in a breeding program. When hand- ling large numbers of plants in a segregating population, the advantage of the ability to select for or against a few traits to achieve the desired breeding objective cannot be over-emphasized. These target traits should not only be easy to evaluate but should also be heritable in order to ensure rapid progress, especially when selecting on a phe- notypic basis. In designing an optimum architecture for beans, Adams (1982) enumerated certain desirable attributes of such a plant structure, which have been presented elsewhere in this dissertation. These traits are not equally important and, besides, cannot all be practically considered in a large breeding program. The purpose of this study is to identify traits which 103 104 are effective indicators of erect bean plant architecture and their relative importance to enable recomendations to be made for target traits in a breeding program for such and objective. Selection is practised in a segregating population and thus this study was designed to find out if the same traits would be identified as important indicators of erect plant architecture in different segregating popu- lations. 6.2 Materials and methods Data from both Experiments (I and II) were used in this study. Using plant architype rating as dependent va- riable and all other architectural traits as independent variables, the data were submitted to the stepwise multiple regression analysis. Each cross, and cycle, as well as the parents, were analysed separately. The traits included in a model were ranked in each analysis on the basis of the magnitude of the partial F values. The frequency of select- ion of a trait as significant by a test of the F value was recorded in each of the five cycles and also in each cross. This served as a basis for determining relative importance of traits. Only traits which were significant at the .05 level or higher were included in a model. The R2 was ob- tained for each model. 105 6.3 Results and discussion 6.3.1 Magnitude of R2 The magnitude of R2, the proportion of variance in the dependent variable explained by variations in the independ- ent variables, indicates the goodness of fit of the regres- sion model. The greater the value, the better the fit. The magnitude of the estimates of this statistic was low for the models obtained for various cycles at East Lansing. The estimates ranged from 7.70% to 28.66%. Each model contained different number of significant variables. The values were higher at Chimaltenango, ranging from 46.06% to 69.83% (Appendix B, Tables 1 to 5). The estimate for the parents was 80.25% (Table 3). The six F3 families produced low to moderate estimates of R2 ranging from 25.72% to 58.35% (Appendix B, Tables 6 to 8). The data seem to suggest a difference in R2 estimates for the parents (pure lines), as compared with the crosses and cycles which were all segregating populations. The low estimates may be due to the fact that architype, the inde- pendent variable, was scored as a qualitative trait instead of the quantitative trait that it is. The battery of mea- surements were unable to explain, adequately, the variance in this subjective estimate. This difference may also have been 106 caused by the inability to distinguish precisely between the wide range of variability in the segregating populat- ions during the scoring process. While parental extremes may have been readily identified and scored appropriately, the numerous intermediates in the cycles and cross populat- ions may frequently have been given the middle score on the scale, leading to a 'blurring' of classification and consequently to lower values of R2. 6.3.2 Frequency of including a trait in a model The model selection procedure identified traits which were similar but not identical from one cycle to another, at a location (Appendix B, Tables 1 to 5). Some traits were selected more frequently than others. Podsmain, hypodiam and branch angle were selected most frequently in cycles in East Lansing while height, podsmid, hypodiam, nodeslow and intnodup were the most frequently selected traits in cy- cles in Chimaltenango (Table 3). In the parents, three variables were retained on the basis of the significance of the F value. These were hypo- diam, podsmain and podslow (Table 4). In the crosses, hypodiam, branch angle and podsup were the most frequently selected traits (Table 3). 107 Table 3. Frequency of selection of a trait by the stepwise multiple regression procedures with architype as dependent variable. Frequency Trait Cycles Cycles F3 families (East Lansing) (Chimaltenango) Hypodiam 4 3 5 Angle 3 2 6 Height 3 5 2 Podsmain 5 0 2 Podsmid 2 4 1 Nodeslow 1 3 2 Podsup 1 1 3 Intnodlow 2 2 1 Intnodup 2 3 0 Nbranch 2 1 1 Nodesmid 2 0 2 Intnodmid 1 1 1 Lowpodht 0 1 2 Nodesup 2 0 0 Hypolen 1 0 0 108 Table 4. Architectural traits selected in the parent population by the stepwise multiple regression procedure with architype as the dependent variable. Trait Partial R2 prob. > F Hypodiam 41.91 *** Podsmain 22.19 *** Podslow 16.15 *** Model 2 80.25% *** : significant at .001 level. The plants at Chimaltenango were shorter and more erect than those at East lensing. This might have contri- buted to height being of importance and selected in all cycles at the former location. The decrease in height caused more pods to be located in the lower parts of the plant. This may also account for the fact that fewer pods were found on the main stem as compared with plants at East Lansing. Based upon the frequency results in Table 3, the selected traits were grouped into two classes as follows: Class A: traits which were selected more frequently, namely, hypodiam, angle, height, podsmain and podsmid, in this approximate order of importance as indicators of erect plant architecture . 109 Class B: traits which were selected less frequently, name- ly, nodeslow, podsup, intnodlow, intnodup, nbranch, nodes- mid, intnodmid, podslow and nodesup, in this approximate order of importance. Reassembling of genes into new combinations notwith- standing, the traits in class A appear to be basic fea- tures around which changes and reorganizations took place. The list produced from the analysis of parents should not be misconstrued to indicate the array of desirable traits. They represent the list that best characterises architecture as it ranges from one extreme (type II) to the other (type III, standard pinto). It may be concluded from the above evidence that the principal indicators of plant architecture in dry beans are high values of hypocotyl diameter, plant height, and the number of pods on the main stem and in the middle of the plant, and low values of branch angle. A pinto architype, in summary, would be tall, have a large hypocotyl, a narrow plant profile and many pods on the main stem. In addition, it would have fewer number of basal branches, and good pod distribution in the plant profile. The internodes in the top region should preferably be shorter than those in the standard pinto parents to eliminate the tendency to Vini- ness 0 These traits are in agreement with those proposed by 110 Adams (1982) . They are also easy to observe and evaluate phenotypically except podsmain which can be readily eva- luated only after the branches have been removed. CHAPTER SEVEN PHENOTYPIC CHARACTER ASSOCIATION AND THE EFFECTS OF RECUR- RENT SELECTION ON ASSOCIATION IN BEANS 7.1 Introduction Phenotypic correlations incorporate contributions from both genetic and environmental sources. The basic nature of genetic correlation is complex and may be due to pleiotro— py, linkage disequilibrium and change in gene frequencies upon selection (Rutledge g; 31, 1973). Two measurable traits are likely to be correlated if they share at least a proportion of the genes that are involved in their expres- sion (Ecochard and Ravelomanatsoc, 1982). Four forces are capable of altering the initial cha- racter association in the parents. These are: a. selection b. recombination and reassortment c. effects of environment (genotype x environment interac- tion), and d. sampling error. It must be borne in mind that in the various cycles, the selections were made in the cnsl genetic state (where n 111 112 is a cycle) and hence, essentially, should be considered as members of segregating populations. A segregating population provides new variablity arising from the breakup, partially or fully, of some of the associations which Mather (1973) described as adaptive complexes or functionally-integrated gene blocks, that existed in the parents and that had been maintained over long periods of selfing with selection. The phenotypic expressions in parents would be against a background of interdependence or multicolinearity while in a segregating population, it would be in an environment of relative independence, which will allow greater freedom of expres- sion of relationships. The latter scenario would reduce the incidence of spurious correlations and eliminate weak ones. The correlations from this study are of much wider application since the populations involved exhibit great diversity, involving different classes of Engsgglgs yglga; {is L. Recurrent selection has the effect of breaking linkages and promoting recombination and reassortment of genes. Coupled with selection, recurrent selection would change gene frequencies which should show up as changes in the correlation matrix from one cycle to another. Sometimes, it may be desirable to determine if there are relationships between two sets of data, for example, architectural traits and seed-pod traits in this study, 113 collected on the same subjects, such that components of one group could be an effective predictor of the components of the other. Such predictions are made through abstract unob- served variables called canonical variables. To be able to predict another, it is implicit that the traits have some strong associations which may be extrapolated to suggest sharing of some genes in common, as in a factor analysis. 7.2 Materials and methods Data from the two experiments were used. Simple linear correlations on a phenotypic basis were calculated for the parents, F3 families and all the cycles, separate- ly, for the two locations. All the six F3 families were lumped together for the analysis. The trends with regard to magnitude, significance and sign of the coefficients were examined for pairs of traits for all cycles. For canonical correlation analysis, the two sets of data were architectural and seed-pod traits. In addition to obtaining a canonical correlation matrix, a redundancy analysis was performed to determine the amount of variance of each data set explained by its own canonical variables, as well as the variance of a set explained by the canonical variables of the opposite data set. 114 7.3 Results and discussion 7.3.1 Comparison of correlation at the two locations. The coefficients of correlation among traits in East Lansing and Chimaltenango were generally low to moderate in magnitude. The highest coefficient (r - .943) in Chimalte- nango was produced by the association between seednum and seedwt (Table 6d) . Component compensation as described by Adams (1967) has clearly been violated. In East Lansing, the correlation between yield and podsmid produced the highest coefficient of r - .725 (Table 5b). Trends of the sign of association from Co to C4 were generally similar at both locations for pairs of traits. However, certain stat- istically significant associations showed opposite signs at the two locations. These included the correlations of arch- itype vs height and intnodup vs architype (Table 5a) and, seedwt vs seednum and seedwt vs podsup (Table 5d) , which were all negative at East Lansing but positive in some cycles at Chimaltenango (Tables 6a and 6d) . Similarly, branch angle vs architype (Table 5a), podwidth vs seedwt (Table 5c) and podlen vs seedwt (Table 5e) were positively correlated in East Lansing but negatively associated in Chimaltenango (Tables 5a, c, and e). These reversals in 115 Table 5a. Phenotypic character association (r) among bean traits at East Lansing. Cycle Height Architype Hypodiam Angle Podsmid Architype C0 .095* C1 -.118** C2 .031 C3 -.088 C4 -.248*** Hypodiam C0 .177 .092* C1 .253*** .271*** C2 .367*** .198*** C3 .307*** .241*** C4 .181** .327*** Angle CO -.078 -.064 -.094* C1 -.173*** .139** -.266*** C2 .048 .030 -.053 C3 -.O73 .146** -.142** C4 -.123** .178*** -.183** Podsmid C0 .369*** .143*** .224*** -.210*** C1 .465*** .242*** .465*** -.286*** C2 .284*** .197*** .474*** -.025 C3 .176*** .299*** .398*** -.239*** C4 .171*** .177*** .314*** -.111* Podsmain C0 .055 .214*** .008 .001 .208*** C1 .101* .254*** .110* -.005 .219*** C2 .126** .156*** .162*** -.019 .224*** C3 .074 .213*** .146** -.022 .240*** C4 .027 .145** .102* .101* .216*** Intnodup C0 .473*** -.061 .104* .014 .231*** C1 .304*** -.140** .031 -.035 .231*** C2 .276*** -.194*** .202** -.045 .101* C3 .422*** -.137** .140** .016 -.023 C4 .145* .014 .044 -.036 -.044 Nodesup C0 .056 -.064 .099*' -.097* .096* C1 .333*** -.163** .158** -.035 .111 C2 .217*** .005 .262*** .018 .177*** C3 .153** .029 .184*** .029 .086 C4 .156** -.044 .090 -.100* .045 ***' **’ * 3 significant at .001, .01, and .05 levels, respectively. 116 Table 5b. Phenotypic character association (r) among bean traits at East Lansing. Cycle Height Architype Hypodiam Angle Podsmid Seedwt CO .100* -.032 -.016 -.017 -.005 C1 .063 -.041 -.043 .016 -.045 C2 .094* -.021 -.005 .031 -.044 C3 .095* -.062 .003 -.029 -.029 C4 .062 -.001 -.066 -.013 -.058 Podwidth C0 -.009 .034 .009 -.089 -.111 C1 .202*** .014 .036 -.141** .106* C2 .113* -.094* -.003 -.004 -.134** C3 .113* -.120 .081 -.004 -.103* C4 .083 -.039 .023 -.073 -.O44 Podlen C0 .098* -.O32 .105* -.219*** .084 C1 .085 -.002 .083 -.005 .072 C2 .130** .073 .221*** -.069 .094 C3 .227*** .013 .237*** -.133** .141** C4 .165** .064 .214*** -.179** .280*** Seednum C0 .091 .044 .023 -.O4O .083 C1 .211*** .147** .254*** .016 .238*** C2 .119** .138** .296*** -.056 .225*** C3 .228*** .045 .152** -.166*** .076 C4 .141** .127** .275*** -.249*** .233*** Yield C0 .455*** .146** .244*** -.363*** .581*** C1 .415*** .214*** .431*** -.380*** .725*** C2 .327*** .195*** .447*** -.067 .458*** C3 .340*** .198*** .409*** -.368*** .648*** C4 .308*** .117* .403*** -.211** .593*** Podslow C0 .403*** .034 .272*** -.105* .287*** C1 .384*** -.140** .105* -.284*** .314*** C2 .297*** -.014 .217*** -.093 .054 C3 .344*** -.120** .134** -.161** .081 C4 .192** -.097 .091 -.147** -.003 Podsup C0 .229*** .109* .194*** -.183*** .279*** C1 .086 .241*** .365*** -.O79 .222*** C2 .015 .180*** .283*** -.045 .102* C3 .037 .220*** .333*** -.172*** .252** C4 .084 .163** .259*** -.040 .163** ***, **, * : Significant at .001, .01, and .05 levels, respectively. 117 Table 5c. Phenotypic character association (r) among bean traits at East Lansing. Cycle Podmain Intnodup Nodesup Seedwt Podwidth Intnodup C0 -.009 C1 -.111* C2 .097* C3 -.051 C4 -.122* Nodesup C0 .107* -.039 C1 .066 -.069 C2 .041 .107* C3 -.046 .044 C4 .072 .l78** Seedwt C0 -.118** .083* -.014 C1 .033 .088* .081 C2 -.138** -.028 -.001 C3 -.078 .078 .094 C4 -.257*** .229*** .097 Podwidth C0 -.138** -.130** .075 .100* C1 .104* -.011 .201*** .331*** C2 -.068 .132** .043 .437*** C3 -.020 .091 -.017 .291*** C4 .034 .076 .040 .251*** Podlen C0 -.l38** .091* .075 .052 .367*** C1 .005 .046 .107* -.009 -.020 C2 -.120** -.005 .044 .153** .197*** C3 -.003 .019 .003 .104* .229*** C4 .028 -.069 .108* .151* .075 ***, **, * : significant at .001, .01, and .05 levels, respectively. Table 5d. 'Phenotypic character association traits at East Lansing. Seednum Yield Podslow Podsup 118 (r) among bean Cycle Podsmain Intnodup Nodesup Seedwt Podwidth C0 C1 C2 C3 C4 C0 C1 C2 C3 C4 C0' C1 C2 C3 C4 C0 C1 C2 C3 C4 -.O71 .115* -.011 -.152** -.223*** .173*** .257*** .196*** .152** .097 .153** .133** .298*** .129** .157** .182*** .213*** .147** .129** .169** .046 .115* .049 .155** -.022 .285*** -e029 .007 .071 -.089 .293*** -.013 .183*** .181*** -e082 .082 -e082 “.140** -e 113* '.091 -.059 .026 .110* .066 .092 .175*** .146** .140** .137** .111* .088 -0 069 .052 .037 -.025 -e012 “.069 .107* .131** .028 -.O36 -.039 -.264*** -.102* -.246*** -.113* -.O47 -.063 .128** .095* .125** .248** .206** .056 .002 .031 .075 .003 -e 074 ‘.104* -.059 -.150* -.071 .216*** .026 .053 .033 -.125** .138** .108* .134** .047 -.034 -.170*** -.173*** -.O92 -.159** -.062 l ee, respectively. * e significant at .001, .01, and .05 levels, Table 5e. at East Lansing. Cycle Seednum C0 C1 C2 C3 C4 Yield C0 C1 C2 C3 C4 Podslow C0 C1 C2 C3 C4 Podsup C0 C1 C2 C3 C4 Podlen .116** .147** .625*** .636*** .151** .184*** .035 .120** .338*** .458*** .018 .016 .067 .041 .066 .035 .026 .077 .143** .077 119 .085 .361*** .149** .358*** .437*** .015 .081 .012 .054 .127* .072 .122** .083 .049 .244*** Seednum Yield .492*** .415*** .320*** .357*** .306*** .366*** .345*** .141** .280*** .334*** Phenotypic character association (r) among traits Podlow Podsup .053 .419*** -.153*** -.139** -.010 *** r **r * e respectively. significant at .001, .01, and .05 levels, Table 6a . Phenotypic character association traits at Chimaltenango. 