AN ATTEMPT TO OVERCOME THE YIELD-DAMPENING EFFECT OF NEGATIVE CORRELATIONS AMONG YIELD COMPONENTS IN BEANS (Phasequs vngaris L.) Thesis for the Degree of Ph. D. MICHIGAN STATE UNIVERSITY OSWALDO VOYSEST VOYSEST 1970 Taiwan-m , T w 9 .- THES! LIfiRA‘JEY 2., h’llClegan State nivezsity —-w This is to certify that the thesis entitled An attempt to overcome the yield-dampening effect of negative correlations among yield components in beans (Phaseolus vulgaris L.) presented by Oswaldo Voysest Voysest has been accepted towards fulfillment of the requirements for Ph.D degree in CrOp Solence ‘ Major professor Dat 4' ’ ~ " . , ”1/ /“//‘/7’(7 r swims av "’ 2 -- ‘ HMS e sous l nnnv Rm av nun ABSTRACT AN ATTEMPT TO OVERCOME THE YIELD-DAMPENING EFFECT OF NEGATIVE CORRELATIONS AMONG YIELD COMPONENTS IN BEANS (Phaseolus vulgaris L.) BY Oswaldo Voysest Voysest Negative correlations among the several components of yield in field beans (Phaseolus vulgaris L.) impede prog- ress for higher yield when individual components become the direct object of selection. A plan in which the seed number components are held constant, in the genetic context, while selection pressure is placed on the seed size component, is prOposed as one practical method of overcoming the effects of the negative correlations. The rationale of this approach implies the following premises: a. Additive behavior of genes for number of pods per plant (X), number of seeds per pod (Y) and seed weight (Z). b. Low heritability for X and Y; high heritability for Z. c. The identification of high seed number types (XY) by selecting from among small Z lines, thus taking advantage of the negative relationship between seed Oswaldo Voysest Voysest number and seed size to offset, to some extent, the low heritability of XY. Crosses were made between lines showing low Z (high XY) and large Z (low XY). Two successive generations of backcrosses to the small Z parents were produced but selec- tion was practiced for large Z. Studies on the nature of the gene action and esti- mates of heritability for yield and its components confirmed satisfactorily the validity of the assumptions on which this work was based. Negative correlations among some of the components of yield were shown to exist. These negative associations persisted through the BCl and BCll generations. Through path coefficient analysis X was found to be the most impor— tant component influencing yield in a direct as well as in an indirect way. When the effects of correlation of X on Y and X and Y jointly on Z were removed, based on the premise that the characters first in the sequence of deve10pment influence the expression of those following them in the sequence, variations in the degree of influence of the different sources of variation (genotypic, environmental and their interaction) on the expression of the traits were found as compared with the reported influence of these sources of variation when correlations were present. Variation in the heritable value of Z was also noticed. It is postulated Oswaldo Voysest Voysest that the genetic variance of X is reflected in the genetic variance of Z. The genetic variance of Z then would be composed of a part that is common to X and another which is independent of X, both of which are available for selection. Through backcrossing the variance of X would have been made to vanish and selection would have been based rather on the portion of the genetic variance of Z which is independent from X. As expected, the genetic complex for seed number represented by the recurrent parent was recovered through recurrent backcrossing. When individual components for the seed number trait were considered, however, significant variations were noted with respect to the expected values. These deviations were attributed mainly to component compensation. Selection for seed size in the BCI was effective in about half of the populations studied. A regression toward the Z-values of the recurrent parent was evident in the pOpulations where selection for large Z was not effective. A narrow genetic base in the parent pOpulation was singled out as the most probable cause of lack of success in selec- tion for large Z. In the populations where selection for Z was effective, the regression towards the recurrent parent values was successfully overcome. Increases over the pro- genitor ranged from 10 to 31%“ Selection in certain crosses of the BCI might have successfully isolated a genetic portion more associated with Oswaldo Voysest Voysest the mid-parental performance than with that of the recurrent parent. This was confirmed by the similar percent increase in seed size of the BCl and BCll with respect to the recur- rent parent. With respect to yield most lines showed a numerical increase over the recurrent parent although only 6 lines showed significance. A summary of the changes in the pOpu- lations studied with reSpect to their components and yield presents the following picture: of the 20 populations studied in 12 of them there was no significant gain in seed size; stability of the seed number component was maintained but no gain in yield was evident over the recurrent parent with the exception of 2 pOpulations where significant in- crease in X and Y, respectively, accounted for most of the increase in yield. This performance was attributed to complementary gene action. In the other 8 populations where selection for Z was effective in 4 of them there was signif- icant gain in yield and in 4 of them increases in Z were unable to compensate for variations in the X or Y components. Lack of genetic gain in yield in these crosses was attributed to the narrow genetic base among the parent pOpulations and to the lack of an outstanding recurrent parent. Average yields of BCl and BCll exceeded the recur- rent parent by 28% and 32%, respectively. It appeared from data derived from BClSl and BC182 that yield performance of the BCI was influenced favorably by heterozygosity. Oswaldo Voysest Voysest Our data support the idea that new levels of yield can be attained by increasing the level of expression of the component most highly heritable through selection, while holding constant the levels of expression of the less heri— table characters through recurrent backcrossing. Ample genetic diversity for the character under selection, and high levels of expression for the traits to be stabilized «I . . are sone qua non requirements for the success of this approach. AN ATTEMPT TO OVERCOME THE YIELD-DAMPENING EFFECT OF NEGATIVE CORRELATIONS AMONG YIELD COMPONENTS IN BEANS (Phaseolus vulgaris L.) BY Oswaldo Voysest Voysest A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Crop and Soil Sciences 1970 ACKNOWLEDGMENTS The author wishes to thank Professor M. W. Adams who generously supplied advice and encouragement during the course of this investigation and the whole period of my studies. His indefatigable efforts in revising my rather Spanish-sounding manuscript are greatly appreciated. Grateful thanks are due to Dr. C. E. Cress for a critical reading of the manuscript and for a number of constructive suggestions. I am also indebted to Mr. John Barnard, a fellow