120 (r) among bean Cycle Height Architype Hypodiam Angle Podsmid Architype C0 .567*** C1 .452*** C2 .633*** C3 .566*** C4 .537*** Hypodiam CO .387*** .330*** C1 .200* .264** C2 .240** .334*** C3 .523*** .647*** C4 .301** .059 Angle C0 .174 -.022 .014 C1 .267** -.186* .009 C2 .169 -.351*** -.199* C3 .190* -.081 -.104 C4 .120 -.178 -.150 Podsmid CO .084 .006 .0288 -.220* C1 .218* .539*** .353*** -.286** C2 .252** .516*** .162 -.310** C3 .263** .397*** .265** -.085 C4 .034 .255** .199* -.261* Podsmain C0 .157 .150 -.164 .119 .335*** C1 .328** .366*** -.201* -.288** .525*** C2 .266*** .365*** .172 -.264** .564*** C3 .251** .354*** .248** -.116 .433*** C4 .397*** .305** .176 -.O69 .405*** Intnodup C0 .078 -.095 .205* -.062 .014 C1 .528*** .273** .104 -.134 .209* C2 .410*** .206* .119 .122 .130 C3 .674*** .225* .233** -.036 .092 C4 .629*** .049 .288** -.O44 .015 Nodesup C0 .053 .051 .012 -.065 .130 C1 .352*** .258** .085 -.120 .290** C2 .237** .206* .126 .053 .271** C3 .486*** .198* .223* .063 .067 C4 .200* .296** -.O38 -.083 .001 ***, ** * significant at .001, .01, and .05 levels, respectively. 121 Table 6b.Phenotypic character association (r) among bean traits at Chimaltenango. Cycle Height Architype Hypodiam Angle Podsmid Seedwt CO -.028 -.193* .165 .152 -.380*** C1 .106 .072 -.017 .135 -.005 C2 -.235** -.125 .159 .103 -.146 C3 -.074 -.081 -.191 -.036 -.116 C4 -.234** -.217* -.360** .152 -.360*** Podwidth CO .088 .187* .044 -.175 -.180* C1 .090 .007 .122 .010 .060 C2 .251** .116 -.047 -.204 .146 C3 -.027 -.061 .006 .038 -.145 C4 .241** -.044 .077 .007 -.088 Podlen C0 .167 .187** -.051 -.101 .272** C1 -.004 .002 -.077 -.297** .046 C2 -.140 .013 .134 -.020 .067 C3 .090 .218* .129 .060 .176* C4 .161 .202* .167 -.O42 .208* Seednum C0 -.014 -.128 .175 .114 -.339*** C1 .101 .056 -.048 .122 -.001 C2 -.322** -.153 .121 .136 -.126 C3 -.055 .042 .099 .118 .126 C4 e118 0044 e234** -e014 “.044 Yield C0 .128 .170 .069 .093 .048 C1 .172 .319** .083 -.015 .208* C2 .030 .093 .127 -.198* .260** C3 -.055 .087 .036 -.045 -.055 C4 .101 .101 -.140 -.153 .088 Podslow C0 .069 .024 .028 .003 .086 C1 .437** .393** .146 -.170 .369** C2 .164 .015 .003 .103 .130 C3 .561*** .453*** .347*** -.088 .296** C4 .629*** .320** .024 -.115 -.220* Podsup C0 -.169 -.089 -.022 -.193* .160 C1 -.021 .098 -.173 .097 -.198* C2 -.040 -.009 .047 -.184 .104 C3 -.142 .153 .136 -.009 -.055 C4 -.116 .123 .054 -.424*** .278* *1", Hr, * significant at .001, .01, and .05 levels, respectively. 122 Table 6c. Phenotypic character association (r) among bean traits at Chimaltenango. Cycle Podsmain Intnodup Nodesup Seedwt Podwidth Intnodup C0 .035 C1 .346*** C2 .234** C3 .235** C4 .162* Nodesup CO .334*** -.099 C1 .274** .206 C2 .357*** .104 C3 .248** .460*** C4 .089 -.074 Seedwt CO -.295** -.054 -.017 C1 -.280** .027 .157 C2 -.158 -.086 -.130 C3 -.002 .002 .157 C4 -.529*** -.119 .036 Podwidth C0 -.091 -.142 -.058 -.006 C1 .053 .118 -.118 -.359*** C2 -.043 .123 .172 -.410*** C3 -.309*** -.019 -.056 -.174 C4 .107 .322** -.O79 .156 Podlen C0 .284** -.059 -.004 -.741*** .219** C1 .286** -.008 -.113 -.86l*** -.O75 C2 -.158 -.075 -.142 .449*** -.075 C3 .071 , .124 -.O4O -.147 .229** C4 .237* .117 -.277** -.039 .433*** ***, **, * : significant at .001, .01, and .05 levels, respectively. 123 Table 6d. Phenotypic character association (r) among bean traits at Chimaltenango. Cycle Podsmain Intnodup Nodesup Seedwt Podwidth Seednum C0 -.305** -.118 -.017 .028 .028 C1 -.268** .016 .170 .943*** -.376*** C2 -.121 -.109 -.221* .836*** -.528*** C3 -.045 -.027 -.326*** -.079 .178* C4 .219* .138 -.189 -.244** .164 Yield C0 .134 .062 -.200* .075 -.068 C1 .064 .037 .267** .410*** .047 C2 .052 .121 -.204 -.039 .026 C3 -.125 -.O92 -.134 .110 .057 C4 .085 .158 .004 .045 .126 Podslow C0 .073 .369*** -.261** .018 .011 C1 .417*** .512*** .302*** .105 .092 C2 .298** .528*** .038 -.021 -.O62 C3 .430*** .240** .269** .140 -.195* C4 .331** .325** .049 -.221 .166 Podsup C0 -.033 -.116 .137 .249** -.053 C1 .070 -.080 .165 .254** -.326** C2 .288** -.172 .260** .006 -.O76 C3 .212* -.077 .028 .097 -.O45 C4 .080 -.053 .024 -.213 -.152 ***, “I, * : significant at .001, .01, and .05 levels, respectively. Table 6e. Phenotypic character association (r) among bean traits at Chimaltenango. Cycle Podlen Seednum C0 C1 C2 C3 C4 Yield C0 C1 C2 C3 C4 Podslow C0 C1 C2 C3 C4 Podsup C0 C1 C2 C3 C4 -.647*** -.825*** .555*** -.147 .114 -.118 -.306*** “.119 .071 .067 -.067 -.057 .114 -.161 .054 -.204* -.220* .022 .231** -.016 Seednum .040 .393*** .076 .110 .077 .015 .109 .056 .129 .149 .252** .222** .072 .041 .008 Yield Podslow .078 .141 -.027 -.063 .242* -.024 -.024 .113 -.088 -.023 -.130 .163 -.069 .188 -.233* ***’ **’ * 0 levels, respectively. significant at .001, .01, and .05 125 sign are attributable to genotype x environment interact- ion. Stress and differences in environments have been known to change phenotypic correlations (Grafius, 1964: Adams, 1967) . Falconer (1952) suggested that a trait measured in two environments should not be considered as one but two traits associated by genetic correlation. Differences in plant density could be a reason for the observations only for the fact that the plants at Chimaltenango were smaller in size and, thus, even though the spacings between plants at the two locations were identical, competition among plants was different at the two locations. It is probable that sampling error played a role since the number of selections at Chimaltenango was half that at East Lansing. Plants at Chimaltenango were observed to be more erect, shorter and of compact, narrow profile. This may have contributed to the observed association in architype vs height and architype vs intnodup. It is expected that larger seeds would require wider pods while longer pods would be needed for more seeds per pod. The unexpected negative associations between seednum vs podlen and pod- width vs seedwt, and the positive association between seed- num vs seedwt at Chimaltenango may be due to the problems of adaptation. Large pods did not necessarily mean large seeds and long pods failed to fill properly. In Figure 17, 126 podwidth in Chimaltenango was larger in all cycles than at East Lansing but in Figure 18, the reverse was true for seedwt. It is evident from the correlations that negative associations disappeared or became statistically non-signi- ficant in the advanced cycles (Tables .6a, c and e). The early cycles had a high proportion of the pinto genes from the pinto group that were actively retained. 7.3.2 Patterns of association at two locations a. None or only occasional significant associations at both _locations. Traits in this category of associations included int- nodup vs angle and podwith vs nodesup (Table 5a) and pod- width vs architype, podwidth vs nodesup and podwidth vs angle (Table 5b). Others were podwidth vs nodesup, podlen vs nodesup, intnodup vs angle and seedwt vs nodesup (Table 5c). Seedwt correlated significantly with very few of the architectural traits. It correlated significantly and nega- tively with only podsmain at both locations (Table 5c) and with podsmid at Chimaltenango (Table 6c). These two traits have earlier been identified as key traits in plant archi- 127 tecture. At East Lansing, seedwt correlated negatively with podsup (Table 5d) but the association was positive in the early cycles at Chimaltenango (Table 6d). Low correlation coefficients for pairs of traits indi- cate that selection for them could be carried out independ- ently without the undesirable effects of negative correla- tions (Ghaderi g; 31, 1984). Host of the correlations in this group involved seed-pod traits with architectural traits. With the observed in 3959 recovery of architecture in the early cycles, the trait might be controlled by a block of genes which are tightly linked and inherited en hlgg. Several rounds of intermating were necessary to break this linkage allowing recombination to occur in the region. Stated in another way, this could be a situation of 'linkage freeze' on free and random recombination for ef— fects regulated by genes in the gene blocks, alluded to by Kelly and Adams (1987) , as a consequence of intermating between divergent germplasm pools. Looking at the parent correlation analysis, it is seen that seedwt and architype rating were highly significantly (r - -.646 ***) and negatively correlated (Appendix C, Table 1). This correlation, however, is almost completely dissipated to a paltry yet statistically significant (r a - .089*) value in the F3 (Appendix C, Table 2). This suggests an association which was weakened after only one round of 128 intermating. Seedwt and architype were negatively corre- lated in all cycles but this association was not signifi- cant at East Lansing (Table 5b) . At Chimaltenango, the association was significant only in the Co and C4 (Table 6b). Crossing elite parents, as was the case in this study, would represent a situation in which seed size and extreme architecture genes would be in repulsion phase association. This being the case, recurrent selection would be an effec- tive method for assembling architecture and large seed size in one genotype. The report by Kelly and Adams (1987) underscores the last statement. b. No association in Co but significant association in later cycles. There were many associations which were non-signifi- cant in the Co but became very significant in some or all subsequent cycles, at both locations. These included angle vs height, angle vs architype, podsmain vs height, podsmain vs hypodiam and intnodup vs architype (Table 5a). Others were seednum vs height, seednum vs architype, seednum vs hypodiam (Table 5b) , and, seednum vs seedwt, seednum vs podwidth, seednum vs nodesup and seednum vs intnodup (Table 5d) . 129 Many such associations were between seednum and archi- tectural traits. The hoped-for effect of recurrent select- ion is to increase the frequency of desired alleles in a population. Changes in gene frequencies for two or more traits in a multiple trait selection program is, as stated by Rutledge et a1, (1973), a source of genetic correlation. Recombination and reassortment can organize genes into new genetic matrices and introduce new kinds of association. c. Associations remaining strong and/or getting 'stronger' from one cycle to another. These associations were predominantly positive and oc- curred among architectural traits. The traits were ones that have been selected from the multiple regression analy- sis be principal indicators of bean plant architecture. With selection progressively biased towards these traits, their gene frequencies in the population would have in- creased and contributed to stronger genetic correlations. Some of these associations were architype vs height, hypo- diam vs height, podsmid vs architype, hypodiam vs architype and hypodiam vs podsmid (Table 6). 130 d. Associations getting 'weaker' from one cycle to another. Two examples may be cited from this analysis. These are nodesup vs height (Table 5a) and intnodup vs podsmid (Table 6 a). Both were non-significant in the parents (Appendix C, Table 1) but were significant in the F3 fami- lies (Appendix C, Table 2). This suggests that these were new associations brought about by intermating with select- ion. By selecting for shorter internodes and more nodes, the erectness of the plant became more pronounced and well defined, as the vininess of the central axis was curtailed. However, as selection proceeded for taller plants, the internodes in the upper region of the plant got longer and hence fewer nodes and pods were recorded for that region. With longer internodes, fewer nodes were recorded in the mid-section thus weakening the association. e. Significant associations changing in sign from one cycle to another. These associations were found at Chimaltenango and oc- curred among seed-pod traits, involving seednum vs other traits. The sign change took place in or after C2. From C3, the sign for the significant associations were the same at 131 the two locations. Seednum vs seedwt was expected to be a negative correlation while seednum vs podlen was expected to be positive since, for the same situation, pods with larger seeds would have fewer seeds per pod while longer pods had more seeds. This was not the case in the early cycles at Chiamltenango (Tables 6d and e). This observation is attributable to genotype x environment interaction. f. Associations between yield and its components and among components. Correlations between yield and its components were positive in all cycles but not significant in every cycle at Chimaltenango. Podsmid produced the highest coefficients among the pod distribution traits (Tables 5a and 6a). Seednum and seedwt contributed significantly to yield at Chimaltenango in C2 only, but at East Lansing, their con- tributions were significant in all cycles except in C0° The signs of the correlations among yield components have been summarized in Table 7. Seednum correlated positively with podsup and podsmid but negatively with podslow and seedwt. These could be residual relationships from the parents. Seedwt correlated negatively with podsup and podsmid but positively with podslow, the last two being statistically non-significant. This relationship reflects the structural 132 Table 7. Sign of correlations among grain yield components in the PRS cycles. Seednum Seedwt Podsup Podsmid Podslow Seedwt - (-) Podsup + (-) - (-) Podsmid + (+) - (-) + (+) Podslow - (+) + (-) - (+) .1. (+) Sign of associations in parents are in brackets organisation in the pinto seed and plant type where pods are predominantly set in the lower third of the plant and are large-seeded. Pods in the upper parts of the plant tend to have smaller seeds. The parental correlations indicated that increasing the number of pods in any region decreased the seedwt (Table 7). Pods in the lower region of the plant had more seeds per pod than those in the upper parts but the correlations in some cycles for seednum vs podsup were positive while seednum vs podslow were negative, suggesting that new correlations were established. By deploying pods to the upper regions, the 133 negative correlation between podsup vs seednum in the pa- rents changed to positive while the positive correlation between podslow vs seednum changed to negative in C4. The observation that podsmid produced the highest Coefficient among the pod distribution traits and the fact that it was extracted as one of the principal indicators of architecture in the regression analysis suggests that when breeding for high-yielding architypes, plants with more pods in the middle should be a selection criterion. The problem of adaptation is encountered again. Seed- num and seedwt contributed significantly to yield in C2 at Chimaltenango. With respect to associations among yield components and especially to the East Lansing data since the Chimaltenango data had problems with adaptation, it is seen that, frequently, the associations were negative. This agrees with the observation by Adams (1967) of negative correlations among yield components of the field bean. The correlations were attributed to developmental rather than genetic sources. The primary yield components were postu- lated by Adams to show an interdependence which enables them to compensate for each other in the face of stress in the environment, such that the optimal geometric configu- ration of the yield construct is attained. In this study, numbers, sizes and positions of plant parts were reorganiz- ed from one cycle to another and attempts were made through 134 intermating to break up associations. It appears these developmental associations are not easily broken up. It is noteworthy that seednum correlated negatively with seedwt, but with two of the pod distribution traits (podsup and podmid), the associations were positive. Seednum correlated negatively with podslow, the third pod distribution trait. Seedwt also correlated negatively with podsup and podsmid but positively with podslow. When a plant has a high pods- low value, it resembles a standard pinto and would be likely to carry also the large seed of the pinto, leading to low seednum as in the pinto. Pods in the lower third of the plant have heavier seeds. But as pods are deployed to the upper parts of the plant where seeds are smaller, yield loss is compensated for by an increase in pod and seed numbers. g. Negative associations among architectural traits It is noteworthy that significant negative associat- ions were found predominantly in associations involving branch angle and all three pod distribution traits (Table 5a and b). This suggested that there is a limit to the emphasis that should be placed on selection for plant profile. When plants get too narrow, plant yield will be 135 drastically reduced through reduction in pod numbers thro- ughout the plant profile. Narrow branch angle may impose competition for space by the pods in the plant profile. Selection for moderate branch angle (60° to 70°) may be recommended. On the other hand, since yield is more a population than individual phenomenon, yield could be in- creased by planting plants with narrow profile at higher densities. Plant height was negatively correlated with architype rating and branch angle. The non-architypes tended to be prostrate. With intermating and recombination, the pros- trate nature was reduced so that plants became more erect and tall but with long vines. Selecting against long vines reduced the plant and improved lodging resistance. As vine lengths were reduced the plants became relatively shorter but had narrower profiles due to more acute branch angles. h. Negative associations between seed-pod traits and archi- tectural traits. The associations in this group included podwidth vs podsup, seedwt vs podsmain, podwidth vs podsmid, podwidth vs podsmain, seednum vs angle, and podlen vs angle. How- ever, these associations were non-significant in all cy- cles. 136 7.3.3 Canonical correlation analysis None of the canonical correlations observed at Chimal- tenango was significant, except for C3. At East Lansing, three significant correlations were observed in all the cycles, except Co in which only two were significant (Ap- pendix D, Table 1). This indicates that there were two to three independent dimensions of the architectural traits set which were significantly related to corresponding di- mensions of the seed-pod traits. Loadings of opposite signs were frequently encountered in the standardized canonical coefficients matrix with some reversal in sign in the canonical structure (correlation between the original variables in a set and their canonical variables). In the redundancy analysis in this study, the variance of the architectural traits explained by their canonical variables ranged from 9.70% to 25.53%. over the cycles at East Lansing. The variance explained by the opposite set of variables (seed-pod traits) ranged from a mere 2.41% to 5.84%. On the other hand, the variance of the seed-pod traits explained by their own canonical variables ranged from 75.04% to 81.99% over the five cycles. This suggests a stronger within-pool relationship for the seed-pod traits than for the architectural traits. However, the variance of 137 the seed-pod traits explained by the architectural traits was still low, being 8.42% to 18.15%, over the cycles. An example of the analysis is presented in Appendix D, Tables 2a and b. Since the results were non-significant it would serve no useful purpose to present the voluminous data on these variates. From the squared multiple correlation matrix, it was observed that the canonical variables had very small load- ings (Appendix D, Tables 3 and 4). It was clear from the redundancy analysis that relat- ionships between the two data sets which characterised the two germplasm pools were weak. This will prevent any relia- ble conclusions from being made from the analysis. The squared multiple correlation matrix indicates further that none of the canonical variables had loadings large enough to be considered to have predictive power for any other variables. It would not be possible to make reliable predict- ions between gene pools about architecture on the basis of seed-pod data, and vice versa. CHAPTER EIGHT ANALYSIS OF RECOMBINATION AMONG BEAN TRAITS 8.1 Introduction Kelly and Adams (1987) were unable to find recombin- ants for large seed size and erect plant‘ architecture in the early cycles of recurrent selection. They attributed this to a linkage probably in the repulsion phase. By analysing the recombination patterns in various cycles, it may be possible to identify the cycle in which recombinat- ion for the above-mentioned traits first occurred. This would indicate the stage at which the postulated linkage was broken. The analysis would also be able to identify traits which are involved in recombination in each cycle. Anderson (1939) proposed a procedure by which the extent of recombination among three selected traits could be demonstrated using raw data. This procedure limits the study of recombination in this fashion to three traits. The use of principal component analysis would allow more traits to be considered, as will be considered in the following presentation. 138 139 8.2 Materials and methods In this study, data from the F2 and F3 populations as well as five recurrent cycles were independently submitted to principal component analysis usisng the SAS (1985) PRIN- COMP routine. From the factor patterns, traits were fol- lowed through consecutive cycles to find out the changes in the magnitude and sign of their loadings from PC1 to later PCs and from one cycle to another, where applicable. Notice was taken of whether or not a trait was loaded with large values in one or several PCs. The proportions of variance due especially to the first three PCs were compared among the various populat- ions. The contribution by PC2 was converted to a length relative to the length of PC1 which was proportional to the variance it contributed. The extent of recombination was diagramatically repre- sented as a spindle in a multidimensional space as proposed by Anderson (1939) except that the elipsoid was drawn with straight sides due to difficulty of judging perspective correctly. 8.3 Results and discussion 8.3.1. Recombination F2 and F3 populations. 140 The first PC accounted for only 17.01% of the total variance and it required five and six PCs to account for 55% of the total variance in the F2 and F3, respectively (Appendix E, Tables 1 and 2). PC1 showed loadings of oppo- site sign but the trend, with regard to sign of loading, was similar to PC1 in the parents. Changes in sign were observed in hypolen, angle, podwidth and podlen (Appendix E, Table 1) . Seedwt was the only variable with high nega- tive loading. The contribution from internodes and number of branches decreased. The loadings on PC2 and later PCs frequently varied in sign and magnitude from those in the parents. The proportion of contribution by PC1 and PC2 in the F2 were similar (17.01% and 15.60%) while in the F3 the ratio was approximately 2:1 in favour of PC1, as was the case in the parents (Table 8). The almost 50% reduction in the contribution to variance by PC1 from the parents to the segregating populations may be explained by the obser- vation that traits such as height, hypodiam and podsmid, whose loadings were among the highest and confined to PC1 in the parental population, resolved into several PCs in the segregating populations. That is, they loaded signifi- cantly in more than one, usually successive, PCs (Table 9 and Appendix E, Table 1). This is attributable to recombi- nation from intermating whose effect is breaking up of associations and assorting genes to establish new rela- tionships. This caused the contribution to variability to 141 Table 8. Contributions to variance by the first three princi- pal components in parents, F2 and F3. PC1 PC2 PC3 Cumulative Parents 38.24+ 16.97 10.23 65.45 F2 17.01 15.60 9.55 42.17 F3 18.20 10.25 8.27 36.42 +, expressed as percentage of total variance 142 Table 9. Loadings in the first six most important principal components in the parents. PC1 PC2 PC3 PC4 PCS PC6 £31311; '''' 2553 "'TSSI3""?321;""TIEZSmTESEmTIZ32"" Nbranch ‘Zgfifi ‘2121 -.1270 -.1000 -.0101 ‘5219 Hypolen -.1886 $2311 ‘5018 .0134 .0681 .0167 Hypodiam $1912 .0426 .0565 -.1975 -.2740 .1168 Angle .1458 $2592 ‘1211 .0498 .0969 -.1476 Podsup $251; .1951 -.1281 -.3943 .1340 .1077 Podsmid ‘1212 .1255 -.O121 -.2128 -.0335 .1370 Podslow ‘ZZQQ -.3086 .0332 .0790 -.0356 .1960 Nodesup .1027 -.3243 -.1233 -.4380 $2265 -.2011 Nodesmid .0511 -.2783 ‘1256 .0463 -.3575 ‘2211 NOdBBlOW ‘2618 -.1725 .0618 .1122 ‘5212 12251 Lowpodht .1161 ‘1121 -.0791 .1085 -.0844 -.1448 Podsmain .1544 -.0192 ‘15:: ‘2118 &Z§2§ .0659 POWidth -.2357 .0331 .0178 .0370 -.2783 ‘3586 Podlen -.2711 -.0809 -.2085 .0054 .1187 11119 Seednum .1237 -.4050 -.0192 .1135 .0830 -.1004 Seedwt -.2891 .0806 -.1389 &QZ§A .1795 £1001 Intnodup .1945 -.0787 -.3366 $5151 .0413 -.0156 Intnodmid $2212, $2299 -.2245 &2§§Q_ .0659 -.1621 Intnodlow ‘ZQZZ -.0918 -.1173 .1694 -.5625 -.1301 PROPORTION 38.24+ 16.97 10.23 6.49 5.97 4.92 CUMULATIVE 38.24 55.21 65.45 71.95 77.92 82.85 +, expressed as percentage of the total variance 143 be distributed thinly over several more effective sources of variation. The F3 required more PCs to account for the same amount of variation because during the selfing of the F2 the residual heterozygosity from the F2 provided material for further recombination. Seed-pod traits were significantly positively loaded in PC2 through PC5 in the F2 populations. In the F3 fami- lies, their effects were non-significant as indicated by the lack of significant loading in the first six PCs. The tendency to be loaded significantly in more than one PC suggests that genes for these traits were involved in the recombination and reassortment processes. Number of branch- es and branch angle as well as the internode length in the upper and lower thirds of the plant were traits which, hitherto, contributed significantly to variance by virtue of their being loaded in the PC1 in the parents, but failed to be significantly loaded in the PC1 in the F2. This may suggest that these traits may have undergone reorganisation through recombination. Further, the reversal of sign for the pod dimension traits indicates that new associations between the two germplasm pools, even though weak, were begining to form. However, this did not include seedwt which maintained its negative sign throughout (Table 9 and Appendix E, Table 1). 144 9.3.2 Recombination in cycles. The contributions to variance by various PCs were similar from one cycle to another. The first six PCs ac- counted for a total of less than 60% of the total variance in each cycle (Tables 10 to 14). Height, hypodiam and podsmid were consistently highly positively loaded in all cycles. Branch angle was also consistently negatively loaded. The results reinforce previous ones and compels the conclusion that, indeed, height, hypocotyl diameter and pods in the middle part of the plant are the most important predictors of bean plant architecture. Branch angle was positively associated with PC1 in the parents but after intermating in the F2, it remained negative throughout the cycles. In effect, this change in relationship between architecture and branch angle came about when Changes in pod dimensions of the architype were initiated by recombi- nation. It would be recalled from the correlation analysis that significant negative correlations among the architect- ural traits were found predominantly in those involving branch angle and pod distribution traits (podsup, podsmid, podslow). For the new pinto architype to maintain its large pods, the branch angle would have to be smaller in value than in the parent navy architype. The branch angle for the 145 Table 10. Loadings in the first six most important principal components in Co. PC1 PC2 PC3 PC4 PC5 PC6 13213;; """ 3353. "73333"'IZEE"3T3§E§"'E§3"3TS35;"-' Nbranch ‘19:; .1752 -.1396 .1000 -.4094 -.1273 Hypolen -.1998 .1850 12165 12661 15258 -.2533 Hypodiam .1608 .1485 -.0267 $2109 -.1033 14120 Lowpodht -.1466 .1064 ‘2182 ‘3512 .0313 $3222 Angle -.1139 -.3621 .1044 -.2523 .0608 .1384 Podsup .1834 -.0321 -.1073 $5121 .1730 .0110 Podsmid $3521 .0891 -.1406 $2402 -.0818 .0105 Podslow 11680 -.0167 -.1093 -.2408 .0252 -.1979 Nodesup .1067 .1840 -.3098 -.2295 .0452 13181 Nodesmid .0285 13281 -.1482 -.1920 ‘3121 .0285 Nodeslow 13183 .0330 -.1050 -.1031 .1696 -.1654 Podsmain .1050 -.1928 -.3315 .1062 13125. .1043 Intnodup ‘11:; -.1418 ‘1122 -.0403 .0167 .0346 Intnodmid 12462 -.3399 12812 -.0223 -.2177 .0910 Intnodlow .1872 -.0096 13823 -.1185 .1829 13181 Podlen .0603 11128 .1960 -.0009 -.2928 .0090 Podwidth -.1071 11133 .1634 -.1918 -.1015 .0998 Seednum .0603 .0617 .1513 ‘2252, -.1011 -.4245 Seedwt .0362 .1176 .1913 -.2933 .0450 -.2254 PROPORTION 16.94+ 9.59 8.31 7.53 6.42 5.44 CUMULATIVE 16.94 26.53 34.85 42.37 48.79 54.24 +, expressed as a percentage of the total variance 145 Table 11. Loadings on the first six most important principal components in C1. PC1 PC2 PC3 PC4 PCS PC6 Height ‘1825 .0930 ‘222fi .0415 -.0443 .1322 Nbranch .1306 ‘fifififi -.1243 -.1232 -.1096 -.3842 Hypolen .0661 -.1017 -.3290 Lilifi -.1638 $1128 Hypodiam ‘Zfififi ‘Zfififi -.0809 .1357 .1400 -.1882 Lowpodht -.0007 .1599 .0353 $5160 ‘3656 .0293 Angle -.2111 -.1251 .1041 .0571 ‘1162 -.1346 Podsup .1028 ‘1951 -.2838 ‘2108 .0307 -.2616 Podsmid ‘lfififi ‘ZQQQ -.1177 .0577 -.1052 -.0716 Podslow .LZQQQ -.0392 -.0227 -.3370 -.4387 .0557 Nodesup ‘QQQZ -.3223 .0715 -.O701 ‘2921 -.0192 Nodesmid ‘1112 -.2811 -.0746 -.0095 .1929 -.0894 Nodeslow ‘1411 .0159 .1781 -.1930 .1172 -.0906 Podsmain .1237 -.O165 -.2124 .1920 -.1261 .0978 Intnodup .0197 ‘2121 ‘Afilfi .0253 -.0823 .1987 12211 Intnodmid -.1833 ‘1321 .0723 -.1797 .1082 Intnodlow 12113 -.0947 13122 .1321 .1942 -.0077 Podlen .0728 .0543 .0935 -.1349 .1758 $1315 Podwidth .1424 -.2347 .0605 yfillfi -.3804 .1160 Seednum .1541 ‘2559 -.1391 -.0884 ‘2052 ‘4291 Seedwt .0239 -.1788 ‘12:; ‘1111 -.2887 -.2851 PROPORTION 18.38+ 11.12 9.62 7.24 6.92 5.75 CUMULATIVE 18.38 29.50 39.13 46.37 53.20 59.04 +, expressed as a percentage of the total variance 147 Table 12. Loadings in the first six most important principal components in C2. PC1 PC2 PC3 PC4 PC5 PC6 ESISEE """ LEE-"3559'"TIEZE"ITSSII"'TISSImTBES"" Nbranch ‘31:; -.1537 -.1785 -.0135 -.4185 .0229 Hypolen -.1255 $3551 -.0569 -.0360 13632. -.0379 Hypodiam ‘4321 -.025 -.0408 .0520 -.0734 -.0379 Lowpodht -.0029 .1710 -.2050 ‘2112 -.1759 ‘2208 Angle -.0356 .1056 -.044a -.0804 -.00049 13521 Podsup .1309 -.2384 -.2480 -.0431 -.1156 -.0625 Podsmid ngzg -.0688 -.1057 -.0916 -.0496 -.0256 Podslow .1930 .1105 ‘1121 -.1517 .0514 -.3024 Nodesup ‘24:: .1668 -.1007 -.0706 .0912 ‘1914 Nodesmid 12268 $3511 -.2359 -.2506 .1836 .1486 Nodeslow 13216 .0493 .1239 -.1429 -.1741 .0244 Podsmain .1428 -.0874 ‘2222 -.2828 12488 -.2658 Intnodup .1854 .0144 14258 .1250 .0161 .1762 Intnodmid -.0014 -.2721 14185 11013 -.1360 .1405 Intnodlow .0605 .0136 .1817 $2394 page; ‘5245 Podlen .1643 .0364 -.2110 12581 .1926 -.2703 Podwidth -.0339 11388 .1551 12135 -.0791 -.1997 Seednum ‘2459 -.2173 -.1900 13338 13312 -.1228 Seedwt -.a309 11161 .0099 .1978 -.4925 -.1819 PROPORTION 15.79+ 9.92 9.36 8.65 6.19 5.92 CUMULATIVE 15.79 25.71 35.08 43.73 49.94 55.85 +, expressed as a percentage of the total variance 148 Table 13. Loadings in the first six most important principal components in C3. Height .1121 .2111 .1094 .1570 .0131 -.1924 Nbranch .2112 -.3546 -.1706 -.1150 -.1983 .0708 Hypolen -.1708 .1097 .1111 .1047 .0793 -.0044 Hypodiam .1111 -.0883 -.0258 -.0058 .1147 .1832 Lowpodht .0757 -.0437 .0925 -.1702 .1180 .1933 Angle -.1492 .1699 -.2465 -.0704 -.1445 -.0774 Podsup .1833 -.3294 -.0993 -.1885 .2112 .1935 Podsmid .1111 -.3030 -.0219 .1406 .0899 .0237 Podslow .1704 .1440 .0124 .1212 .1418 .0189 Nodesup .1859 -.0110 -.0795 .0246 -.3729 -.0062 Nodesmid .1878 -.1004 .2111 .1211 -.2584 .3227 Nodeslow .0085 -.1971 .0958 -.3237 .0703 E Podsmain .0802 -.0612 -.0685 .1111 .1111 .0786 Intnodup E .1211 -.1858 -.0481 -.0048 -.1250 Intnodmid .1239 .1111 -.3204 -.2633 .1529 .1850 Intnodlow .1863 .1111 -.0856 -.0743 .1808 -.2381 Podlen E .0286 .1111 -.3382 .1390 .0617 Podwidth .0422 .2111 .2111 .0688 -.0717 .1211 Seednum .2111 .0239 .1111 -.4031 .0257 -.2957 Seedwt .0384 .1970 .1966 .1096 -.3240 .1211 PROPORTION 15.49+ 11.83 8.80 8.33 6.49 6.22 CUMULATIVE 15.49 27.33 36.14 44.46 50.96 57.18 +, expressed as a percentage of total variance 149 Table 14. Loadings in the first six most important principal components in C4. PC1 PC2 PC3 PC4 PCS PC6 £21313; """ 23;; "'T3352"'3§£m73;§;"'E§_E"3TI§2§"" Nbranch .2222 -.2063 -.1495 .0259 -.4171 -.1619 Hypolen -.1825 -.0743 .0641 .2221 p.222; —.2448 Hypodiam p.2122 —.0486 -.0691 -.1134 .0215 .0267 Lowpodht -.0356 .1054 -.3282 .2222 .1482 .1511 Angle -.2364 .0840 -.0174 -.1434 .0709 .2122 Podsup .2121 -.0083 -.2686 -.1876 .2222 .0441 Podsmid .2212 -.0824 -.0723 -.1576 .0063 .0700 Podslow .0973 -.2259 .2222 -.2946 -.1093 -.2594 Nodesup .1529 .0986 .1927 .1291 .2221 .0982 Nodesmid .0178 —.3559 .2222, .1826 .1122 -.1108 Nodeslow .2212 .0506 .1495 .0071 -.0993 .1642 Podsmain .0585 .0833 .0894 -.5204 .2222 .1469 Intnodup .1101 .1221 .1919 .0356 -.0770 -.1407 Intnodmid .1258 .2212 -.1603 -.0980 -.1299 -.2044 Intnodlow .1182 .2412 .1881 .1031 .0862 -.1507 Podlen .2222 -.1486 .0404 .1872 .0849 .2111 Podwidth -.0339 .0788 .2222 .0411 -.0129 .2222 Seednum .2221 -.0504 -.2534 .2222 .0921 .0023 Seedwt .0307 .1017 .2222 4.2122 -.3717 .2222 PROPORTION 13.74+ 11.70 9.48 8.86 6.46 6.09 CUMULATIVE 13.74 25.45 34.93 43.80 50.26 56.35 +, expressed as a percentage of the total variance 150 navy check parent was 23.33° while it was 28.84° in the C4 (Appendix A, Tables 4 and 15). Seedwt loaded positively in PC1 in all cycles except C2' the magnitude of the loading being negligible each time. However, the magnitude of seedwt loadings was quite large and positive in the P02 in all cycles, and, along with podwidth was the most important variable in PC2 in C2 (Table 12). It is noteworthy that while pod traits, namely, podlen and podwidth, on the whole were mostly positive in all the cycles and generally were loaded with increasing magnitude of the coefficients from Co to C4, seedwt only maintained nonsignificant positive loadings on the PC1s. This suggests that when recombining architecture and seedwt, new relat- ionships created in the recombinants were stronger between the pod dimension traits and architectural traits than between archtectural traits and seedwt. Podwidth and seedwt were usually loaded with identical sign in the PCs and the two were positively correlated. This may indicate that the association of seedwt and architecture in the pinto archi- type may be via podwidth. Seednum loaded positively and of significant magnitude along with the architectural traits in PC1 in all cycles except Co. This confirms that this trait is more of an architectural attribute than it is a seed-pod trait. Seed- num depends on the number of racemes which in turn depends 151 on the number of nodes, the latter being an architectural trait. With this relationship, it is not surprising that seednum loaded in the PC1 along with architectural traits. The ratio of proportion of contributions to total variance by the first two PCs indicate a relationship of approxi- mately 2:1 in favour of P01, from Co to CZ, as was the case in the F3. Thereafter, the two contributions were similar. The value would indicate a greater amount of recombination after C2' As was reported earlier, the pod traits loaded with increasing magnitude for the coefficients on the P01 as cycles advanced. Kelly and Adams (1987) failed to reco- ver recombinants in the early cycles. The reason could be that recombinants in the early cycles involved mainly architectural traits. Significant recombination between seed-pod traits occurred in the C3, the cycle in which Kelly and Adams first observed satisfactory recombinants, and beyond. ‘ The fact that the primary architectural traits were significantly loaded in P01 in all cycles suggests that the basic structure for architecture was recovered in C0 and maintained as such, with minor modifications, as seed-pod traits were added. The failure to recover satisfactory recombinants in the early cycles should not be miscon- strued to mean a lack of recombination at all between seedwt and architecture. Figure 37 indicates that while 152 architecture may have been recovered in 2922 in Co, seedwt changed gradually. It has been suggested earlier in this discussion that pod dimensions recombined with architecture in the early cycles. 