graduate student, for his continual assistance in preparing the computer programmes. I would be remiss if I did not acknowledge the affectionate toleration accorded me by my wife and children through three years of dull and plodding but happy scholar- ship; their forbearance, who have survived the strain of my labors, is appreciated. It is a pleasure to express my gratitude to the Rockefeller Foundation for their financial and moral support which enabled me to enjoy the benefits of a quality educa- tion and undertake the present study. ii TABLE OF CONTENTS INTRODUCTION . . . . . . . . . . . . . . . . . REVIEW OF LITERATURE . . . . . . . . . . . . . MATERIALS AND METHODS . . . . . . . . . . . . Plant Materials . . . . . . . . . . . . . General Scheme of the Experiment . . . . . Greenhouse, 1967 . . . . . . . . . . . . . Field Trials, 1968 . . . . . . . . . . . . Greenhouse, 1968 . . . . . . . . . . . . . Field Trials, 1969 . . . . . . . . . . . . RESULTS . . . . . . . . . . . . . . . . . . . Analysis of the Parent Population . . . . Study of Correlations . . . . . . . . . . Genetic Advance . . . . . . . . . . . . . Heritability estimates . . . . . . . . Test of additivity for seed size . . . Response to selection . . . . Heterozygosis-performance relationship DISCUSSION . . . . . . . . . . . . . . . . . . Correlation Among Traits . . . . . . . . . Z Trait Responses to Selection . . . . . . Stability of the Seed Number Components . Genetic Advance in Yield . . . . . . . . . SUMMARY AND CONCLUSIONS . . . . . . . . . . . LITERATURE CITED . . . . . . . . . . . . . . . iii Page 10 10 12 12 13 15 16 24 24 3O 42 42 47 47 59 74 74 83 86 88 96 100 LIST OF TABLES Table Page 1. Mean plant performance of the original parent pOpulation evaluated at East Lansing, Michigan, in 1967 . . . . . . . . . . . . . . . 11 2. Backcross combinations obtained from cross— ing small-seeded lines x large-seeded lines, small—seeded lines being the recurrent parents . . . . . . . . . . . . . . . . . . . . 14 3. Variance analysis and mean square expecta- tions for data from two years at one location . . . . . . . . . . . . . . . . . . . l7 4. Genetic material representing four levels of heterozygosis . . . . . . . . . . . . . . . 20 5. Parent increase (+) or decrease (-) of BCl values based on performance of parents in 1968 and 1969 . . . . . . . . . . . . . . . . . 21 6. Comparative mean plant performance of the small-seeded pure lines evaluated at Saginaw, Michigan, in 1967, 1968, and 1969 . . 25 7. Comparative mean plant performance of the large-seeded pure lines evaluated at Saginaw, Michigan, in 1967, 1968, and 1969 . . 26 8. Analyses of variance of grain yield and the components of yield measured for eleven parental lines grown at one location for two years . . . . . . . . . . . . . . . . . . . 28 9. Simple correlation coefficients among three yield components and grain yield in common beans . . . . . . . . . . . . . . . . . . . . . 31 10. The path-coefficient analyses showing direct and indirect effects of the components of grain yield for the small-seeded parent pOpulations . . . . . . . . . . . . . . . . . . 33 iv Table 11. 12. 13. 14. 15. 16. 17. 18. The path-coefficient analyses showing direct and indirect effects of the components of grain yield for the large—seeded parent pOpulation . . . . . . . . . . . . . . . . . . The path-coefficient analyses showing direct and indirect effects of the components of grain yield for the second backcross generation . . . . . . . . . . . . . . . . . . Mean squares of analyses of variance for uncorrelated data for grain yield and two components of yield from eleven bean lines evaluated for two years at Saginaw, Michigan . . . . . . . . . . . . . . . . . . . Estimates of variance components of grain yield and the components of yield for eleven bean lines grown for two years at Saginaw, Michigan and analyzed with respect to two sets of data, (a) actual data, (b) trans- formed data . . . . . . . . . . . . . . . . . . Estimates of variance components expressed in percent of the total variance for each trait within each set of data (from Table 9) . . . . . . . . . . . . . . . . . . Estimates of variance components and heritability computed for single plots for grain yield and components of yield for the parental bean lines grown for two years at Saginaw, Michigan . . . . . . . . . . . . . . . Means of the seed size trait for a BC population, its selected portion and fheir respective selfed generation, in twenty sets of crosses of small- and large—seeded lines of beans . . . . . . . . . . . . . . . Realized heritability eStimates for seed size based on actual response from selection practiced in a first backcross generation in a set of crosses between small- and large- seeded bean lines . . . . . . . . . . . . . . . Page 34 35 38 39 4O 42 44 45 Table 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. Estimates of variance components and heritability for single plots for grain yield and components of yield, with effects of correlations removed . . . . . . . . . . .Estimates of the heritability of yield and its components in a bean population with Operating correlations among components . . t-test and mean values for seed size for twenty first-generation backcrossed lines and their expected values under an additive model . . . . . . . . . . . . . . . . . . . Expected means for two backcross generations under no selection and under 8% selection intensity on the BCI for the character seed we ight O O I O O O O O O O O O O O O 0 O 0 Actual seed size means of the BC11 lines as weight of 100 seeds, under an additive model when selection is based on seed size Differences in seed size of the BCl and BCll generations of twenty bean populations, expressed as percent change over the recurrent parent . . . . . . . . . . . . . Observed and expected changes on seed number and seed number components in the BC11 generation under two successive backcrosses to the small-seed parent and selection in the BCI for large seed . . . . . . . . . . Grain yield and percent change in yield and its components with reference to the recurrent parent for twenty BCll pOpulations . . . . . . . . . . . . . . . . Observed grain yield for the first and second backcross generation of twenty bean populations . . . . . . . . . . . . . . . . Comparison of grain yield among the BClsl and BC1S1 vs BCll generations derived from selected BCl pOpulations . . . . . . . . . 0 Page 46 46 48 51 52 54 55 57 6O 61 Table Page 29. Means of yield and the components of yield at four levels of heterozygosity in six bean pOpulations . . . . . . . . . . . . . . . 62 30. Test for curvilinear regression of the heterozygosis-performance relationship for yield and its components, by ortho— gonal polynomials . . . . . . . . . . . . . . . 68 31. Comparison between filial and backcross generations having the same level of heterozygosis. Plus (+) or minus (-) signs used to characterize the group exceeding (or not) the other . . . . . . . . . . . . . . 7O 32. Comparison between backcross generations derived from a first backcross where selection was practiced for seed size . . . . . 