8.3.3 Recombination spindle In Figures 38 and 39, the shaded portions indicate, proportionally, the fraction of the multi-dimensional space which represents realized recombination. Complete recombina- tion would be a rectangle represented by ACBD. AB represents P01 and is equal in length to CD. Partial recombination would produce a parallelogram defined by Ach. PC2 is drawn along CD. It is difficult to present the 'spindle' in three dimen- sions but by being consistent in presentation, the diagrams would reflect the differences in the data. By setting a length for AB, the length of cd can be obtained. The proportional lengths of the various genetic populations are presented in Table 15. The F2 population has the highest value for the length of the PC2 axis while the parents have the smallest. The area Ach for the F3 was nearly a rectangle (Figure 38). F2 is the genetically most variable population in a cross. Maximum recombination takes place in this generation. With one round of selfing (F3) the length of P02 dropped to near that of the parents. Popula- tions become progressively homozygous with selfing, reducing 153 Recombination analysis in F2 and F3 generations Figure 38. of bean crosses, using principal components. u *u fl? 1‘!” I l \i“ l i ““n W lysis in five phenotypic recur- iOn ana Recombinat Figure 39. 155 the residual variability available at meiosis for recombi- nation. The value for Co was almost identical to that for the F3 (Table 15). This was not surprising since the C0 con- sisted essentially of groups of F3 families. It is observ- ed from this table that the PC2 length progressively in- creased from C0 to C4. The parallelogram in C0 changed to near-rectangular in C4 (Figure 39) It would be recalled that Kelly and Adams (1987) reported failure to observe recombination in the early cycles between the two diverse germplasm sources. They first selected the desirable recombinant (large seed size and good architecture) in C3. The frequency analysis for seedwt showed that there was a generally steady progress in seedwt increase from C0 to C4 indicating recombination between architecture and seedwt, since the former, it was observed, was recovered in the Co. As the cycles advanced, the 'linkage freeze' suggested by Kelly and Adams (1987) succumbed to the intermating and allowed recombination to occur 0 156 Table 15. Length of PC2 axis in various bean populations. Population Length of PC2 Parents 3.55 Cycles Co 4.52 Cl 4.84 C3 6.11 c. 6.81 CHAPTER NINE IDENTIFICATION OF FUNDAMENTAL AND FUNCTIONAL RELATIONSHIPS IN BEAN TRAITS 9.1 Introduction In a breeding program, a breeder may target one or several traits for selecting. To be able to handle a large number of plants in a segregating population, the breeder needs to know a few traits are effective indicators of his objectives. Some traits which are fundamentally related to others in that they influence the same general function and may be under the same kind of genetic control. Using traits which are functionally related as target traits may tanta- mount to unecessary duplication and waste of time and resources in a breeding program. The breeder may be better of chosing traits from different functional groups to offer him a broader and more effective basis for selecting to- wards his breeding objectives. This study was conducted to identify such functional groups among all the bean traits scored. 157 158 9.2 Materials and methods Data from Experiment I were used in this study. The traits measured were separated into two classes, seed-pod traits (four traits) and architectural traits (15 traits), to reflect the two diverse sources of germplasm employed. This allowed three sets of analysis to be made, two for the classes independently and one for the classes combined. This would offer an opportunity to examine both inter- and intra-class relationships. In factor analysis, the choice of traits to include has a direct bearing on the outcome. In this study, traits which were considered response variables in that they were products of other traits, or derived traits which were calculated from other data, were excluded. For example, yield is a product of seedwt x seednum; height is a func- tion of internode number and their lengths: total number of pods was derived from podsup, podsmid and podslow. By so doing, a chance was given for the analysis to reconstruct these and other concepts without bias and in the process supply information on possible genetic relationships. Variables whose loadings were positive and of large magnitude in the factors were also highly correlated with each other as indicated by the correlation analysis. Similar- ly, variables with high negative loadings were found to be 159 negatively correlated with those with high positive load- ings in the same factor. In factor' analysis, it is desirable eventually to associate a factor with a concept (biological in this case). The traits which showed high negative loading coef- ficients were found to be 'anti-concept' , that is, they worked to suppress the expression of the identified biolo- gical concepts. The first two factors accounted for most of the variance but their contribution was not of large enough magnitude in the cycles such that a plot of these factors would serve any useful purposes. 9.3 Results and discussion 9.3.1 Relationships among the seed-pod traits The factor patterns at the two locations were similar, as confirmed by the positive correlations among factor loadings in the various cycles at the two locations (Ap- pendix F, Table 1) . Two principal factors (PF) were ex- tracted in each cycle. The traits with the highest loadings were essentially the same in each cycle at both locations except in C0 where seedwt had the highest loading at Chima- ltenango while seednum loaded most significantly in East Lansing in PF2. In Cl, the traits switched between factors 160 at the two locations; podlen and seednum loaded in PF2 at East Lansing but in PF1 at Chimaltenango (Tables 17 and 22). In (:0, podlen and podwidth were associated in one factor from the seed traits. However, starting from C1, seednum and podlen were associated in one factor while podwidth and seedwt were associated in another. It should be noted that the association between seed- num and seedwt was inverse in the same factor and further, that in Co, these were the highest-loading in PF2 at both locations. This was not the case in subsequent cycles. Co was an unselected population. The negative association in the same factor suggests a relationship in which the two traits may be governed by two sets of genes which are inversely related. The two sets of genes were contributed by different elite parents, seednum being associated with architectural gene pool while seedwt is a pinto trait. The inverse relationship, depicting a developmental compensato- ry relationship, may exist in the repulsion phase because of the sources of the genes. Table 26 offers an alibi to this suspected repulsion phase linkage in the parents. The two factors extracted were highly loaded by seedwt in the PF1 and seednum in PF2. In PF1, the two traits were in- versely related. There, obviously, was no dissociation in this linkage and hence no opportunity for recombination in this region, in Co. As the cycles advanced, the linkage was 161 Table 16. Loadings on the first two most important principal factors in Co for seed-pod traits in East Lansing. Podlen .1212 .1463 Podwidth. .1121 -.2149 Seednum .1989 .1112 Seedwt .2477 -.2122 PROPORTION 35.04+ 26.54 CUMULATIVE 36.04 61.58 +, expressed as a percentage of the total variance Table 17. Loadings on the first two most imporant principal factors in C1 for seed-pod traits in East Lansing. Trait PF1 PF2 "€355; """" SETITISEQ" Podwidth .1111 .0580 Podlen .1591 .1111 Seednum -.3919 .2221 PROPORTION 37.36+ 26.41 CUMULATIVE 37.36 63.78 +, expressed as a percentage of the total variance 162 Table 18. Loadings of the first two most important principal factors in C2 for seed-pod traits in East Lansing. Trait PF1 PF2 £§2§£§£ """ I££25"'ITZEEI' Podlen .1211 .2548 Seedwt -.0753 .2222 Podwidth .0731 .1221 PROPORTION 40.83+ 38.63 CUMULATIVE 40.83 79.46 +, expressed as a percentage of the total variance Table 19. Loadings of the first two most important principal factors in C3 for seed-pod traits in Lansing. Trait PF1 PF2 £22533; """ IEIE§"'3TIZEZ' Podlen [.2212 .2204 Podwidth .0810 .2112 Seedwt -.0245 .1212 PROPORTION 41.93+ 32.61 +, expressed as a percentage of the total variance 163 Table 20. Loadings of the first two most important principal factors in C4 for seed-pod traits in East Lansing. Trait PF1 PF2 Seednum .2222 -.1916 Podlen .2221 .1967 Podwidth -.0842 .1222 Seedwt .0874 .1212 PROPORTION 39.79+ 32.64 +, expressed as a percentage of total variance Table 21. Loadings of the first two most important principal factors in Co for seed-pod traits in Chimaltenango. Traits PF1 PF2 "1335;; """" :35; ""3333" Podwidth .1211 .0621 Seedwt .1637 (.2112 Seednum .5943 -.2122 PROPORTION 42.40 28.83 +, expressed as a percentage of the total variance 164 Table 22. Loadings of the first two most important principal factors in C1 for seed-pod traits in Chimaltenango. Trait PF1 PF2 E352; """" 2313""355" Seednum .2211 -.2256 Podwidth .1790 .2111 Seedwt -.2872 .1111 PROPORTION 31.10 26.80 CUMULATIVE 31.10 57.90 +, expressed as a percentage of the total variance Table 23. Loadings of the first two most important principal factors in C2 for seed-pod traits in Chimaltenango. Trait PF1 PF2 Podlen .2221 .2458 Seednum .2122 -.2205 Podwidth .2884 .1222 Seedwt -.2401 .1212 PROPORTION 40.11 28.10 CUMULATIVE 40.11 68.21 +, expressed as a percentage of the total variance 165 Table 24. Loadings on the first two most important principal factors in C3 for seed-pod traits in Chimaltenango. Trait PF1 PF2 ;;ednu;—_= .22.. .163;— Podlen .1212 -.3378 Seedwt . 1032 .2222 Podwidth .3719 -.1111 PROPORTION 41.20 28.75 CUMULATIVE 41.20 69.95 +, expressed as a percentage of the total variance Table 25. Loadings of the first two most important principal factors in C4 for seed-pod traits in Chimaltenango. Traits PF1 PF2 '333I2R”""'T§§3§""T3§EZ’ Seednum .6958 .5505 Podwidth .5680 -.2808 Seedwt -.3227 .8353 PROPORTION 35.68 + 26.32 CUMULATIVE 35.68 62.00 +, expressed as a percentage of the total variance 166 Table 26. Loadings of the first two principal factors in the parents for seed-pod traits. Trait PF1 PF2 E3312; -------- 323"":3312" Seedwt .1212 -.4795 Seednum :19225 Lillfi Podwidth - .4379 -.4729 PROPORTION 90.42+ 9.10 CUMULATIVE 90.42 99.52 +, expressed as a percentage of the total variance 167 broken, the negative coefficient dwindling in magnitude (Tables 16 to 19). In effect, it was not possible to reco- ver large-seeded pods with many seeds (recombinants) in the early cycles until after C2, which is in consonance with the report by Kelly and Adams (1987) who first encountered desirable recombinants in C3. Chronologically, seedwt and seednum were independently extracted in different factors, in the parents, but they came together in C0 in an antagonistic relationship, and had to separate under the pressure of intermating with selection, starting from C1. In the last separation, it appears a truce, so to speak, had been achieved to permit limited exchange of genes across the genetic borders of the two sets of seed genes. To accommodate this recombination which was to permit seeds in a pod to be numerous while getting larger, pod dimension traits had to reorganize. In the parents and Co, they were associated together in PF1, but subsequently, seedwt and podwidth were associated in one factor while seednum and podlen were associated in another (Tables 16 to 20). This new arrangement is logical; large seeds need large pods while many seeds need longer pods for accommodation. The only notable descrepancy in these trends arose in C3 in Chimaltenango, where podwidth and seedwt were, unex- pectedly, inversely related in PF2 (Table 24) . It would be 168 recalled from an earlier discussion and especially from Figure 17, that podwidth at Chimaltenango was one of three traits which were consistently larger in value in all cycles than those at East Lansing. Seedwt, however, did not follow this aberrant pattern (Figure 18) . This means the correspondence between seedwt and podwidth at the two lo- cations had to be inverse. Large pods at Chimaltenango did not necessarily carry heavier seeds. This might have been a problem with genotype x environment interaction. It is customary, in factor analysis, to attempt the task of assigning of meaningful concepts which reflect a functional relationship of traits significantly loaded in a factor. Tables 2a to f (Appendix F) summarize the concepts for seed-pod traits in the cycles and parents. It is very clear in the tables that there are a set of genes whiCh control seed number. Looking at Figure 36, it would be difficult to exceed a certain maximum seed number for beans without adverse consequences. In the Co, we can identify a pod dimension factor (PF1) in addition to seed number in PF2. Generalizing from the other cycles, two concepts may be proposed for bean seed-pod traits: 1. Size factor: Comprising seedwt and podwidth, this factor is concerned with genes which promote seed size, and there- fore pod size. ii. Number factor: This consists of pod length and seed 169 number, and suggests that these traits are under the same genic regulation, and responsible for defining seed number and pod length jointly. The pod dimension factor identified in Co was a tran- sient genetic system in the process of recombining two diver- se gene pools, since the C4 concepts compare with the parent- al concept. 9.3.2 Relationships among the architectural traits Linear correlations among loading coefficients at the two locations indicated high significance for the first three factors in all cycles (Appendix F, Tables 3 to 7) . Correlations in C3 especially were low. Factor loadings of above .50 were underlined for use in obtaining a name for each factor but emphasis was placed on higher loading coefficients in the factor patterns. Six factors were retained in each cycle in the East Lansing data while five or six were retained in the Chimal- tenango analysis. The retained factors together accounted for between 68.93% and 71.35% of the total variance in Chimaltenango, the first two factors accounting for between 34.96% and 46.05% of the total variance (Tables 27 to 31). In East Lansing, the six retained factors accounted for a total of between 62.09% and 68.84% of the total variation while the first two factors accounted for 30.18% to 34.92% 170 Table 27. Loadings of the first six most important principal factors in CO in Chimaltenango for architectural traits. PF1 PF2 PF3 PF4 PF5 PF6 EREQQES'EL?ITSEEI""T3§§S"”333;?"'TISSQ'mTSSES" Intnodlow .1111 .1978 .0194 .1608 .0394 -.1103 Intnodup .1211 -.2006 .1810 -.2255 -.1130 -.0415 Nodeslow ‘.1121 -.5125 .0429 .2265 -.2787 .3507 Nodesup .0573 .1111 -.2465 -.0126 -.1572 .0219 Nodesmid .0502 .2111 .1892 .3199 -.0856 .1452 Podslow .4027 -.6489 .0981 .0743 -.1085 .2170 Hypodiam .2541 -.0168 .1111 .0027 .0569 -.O9l3 Nbranch .0093 -.1170 .1111 .0269 -.0430 .0119 Podsmid .0488 .0222 .0164 .1112 -.0406 .1184 Podsup .1246 .0497 -.0076 .1121 .1008 -.2369 Hypolen .0729 -.1062 -.1780 .0870 .1111 -.O766 Lowpodht -.1094 -.0065 .4644 -.0503 .2111 .1044 Angle .0126 -.2020 .0327 -.l751 .1211 .1122 Podsmain .0893 .3914 -.1489 .1390 -.2035 .2112 PROPORTION 21.18+ 13.78 11.15 8.87 8.47 7.86 CUMULATIVE 21.18 34.96 46.11 54.97 63.45 71.31 +, expressed as a percentage of the total variance 171 Table 28. Loadings of the first five most important principal factors in Cl in Chimaltenango for architectural traits. PF1 PF2 PF3 PF4 PFS mEESSGE'CQE’TSQE2"‘3T33ES"’I'.'IESZ"’ITIS;3 """" Intnodmid .1112 .1083 .0077 .2814 .1991 Intnodlow .1212 .0110 .2038 -.0908 .1237 Podslow .2111 .4694 .0939 -.2533 -.0938 Nodeslow .1111 .4646 .1250 -.2527 .0733 Podsmid .2006 .2121 .4952 -.0215 .1620 Podsmain .3531 .2111 .2119 .2226 -.1465 Nodesup .3898 .4746 .2367 .3251 -.0639 Ang1e .0599 -.7872 .1290 .1356 -.l450 Hypodiam -.0697 -.0594 .1111 -.1102 -.0499‘ Nbranch .1802 .1774 .1111 -.0418 -.0876 Nodesmid .3664 .2878 .4672 -.3297 -.l778 Podsup -.1725 -.0280 -.2207 .1111 -.0054 Lowpodht .1671 .0859 -.0201 .3088 .2211 Hypolen -.0401 .0209 -.1177 -.2417 .1112 PROPORTION 32.98+ 13.08 9.47 8.67 7.15 CUMULATIVE 32.98 46.06 55.53 64.20 71.35 +, expressed as a percentage of the total variance 172 Table 29. Loadings of the first five most important principal factors in C2 in Chimaltenango for architectural traits. PF1 PF2 PF3 PF4 PFS 2323321213213;-':15;S""TE's'SmT-TII3'2m33LIES"' Intnodlow .2212 .3165 -.0377 -.3752 .0549 Podslow .2212 .0772 .0170 .2719 .3396 Intnodup .2221 .0093 -.1523 .2063 .1157 Nodeslow .2221 -.3365 .3250 .1356 -.0909 Podsmain .4779 .1362 .4679 .3857 -.3448 Hypolen .0553 .2122 -.0062 -.0891 -.0764 Nodesmid -.0450 .2222 -.0216 .2546 -.0004 Hypodiam .0884 .0332 .2222 .1375 .4039 Podsmid .3953 .0053 .2112 .3095 -.1326 Angle .0977 .0311 -.7956 .2079 .0393 Nodesup .1291 .2127 .0797 .1211 .0632 Lowpodht -.0828 .4956 .1369 -.6179 -.1446 Nbranch -.0213 -.0512 .0852 .1140 .2122 Podsup -.2938 .3672 .3033 .3837 -.5046 PROPORTION 22.87+ 15.22 11.43 10.95 8.46 CUMULATIVE 22.87 38.09 49.51 60.47 68.93 +, expressed as a percentage of the total variance 173 Table 30. Loading of the first five most important principal factors in C3 in Chimaltenanago for architectural traits. PF1 PF2 PF3 PF4 PFS InEQSEGfiumu-TBZII““T3§§I""TS;-7§""TBESS"" Intnodlow .2222 .1386 -.1936 .0123 -.1596 Intnodmid .2221 .1340 -.2363 -.1778 .1387 Nodesup .2222 .1203 .2460 .0098 .1092 Nodeslow .2221 .4852 .1535 .0396 .1408 Podsmid .0006 .1212 .0623 -.0882 .0504 Podsmain .3263 .1222 -.0049 -.3652 -.1326 Podslow .3754 .2122 -.1510 .2611 -.1015 Nodesmid -.2321 .4105 .1166 .0862 .3976 Angle -.1070 -.1732 .2211 .0954 .0086 Nbranch .1409 .2435 .2212 -.0268 .0963 Hypolen -.0985 .0740 .1379 .1121 .2801 Podsup -.1235 .1774 .0583 -.7382 .3122 Lowpodht .1649 -.1439 .0574 .0342 .2112 Hypodiam .4434 .4123 -.0254 -.2501 .2121 PROPORTION 28.58+ 12.72 11.43 8.71 7.50 CUMULATIVE 28.58 41.30 52.73 61.44 68.94 +, expressed as a percentage of the total variance 174 Table 31. Loadings of the first five principal factors in C4 in Chimaltenango for architectural traits. PF1 PF2 PF3 PF4 PFS ESSSST'ESEK'TISSS""TSSSS""TS§ET'ZTZEZE" Nodeslow .2222 .2057 -.2318 .1288 .0543 Nodesup .2111 -.ll78 -.1272 -.1473 .2525 Intnodmid .0730 .2111 -.O648 -.1137 .0602 Intnodup .1953 .1211 .1826 -.0330 .0567 Hypolen .3306 -.5280 .2487 -.1880 .0387 Angle -.2944 -.0891 .1211 -.1123 -.1772 Intnodlow .2467 .3424 .2222, .0954 .3041 Podsup -.0430 .1296 -.6832 .1975 .4436 Lowpodht -.0798 -.0116 .1197 .2222 .2026 Nbranch .0773 -.2442 -.3162 .1221 .1208 Hypodiam .1043 .3536 -.1734 .2222 -.0203 Podsmid -.0251 .0069 -.1592 .3200 .2122 Podsmain .2222 .1905 .0592 .0021 .2112 Nodesmid -.0372 -.1685 .1331 -.0804 .0298 PROPORTION 21.31+ 17.31 13.09 10.31 8.60 CUMULATIVE 21.31 38.61 51.70 62.01 70.60 +, expressed as a percentage of the total variance 175 of the variance, over the five cycles (Tables 32 to 36). In Chimaltenango, internode length measurements were consistently the highest loading variables in PF1 in all cycles except C4 in which they dominated PF2. In East Lan- sing, intnodup, intnodmid and intnodlow were frequently loaded together in one factor. They became progressively more important as the cycles advanced, moving from PF3 in Co to PF1 in C4 (Tables 32 to 36). In East Lansing, PF1 was frequently loaded by node and pod distribution varia- bles along with traits such as hypocotyl diameter and number of branches. Factors were found sometimes to resolve into others in the sense that traits could be highly loaded in more than one factor, or related measurements such as podsup, podsmid and podslow could be loaded in different factors. PF2 and PF3 were significantly loaded by more than one trait at both locations. In other words, these factors were frequently competitively loaded by more than one trait. In East. Lansingy PF4 'to PF6 ‘were frequently independently loaded by variables such as podsmain and branch angle. The relative importance of traits and the composition of fac- tors on the basis of the magnitude of loading coefficients was variable from one cycle to another at both locations, especially, between PF2 and PF4. 176 Table 32. Loadings of the first six most important principal factors in Co in East Lansing for architectural traits. PF1 PF2 PF3 PF4 PFS PF6 333;;IS""ZES"'T§ZEI""TIEESmITS'v'EE’mTSSSE""3331 Nbranch .2112 .3253 -.0106 -.0846 .2135 -.3741 Podsup .2112 -.l683 .0414 -.1317 .0360 .4620 Angle -.6106 .0173 .0548 -.3029 .1420 .0322 Podslow .2478 .2222 .3125 .0766 .0248 -.0258 Nodeslow .3001 .2211 .1963 .0675 -.0148 .1634 Lowpodht .1167 .2222 .1490 .0274 -.0906 -.1049 Intnodlow -.0706 -.0812 .1222 .1493 .1446 -.0427 Intnodup .1538 .2004 .1212 -.2421 -.0778 -.0083 Nodesmid .0636 .1004 .0512 .2122_ .0314 -.0857 Intnodmid .0300 .2067 .2222 -.6034 .0515 .0335 Hypodiam .3429 -.2661 .1443 .0209 .2222 .0652 Nodesup -.0658 .2333 -.0191 .4024 .2222 .2091 Hypolen .0379 -.4427 -.0041 .2713 -.6358 .1913 Podsmain .0161 .2304 -.0547 -.0539 .0505 .2222 PROPORTION 19.50+ 11.41 9.69 8.36 7.13 6.88 CUMULATIVE 19.50 30.91 40.60 48.96 56.09 62.09 percentage of the +, expressed as a total variance Table 33. 177 Loadings of the first six most important principal factors in C1 in East Lansing for architectural traits. Nodesmid Nodesup Intnodlow Nodeslow Nbranch Hypodiam Podsmid Podsup Intnodup Intnodmid Lowpodht Podslow Hypolen Angle Podsmain 11122 11123 11251 15125 -.1517 .3271 .2676 -.1640 .1200 -.3827 .0698 .2318 -.0928 -.0977 .0493 .0001 .0435 .1533 .1565 -.0772 -.3056 .0913 PROPORTION 20.75+ 13.67 CUMULATIVE 20.75 34.42 .0288 -.2580 -.1185 -.0601 11.35 45.71 .1333 -.1269 .1936 .0142 .0650 -.7419 .1578 .2883 -.1207 9.41 55.18 .0742 .2665 -..0381 -.0236 -.1162 .1460 .2391 767 -.6556 .0515 6.88 62.06 .1044 .1331 .3650 -.0899 .0122 -.0282 .0902 .2091 .1990 6.79 68.84 +, expressed as a percentage of the total variance 178 Table 34. Loadings of the first six most important principal factors in C2 in East Lansing for architectural traits. PF1 PF2 PF3 PF4 PP5 PF6 £32232?"'25;-"T32;§2"I?BETTE;§S"'3T3;33"'33123 Hypodiam .1122 .1484 .0250 .2707 .2259 -.0529 Podsmid. .2212 .1759 -.0220 .2397 .0375 .0478 Nodeslow .2222 .1215 .4078 .0900 -.1283 .2010 Hypolen -.4893 .3845 -.1190 .2567 .0986 .0918 Nodesmid .1776 .2222 .0938 .0138 .0806 .0096 Nodesup .3044 .4680 .1319 -.0247 .3139 .0447 Intnodmid .0520 -.7637 .2215 .0709 .3554 .0220 Podslow .1143 .0807 .2122 .3527 -.1024 -.2276 Intnodup .1879 -.2172 .2122 .0791 .3540 .0545 Podsup .3911 -.1200 -.6455 .3386 .0285 -.1043 Podsmain .0680 -.0338 .1028 .2112 -.0615 .0173 Intnodlow -.0448 -.0578 .0825 .0039 .1222 -.1121 Lowpodht .0059 .1566 -.3144 -.1786 .4384 .2214 Angle -.0331 .0104 -.0215 .0094 -.0333 .2221 PROPORTION 17.98+ 12.41 9.65 8.61 7.28 6.77 CUMULATIVE 17.98 30.39 40.03 48.64 55.92 62.69 +, expressed as a percentage of the total variance 179 Table 35. Loadings of the first six most important principal factors in C3 in East Lansing for architectural traits. PF1 PF2 PF3 PF4 PF5 PF6 ;;;;;;"“:;;;i":t;;z;'“'t3;;;‘“:t;;;;““t3;;;“it;63. Podsmid (.1121 -.1106 .2291 .3110 .0964 -.2642 Nodeslow .1111 .3055 .3740 -.0798 -.1879 .0351 Podsup .1111 -.1533 -.1054 .1427 .4969 -.0612 Hypodiam .4665 .2884 .3064 .2473 .3714 -.1726 Hypolen -.6558 -.1355 .1801 -.0465 .1341 -.2819 Intnodup .0411 .1111 .0589 -.0717 -.1604 -.1023 Intnodmid .0781 .1211 -.3719 -.0721 .0502 .0660 Intnodlow -.1423 .1121 .1476 .2008 .1856 .2198 Nodesmid -.0180 -.1380 .1111 .0431 -.0379 -.1781 Nodesup .2191 .1084 .1112 -.0620 .1383 .3942 Podsmain .0295 -.0508 -.0586 .2211 .0269 .0412 Podslow .0071 .2377 .2257 .4951 .4670 -.3008 Lowpodht -.0684 .0663 .0608 -.0359 .1121 -.0749 .Angle -.1171 .0382 -.0561 -.0109 -.0980 .2222 PROPORTION 17.98+ 13.93 10.09 8.27 7.77 6.91 CUMULATIVE 17.98 31.91 42.00 50.27 58.04 64.95 +, expressed as a percentage of the total variance 180 Table 36. Loadings of the first six most important principal factors in C4 in East Lansing for architectural traits. PF1 PF2 PF3 PF4 PF5 PF6 RESET-£52m};E’mTSZIEmITEESS'"'T333'2'""TIZBE Intnodmid .1121 .0807 -.1332 .1420 -.0022 -.3609 Intnodlow .1111 -.0018 -.0046 -.0558 -.0092 .2319 Nodeslow .1503 .1111 -.0088 -.1251 .0161 .2098 Podsmid -.0762 .1111 .0113 .3433 -.1393 .0408 Hypolen -.1309 -.5598 -.1992 -.0942 -.1022 .4689 Podslow -.1164 .1159 .1121 -.1094 -.1458 .0710 Lowpodht -.0110 .0445 -.8307 -.0477 -.0179 .1127 Podsup -.0762 .0513 -.0897 .1111 -.0988 -.0094 Podsmain .0964 .1107 .3924 .1111 .4454 .1543 Hypodiam .0215 .3902 .0475 .4582 -.3897 .1003 Angle -.1284 .1170 -.1603 -.0892 .1111 -.1627 Nbranch -.1833 .3960 -.0310 .0298 -.6480 -.2065 Nodesup .1982 .1223 -.0401 .1313 .0213 .1111 Nodesmid -.4247 .1692 .1923 -.4333 -.1029 .4799 PROPORTION 15.67+ 14.50 10.36 9.55 7.90 7.22 CUMULATIVE 15.67 30.18 40.54 50.09 57.99 65.21 +, expressesd a percentage of the total variance 181 The populations under consideration in this study are segregating populations. Identifying individual factors by concepts on a cycle basis alone may not be a useful excer- cise since recommendations for selection would not be made on that basis but general for a breeding program. A more useful and worthwhile approach would be: i. Identify associations within factors: This would help in recognizing the traits which are likely to be defining or influencing the same biological function. Further, it would also help in the recommendation of one or two traits which are easy to evaluate, from the group, for use in selection in a breeding program. ii. Observe the relative ranking with regard to PFs: Those which are frequently loaded in the first two to four PFs may be considered more important indicators of what the traits represent (architecture in this case). iii. Compare the outcome with results from the regression analysis for the purpose of corroboration of evidence. In Table 37, PF1 for the parents is loaded by branch number and pod distribution traits just as PF1 in Co in East Lansing (Table 32). It may be noted that in C0 branch angle was loaded in PF1 by a coefficient of similar magni- tude, except that it had a negative sign. Since most pods are borne on the branches, the more of the latter, the more of the former. But the number and how they are distributed in the profile depends on the branch angle. 182 For the same number of pods, wider angles would cause more pods to be located in the lower region of the plant. Path coefficient analysis by Duarte and Adams (1972) in dry beans suggested that the number of pods per plant may be influenced through the number of nodes and the number of leaves in this sequence. Included in the PF1 in the parents is hypocotyl diameter. It influences the number of branches via plant height. It may not have many genes in common with pods and number of branches. PF2 in the parents was principally a nodes factor (Table 37). The moderate loading coefficient of podslow was not unexpected since Adams (1982) suggested that nodes influence the number of pods via the number of racemes, which must form only at an axillary position (which means leaves and nodes). Internode length measurements dominated PF3 and since plant height, in part, is a fucntion of internode length, this PF may be called a height factor. PFs and PF6 are branch angle and pods on the main stem factors, respectively. For selection purposes, number of branches, number of nodes in the upper- third of the plant, branch angle, and the number of pods on the main stem would be recommended from this analysis. These were among traits identified previously as substant- ive indicators of architecture. In the cycles, the internode measurements loaded to- gether in the same factor in each cycle and at both locat- ions. This suggests that the three traits are strongly 183 associated and any attempt to change the length in one region would be accompanied by changes in the other two. This particular association was stronger at Chimaltenango, where the three internode lengths dominated PF1 from Co to C3 and in PF2 in C4. The low contribution of factors to total variance in the cycles as compared to the parents indicates the amount of change due to recombination with selection that took place. To follow cycle-to-cycle Chang- es, concepts were assigned to factors after examining the analysis and observing specific patterns of association and their possible roles in plant architecture. The concepts are as follows: a. Height (elongation) factor: This factor comprised traits which promoted stem elongation, the sum total of which indicated plant height. The traits from the factor pattern were intnodup, intnodmid and intnodlow (internode length measurements) which were most of the time associated with the same factor. b: Structural (skeletal) factor: Traits in this factor are those responsible for the framework of the plant and may be further partitioned into} i. Sturdiness factor: Comprising hypodiam and hypolen, these traits are anti-lodging and ensure the erectness of the plant. ii. Profile factor: This is made up of branch angle 184 and number of branches, traits which define the plant profile. c. Distribution (number) of reproductive parts factor: These traits are concerned with the number of units or reproductive components within the plant frame. The traits are podsup, podsmid, podslow, podsmain nodesup, nodesmid, nodeslow and lowpodht. Tables 8 to 12 (Appendix F) present the factor pat— terns in the concepts for various cycles and locations. The height factor was consistently the most important factor in Chimaltenango in all cycles. Height at East Lansing became progressively more important from its third position in C0 to first in C4. This indicates that height is one of the reliable indicators of architecture. The structural factor also became progressively more important from its fifth position in C0 to first in C3. The most important structur- al traits in the cycles were hypocotyl diameter and number of branches. Together with height, these three traits were clearly the most important determinants of plant architect- ure in dry beans. This evidence corroborates that from the multiple regression analysis. Further, it supports the suggestion by other researchers, including Bramel 21; 21 (1984), that preceding, for example, a multiple regression analysis with a PFA will enable summarization of the data for selecting traits for inclusion in the prediction equat- ion while eliminating bias due to multicolinearity. 185 With minor exceptions in C1 and C3 in Chimaltenango, and C4 in East Lansing, all five biological concepts des- cribed above were found in each cycle at both locations. The order of extraction of these concepts was not, however, the same in each cycle, indicating that different traits were important in different cycles, and this was due to changes in selection pressure and targets from one cycle to another. 9.3.3 Relationships among all traits combined. For the parents, the first five PFs accounted for 81.09% of the total variance. Combining all traits in one analysis jproduced, only’ one significant change. PF2 was loaded by seed-pod traits, shifting the loadings in Table 37 (architectural traits only) one PF later. PF2 may be described as a seed-pod factor. PC1 remained the same at the top as when only architectural traits were considered. All architectural traits, except nodesmid, were positively loaded while all seed-pod traits had negative loadings. The reverse was true in PF2, except for podslow (Table 38). In each case, the exceptions had negligible coefficients. This, once again, confirms that there were genes from two divergent pools in the breeding program. These sets of genes were 'anti-each-other' (or antagonistic). 