71 33. Heterotic response for grain yield and the components of yield in six bean populations (percent increase in F1 as compared with parents) . . . . . . . . . . . . . . . . . . . 72 vii Figure LIST OF FIGURES Graphical representation of the values for given yield and the components of yield in the 1969 experiments expressed in percent of the values from 1968 trials . . . . . . . . . . . . . . . . . . Graphical representation of the deviations of BC means for seed size expressed in percent of the mid-parents grown in two years . . . . . . . . . . . . . . . . . . Heterozygosis-performance relationship for yield in six bean pOpulations . . . . Heterozygosis—performance relationship for number of pods per plant in six bean pOpulations . . . . . . . . . . . . . Heterozygosis-performance relationship for number of seeds per pod in six bean populations . . . . . . . . . . . . . Heterozygosis-performance relationship for seed weight in six bean populations . viii Page 29 50 63 64 65 66 INTRODUCTION In beans, as in many other crOps, efforts directed at raising grain-yield potential, based on selection of this character p§£_§§J have often been in vain. A widely-used approach to understanding the in- heritance of yielding ability in grain crOps has been the analysis of the components of yield. In the case of common beans the primary components of yield are number of pods per plant, number of seeds per pod, and seed weight. Since yield is the multiplicative product of these components, all three assume importance in efforts to understand the basis of yield and in efforts to attain new levels of productivity. If the object of a breeding program is to increase the level of yield, then a positive correlation among the components may be considered an asset while negative cor- relations would be detrimental. Progress by selection for components of yield rather than yield pg£_§g_has been lim- ited by moderate to strong negative correlations among the components. Gains in a single yield component offset by decreases in one or both of the other components have impeded progress for higher yields. The net result in selection programs where individual components have become the direct object of selection have not differed substan- tially from those based on selection for yield alone. A compensatory mechanism has been postulated to control the relationships among components. Evidence seems to suggest that negative correlations arising from this system of compensation are primarily develOpmental in nature, i.e., components compete for a common limited pool of re- sources produced by or available to the plant, and in order to attain a typical yield a compromise is established among the components with respect to their levels of expression. The gradual attainment, however, of new higher levels of yield is clear indication that these negative correlations among yield components may be at least par- tially surmounted. The aim of this thesis is to test whether yield limitations imposed by negative associations can be overcome by shifting only one of the traits composing the complex character from its typical value while holding constant the genetic basis of the other yield-comprising traits. A concurrent objective is to explore the idea that the penetrance of the genes which regulate the develOpment of the yield components is not affected by the persistence of the negative relationships since it is not encumbent on this procedure that negative associations be made to vanish, only that the yield be improved within a framework where negative correlations have been shown to exist. REVIEW OF LITERATURE Efforts to improve grain yield in crOp plants in- volve two general kinds of approaches. .Some workers have emphasized the study of the physiological characters under- lying differences in yield capacity; some papers in beans (19, 32, 33) and in small grains (6, 30, 34) may be cited as examples. Others have preferred to deal with characters more amenable to observation, that is, end points of pheno- typic expression that could be evaluated in terms of size, morphology or number and that either comprise yield or can be associated with it. A more subtle kind of controversy has arisen in- volving the yield structure and ways to define it. The view that hereditary control of yield may be studied best at its component level (16) was challenged on the grounds of a dubious cause and effect relationship between yield and the components closer than that of genes for yield per s3 (23). The argument that yield is indeed the product of a set of yield components and that there can be no genes for yield which by-pass the components (14) has remained unchallenged. The use of yield components as an approach to vari- etal improvement has been criticized (22) on the grounds that components are nothing else than manifestations of yield, with value only as indicators of the general trends taking place during plant growth, or valuable only in pro- viding a model when selecting for particular ecological conditions. On the other hand, the importance of breeding for yield utilizing knowledge of yield components and their genetic relationships, has long been emphasized for self- pollinated crOps (37). Selection programs for yield based on component anal- ysis are no more widespread than those using the strictly statistical-genetic approach, primarily because of the nature of the interdependence of the components and their sometimes nonsignificant effect on the levels of expression of the complex trait itself, as indicated by numerous studies on phenotypic (correlations) and genotypic (herita- bilities and genetic correlations) parameters of yield and its components. Total seed yield has been reported unanimously as a character of low heritability of soybeans. Estimates of heritability for pods per plant and seeds per pod have varied from intermediate to low, but seed weight has been reported in most cases as highly heritable (4, 18, 20, 35). A similar pattern has been observed in common beans. Heri- tability estimates in the broad sense showing values such as 51.1% for number of pods per plant, 82.9% for number of seeds per pod, 84.8% for seed size, and 15.T% for yield have been reported (9). Other reports present very low heritabil- ity estimates for total yield and each yield component (8). Interdependence among the components of yield in common beans is clearly indicated by almost all the numerous studies where the correlation coefficients have been calcu- lated (5, 7, 9, 10, ll, 17, 26, 27). The values of the correlation coefficients between yield and the components, number of seeds per pod and seed weight are, in general, small or negligible. Number of pods per plant is the only component whose correlation with yield has been consistently reported as high. Correlations among components themselves are reported mostly as negative. When positive, the values are of small magnitude. Duarte (11) used a path coefficient analysis to separate the correlation coefficient into components of direct and indirect effect. Number of pods per plant was the component which showed the greatest direct effect on yield. Seed weight, on