186 Table 37. Loadings of the first six most important principal factors in parents for architectural traits. PF1 PF2 PF3 PF4 PF5 PF6 322;;13"155-"3333""TISESm'TBIES'""3232""TEE?" Nbranch .2211 -.2353 .1622 .0285 -.0389 .1166 Podsmid .2122 .2017 .1365 .3280 .2892 .1968 Hypodiam .6620 .1063 .0280 .4969 .2555 .1305 Nodesup .0631 .2112 .0274 .0584 -.1160 -.0039 Intnodup .1087 .0514 .2122 .2300 -.0732 .1395 Intnodmid .4137 -.0978 .5830 .1565 .4759 -.0003 Hypolen -.2198 -.4S77 -.5177 —.3009 .1846 .1953 Intnodlow .1755 .0148 .2653 .2121 -.0035 .0133 Podslow .1221 .4721 .1721 .5422 -.0697 .4609 Angle .1940 -.1105 -.1026 -.0312 .2221 .2923 Lowpodht .3978 -.4012 .1504 .0875 1.4924 -.1009 Podsmain .0976 -.0637 .0119 .0630 .1765 .1221 Nodeslow .3064 .4342 .3779 -.0056 .1540 .5840 Nodes -.0734 .0648 -.0552 .1720 .0358 .1938 PROPORTION 40.18+ 21.10 13.46 8.60 7.18 5.00 CUMULATIVE 40.18 61.28 74.73 83.33 90.52 95.52 +, expressed as a percentage of the total variance 187 Table 38. Loadings of the first six most important principal factors in the parents for all traits. PF1 PF2 PF3 PF4 PF5 PF6 REESE-"22227317773137"'TIZEI'WTSEE""3315? Podsup .1111 -.2286 .2231 .1263 .0004 .1100 Podsmid .7781 -.3397 .1778 .1426 .2791 .2647 Hypodiam .6096 -.5145 .0185 -.0006 .4109 .1843 Podlen -.2493 .1111 -.0765 -.2203 -.1257 -.2834 Seedwt -.3084 .1211 -.2145 -.0216 -.2530 -.1394 Nodesup .0194 -.1474 .2121 -.0076 .0437 -.1181 Intnodup .1101 -.0734 .0256 .2111 .2138 -.0985 Intnodmid .3757 -.2544 -.1043 .6012 .1183 .3954 Intnodlow .1246 -.2622 -.0128 .2272 .1111 -.0528 Podslow .1814 .0432 .4425 .1788 .5882 .0667 Angle .1544 -.2419 -.1149 -.0657 -.0417 .1111 Seednum -.1030 -.1138 .2054 .1725 .0997 -.1543 Nodeslow .3290 -.0396 .3833 .3716 -.0082 .2540 Nodesmid -.0712 -.1627 .0327 -.0671 .1466 .0694 Lowpodht .3552 -.1888 -.3758 .1741 .0602 .3994 Podsmain .0711 -.1787 -.0363 .0273 .0589 .1631 Podwidth -.2417 .2378 -.1089 -.1166 -.1667 -.0922 Hypolen -.1967 .1266 -.3782 -.3985 -.2654 .1482 PROPORTION 38.11+ 18.77 11.11 6.86 6.23 5.10 CUMULATIVE 38.11 56.89 68.00 74.86 81.09 86.19 +, expressed as a percentage of the total variance 188 The correlations among the factor loadings from the two locations were generally significant and positive (Ap- pendix F, Tables 13 to 17). Between six and eight factors were extracted from the data at both locations. The factors retained in Chimaltenango accounted for 68.82 to 80.17% of the total variance, the first two accounting for 29.19% to 38.47% (Appendix F, Tables 18 to 22). In East Lansing, the retained factors accounted for 59.02% to 72.04% of variance while the first two contributed between 25.29% and 28.67%, over the cycles (Appendix F, Tables 23 to 27). The combined analysis for the cycles, similar to the parents, yielded little significant changes. The seed-pod traits were loaded together in nearly identical manner to that obtained in the seed-pod traits PFA (Appendix F, Tables 16 to 20). In Co, pod dimension traits were loaded in PF6; in C1, seedwt and seednum were loaded with inverse signs in PF6 with, podwidth loaded in PFS. By C2, the pairing had changed to the expected podlen + seednum and podwidth + seedwt in PF3 and PF4, respectively (Appendix F, Table 25) . This pattern was maintained up to C4 by which stage seednum and podlen were loaded in PF2 with seedwt loaded fairly highly in PF1. It would be recalled that architype was shown to have been recoverd in 1922. This means that emphasis was placed on incorporating seed-pod traits into architecture as the cycles advanced, confirming 189 the earlier suspicion that target traits as well as select- ion pressure changed from one cycle to another. This may be the reason for the seed-pod traits becoming gradually more important from PF6 in C0 to PF2 in C4. There were occasions in which the loadings of seed-pod traits were associated with fairly large loadings from architectural traits (Ap- pendix F, Table 27) . Some of such associations involved podwidth with either hypocotyl traits or number of branch- es. But this rare observations may indicate that seed-pod trait genes are quite unique from architectural trait genes. There may be a direct association between seed size and architectural traits. In fact, where architectural traits loaded significantly and positively, seed-pod traits were weakly to moderately negatively loaded. Parents showed highly significant negative correlations between seedwt and architype rating, height, hypocotyl diameter and pods in the middle-third of the plant. Thus, as expected, intermat- ing reduced the strength of associations. To obtain a tall, large-seeded plant, the negative association between seedwt and.height must be broken. The negative association did not appear to be developmental but rather genetic, having dis- sipated after the initial rounds of intermating as was evident in the East Lansing results. The combined data may be summarized as was done for 190 the previous categories by combining the concepts. The seed-pod traits were called 'economic traits'. Height again showed up as one of the most important concepts, the econo- mic factor appearing in PF3 (Appendix F, Tables 28 to 32). Except for height, the other concepts were frequently loaded in more than one factor in each cycle. CHAPTER TEN GENETIC DIVERGENCE AMONG PARENTS AND CYCLES OF RECURRENT SELECTION OF BEAN 10.1 Introduction The germplasm utilized in the phenotypic recurrent se- lection by Kelly and Adams (1987) was obtained from two sources which displayed certain readily descernible con- trasts in morphology, especially in seed size and gross plant architecture. Workers, including Singh and Gutierrez (1984), have reported that genetically controlled hindrance to hybridization exists in some crosses between the large- and small-seeded classes. Kelly and Adams (1987) did not report any widespread dysgenic events in their program to indicate prevalence of this problem. _ This study was designed to find out how divergent the parents from the two germplasm pools were and also to identify the traits which are principal sources of diverg- ence. By studying the divergence from one cycle to another, it would be possible to determine if significant genetic shifts were made, and between which cycles most changes were effected. This should shed some light on the patterns 191 192 of recovery of traits in the above-mentioned breeding prog- ram. 10.2 Materials and methods Two and three representative parents from the pinto germplasm pool and architectural pool, respectively, were investigated in this study, in addition to 100 selections fro each of the five recurrent cycles. Principal component analysis was performed on the parents to determine traits which were responsible for most of the variance. The pro- cedure may also identify fundamental relationships among the traits which may indicate the divergence between the two sources of germplasm utilized in the breeding program by Kelly and Adams (1987). Hahalanobis' D2 distances among the five parents were calculated independent of the distances among the five cy- cles. In each case, the biological distances were estimated on the basis of architectural traits and seed-pod traits, separately. In addition to a D2 analysis, the populations were submitted to canonical discriminant analysis, using the two sets of traits separately and then together as measurement batteries. By calculating the standardized canonical coef- ficients for each set of traits, it was possible to obtain 193 an indication of traits in each set which were responsible for most of the divergence among populations. The first two canonical variates were plotted in addition to constel- lations of the cycles on the basis of the D2 analysis. 10.3 Results and discussion 10.3.1 Divergence among parents The first six principal components (PC) accounted for 82.85% of the total variance, PC1 alone accounting for 38.24% (Table 9). Loadings of opposite sign were encount- ered in PC1: all architectural traits had positive loadings (except hypolen), while all seed-pod traits were negatively loaded (except seednum). The highest positive loadings were given by height, hypodiam and podsmid, while the highest negative loadings were produced by podwidth, podlen and seedwt. Height, hypocotyl diameter and pods in the middle of the plant, it would be recalled, were among traits identi- fied as the principal indicators of architecture in the multiple regression analysis. These traits hence may be considered the most representative of the architectural germplasm pool. The highest negatively loaded traits were 194 all seed-pod traits and, similarly, may be taken to be representative of the large seed (pinto) germplasm pool. It is significant to note that seednum (number of seeds per pod), even though biologically and technically a seed-pod trait, was the only positively loaded trait of the group. This is because high seed number is actually an attribute of architecture. In fact, in PC6 which was dominated by high positive loadings from seed-pod traits, seednum, this time, was the only trait with a negative loading coeffi- cient (Table 9). Unlike traits such as nbranch and hypolen which contributed significantly and positively to variance in more than one PC, these architectural traits mentioned above contributed to variance only in PC1, the most import- ant PC. This may further indicate the primary role of these traits in bean plant architecture. The opposite signs of the loading coefficients shown by the two groups of traits suggest negative association between them; traits which promote architecture are anti- seedwt. It may be said, also, that the architectural traits promote seed number and seed number is 'anti' seedwt. Further, the fact that the loadings of the most important principal component, PC1, could be grouped clearly into two "sub-factors" according to sign and attributed to biologic- al concepts, namely, architecture and seed-pod traits, which reflect the nature of the parental gene pools, would 195 indicate the existence of two functionally distinct gene groups. To achieve recombination between the two groups, the negative association had to be broken. This was achieved by the phenotypic recurrent selection in this study as evi- denced by the change in association, the initial negative correlation in the parents (r = -.646 ***) dissipating to r - -.096 * in the F3 generation and being non-significant in the cycles. The internode measurements (intnodup, intnodmid,int- nodlow) frequently were loaded alike as in PC1, PC3, PC4, and PC6 (Table 9). The other important architectural traits such as nbranch, angle, podsmain and podslow were all extracted.*with. significant loadings in the first three PC's. These results confirm the findings of the regression analysis that these traits have causative influences on bean plant architecture. ' The representative samples from the two germplasm pools differed significantly in terms of architectural traits, according to the D2 estimates. The results further show that there were similarities in cultivars within the architectural pool for these traits (Table 39 ). Seed-pod traits produced very highly significant differences bet— ween the two pools (Table 40). The Wilk's lambda test of the discriminating power of the measurement battery for 196 Table 39. Mahalanobis' D2 distances between parents on the basis of architectural traits. Olathe UI 114 X80149 Midnight c-20 UI 114 2.91 X80149 2.92 2.69 Midnight 5.29* 5.65* 4.21 c-20 7.14* 7.50** 6.34* 3.38 **, *: significant at .01 and .05 levels, respectively. Table 40. Mahalanobis' D2 distances between parents on the basis of seed-pod traits. Olathe UI 114 X80149 Midnight C-20 UI 114 1.83 X80149 4.51** 5.16*** Midnight 5.52*** 6.20*** 1.25 C-20 6.23*** 7.18*** 2.49 1.57 ***, **, significant at .001, .01 levels respectively. 197 Table 41. Standardized canonical coefficient for seed-pod traits in parents. CANl CANZ CAN3 lac-.5513"'"TZEZI"""TS§§I'""3335" Podlen -.4517 .4062 -1.6198 Seednum .3124 1.1875 .6183 Seedwt 3.2689 -.0515 1.7075 PROPORTION 93.39 .0604 .0050 CUMULATIVE 93.39 99.43 100.00 198 the grouping criterion was significant at the .0001 level. The first two canonical variates accounted for 99.43% of the total variance, indicates that the first vector is the predominant axis of variation. Traits loaded on this axis are the most important sources of variation. Using the absolute magnitude of the coefficients, the relative im- portance of traits in the primary axis can be obtained. Seedwt, clearly, is the most important source of divergence in the two germplasm pools. Vector 2 indicates seednum to be the next most important source of divergence. These results suggest that the parent germplasm sources differed in seedwt, especially, and seednum. Seednum has been shown to be more of an architectural attribute than seed-pod. It appears the parents did not differ architecturally as dras- tically as in seed size and pod characteristics. Morpholo- gically, all plants from the two pools looked alike in the early growth, standing erect until later stages of growth when the pinto group became viny and assumed a decumbent growth form. From Appendix A, Tables 1 to 11, it is evident that clearcut differences between the pools were observed in very few traits including height, podsmid and intnodlow. Seedwt ratio for the two germplasm pools was about 2:1 in favour of the pinto group. Such a dramatic difference was not found, generally, among the architectural traits. In the plot of the first two canonical variates, the navy 199 group clustered to the left while the pinto group clustered to the right (Figure 40). 8.3.2 Divergence among cycles a. Architectural traits as measurement battery. The first and second canonical variables accounted fOr 96.63% of total variance at East Lansing and 84.88% at Chi- maltenango (Tables 42 and 43). Wilk's lambda test was signi- ficant at the .01 level. A plot of the first two canonical variates shows that there is an overlap, but both Co and C1 separate out fairly clearly; C2 clusters out to the right portion though it is rather dispersed as a group. C3 and C4 are most similar, being located at the periphery of the general cluster (Figure 41). This indicates that the architectural traits were recovered in the early cycle of selection, recovered 111 2222 as Kelly and Adams (1987) observed. The later cycles only fine-tuned the architectural traits complex to accom- modate the seed-pod traits introduced from the pinto group. The D2 estimates of biological distances between cycles when architectural traits alone were used as the basis for estimating distance indicated that the distance between C3 and C4 was not significant at East Lansing. 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A Tj ¢.?+ I... a... . i .5 s ww.» o o o O N o nemwu 0 ~. u u o ~ :6 u o 2. . o 68:33 ofl..1~u ”a 8 . us .334... . o o 0 ON. _M& N ~_W_:u ~ . _. ~. u _ “O W m m o _w No Nu n>z _ flnOC1u bu. van" 0* ~30 +n1nn n10 nmnonmnma anmnwwawsmaw «cannpoau cmuao mun n1ewna +01 a10cunao. zcaamfim w: #30 Una" pannnmnm <01nocm n F Trait prob. > F m"""'BSS;;;I;""'III """""" EQIQEZ'm'III """" Height *** Intnodlow ** Intnodup ** Intnodup ** Nodesup * Hypodiam ** Hypodiam * Podsmid ** Angle * Angle * Intnodlow + Nodeslow + Nbranch + Podsmain + R2 : 11.12% - 12.51% 46.06% - 47.35% *88, *8, *, + : significant at .001, .01, .05, and .10 level, respectively. 259 Table 2. Architectural traits selected in C1 by four different stepwise multiple regression procedures from data from two locations, with architype as dependent variable. Location East Lansing Chimaltenango Trait prob. > F Trait prob. > F """"" fi;;§§§£""l§l"""""'"ESSSQIE’WIIT"m" Angle *** Height *** Podsmid *** Nodeslow *** Podsmain *** Lowpodht *** Hypolen ** Podslow ** Height ** Podsup * Nodesup ** Intnodmid + Podslow ** Nbranch + Intnodlow ** Hypodiam + Nodeslow + Nodesup + R2: 31.45% - 33.72% 57.04: - 58.43% ***, **, *, +: significant at .001, .01, .05,and .10 level respectively. 260 Table 3. Architectural traits selected in C2 by four different multiple regression procedures from data from two locations, with architype as dependent variable. Location East Lansing Chimaltenango Trait prob. > F Trait prob. > F """""i;2;33;;""112 """"""" ;:;;;;““'::: """" Intnodmid *** Podsmid *** Nodesmid *** Hypodiam * Hypodiam *** Podslow * Podsup *** Angle * Podmain * Intnodmid + Podslow * Lowpodht + Intnodlow + Podsup + R2 : 16.73% - 17.40% 58.08% - 61.42% ***, **, *, + : significant at .001, .01, .05, .10 level, respectively. 261 Table 4. Architectural traits selected in C3 by four different stepwise multiple regression procedures from data from two locations, with architype as dependent variable. Location East Lansing Chimaltenango Trait prob. > F Trait prob. > F """"" 557""":::"’““““'“;;;;;;;“"':::“""‘ Podmain *** Nodesmid *** Nbranch *** Intnodup ** Hypodiam *** Height ** Podsup *** Hypodiam ** Nodesmid ** Podsup ** Hypolon ** Intnodmid * Intnodup * Intnodlow * Podsmid * R2 : 28.40% - 29.01% . 72.87% - 72.98% ***, **, * : significant at .001, .01, .05 levels, respectively. 262 Table 5. Architectural traits selected in C4 by the stepwise multiple regression procedure for data from two locations, with architype as dependent variable. Location East Lansing Chimaltenango Trait prob. > F Trait prob. > F """" 12;;3312;"""III""""""§;Z;£E"'"III"""" Height *** Podsmid ** Angle *** Intnodup ** Nbranch *** Hypodiam * Podmain * Podsup + Intnodmid + Lowpodht + R2 : 29.66% - 30.58% 48.24% - 55.98% ***, **, *, + : significant at .001, .01, .05, .10 levels, respectively. 263 Table 6. Architectural traits selected in two crosses by the stepwise multiple regression procedure, with architype as dependent variable. Cross 1 2 Trait prob. > F Trait prob. > F """" EQSEZ;"““':::""""';;I;""""':::“““ Nbranch ** Hypodiam *** Angle ** Intnodmid * Height * Podsmain * Nodesmid * Intnodlow + Podsup * Nodeslow * Intnodlow * R2 ***, **, *, + : significant at .001, .01, .05, and .10 levels, respectively. 264 Table 7. Architectural traits selected in two crosses by the stepwise multiple regresssion procedure with architype as dependent variable. Cross 3 4 Trait prob. > F Trait prob. > F """"" 55351;;"m37’"""";;§;;;I;""':::“"" Angle *** Angle *** Nodesup * Hypodiam *** Lowpodht * Podslow *** Intnodup + Nodesmid ** Hypolen + Lowpodht ** Podsmid * Intnodlow * R2 ***, **, *, + : significant at .001, .01, .05, and .10 levels respectively. 