the Other hand, had the least in- fluence upon seed yield. Coyne (8) calculated partial correlation coeffi- cients between total seed yield and yield components. Based on the high values of the partial correlation coefficients between total yield and each yield component, he concluded that each component was about equal in importance in deter- mining total seed yield. The fact that the majority of the partial correlation coefficients were low and positive was interpreted as an indication that it.would be possible to select for an increased value of one yield component without producing a reduction in value of the other components. There are only a few studies on the genetics of the components of yield. Dickson (10) reported that number of pods per plant, number of seeds per pod, and number of seeds per plant were determined by a simple additive gene system. In the case of pod number some incomplete degree of domi- nance was reported with high pod number being mostly deter- mined by recessive genes. Coyne (8) reported complete dominance for higher number of pods per plant and lack of dominance for mean seed weight. The nature of gene action and the complex structure of yield bears a close relationship to the presence or absence of heterotic behavior. Evans (13) has reported significant positive heterosis for seed yield per plant and number of pods per plant in beans. She noticed that some crosses involving determinate and indeterminate types of plants did not maintain their heterotic behavior through the second generation whereas others involving only determinate types showed a considerable amount of heterosis in the F2 generation. She concluded that morphological differences between the two types of plants are associated with differ- ences which produce superior Fl combinations but not well- balanced segregates in advanced generations. Adams and Duarte (2) explained heterosis for a complex trait as a result of component interaction. Their studies with total leaf area as a complex character con- firmed other reports (15, 36) that the multiplicative interaction between components can successfully explain heterosis in a complex trait. The component traits, leaf area and leaflet number, were influenced by an additive and a dominant gene system, respectively. Selection studies based on components of yield have not succeeded in raising the level of productivity in beans. Duarte (11) applied recurrent selection methods for yield and each of the components of yield for three levels of expression in a bean population. No progress was attained for yield itself during two cycles of selection. Progress in each of the components of yield was offset by an Opposite response in the other components. Coyne (8) selected the top 5%.of the F2 of a cross between two bean varieties on the basis of total yield and separately for each of the three yield components. No yield improvement was realized for any of these traits. These results were attributed to the large environmental effect on the expression of these traits,which made it difficult to identify genetically superior individuals, or to low additive genetic variance. In barley, Nickell and Grafius (25) failed to real- ize the expected genetic gain after one generation of selec- tion based on yield and the seed size component. Different environmental conditions requiring different Optima in the gene pool for yield components and their interrelationships for attaining maximum yield was suggested as an explanation for this negative response to selection. Increases in yield by selecting for morphological components have been reported in other crOp species. Torregroza and Harpstead (31) obtained an increase of 28% in the number of ears per plant and 14% more yield than the original population in the fifth cycle of selection for multiple ears in corn. In single-eared selections yields were reduced by 5%.while the number of ears decreased by 7%. Rasmusson and Cannell (29) carried on selection ex- periments on the basis of yield and its components in two populations of barley. The results were not consistent for the four selection criteria for the two populations. Selec— t:ion for number of heads per plant was effective in one of tflie two pOpulations studied; the positive correlation with )nield was high. Selection for kernel weight was effective :fcxr both pOpulations but its positive correlations with yield was high in only one population. Selection for ker- rieals per head was successful in one population and failed 2111 'the other. Yield was reduced when selection for kernels EP€azr head was effective. All these studies of grain yield in terms of the cICOIIrlponents showed that the varieties achieve their yield 3111 Idifferent ways, i.e., either through an increase in the Seed number components or through an increase in seed size. However, because components of yield are interdependent, increases in one are often accompanied by decreases in one (Dr' nuore of the others. The nature of these responses are both genetic and environmental as suggested by Adams (1) in beans and Rasmusson and Cannell (29) in barley. The associations between components are described by Adams as deriving from develOpmentally-induced relationships between these attributes of yield whereas Rasmusson and Cannell ascribed these relationships to genetic linkage. MATERIALS AND METHODS Plant Materials Plant material for this study consisted of eleven lines of navy-type beans (Phaseolus vulgaris L.) selected from among 227 lines grown in 1967 and previously classified by seed size. The lines were divided into two sets: the first, on the basis of small seed size and high seed number, the second, on the basis of large seed size. In addition, two large-seeded varieties, Great Northern (selection #27) and Perry Marrow, were included in the second set. Because of the negative associations between seed size and seed number in navy beans, and the lower heritabil- ity of seed number, it was deemed advantageous to select the Iiigh seed number lines partially on the basis of their small seed size. For this reason, the recurrent parents, which ccuitribute genes for high pod number and/or high number of seeds per pod to the crosses, are often referred to as the smallrseeded parents. The characteristics of the original parent popu- lation are shown in Table 1. Parents will be referred hereinafter as P-Ol, P-OZ...P-12 and P-13. 10 11 Table 1. Mean plant performance of the original parent population evaluated at East Lansing, Michigan in 1967 Yield Weight/100 Seeds Seed Number per Plota Lines (in gms) per Plota (in gms) Small Seed Set P-Ol 16.8 1434 240.9 P-02 15.6 1327 207.0 P-03 14.9 1396 208.0 P-04 14.0 1471 205.9 P-05 14.0 1328 205.9 Mean 15.1 1391 209.5 Large Seed Set P-06 19.5 953 185.9 P-07 19.6 969 189.9 P-08 19.5 1112 216.8 P-09 18.2 1111 184.0 P-10 17.8 1253 223.0 P-ll 16.6 1337 222.0 Mean 18.5 1122 203.4 P-12 (G. Northern) 28.9 . P-13 (P. Marrow) 35.9 . aFive-foot plots. 