265 Table 8. Architectural traits selected in two crosses by the stepwise multiple regression procedure with architype as dependent variable. ‘ Cross 5 6 Trait prob. > F Trait prob. > F ’ """ £332£I§""“"III """""" REES-""717" Podsup ** Angle *** Intnodmid ** Height ** Lowpodht * Nodeslow ** Angle * Podsup ** Nodesmid * Hypolen * Hypodiam + Podslow * Nodesup + Intnodlow + 122: ***, **, *, + : significant at .001, .01, .05, and .10 levels, respectively. 266 Appendix C Phenotypic character associations among bean traits in parents and F3 families. 267 Table 18. Phenotypic character association (r) among bean traits in the parents. Architype Nbranch Hypolen Hypodiam Angle Podsup Podsmid Podslow Nodesup Nodesmid Nodeslow Lowpodht Podsmain Podwidth Podlen Seednum Seedwt Intnodup Intnodlow Height .543** .530** .395* .757*** .445* .547** .822*** .655*** .174 .156 .769*** .271 .495** .508** .678*** .312 .655*** .569** .459** .390* -.020 .647*** .528** .420* .619*** .083 -.052 .066 .331 .470* .600*** -.463* -. 705*** .029 -. 646*** .052 .232 -.295 .578** .166 .677*** .659*** .108 -.l79 -0088 .353 .399* .177 -.255 -.289 -0145 -e260 .238 .203 -e342 .247 -.236 -.331 -.444* -.513** -.051 -.462* .117 .169 .330 .237 -.490** .388* -.564** -.468** Architype Nbranch Hypolen Hypodiam .351 .592** .829*** .476** .138 .180 .478*** .310 .217 .433* .623*** .220 .775*** .220 .552** Angle .262 .409* .042 -.198 .145 .294 .473** .411* -.225 -.523** -.204 -.337 -.l34 -.013 .05 levels, **' : significant. at respectively. .001, .01, and Table lb. traits in the parents. Podsmid Podslow Nodesup Nodesmid Nodeslow Lowpodht Podsmain Podwidth Podlen Seednum Seedwt Intnodup Podsup Podsmid .840*** .191 .239 -.185 .370* .441* .091 -.502** -.479** -.076 -.515** .212 Intnodlow .198 .469* .229 .023 .508** .449* .292 .488** .635*** .107 .664*** .309 .437* 268 Podslow Nodesup Phenotypic character association (r) among bean Nodesmid Nodeslow .216 -.410* .275 .112 -.214 .382 -.308 -.O3O .210 -.045 .481 -.502** -.389* .511** -.465* .486** .149 **' * 3 respectively. significant. at .4727** .347 .097 .630*** .412* -.256 -.416* .341 -.O38 -.315 -.216 -.236 -.145 .539*** .368 -.436* -.373* .386 .082 .556** .093 .001, .01, .05 levels, 269 Table 1c. Phenotypic character association (r) among bean traits in the parents. Lowpodht Podmain Podwidth Podlen Seednum Seedwt Int'up Podsmain .015 Podwidth -.133 -.377* Podlen -.291 -.484** .432* Seednum -.377 .138 -.380* -.082 Seedwt -.l73 -.314 .569** .756*** -.429* Intnodup .165 .100 -.303 -.292 .357 -.230 Intnodlow .148 .132 -.360 -.404* .206 -.491** .442* ***, **, * :significant at .001, .01, and .05 levels, respectively. 270 Table 28. traits in the F3 families. Height Architype Nbranch Phenotypic character association (r) among bean Hypolen Hypodiam Angle Architype-.020 Nbranch .199*** -.063 Hypolen .066 .025 -.112** Hypodiam .427*** .211*** .354*** Angle -.102* .278*** -.204*** Podsup .207*** .001 .256*** Podsmid .470*** .077 .463*** Podslow .465*** -.041 .308*** NOdesup .103* -.019 -.038 Nodesmid .206*** .001 .028 Nodeslow .482*** .070 .157*** Lowpodht .105* .083 -.021 Podsm8in .138** .219*** -.108** Podwidth .045 -.227*** -.095* Podlen .017 .068 .078 Seednum .155*** .150*** -.009 Seedsize .004 -.089* .045 Intnodup .437*** -.096* .131** Intnodlow .336*** .012 -.046 **’ * e respectively. . significant at .001, -.037 .060 -.228*** -.016 .312*** -.082 -.019 .517*** -.289*** -.l49*** .321*** -.l73*** -.066 .101* -.002 .134** .145*** -.001 -.155*** .303*** -.108** .211*** .073 .018 -.098* .l60*** -.016 -.023 -.065 -.l43*** -.057 .150*** -.027 .102* .247*** -.035 -.038 -.027 -.l48*** -.049 .073 -.095* .025 .191*** -.085 .01, and .05 levels, 271 Table 2b. Phenotypic character association (r) among bean tratis in F3 families. Podsup Podsmid Podslow Nodesup Nodesmid Nodeslow Podsmid .370*** Podslow -.006 .297*** Nodesup .060 .029 .001 Nodeslow .060 .169*** .029 .250*** Lowpodht .192*** .304*** .496*** .157*** .146*** Podsmain .146*** .021 -.314*** -.012 .125** -.l35** Podwidth .17l*** .l92*** .250*** .080 .051 .245*** Podlen -.O71 -.038 .037 .023 .030 .059 Seednum .032 .020 .180*** .052 -.097* .065 Seedwt .116** .163*** .023 .059 .156*** .112** Intnodup .056 .180*** .356*** -.051 -.175*** .292***GZ Intnodlow.092* .162*** .105* .096* -.020 .047 *1", **, * : significant at .001, .01, and .05 levels, respectively. 272 Table 2c. Phenotypic character association (r) among bean traits in F3 families. Lowpodht Podsmain Podwidth Podlen Seednum Seedwt Int'up Podsmain -.081 Podwidth -.008 -.015 Podlen -.029 -.034 -.005 Seednum .139 .038 -.011 .083* Seedwt -.106*-.094* .033 -.021 -.211*** Intnodup -.069 .092* .015 .077 -.074 .074 Intnodlow .116**.123** .022 .057 .008 -.026 .301*** MM, Hr, * : significant at .001, .01, and .05 levels, respectively. 273 Appendix D Canonical correlations between architectural traits and seed-pod traits in five phenotypic recurrent selection cycles 274 Table 1. Canonical correlation between architectural traits and seed-pod traits in various selection cycles in East Lansing. Cycle Canonical C0 C1 C2 C3 C4 variable 1 .409*** .497*** .428*** .426*** .622*** 2 .311* .319*** .352*** .380*** .455*** 3 .213 .290* .283** .317** .358* 4 .157 .186 .217 .169 .319 ***, **, *, significant at .001, .01, and .05 levels, respectively. 275 Table 28. Canonical redundancy analysis. Standardized variance of the seed-pod traits explained by: a.Their own canonical b. the architype variables variables '"ELSQSEZZSQ """ 23;;IQZI;;"’"";;;§3;EI;; """ EEQQIQZECQ’ .2204 .2204 .0545 .0545 .1940 .4144 .0198 .0743 .3309 .7453 .0280 .1023 .2547 1.0000 .0088 .1111 Table 20. Canonical redundancy analysis. Standardized variance of the architype traits explained by: a.Their own canonical b. the seed—pod variables variables "EESESEZISR """ 3;;31;ZI;; """" £§3§2§EZS§'"'E;;;I;ZI;;" .1173 .1173 .0290 .0290 .0934 .2108 .0095 .0385 .0872 .2980 .0074 .0459 276 Table 3. Squared multiple correlations between the architecture variables and the canonical variables of the seed-pod traits. Canonical variable Architype Nbranch Hypolen Hypodiam Lowpodht Angle Podsup Podsmid Podslow Nodesup Nodesmid Nodeslow Podsmain Intnodup Intnodmid Intnodlow .038 .007 .059 .004 .060 .028 .028 .046 .006 .024 .001 .013 .004 .056 .008 .060 .004 .068 .029 .029 .046 .030 .027 .020 .028 .029 .067 .013 .062 .022 .073 .029 .052 .051 .030 .027 .020 .028 .071 .019 .062 .022 .076 .029 .054 .051 .032 .027 .021 .028 .060 277 Table 4. Squared multiple correlations between the seed- pod traits and the canonical variables of the architure traits. Canonical variable Trait l 2 3 4 1323;:"T333"""T32§"""'TSSS""'T3§Z' Podwidth .131 .137 .170 .170 Seednum .086 .109 .143 .144 Seedwt .000 .028 .064 .074 278 Appendix E Principal component analysis of F2 populations and F3 families of beans. Table 1. Loadings on the first six most important principal 279 components in the szopulations. P01 902 903 904 905 PC6 {1223132 '''' I395; "-3552":TI1'25"ITIBII"IT3;ZE"'TSEEZ"" Nbranch .0277 .1219 .0542 19921 .0142 13210 Hypolen 12034 -.1211 .0494 12401 -.3484 -.l6ll Hypolen 19292 .0483 .0459 .1986 12021 .1236 Angle -.0280 -.2266 .0717 -.0927 -.0956 13911 Podsup 13121-.0890 12919 -.0012 -.1674 .1726 Podsmid 43032, ‘20:; .1238 .0532 13304 -.2066 Podslow .0423 13129 -.2124 -.1536 14015 .1759 Nodesup .1920 -.3295 .0915 -.1093 13193 -.0795 Nodesmid 12315 -.3159 -.1838 -.1459 -.0192 .0021 Nodeslow 12929 .1675 -.2001 .1386 -.0527 15444 Lowpodht 13991 -.1108 .1428 12319 -.2812 -.2272 Podsmain ‘2112 -.0397 .1368 -.2016 $2124 .1794 Podwidth .0187 .0530 12919. ‘3525 13105 -.3592 Podlen .0486 12911 -.5035 .1449 -.1333 -.2079 Seednum 12999 -.1063 -.5220 -.0042 .0026 -.2512 Seedwt -.2170 ‘2032 .0224 ‘2311 -.0869 .1728 Intnodup .0133 19999 $2114 -.2436 -.1151 -.0595 Intnodmid .0644 13944 12513 -.1803 -.1511 -.1935 Intnodlow .1914 .0987 .0808 -.3013 -.3003 .0112 PROPORTION 17.01+ 15.60 9.55 7.29 6.68 5.78 CUMULATIVE 17.01 32.68 42.17 49.45 56.14 61.93 +, expressed as a percentage of total variance 280 Table 2. Loadings of the first components in the F3 families. six most important principal 901 902 903 904 905 906 13213;; """ E---:;;;;---:;;;;---:;;;;---:;;;;---:_;_:.E---- Nbranch .2505 .0571 -.1554 -.5195 .0185 .0526 Hypolen -.0691 12251 .2224 .0372 $2802 .1521 Hypodiam .1511 .2959 .0171 -.1598 -.0451 -.0589 Angle -.1802 .0419 .0732 12911 -.3571 ‘1210 Podsup .211; .2050 .1658 -.2054 -.2358 -.2968 Podsmid .3151 .1776 .0078 -.2267 .0146 -.0617 Podslow .11123 -.1479 -.3292 .1155 -.0148 12519 Nodesup .0727 .1578 -.0644 .3422 .0797 -.4370 Nodesmid .0659 .4551 -.1095 12191 .2111 .0065 Nodeslow 12212 .0357 -.2609 12912 -.0286 .1054 Lowpodht -.0219 12:91 11522 -.0839 .1520 -.0235 Podsmain .1690 .0119 -.0567 .1520 -.3309 -.2490 Podswidth .0062 -.0702 -.0450 .1903 14016 -.2120 Podlen .0873 -.0621 -.0460 -.0792 -.2149 .1366 Seednum .1021 .1221 .1267 .0741 -.1519 .1625 Seedwt -.0046 -.1915 -.2137 -.1154 11§21 -.0784 Intnodup 12521 -.3794 .1603 .1022 .0604 $2222 Intnodmid .1931 -.4304 12999 -.0278 -.0566 -.1477 Intnodlow .2015 -.1708 .4281 .1982 .0855 -.1466 PROPORTION 18.20 10.25 8.27 7.21 6.28 5.54 CUMULATIVE 18.20 28.45 36.72 43.94 50.22 55.76 +, expressed as a percentage of total variance 281 Appendix F Principal factor analysis: Biological concepts associated with factors, correlations between factors at two locations and the factor loadings on the basis of all traits for various cycles. 282 Table 1. Correlation between principal factors extracted from data from the two locations. Cycle PF1 x PF1 PF2 x PF2 0 0.830 * 0.957 * 1 0.998 *** 0.883 * 2 0. 858 * 0. 664 3 0.914 * 0.158 4 0. 608 0. 102 '—.—_m-n-“~-.~—_~o-n...---—-.-—-—--——---—_—.-_-——-— *, ***, significant at 0.05 and 0.001 levels respectively. 283 Table 2a. Biological concepts associated with principal factors extracted from parents for seed-pod traits. Factor Concept 1 Size (Pod length Seedwt) 2 Number (Seed number) Table 2b. Biological concepts associated with principal factors in Co at two locations for seed-pod traits. Location Chimaltenango East Lansing Factor Concept Concept "'1 """ £33332;1337333557'EZS’EIQQQQZSE’EERQEJ"n width) width) 2 Number (Seed number) Number (Seed number) 284 Table 20. Biological concepts associated with principal factors in C1 at two locations for seed-pod traits. Location Chimaltenango East Lansing Factor Concept Concept 1 Number (Pod length Size ( Seedwt Seed number) Pod width) 2 Size (Pod width Number (Pod length Seedwt) Seed number) Table 2d. Biological concepts associated with principal factors in C2 at two locations for seed-pod traits. Location Chimaltenango East Lansing Factor Concept Concept '"I """ £$§§7£3$I§3§E£ """ ESEQ;'I§;;§';E;SQI—"" Seed number) Pod length) 2 Size (Pod width Size (Seedwt Seedwt) Pod width 285 Table 2e. Biological concepts associated with principal factors in C3 at two locations for seed-pod traits. Location Chimaltenango Lansing Factor Concept Concept 1 Number (Seed number Number (Seed number Pod length) Pod length) 2 Size (Seed size Size (Pod width Pod width) Seed size) Table 2f. Biological concepts associated with principal factors in C4 at two locations for seed-pod traits. Location Chimaltenango East Lansing Factor Concept Concept "'1 """ §£§£§£7§§2§££££2§ """ REQETQQEE‘QGQSET" Pod length) Pod length) 2 Size (Pod width Size (Pod width Seedwt) Seedwt) 286 Table 3. Correlations among factor loadings in Co at two locations for architectural traits. PF1 PF2 PF3 PF4 PFS PF6 PFl_ .450* PF2 .830*** PF3 .634** PF4 .068 PFS- ,510** PF6 .534* ***, **, *, significant at .001, .01, and .05 level, respe- ctively. Table 4. Correlations among factor loadings in C1 at two locations for architectural traits. PF1 PF2 PF3 PF4 PFS PF1 .776*** PF2 .711*** PF3 .545* PF4 .360 PFS -.501* ***, *, significant at .001, and .05 levels, respectively. 287 Table 5. Correlations among factor loadings in C2 at two locations for architectural traits. PF1 PF2 PF3 PF4 PFS PF1 .506* PF2 -.286 PF3 .649** PF4 .476* FPS .093 **, * , significant at .01, and .05 levels, respectively. Table 6. Correlations among factor loadings in C3 at two locations for architectural traits. PF1 PF2 PF3 PF4 PPS PF1 .159 PF2 .601** PF3 .646** PF4 .337 PFS .356 **, significant at .01 level. 288 Table 7. Correlations among factor loadings in C4 at two locations for arhitectural traits. PF1 PF2 PF3 PF4 PF1 PF2 PF3 .840*** .730*** .084 PF4 PFS PF6 .543* -.O37 *, significant at .001 and .05 levels,respectively. 289 Table 8. Biological concepts associated with principal factors in Co at two locations for architectural traits. Location Chimaltenango East Lansing Factor Concept Concept 1 Height Distribution (Pods) Structural (nbranch) 2 Distribution (Nodes) Distribution (Pods) 3 Structural (Sturdiness Height /profile) 4 Distribution (Pods) Distribution (Nodes) 5 Structural (Sturdiness) Structural (Sturdiness) 6 Structural (Profile) Distribution (Pods) Table 9. Biological concepts associated with principal factors in C1 at two locations for architectural traits. Location Chimaltenango East Lansing Factor Concept .Concept I """ 1221;; """"""""" BEEQI-ISQEESQ’ZEéS """"" 2 Distribution (Pods) Structural (Profile) 3 Structural (Sturdiness Height / profile) 4 Distribution (Pods) Distribution (Pods) 5 Distribution (Pods)/ Structural (Sturdiness) Structural (Sturdiness) 6 Distribution (Podsmain) 290 Table 10. Biological concepts associated with principal factors in C2 at two locations for architectural traits. Locations Chimaltenango East Lansing Factor Concept Concept 1 Height Structural (Profile /sturdiness) 2 Structural (Sturdiness) Distribution (Nodes) Distribution (Nodes) 3 Structural (Sturdiness) Height Distribution (Pods) Distribution (Pods) 4 Distribution (Nodes) Distribution (Pods) 5 Structural (Profile) Height 6 Structural (Profile) Table 11. Biological concepts associated with principal factors in C2 at two locations for architectural traits. Location Chimaltenango East Lansing Factor Concept Concept 1 ' 'EQIQEE """""""""" QEEZEQEQI’ZEESEIIS ””” 2 Distribution (Pods) Height 3 Structural (Profile) Distribution (Nodes) Structural (Sturdiness) Distribution (Pods) 01-h Distribution (Pods) Distribution (Pods) 6 Structural (Profile) 291 Table 12. Biological concepts associated with principal factors in C4 at two locations for architectural traits. Location Chimaltenango East Lansing Factor Concept Concept "T""'31;;21332123713332.3323"$5.312; """"""""" 2 Height Distribution(NOdes/pods) 3 Structural (Profile) Distribution (Pods) 4 Structural (Sturdiness Distribution (Pods) /profile) 5 Distribution (Pods) Structural (Profile) 6 Distribution (Nodes) Distribution (Nodes) 292 Table 13. Correlations among principal factors extracted at the two locations in Co for all traits. PF1 PF2 PF3 PF4 PFS PF6 PF7 PF1 .822*** PF2 .247 PF3 .543** PF4 .745*** PFS .668*** PF6 .498* *1”, 1”, *, significant at .001, .01, and .05 level, respectively. Table 14. Correlations among principal factors extracted at two locations in C1 for all traits. PF1 PF2 PF3 PF4 PFS PF6 PF1 .611** PF2 .610** PF3 .340 PF4 -.287 PFS -.150 **, significant at .01 level. 293 Table 15. Correlations among principal factors extracted at two locations in C2 for all traits. PF1 PF2 PF3 PF4 PPS PF6 PF7 PF1 .604** PF2 .801*** PF3 .723*** PF4 .385 PF5 .352 PF6 .327 PF? .383 ***, **, significant at .001, and .01 levels, respectively. Table 16. Correlations among principal components extracted at two locations in C3 for all traits. PF1 PF2 PF3 PF4 PF5 PF6. PF7 PF1 .666*** PF2 .301 PF3 .554** PF4 .144 FPS .044 PF6 .497* PP? .299 *1”, Hr, * : significant at .001, .01, and .05 levels, respectively. 294 Table 17. Correlations among principal factors at two locations in C4 for all traits. PF1 PF2 PF3 PF4 PFS PF6 PF? PF1 .677*** PF2 .346 PF3 -.195 PF4 -.048 FPS -.463* PF6 .674*** ***, **, * : significant at .001, .01 and .05 levels, respectively. 295 Table 18. Loadings of the first six most important princi- pal factors in Co in Chimaltenango for all traits. PF1 PF2 PF3 PF4 PPS PF6 $323333;-"EEmTSIZSmIISS2““?3ZZE"':IIS§""TI§§I' Intnodlow ‘8221 .2462 .1917 .0718 .0787 .0101 Intnodup ‘1261 -.1502 -.2841 .2160 -.2346 -.1210 Nodeslow ‘6562 -.3664 .0397 .0012 .2557 -.2382 Nodesup -.0497 ‘1181 -.0890 -.2076 -.0605 -.1519 Nodesmid .0587 $6612 .0801 .1023 .3106 .0293 Podslow ‘504; -.5251 -.0631 .0160 .1280 -.0270 Podlen -.0086 -.0445 ‘8816 .0747 -.0987 -.1732 Seednum -.3022 -.0154 4§A§1 .0296 .1354 .2185 Podwidth .0581 .0766 $6111 -.0808 -.1464 .1585 Hypodiam .2504 -.0134 .0146 ‘8111 .0020 .0913 Nbranch .0004 -.1160 .0449 ‘18:: .0520 -.0621 Podsmid .0810 .0746 -.0801 .0024 1&921 -.0171 Podsup -.1556 .0455 -.0020 .0421 Lfififig .0447 Hypolen .0683 -.1371 .0451 -.1880 .0564 ‘8511 Lowpodht -.1303 -.0129 -.0899 .4280 -.0283 ‘1291 Angle .0972 -.1279 .0591 .0254 -.1415 .0859 Podsmain .1202 .5981 -.0422 -.1857 .1522 -.1820 Seedwt -.0950 .0451 -.0099 .0978 -.1885 .0100 PROPORTION 17.73+ 11.45 9.61 8.68 7.46 7.14 CUMULATIVE 17.73 29.19 38.80 47.48 54.94 62.07 +, expressed as a percentage of the total variance Table 19. 