12 General Scheme Of the Experiment To fulfill the objectives of this thesis, the breeding plan selected to be effective involved combining the high seed number characteristic of one set of lines with the high seed weight characteristic of a second set of lines. Because of the divergent levels of heritabilities of the components it was planned to place major selection pressure on the component of highest heritability, seed weight, so as to regulate the frequency of genes for seed weight, since the heritability of this trait is high enough that selection should be effective. To recover the frequency of genes for high seed number, of lower heritability, recurrent back- crossing to the high-seed-number lines was intended. Inclusion of the Great Northern and Perry Marrow lines--clearly too large to be classified as Navy beans-- represents deliberate overshooting so that a large amount of genetic variance for seed size would be generated and a continual regression in seed size could be tolerated during backcrossing to small—seeded lines. GreenhouseL 1967 Crosses were made in 1967 between small-seeded (high seed number) and large-seeded lines. A total of twenty com- binations were obtained. Plants of the F1 generation were backcrossed to the small-seeded parent to give the BCI generation. The notation used for identification of the l3 backcross material is as follows: two two-digit numbers corresponding to the original parents are shown after the conventional notation for identification of the generations (BCl, F1, F2, etc.). The first two-digit number indicates the progenitor used as female, the second one, the male. The smallest number is always the recurrent parent. For example, BCl-0106 indicates the first backcross generation of the cross P-01 (used as female) with P-06 (used as male), the F1 being backcrossed to P-Ol. As far as the identifi- cation of the particular backcross generation is concerned, the subscript 1 is used to indicate backcrossing to the small-seeded parent. Two backcrosses made to the same re- current parent is indicated by the corresponding subscript written twice. Each small-seeded parent was crosses with at least three large-seeded lines. The 20 combinations obtained are shown in Table 2. F2 seed from 17 of the 20 combinations was obtained by selfing the F1 plants used for the backcrosses. Field Trials, 1968 An experiment including 19 BCl lines, 17 F2 lines, and 13 parental varieties was grown in 1968 at Saginaw, Michigan. The eXperimental design was a randomized block with 4 replications. Each plot consisted of one lS-plant row with a 70 cm (28 inches) distance between rows and a 14 Table 2. Backcross combinations obtained from crossing small-seeded lines x large—seeded lines, small— seeded lines being the recurrent parents Large- Small-Seeded Lines Seeded Lines P—Ol P-02 P-03 P—04 P-05 P-06 BCl-0106 BCl-0206 BCl-0306 BCl-0406 BCl-0506 P-07 BCl-0107 . . " . . .. BCl-0507 P-08 .. .. .. BC1-0408 P-09 BCl-0109 BCl-0209 BCl-0309 BCl-0409 BCl-0509 P-10 .. .. BCl-0310 .. BCl-0510 P-ll ‘ .. .. .. BCl-04ll BCl—051l P-12 BCl-0112 .. .. P-13 ..‘ BCl-0213 BC1-0313 plant spacing of 20 cm (8 inches) in the row. .Moisture conditions were above normal at the beginning of the growing season but two sprinkler irrigations were necessary at the blooming period and during pod and seed develOpment. Twenty-five competitive plants were harvested from each backcross line and twenty from each F2 line° Four competitive plants were chosen from each plot for each parental line. Data were collected for yield (W), number of pods per plant (X), number of seeds per pod (Y), and average seed weight (Z), recorded as grams per 100 seeds. Total grain yield per plant was determined by weighing all the grain 15 produced on each plant. The X component was determined by counting on each plant all the pods with at least one viable seed. The total number of seeds produced by each plant was counted and the number of seeds per pod was estimated by dividing the total number of seeds by the number of pods (Y = (XY)/X). The average seed weight was computed using the total yield per plant and the seed number (Z = W/(XY) x 100). Statistical analyses were made on the basis of plot means. Selection was practiced for seed weight in each BC1 population. Two plants with the largest seed size out of 25 were selected. F2 seed from each line was bulked. Greenhouse, 1968 Seed from each BCl selection was stored as BClSl seed and a part was planted in the greenhouse and back- crossed to the respective small-seeded parent to produce the BC11 generation. Selfed plants from each BCl selection used in the greenhouse produced BClS2 seed. Some crosses were repeated to obtain Fl seed. For the field trials the materials available were: 42 lines of the BCIS1 and BC1§ generations, 37 Bcll’ 17 F3 and 6 Fl lines plus the 13 parental lines, and the non- selected BClS1 generation. 16 Field Trials, 1969 Five field experiments were conducted at Saginaw, Michigan in 1969. The 37 BCll lines and the five small- seeded parents were tested in one experiment using a 6 x 7 rectangular lattice design. The rest of the study involved four additional experiments in which the following material was tested, respectively: (1) BClSl lines, (2) BClS2 lines, (3) F1' F3 and parental lines, and (4) the non-selected BCIS1 generation. The experimental layout in all cases except the last experiment was a 6 x 7 rectangular lattice with 4 replications. Samples from individual BCl plants from the 1968 experiment were tested in a systematic design without replications. Plot characteristics for all five eXperiments were the same. Each plot was formed by one 20-plant row. Spac- ing between rows was 70 cm (28 inches) and plant spacing in rows was 15 cm (6 inches). Five competitive plants were harvested from each plot and data on yield of grain and yield components were collected in the same way as in the 1968 experiments. For the BCISl unselected plants a sample of pods was taken from 17 different plots for each of the 21 backcross combinations. Only data on seed size was collected in this particular experiment. Statistical analyses were made on plot means. Sepa- rate analyses of variance were computed for each experiment, for each trait measured. Further, the 1968 and 1969 data for the parental material were analyzed according to the 17 form of variance analysis presented by Johnson, Robinson and Comstock (20, 21). The form of variance analysis and mean square expectations for data collected in two years and one location are presented in Table 3. Table 3. Variance analysis and mean square expectations for data from two years at one location Source d.f.a Mean Square EXpectationsb 2 2 2 Years y-l 0e + 90 r(yI + rgoy Replications in years y(r-l) o: + gc3(y) . 2 2 2 Lines n-l + r + r 03 09y ch Lines x e rs -1 —l + r02 y a (n )(y ) 0e gy Rep. x lines in years y(n-l)(r-1) a: 3r = number of replications; n = number of genotypes; and y = number of years. bThe variance components estimated were: 02 = Line component due to genetic differences 9 among lines. Ogy = Genotype x year component. a: = Plot error variance. The model used to estimate these components assumes fixed genotypic and random environmental effects. 