296 C1 in Chimaltenango for all traits. Loadings of the first six principal factors in Intnodmid ‘3621 Intnodup 1§§24 Intnodlow yglgg Podslow Nodeslow Nodesup Hypodiam Nbranch Podsmid Nodesmid Podsmain Podlen Angle Podwidth Podsup Hypolen Lowpodht Seednum Seedwt PROPORTION 26.42+ iéfila 15218 .4604 -.0916 .1678 .2804 .3654 .4380 .0576 -.0447 .0707 -.1421 -.0218 .1916 .0274 -.0202 CUMULATIVE 26.42 +, expressed as a .4586 -.1818 -.1824 .0546 percentage of the .3252 -.2845 .0045 .3601 .0710 .3014 -.7564 .0423 .0060 .1295 .3229 .3299 .2618 .2137 -.2752 .1212 .1847 -.0651 .3365 -.2850 .0816 .0050 11211 -.7461 .0403 -.2845 -.1100 -.0627 .1107 -.2236 -.0462 -.0058 .1040 -.0726 -.1942 .0231 -.0466 -.0178 -.0223 .7178 .6582 -.6496 -.0491 7.31 62.82 total variance .1505 -.1888 -.O431 -.2640 -.0123 -.0116 .1340 .1664 -.2033 .1817 -.0568 12115 6.00 68.82 297 Table 20. Loadings of the first six most important princif pal factors in C2 in Chimaltenango for all traits. PF1 PF2 PF3 PP4 PF5 PF6 £3.43; ——E§_6_6—“.077:__“:0473 "T3osZ==='TZSIZ"'ITSI§§' Intnodup ‘1592 .0391 .0588 -.0656 .1323 .0293 Nodeslow ‘5823 .4567 -.3111 -.O499 .0516 -.2351 Intnodlow ‘2181 .1990 .2195 -.0833 -.3892 .2084 Podsmain .2472 &1§ZZ .1916 -.0716 .2391 -.1920 Podsmid .1561 ‘lfilfi .0180 .2572 .2001 .0545 Intnodmid .5321 ‘5522 -.1865 -.0086 -.2156 -.0543 Angle .2483 -.6159 .0930 -.0678 .3249 -.l783 Nodesmid -.0024 -.0129 ‘8502 .0766 .1121 .0038 Hypolen .0715 -.0260 m .1149 -.2492 -.0517 Podsup -.4l9l .3545 .4621 .0851 .2048 -.3544 Seednum .0885 .1093 .0417 ‘QQZQ .0234 -.0624 Podlen -.0681 .0386 .1974 (Llfiflfi -.l613 .2586 Nodesup .1187 .2732 .3587 -.1294 ‘ZQAQ .1589 Lowpodht -.1156 -.0068 .3810 .0228 -.709l -.O809 Podwidth -.0869 .0854 .0274, -.Ol95 -.OO47 ;§§§1 Nbranch .1396 -.l7l7 -.l353 .2633 .2487 $6211 Seedwt -.0369 -.l346 .0618 -.1811 .0342 .0219 Hypodiam .1904 .2968 -.0252 .2928 .0354 .0824 PROPORTION 18.42+ 12.70 10.43 9.49 8.50 6.32 CUMULATIVE 18.42 31.17 41.60 51.09 59.59 65.91 +, expressed as a percentage of the total variance 298 Table 21. Loadings of the first six most important princi- pal factors in C3 in Chimaltenango for all traits. PF1 PF2 PF3 PF4 PF5 PF6 5.23331313555-"TIEE2;""TIEEE"’I‘.'§ZES"'ITBSSImITSZEE' Intnodup $8112 .0062 .0032 .1175 .0409 .0351 Intnodlow ‘1298 .2289 -.0864 -.l664 -.0161 -.2466 Nodesup lelg -.0017 -.1133 .2182 -.l488 .2551 Podsmid -.0614 ‘1612 .1098 .0490 -.1824 -.0227 Nodeslow ‘5219 $6525 -.0021 .1877 .0168 .0487 Podslow .3207 ‘5219 -.4340 -.l419 -.0682 .0808 Hypodiam .4657 $5121 .3449 -.0067 .0053 .0212 Podlen .0382 .0072 ‘1252 *.0049 .1222 -.l628 Podsup -.0251 .0162 12312 -.0400 -.4585 .1959 Angle -.1285 .1297 -.0152 ‘8211 .0347 .0171 Nbranch .1392 .2268 .0637 $1622 .0359 -.0546 Podwidth .0516 -.2011 .2513 -.0153 Llfilfi -.1209 Hypolen -.0815 .0963 -.3087 .1368 ‘&§§1§ .4284 Podsmain .3213 .4963 -.ll37 -.0501 -.5913 -.0497 Seedwt -.0952 -.0037 -.1860 -.l468 -.lO30 $8616 LOWpodht .2221 .0304 .3386 .1556 .1682 ‘5222 Nodesmid -.l334 .1863 .1143 .1293 .0478 .0144 Seednum -.2257 .1980 ‘5655 .1757 .1844 .1545 PROPORTION 22.94+ 11.30 10.03 9.69 7.13 5.99 CUMULATIVE 22.94 34.25 44.27 53.97 61.10 67.09 +, expressed as a percentage of the total varaince 299 Table 22. Loadings of the first six most important princi- pal factors in C4 in Chimaltenango for all traits. PF1 PF2 PF3 PF4 PF5 PF6 £33533.""2.333"2'32;7'":TISEB"':332§""TZ§§E""7313'? Nodeslow ‘1812 .1568 .1748 .0957 -.2626 .1281 Nodesup "6111 .0127 .1621 -.0773 -.2008 -.1845 Intnodup .2153 ‘8211 .0508 -.0558 .1694 .1365 Intnodmid .0644 ‘8885 .0511 -.1215 -.1017 .2195 Hypolen .3515 -.5228 -.0532 -.l725 .1085 .1784 Podsmid -.1068 .0255 ‘8991 .3243 -.l702 .0967 Podsmain .4702 .1127 ‘1528 -.0621 .0641 .0955 Seedwt -.1393 -.0399 -.5882 -.2599 .0066. .2177 Nbranch .0561 -.l764 .1552 ‘1811 -.2343 -.1475 Lowpodht -.0634 -.0597 .1478 ‘1661 .0840 .2255 Hypodiam .0972 .3863 .0205 ‘5219 -.1559 .0044 Angle -.2383 -.0939 -.1596 -.1348 ;121§ -.0682 Intnodlow .2737 .3479 .2735 .0670 ‘6111 .1070 Podsup -.0929 .1380 .4597 .2221 -.5959 -.2919 Podswidth .0935 .1595 -.1401 -.0841 -.0021 .8927 ngii Podlen -.0618 .1175 .2264 .2012 .0577 Seednum .0765 .0948 -.0039 -.0216 -.1150 .1788 Nodesmid -.0530 -.1477 .0427 -.0905 .0786 .0743 PROPORTION 19.31+ 14.81 11.53 8.85 7.78 6.78 CUMULATIVE 19.31 34.12 45.65 54.50 62.28 69.06 +, expressed as percentage of total variance Table 23. Loadings of the first six most important factors 300 in Co at East Lansing for all traits. Podsmid Nbranch Podsup Hypodiam Angle Podslow Nodeslow Lowpodht Intnodup Intnodmid Podlen Podwidth Nodesmid Seedwt Intnodmid Seednum Hypolen Nodesup Podsmain PROPORTION 15.71+ 1:111 -.4678 .2139 .2213 .1397 .0611 .1181 .1607 -.1622 .1044 -.1856 .0314 .1639 -.1780 .1088 .0470 CUMULATIVE 15.71 11912 15221 -.6840 -.0861 .2133 -.0006 -.1223 .0922 .1890 .1984 .0735 -.4221 .2321 .1917 10.04 25.75 .1502 .0819 .2785 .1405 .1074 .0580 -.0399 -.0280 .3312 .15129 -.0405 -.0106 -.0834 -.0434 8.37 34.12 .1274 .1259 -.0214 .0494 11811 11121 .0834 .0196 -.0434 .1180 .1563 .2837 -.1589 7.92 42.04 .0123 *.2747 .0917 -.0465 -.0470 .1396 -.2318 -.0455 .1648 .0834 .4237 -.5855 -.1137 .3367 .1026 -.0915 5.80 47.84 -.3317 -.2129 -.0306 .0037 .0497 -.1443 .1233 .0941 -.0867 .1570 .0349 -.5916 -.1713 5.73 53.57 +, expressed as percentage of total variance. 301 Table 24. Loadings of the first six most important princi- pal factors in CI in East Lansing for all traits. 991 992 993 994 995 996 .3353;-"'35?'ITSEBI"'ITSZ§I"-3333?"TBSEZ""TSSZ§' Nodesmid ‘1493 .1410 -.4090 -.0599 .1702 .0175 Intnodlow 11929 -.0067 .2963 .1390 .0329 -.0926 Nodeslow 15115 .2830 .0830 -.2173 -.1291 .0849 Nbranch -.1147 11216 .0269 -.1447 -.1490 -.0018 Podsmid .2566 19921 .0317 -.1384 .2150 .1276 Hypodiam .3280 19925 .0818 .1325 .0508 .1443 Podsup -.1661 19521 -.1243 .2036 -.0373 .0089 Intnodup .0876 .0247 ‘1230 .0224. -.0191 .0357 Intnodmid -.3963 .0524 .1514, .0734 -.1242 -.0215 Lowpodht .0542 .1787 .0906 19912 .1663 .0350 Podslow .2012 .2075 -.0117 -.7444 .1962 .0099 Hypolen -.1343 -.0245 -.2932 .1053 nggz .1768 Podwidth .1973 -.0724 .0524 -.0304 19991 -.3840 Angle -.0733 -.3524 -.1105 .3312 —.5147 -.1595 Seednum .0837 .1862 .1206 .0308 .1527 ‘1312 Podlen .2159 -.l485 .2542 -.0761 -.0846 .4270 Seedwt .2055 -.0886 .2866 -.0032 .1390 -.6916 Podsmain .0045 .1514 -.1296 -.1005 .1195 .0045 PROPORTION 17.04+ 11.62 9.58 7.61 7.27 5.99 CUMULATIVE 17.04 28.66 38.24 45.85 53.12 59.11 +, expressed as percentage of total variance 302 Table 25. Loadings in the first six most important princi- pal factors in 02 in East Lansing for all traits. PPl PF2 PF3 PF4 PF5 PF6 REEF-"22;;-'"f3273-’7';5;?"33533m37112EmITSEIE' Hypodiam .8122 .1746 .2632 .0941 -.0301 .1920 Nodeslow .8821 .1342 .0126 .0486 .3672 -.0445 POdsmid .8111 .2058 .1671 -.0741 -.0295 .0071 Hypolen -.5328 .3013 .0422 .2499 -.1061 -.0486 Nodesmid .1413 .8181 -.0171 .0467 .0504 .0451 Nodesup .2570 .8881 .0351 -.0076 .0433 .3411 Intnodmid .0940 .7413 .0192 .0070 .1265 .4383 Podlen .0582 -.0255 .8888 .2502 -.0911 -.0134 Seednum .1705 .0130 .8881 -.2569 .0272 .0623 Seedwt .0857 -.0253 -.1025 .8181 -.0586 -.1230 Podwidth -.2123 .0583 .1116 .1888 .1727 .1124 Podslow .1636 .0509 -.0699 .1356 .8111 .0154 Intnodup .2020 -.1748 .0231 .0851 .8888 .4893 Lowpodht .0429 .0871 .0395 .3249 -.4728 .2236 Podsup .3168 -.0855 .0157 -.1133 -.6281 -.O392 Intnodlow -.0881 .0349 .0250 -.0321 -.0789 .8888 Podsmain .0337 -.0378 -.0781 -.1186 .1435 -.0078 Angle -.0322 .0212 -.0505 -.0097 -.0631 -.0426 PROPORTION 15.17+ 10.12 9.34 9.11 6.48 6.21 CUMULATIVE 15.17 25.29 34.63 43.74 50.22 56.43 +, expressed as a percentage of total variance 303 Table 26. Loadings of the first six most important princi- pal factors in C3 in East Lansing for all traits. PF1 PF2 PF3 PF4 PF5 PF6 £3232?"”ZE"ITIEES""TISEZ"'3?6§;§"'ITIEIE""T3§IE Nodesmid .8118 .2423 -.0388 -.0153 .2083 .2594 Podsmid .8882 -.1573 .1856 .3832 -.0969 .1954 Hypodiam .4979 .2080 .2309 .3312 .1245 .1830 Hypolen -.5968 -.2207 .1742 .0684 .2097 .1102 Intnodup .1278 .1118 .1001 .0195 .1043 -.0106 Intnodmid .1262 .1821, -.0249 -.0626 .1569 -.4402 Intnodlow -.1568 .1189 .0923 .1250 -.1094 .1900 Seednum .0428 .1714 .8181 -.l930 -.1448 .1022 Podlen .0048 .0735 .8128 -.0009 .1713 .0033 Angle -.1981 .2816 -.4211 -.2896 -.0980 .0547 Podsmain -.0513 .0337 -.1268 .8181 -.1265 -.0305 Podslow .0776 .1435 -.0280 .8888 .2326 .1312 Podwidth -.0833 .0338 .0932 .0819 .1822 -.1474 Seedwt -.0553 .0355 -.0238 -.0946 .1888 .1720 Nodesmid .0326 -.l442 .1591 .1514 .0001 .1818 Nodesup .2507 .1914 -.1367 -.1659 .0977 .5181 Lowpodht -.0298 .0089 .0380 .0012 .0962 .0466 Podsup .4627 -.l67l .1227 .1495 -.1718 -.l460 PROPORTION 14.90+ 11.47 9.18 8.48 6.83 6.35 CUMULATIVE 14.90 26.37 35.55 44.03 50.86 57.21 +, expressed as a percentage of the total variance 304 Table 27. Loadings of the first six most important princi- pal factors in C4 in East Lansing for all traits. Intnodup .8188 -.0796 .0876 .0151 -.0281 -.0011 Intnodlow .1112 .0467 -.0537 -.0198 .0244 .0793 Intnodmid .8888 .0121 .1398 -.1323 .0401 -.4741 Seednum .0353 .8888 .0737 -.2391 -.1283 .0079 Podlen -.0889 .8888 .1443 .0167 -.0177 .20003 Hypodiam .0310 .8818 .3647 .1256 .1358 -.0500 Podsup -.0785 .4299 .0916 -.0810 .4086 -.2429 Angle -.l786 -.5340 .1806 -.3547 .2843 -.0596 Nodeslow .2076 .0709 .8888 -.0591 -.0367 .3450 Podsmid -.0632 .3494 .8881 .0104 .1898 .0588 Nbranch -.1767 .3006 .4299 .1468 -.4133 -.1248 Hypolen -.0417 ' .0321 -.6413 -.1525 -.0346 .3768 Podslow -.0844 -.0212 .1147 .8881, .0101 .1796 Lowpodht .0107 .0403 -.0126 -.7872 -.1281 .0883 Podsmain .0915 -.0782 .1548 .2466 .8888 .0322 Nodesmid -.2978 -.0640 .0569 .1926 -.2177 .1181 Nodesup .3156 .1824 .0137 -.0781 .2184 .8111 Podwidth .0129 .0101 -.0692 .0774 .0550 -.0554 Seedwt .2208 -.0435 .1150 .0355 -.5081 .1406 PROPORTION 13.89+ 12.31 9.51 9.22 6.59 6.19 CUMULATIVE 13.89 26.20 35.71 44.93 51.53 57.71 +, expressed as apercentage of the total variance 305 Table 28. Biological concepts associated with principal factors in Co at two locations for all traits. Location Chimaltenango East Lansing Factor Concept Concept "'I """ £21332 """""""""" SIQEEZSEEISQ’I """""" Structural (Sturdiness) 2 Distribution (Nodes) Distribution (Pods) 3 Economic (Pod) Height 4 Structural (Sturdiness Economic (Pod) / profile) 5 Distribution (Pods) Distribution (Nodes) 6 Structural (Sturdiness) Economic (Seed) Structural (Sturdiness) Table 29. Biological concepts associated with principal factors in C1 at two locations for all traits. Location Chimaltenango East Lansing Factor Concept Concept I """ QEIQEE """""""""" BIQEEISGEESE'I§;§;;§ """" 2 Structural (Sturdiness) Structural (Profile) /profile) 3 Economic (Pod) Height 4 Economic (Pod) Distribution (Pod) 5 Structural (Sturdiness) Structural (Sturdiness) Economic (Pod) 6 Economic (Seed) Economic (Seed) 306 Table 30. Biological concepts associated with principal components in 02 at two locations for all traits. Location Chimaltenango East Lansing Factor Concept Concept "'I """ BESELISEZISQ'?§3§2;}£S§;§"§E;;EEE;;I'IE;SEZI;}"" sturdiness) 2 Distribution (Pods Distribution (Pods) 3 Distributions (Nodes) Economic (Pod / seed) 4 Economic (Pod /seed) Economic (Seed / pod) 5 Distribution (Nodes) Distribution ( Height 6 Economic (Pod) Heght Table 31. Biological concepts associated with principal factors in C3 at two locations for all traits. Location Chimaltenango East Lansing Factor Concept Concept "'1 """ §;E;£Z """ ' """"""" EZEQZESEQI? """"""" Ditribution (Nodes/pods) 2 Distribution (Pods/nodes) Height 3 Economic (pod) Economic (Pod /seed) 4 Structural ( Profile) Distribution ( 5 Economic (Pod) Economic (Pod / seed) 6 Economic ( Seed) Distribution (Nodes) ------------------------------------------------------------ , 307 Table 32. Biological concepts associated with principal factors in C4 at two locations for all traits. Location Chimaltenango East Lansing Factor Concept Concept m1'"""BIQEZ—ZBGEISQ’I3333;33323"8:23.; """""""" 2 Height Economic (Seed/pod) 3 Distribution (Pods) Distribution (Nodes/pod) 4 Structural (Profile/ Distribution (Pods) sturdiness) 5 Structural (Profile) Distribution (Pods) 6 Economic (Pod) Distribution (Nodes) 308 Appendix G Canonical discriminant analysis: Standardized canonical coefficeints for all traits at two locations. 309 Table 1. Standardized canonical coefficients for all traits at East Lansing. Canonical variable Trait CANl CAN2 CAN3 §;I;EE"'""TSSSE"”"'"IT§;ZS """"""" ITSSZS' Nbranch .1796 -.4897 .1232 Hypolen .4009 .1680 .0382 Hypodiam .0999 .2114 -.0528 LOWpOdht .0603 .0614 .2960 Angle .1853 .0101 .5274 Podsup -.0588 -.2859 -.1217 Podsmid -.2431 .1464 -.l936 Podslow -.4492 .3212 .0222 Nodesup -.0020 .4486 -.2634 Nodesmid -.0197 .0371 .5215 Nodeslow .1067 -.0489 .0753 Podsmain .0002 .0508 .2815 Intnodup -.3433 .2603 .1713 Intnodmid .1421 .0029 .1459 Intnodlow -.1038 .3846 .1242 Podlen .1445 -.0317 -.0100 Podwidth .5626 .0692 .2649 Seednum -.1195 .1440 -.2178 Seedwt .4464 .2385 -.5763 SESSSREEBQ"”§ETSE'I"’"""IIEE""""'T3;;3 CUMULATIVE 85.06 97.01 100.00 +, expressed as a percentage of the total variance 310 Table 2. Standardized canonical coefficients for all traits at Chimaltenango. Canonical variable Trait CAN1 CAN2 CAN3 133;;;;;""'IT§§;;""'""ITS§2§""""'IT§§;I Hypolen .1262 -.0942 -.5173 Hypodiam .1299 -.0256 .5736 LOWpodht -.0436 .2015 .1627 Angle .0854 .3845 .3035 Nodesup .0760 .1621 -.2907 Nodesmid .0471 .0555 -.0883 Nodeslow .2586 -.1043 .1168 Podsup -.0219 -.2938 .4695 Podsmid -.2029 .0142 .0580 Podslow -.2757 .2133 .6865 Podsmain .0902 .5293 .2647 Intnodup -.2641 -.1685 -.l475 Intnodmid -.0077 .2359 -.2909 Intnodlow .1858 .4306 -.0659 Podwidth .8034 .7267 -.0896 Podlen .3049 -.2599 .2396 Seednum -.1867 -.2127 .0263 Seedwt .9160 -.l802 .2796 £§6§3§$§3§""§ZTZE'¥'""""'I§TZE""""TS-71. CUMULATIVE 74.45 92.90 100.00 +, expressed as a percentage of the total variance 311 Appendix H Quantitative genetic studies: Tests of dominant and epistatic gene action in six crosses of beans. 312 Table 1. Test of dominance and epistasis in cross 1 cross 1 Height Architype Nbranch Hypolen Hypodiam Angle 2.6 * $ 0 .51 0.51 0.34 1.14 0.20 6018* -0002 0032 0022 -0001 -0088 0.71+ 0.13 0.13 -0.17 “0.01 '0.85 Podsup Podsmid Podslow Nodesup Nodesmid Nodeslow 1.68 0.18 1.84 0.37 0.54 0.37 1.02 5.00 1.24 0.16 0.13 0.58 1.35 3.36 1.87 0.35 0.11 0.13 Lowpodht Podsmain Podwidth Podlenth Seednum Seedwt 0.81 0.59 0.60 0.27 0.67 4.75** 0.96 0.48 0.11 0.38 0.30 1.51 -0.84 2.04 -0.30 -0.01 0.01 -0.01 $ - difference between parents # - test of dominance: + - tes of epistasis. *, ** a significant at .05 and .01 levels respectively. 313 Table 2. Test of dominance and epistasis in cross 2. Cross 2 Height Architype Nbranch Hypolen Hypodiam Angle 1.27 0.70 0.01 0.33 1.34 2.04** 0031 -0e67 0035 0066 0e24 0022 '0.31 ‘0.39 -0.13 '0.01 0.08 “0.81 Podsup Podsmid Podslow Nodesup Nodesmid Nodeslow 0.52 2.78* 0.79 0.29 0.28 0.34 ”1.12 3013 2036 0.67 0020 0e11- -0.12 “0.12 1.74 ‘0.02 0.17 0.31 Lowpodht Podsmain Podwidth Podlen Seednum Seedwt 0.87 0.33 0.50 0.53 0.14 5.55** -1.l3 “1.13 0.88 0.27 0.23 0.13 ”1.54 0.24 0.27 0.01 0.11 '0.63 # - test if dominance: + - test of epistasis: S-parent * - significant at .05, .01 level,respectively. 314 Table 3. Tests of dominance and epistasis in crosse 3. Cross 3 Height Architype Nbranches Hypolen Hypodiam Angle 8.68** $ 0.80 0.40 1.73 1.73 1.80 10.87# 0.35 '0.14 ‘0.02 0.53 '1.77 2058+ -0036 -0022 -0002 0067 -4050 Podsup Podsmid Podslow Nodesup Nodesmid Nodeslow 1.38 6.67** 4.74** 0.77 0.50 1.59 0.80 5.27 3.57 0.84 0.83 1.41 0.44 4.02 4.53 0.19 0.11 0.80 Lowpodht Podsmain Podwidth Podlen Seednum Seedwt 0.88 1.62 1.47 0.40 0.79 5.75** 0.24 1.13 -0.96 0.06 1.15 3.77 -2.07 1.43 -0.12 0.17 0.34 1.66 $ = difference between parents # = test of dominace: + a test of epistasis. *, ** sinificant at .05. and .01 levels, respectively. 315 Table-4. Test of dominance and epistasis in cross 4. cross 4 Height Architype Nbranch Hypolen Hypodiam Angle 10.74**$ 1.60 0.93 1.60 2.06* 6.69** 0.30# 0.26 -.16 0.29 0.30 -0.75 1.87+ -0.03 0.13 0.44 0.33 -1.59 Podsup Podsmid Podslow Nodesup Nodesmid Nodeslow 8.42** 18.64** 4.74** 0.23 0.06 0.53 -3.52 -2.09 0.23 -0.67 0.04 -0.41 -3.04 -0.83 1.16 -0.46 0.24 -0.17 Lowpodht Podsmain Podwidth Podlen Seednum Seedwt 3.31* 1.80 1.85 1.12 0.03 7.47** -1019 0040 -0031 -0001 -0027 0050 0.13 1.29 0.53 0.07 “0.03 '0.02 # - test of dominance: + - test of epistasis, $ - difference between parents *, **, significant at .05, and .01 levels, respectively. 316 Table 5. Test of dominance and epistasis in cross 5. cross 5 Height. Architype Nbranch Hypolen Hupodiam Angle 16.06**$ 0.06 0.40 0.73 1.86 4.80* 4.10# ”0.02 '0.37 0.05 “0.19 0.50 Podsup Podsmid Podslow Nodesup Nodesmid Nodeslow 6.22** 16.68** 4.95** 0.87 0.19 1.59 -1.40 1.04 1.98 -0.03 0.01 -0.33 -0.88 -0.84 1.93 0.49 0.26 -0.32 Lowpodht Podsmain Podwidth Podlen Seednum Seedwt 2.63* 0.98 1.85 1.85 0.50 6.77** '0.61 ‘1.35 0.31 0.20 0.14 “0.94 ‘1.17 0.68 “0.01 0.11 0.16 '0.13 $ - difference between parents # - test of dominance + - test of epistasis *, **, significant at .05, .01 levels, respectively. 317 Table 6. Test of dominance and epistasis in cross 6 CIOSB 6 Height Architype Nbranch Hypolen Hypodiam Angle 7.46**$ 1.60 0.94 0.16 0.83 3.96* Podsup Podsmid Podslow Nodesup Nodesmid Nodeslow 3.58** 9.77** 2.12* 0.13 0.25 0.96 -0.41 1.92 -3.02 0.36 0.05 -0.01 1.38 1.26 4.16 -0.05 -o.29 0.65 Lowpodht Podsmain Podwidth Podlen Seednum Seedwt 0.80 2.54* 1.47 0.66 0.26 6.55 -0017 -0089 -0022 0002 -0006 -0055 “1.84 1.30 “0.07 1.27 “0.17 “0.56 # = test of dominance; + a test of epistasis. $ = difference between parents *, ** significant at .05, .01 levels respectively