18 Heritability estimates for yield and the components of yield were calculated on a per plot basis by the formula H = GS/SSh where 8; is the estimated variance attributable to genotypic effects and 8:h the phenotypic variance of .A2_22 2 lines (Oph - cg + Ogy + Ca). Heritability values were cal- culated also by other methods. Parent-offspring regression was used with the F1- data and the F2 data were used for the regression of the offspring on the mid—parent. Realized heritability for seed weight was also obtained using the following formula: EBClSls- EBClSl Heritability = ._ _ x 100, XBCls XBCl where the numerator is the selection differential in the BC1S1 generation and the denominator is the difference in performance between the mean of the selected BCl lines and the BC pOpulation mean. 1 Selection was considered effective when the mean values of the progenies of the selected BCl plants differed significantly from the BCls1 pOpulation mean. Realized heritability estimates were used as one means of evaluating the effectiveness of selection. Estimates of expected genetic gain from the selection practiced for seed size in the BCI generation were computed for each backcross line as the product of the heritability estimate based on variance component analysis, the standard— ized selection differential and the estimated phenotypic 19 standard deviation (GA = KSPHH). For the purpose of this work K was given the value of 1.76 which is the expectation in the case of 8% selection (2 in 25) from a normally dis— tributed population. The phenotypic standard deviation was calculated on a per plot basis from the BCl pOpulation. Since the expected genetic gain was calculated assuming a normally distributed population and using heritability estimates in the broad sense, the resulting values were considered only as maximum eXpectations. The expected means for the backcross generations were calculated on the assumption of additive gene action with the midparent value representing the F The expected 1' progress towards the recurrent parent value was one-half of the remainder for each succeeding generation. For the char— acter under selection, seed size, deviations from the addi- tive scheme were considered significant when they fell out- side the ranges of the confidence interval for the observed BCll means. Also, a maximum value for the expected BCll mean due to selection was derived by adding half of the value of the maximum genetic advance to the expected BCll mean calculated under the assumption of additive gene action. The effect of heterozygosis on the grain yield and its components was studied using the genetic material shown in Table 4. The sums-of-squares due to heterozygosis levels were partitioned into single degrees of freedom using 20 Table 4. Genetic material representing four levels of heterozygosis Percent Heterozygosis Genetic Material 0 Inbred lines P1 and P2 25 F3 = F2 selfed 50 F2 = Fl selfed BC1 = ]_X Pl 100 F1 = P1 x P2 polynomial regression to test for the significance of the linear, quadratic and cubic effects. Polynomial coefficients applicable to the unequally spaced levels were derived previously (3). Since the BCll and BC1 generations were grown in a different year from the rest of the material, adjustments were made on X, Y, and Z based on the change experienced by the common sets of parents grown in both years. Only BCl values were used for the 50% level of heterozygosity in the partitioning of the sums of squares. The percentage of adjustments made are shown in Table 5. 21 Table 5. Percent increase (+) or decrease (-) of BCl values based on performance of parents on 1968 and 1969 X Y Z Avg.a Specificb Avg. Specific Avg. Specific 0106 -28.2 -27.1 9.0 11.5 3.0 4.5 0209 -l7.1 -17.3 12.9 13.5 5.9 2.1 0408 -20.0 —17.8 10.8 11.5 4.9 3.0 0506 -20.2 -l9.6 6.2 6.2 4.9 6.0 0510 -20.2 -22.6 6.2 2.6 4.9 3.4 0511 -20.2 —21.5 6.2 7.6 4.9 5.4 aAverage change of all pOpulations with the same genetic background. bChange for the specific pOpulation studied. The interrelationships among plant characters were studied by computing simple correlation coefficients among yield and the components of yield in all possible combina- tions on a plot basis. A further analysis of the corre- lation coefficient was undertaken by the path coefficient method and by multivariate analysis. For the path coefficient analysis four variables were included. The nature of the causal system is repre- sented diagramatically as follows: 22 / (W) < :%5 (W) Total grain yield (X) Number of pods per plant (Y) Number of seeds per pod (Z) Seed weight In the path coefficient diagram the double-arrowed lines indicate the correlation between two variables as measured by the correlation coefficient. Direct effects are represented by single-arrowed lines and measured by path coefficients. The basic relationship between correlation and path coefficients are expressed as follows: r = P + r P + r P xw xw xw yw xz zw r = P + r P + r P yw yw xy xw yz zw r = P + r P + r P zw zw yz yw xz xw The path coefficients were computed from the above set of equations by solving for the P's. 23 Since yield (W) is a multiplicative product of X, Y, and Z, for the correct application of the path coeffi— cient method, a logarithmic transformation of the data was undertaken. A multivariate technique described by Rao (28) was used to remove the correlation effect of number of pods per plant (X) on number of seeds per pod (Y), and the effect of these two components on the seed size component (Z). A program intended to compute the Mahalanobis distance value (24) was adapted in its pertinent parts for our purposes. A 3 x 3 phenotypic variance-covariance matrix was calculated and a matrix of multipliers obtained by a pivotal condensation of the variance-covariance matrix such that the original character means (X, Y and Z) could be transformed to an uncorrelated set (X, Y and Z): the uncorrelated set being defined by the equations: X = X Ne u a I m x N: u N I D) m I D) X where _ covariance YX yz variance X a = covariance ZX ZX variance X covariance ZY — ay ° covariance ZX a = zy variance X RESULTS Analysis of the Parent Population Grain yield (W) and the yield components, number of pods per plant (X), number of seeds per pod (Y), and seed weight (Z) are summarized for parental lines in Tables 6 and 7. The small—seeded lines were on the average more productive than the large-seeded ones. Yields ranging from 22.4 to 30.9 grams per plant are shown for the small-seeded lines. Large-seeded parents recorded yields ranging from 15.8 to 29.8 grams per plant. Number of pods per plant was a highly variable trait, ranging from 39.3 to 46.8 for P-05, from 31.5 to 39.3 for P—02 among the small Z lines and from 12.2 to 22.0 for P—12 and 37.0 to 44.8 for P-08 among the large Z lines. On the average, lines with small seeds produced a greater number of pods per plant than those with large seeds. Although lines with small seeds showed on the aver— age more seeds per pod, the individual examination of the lines did not give evidence of any consistent pattern of variation that could be related to seed size as confirmed by the ranges 3.9 to 5.2 and 3.9 to 4.9 shown by the small and large Z parents, respectively. 24 25 vom.ma emm.es Ame.ea .evm.ms msm.os woo.es .m>m o.eos www.ms em~.ea www.ms omm.ms mmo.es meo.na moms Amsmumv H.Hos oem.ms omm.vs oom.ea omm.ea ome.os omo.na moms mommm oos o.oos nom.ms oeo.vH ooo.vs ovo.ma one.oa cme.oa moms mo passes m.mm oos.ms ooo.es ooo.es oom.es oom.ma oom.oa poms oam.mea osm.oma omm.oea ~em.mea nmm.oms mem.mss .m>« o.om www.moa mme.oms oom.oma mme.vms omo.ovs mam.mos moms mommm mo m.aos mmv.eea mmn.msa emN.emH omo.mks omm.oea mom.0AH moms songs: Hmuoe o.ooa mma.vss ems.mom ome.MAH mom.mma omo.ems ooa.ema moms emm.v mem.v mm~.e vom.v mmm.v mao.m .m>m H.4Ha Hmo.e omn.e mmm.v oom.e neo.e moa.m moms pom pom m.AHH omm.e mem.e. mno.e ooo.e ooo.m omm.m moms mommm mo .02 o.oos soa.v mmm.¢ oem.m mom.m omm.m mmo.e moms van.mm emo.me som.ov mao.se omm.vm mom.em .m>¢ H.6m ekm.om «60.04 .Hnm.om 4mm.me oom.Hm mom.am moms ucmam use m.sm omo.nm oom.mm omo.oe omo.mm omo.em Acme.mm moms moon mo .02 o.oos vme.~e omn.oe ooo.oe H~¢.oe oom.mm omm.mm moms ovm.o~ m~a.u~ ~o~.m~ nmm.om mom.m~ eos.mm .m>< H.60H vm~.- ema.nm «mm.m~ evm.om www.mm Hom.mm moms Amsmumv H.eos mem.e~ mme.o~ mmn.em Hmo.n~ moo.km oom.m~ moms :smum «0 names o.oos mon.m~ mmm.n~ mam.mm eve.- omo.e~ oso.om moss Aooaumomsv .m>m monm eons mono Noun Hons Ham» “smug mmcmnu m>wumamm mmcfiq cocoomIHHmEm moms cam .moas .smms as ammsnosz_.3mcammm um Omumsam>o mocaa munm cocmmmIHHmEm on» mo mocmEHOmumm qua& some o>HumummEOU .O magma 26 0mm.am ham.mm 0mm.mm omh.ha hmo.ha omm.ha mmm.ma MH0.0N mmh.ma .m>m o.mm mm>.HN OmH.Nm oma.mm omm.ma omh.ha omm.®a Own.ma oom.AN omo.ma moma o.ooa ovo.- oon.mm oom.mm oom.ha om¢.ha omm.oa omh.ha ovv.om ov>.ha moma AmEmV mcomm N.OOH OOO.NN oom.mm oom.m~ OO0.0H oom.ha OON.mH oom.ma ooo.ma oom.ma bmma OOH mo usmfimz who.0aa 0mm.mo on~.Ah Ono.hma mmm.ama mhm.aoa mem.ooa omo.mm mom.aoa .m>< v.vm mmm.maa 0mm.m@ 0mm.Vm 0mm.maa mam.mma vON.HmH www.mva mmm.am mmo.oma moma mommm mo o.ooa mmm.maa mmm.H© www.mm mmh.mma Hhh.ona NmN.H~H Nmm.mha mHH.wO mva.mha moma HonEsc Hmuoe mom.¢ mn¢.m mam.v mah.¢ Nmm.v Non.v Omm.m mam.¢ Num.¢ .m>< m.moH mov.¢ mm©.m om¢.v mmo.v mum.v mmm.v mmm.m mnm.¢ mum.v moma pom Mom o.ooH bma.¢ mmm.m 5mm.m mom.v 0mm.¢ 0mm.v mam.m Om~.v Ohm.¢ moma women m0 oz www.mm oma.ma mna.ha oma.mm who.vm mnm.¢m oom.o¢ th.HN www.mm .m>¢ m.m> Hmn.mm ooo.mH OON.NH Omm.mm om¢.0m omm.am ooo.hm OOH.ON oom.om moma pamam mom 0.00H VmN.Nm anm.ma mva.mm Hmv.~m ooo.mm 00¢.hm oom.vv omN.mm omm.ov moma mcom mo .02 Naa.v~ mmm.mm Amm.ha aaa.¢~ Hmm.mm omm.om mmo.mm NHH.mH mmh.mm .m>¢ m.mm www.mm www.ma mmm.ma vmo.mm www.mm www.mm mo~.o~ www.ma www.mm moma Amemv 0.00H wmm.mm mmn.¢m mvH.o~ emm.mm www.mm oma.hm mom.m~ mmN.mH omo.mm wmma Camum mo Gama» AooHnmomav .m>< MHIm NHIm HHIm OHIm mOIm QOIm hOIm OOIm Mme» pawns mmcmcu m>Humaom nosed cocoomlomnmq mama can .moma .noma Cw cmmHLon .Bmchmm um Ooumsam>m mmcfla whom pooommImmumH mcu mo mocmEHOMHom unmam some o>flumummeou .h magma 27 A negative association of total number of seeds with seed size was observed. The average difference in lOO—seed weight between small- and large—seeded parents was 6.4 grams. Consistency of performance of the traits over two years is illustrated by the analysis of variance shown in Table 8, the measurements being expressed as percentage values to those of 1968, taken as reference, and presented in Figure 1. There were no significant differences from year to year in yield of grain, total number of seeds, and seed size. Significant differences were found for number of pods per plant and number of seeds per pod. Seed size behaved as the more stable character, showing only slight changes due to seasons. Components X and Y, on the other hand, showed marked changes from year to year. Values of these two components varied in Opposite directions consis- tently for the two sets of lines tested. This compensatory action of X and Y resulted in an almost stable seed number component. Whereas in the small Z population the components X and Y varied by the same amount, percentage-wise, though in Opposite directions, in the large Z lines some limitation impeded the upward change in the Y component necessary to compensate for the rather large decrease in the X component. The final outcome is a reduced total number of seeds in large seeded populations as compared with its counterpart. 28 .HO>OH RH OSU um UCMUHHHCmAmst OOOmV.O HVOON.OmOH bwmho.o ONhN0.0¢ MHmmm.mN OO Honum OHmHh.O mHowm.mmm ssmOHOm.O OHOOh.NH hHth.NN OH mommuocom x mumow ssommmo.¢m ssmmmHm.mmom ssmommo.o sseomom.mmm voomm.mm OH mommuocom «somfimm.m MOmHO.m¢mm ssmHmmh.m ssmhmnO.Hmm OOOON.v H Hmmw Omvmv.O NOmm0.0mMH NOBO0.0 HOmOh.mm mvom>.o¢ O How» m cHnuH3 .mmmm mpoom OOH HOQEOZ pom Mom DGMHm mom OHOHN mo mousom mo cameos comm Hmuoe mcsmuo.oz moom mo .02 mumsvm cmoz munch o3u How coHumooH oco um czoum mocHH Hmucmnmm cm>mHo Mom Oomsmmoe OHOHN mo mucmcomaoo may cam OHth :Hmum mo mocmHHm> mo mommHmcm .m OHQmB 29 /. / WWMMMWMMZMMMMWW%%%W 65 8 H 115 f? c I- m . g r 110 ‘- H h m . g . 3 105 .. o . II .I (D 101 ‘I— 8 #1: 99]: C Q a, b O Os ,_ :3 98 95 ~- m m I. H b “a Z 90-h 33 u u ,E o . C: 85 '1- .H I" g b a, I- g L m 80': 5 H m E‘. Figure 1. J No. Seeds Seed per Pod Size Yield of No. Pods Total Seed Grain per Plant Number Graphical representation of the values for grain yield and the components of yield in the 1969 experiments expressed in percent of the values from 1968 trials. Hachured blocks refer to small-seeded lines, white blocks represent large-seeded parents. 30 Study of Correlations Phenotypic correlation among the yield components, and grain yield for the parent pOpulation and the backcross generations are given in Table 9. Number of pods per plant was more closely associated with high seed yield than any other component. The values of the correlations were similar for the parent and back- cross pOpulations. Number of seeds per pod was signifi- cantly associated with yield in the small-seeded parents. No correlation was found between these two variables in the large Z pOpulation. The degree of correlation between Y and W appears to be related to seed size. When the whole BC 11 population was compared with BCll pOpulations where selec- tion for high seed size was effective, the results were the same as when small and large seeded pOpulations were com- pared. This was expected inasmuch as the comparison between the BC11 pOpulations was in reality a small versus a large seed comparison. In general, the values of the correlation coeffi- cients among components of yield were negative and they ranged in size from negligible to moderate. Ten out of twelve of the coefficients were negative in the four pOpu- lations studied. Although only four were statistically significant the trend for negative relationships among the components was evident and in accordance with previous findings. 31 .o>Huoommo 003 N MOM coHuooHom OHOSB mcoHumHsmo HA m 000 .coHumHnmom HHOm mHocz Q .H00.0 u s; 00 :0. 1000.0 n *0 00 .4. 50000H0 00 0004000 00 £043 100 .000.0 I ss 00 .H. “00H.0 u s0 00 .4. 5000000 00 0004000 00H nuns Lev .0HH.0 u my 00 .u. 4000.0 u *0 00 .4. 2000000 00 mmmumme 000 Bus: 100 .m0~.0 u ea 00 =H. “AH~.0 u s0 00 .4. soemmum 00 0004000 0» £003 100 .000.0 I s0 00 .0. .00H.0 u.x0 00 .u. soemmum 00 mmmumme 00H nuns Lava 44400.0- 000.0- 400H.0u 000.0 44000.0- 0000 0000 0> 000\mcs040 .02 4000.0- 44000.0- 000.0- 004.0- 44000.0- 0040 0000 0> 000H0\0000 .02 000.0- 000.0- 000.0- 000.0 000.0- 000\mcsmum .00 0> ucmamxmcom .02 000.0 0HH.0 44050.0 000.0 00H.0I 0040 0000 0> cause 000.0 44000.0 4400H.0 44050.0 000.0 000\mcsmum .0: 0> eases 44HH0.0 44000.0 440vn.0 44000.0 44000.0 ucmsm\0eom .0: 0> names HH HH H muconmm mucoumm OODMHOHHOU mumuumumno o om n om om N HH080 N mmums 10V Ass 100 Ame 1H0 000a 0004 OHmHm chHm cam mucocomfioo OHon moms» OCOEm mucmHOHmmooo coHumHouHoo OHQEHm cocoon GOEEOO CH .0 magma 32 In Tables 10, 11, and 12, path coefficient analyses of the relationships among yield and its component charac- ters are shown for the small- and large-seeded parents and the Bcll pOpulations, respectively. The simple correlation between X and W was high and positive. The direct path effect of X and W was likewise high and positive. The indirect effects via Y and Z were very small. This same pattern was the same for both sets of parents and was not altered by the process of backcross- ing. The simple correlation between W and Y was positive and intermediate in level for small Z parents. This value was determined mainly by the direct effect (ryw = 0.473 vs wa = 0.423). The indirect effects via X and Z were posi- tive but small. In the large-seeded parents the direct effect and the indirect effect via X were near the same magnitude as in the small seeded parents. In Spite of this, however, the correlation coefficient of W and Y was very small and nonsignificant due to the decisive influence of a negative indirect effect of Y via seed size. The BCll pOpulation showed a significant positive correlation between W and Y (r = 0.238). Most of this WY relationship was ascribed to the direct effect of Y (P = 0.297). The indirect effect via the other two YW components X and Z were negative but unimportant. When only the crosses where selection for seed size was effective 33 Table 10. The path-coefficient analyses showing direct and indirect effects of the components of grain yield for the small-seeded parent pOpulations Direct Indirect Pathways of Association Effect Effect r Yield vs No. of Pods/Plant O.8494** rDirect effect 0.8695 Indirect effect via no. grains/pod 0.0221 Indirect effect via seed size -0.04l6 Yield vs No. of Seeds/Pod 0.4732** Direct effect ' - 0.4226 Indirect effect via no. pods/plant 0.0454 Indirect effect via seed size V 0.0052 Yield vs Seed Size 0.0641 Direct effect 0.2192 Indirect effect via no. pods/plant -0.l651 Indirect effect via no. grains/pod 0.0100 34 Table 11. The path-coefficient analyses showing direct and indirect effects of the components of grain yield for the large-seeded parent pOpulation Direct Indirect Pathways of Association Effect Effect r Yield vs No. of Pods/Plant 0.8560** Direct effect 1.1684 Indirect effect via no. grains/pod -0.0156 Indirect effect via seed size -0.2969 Yield vs No. of Seeds/Pod 0.0381 Direct effect 0.3874 Indirect effect via no. pods/plant -0.0470 Indirect effect via seed weight -0.3026 Yield vs Seed Size -0.1440 Direct effect 0.6131 Indirect effect via no. pods/plant -0.5657 Indirect effect via no. grains/pod —0.l9l4 Table 12. 35 The path-coefficient analyses showing direct and indirect effects of the components of grain yield for the second backcross generationa Direct Indirect Pathways of Association Effect Effect r Yield vs No. of Pods/Plant 0.9114** (0.8604**) Direct effect 1.0548 (0.9670) Indirect effect via -0.0082 no. grains/pod (-0.0127) Indirect effect via -0.1l75 seed size (—0.0938) Yield vs No. of Seeds/Pod 0.0060 (0.2582**) Direct effect 0.2731 (0.2966) Indirect effect via -0.0318 no. pods/plant (-0.0414) Indirect effect via -0.2409 seed size (-0.0170) Yield vs Seed Size 0.0846 (0.1147) Direct effect 0.4805 (0.3721) Indirect effect via -0.2579 no. pods/plant (-0.2439) Indirect effect via —0.1369 no. seeds/pod (-0.0135) 8Numbers in parentheses indicate values for the Whole BC11 pOpulation. where selection for seed size was effective. The others are values for the Bell 36 were analyzed, the results were almost the same, with the exception of the relationship between yield and number of seeds per pod. No correlation was found for W and Y in these crosses. The direct effect was almost of the same magnitude as that of the whole BCll population (wa = 0.297 vs wa = 0.273), however, the indirect effect via seed weight, was negative and almost of the same value as the direct effect (wa = 0.273 vs P rzw = -0.24l). YW The simple correlation between W and Z was small in the three pOpulations: positive but unimportant in the small Z lines and the BCll generation and negative but equally small in the large-seeded parents. In all cases, however, the direct path effects were moderately high, 0.219 in the case of small-seeded parents, 0.613 for the large- seeded lines and 0.480 for the backcross generation. In the three pOpulations a comparatively high negative influence of Z upon W via pods per plant (r = -0.165, -0.566, and szwx -0.258, respectively) offset the direct effects, rendering the correlations small and unimportant. Since we are dealing with sequential characters, the correlations describing the associations between the traits will reflect the influence of the initial trait or traits upon the subsequent ones in the sequence of develOpment. To remove the effect of correlations would then mean in this case to free a particular trait from the influence of the previous traits in the develOpmental sequence. 37 Table 13 shows the mean squares from the analyses of variance for the parent population calculated after the effects of correlations were removed. The mean squares of correlated (actual) minus uncorrelated (transformed) data for yield and two of its components are also shown. The correlation effect of X was removed from Y and the effects of these two components were removed from Z. A significant effect due to genotype, years, and the interaction of genotype x years was observed for X and Y (Table 8). The genotypic and environmental effects were reported significant for Z and none of the sources of vari- ation is significant for yield. For X and Y the effects due to environment seemed to predominate over the genotypic effects; the Opposite was true for the Z component. When the effects of the correlations were removed, significant contributions of genotype, years, and genotype-environment interaction were detected for W, Y, and Z, as shown in Table 13. The variance compOnents for years, genotypes and the interaction at years by genotypes were calculated for yield and the components of yield making use of the trans- formed data for the parent pOpulation. The values obtained are shown in Table 14. The relative importance of each of the variance components with respect to the total variation represented by their sums is expressed on a percentage basis for each trait for each set of data, in Table 15. 38 .00>00 s0 000 00 0000000000044 00000.0 00000.0 00000.00 00 00000 4400000.000 4400000.0 4400000.000 00 00000000 x 000» 4400000.000 440000~.~ 4400000.000 00 00000000 4400m00.000 440m000.00 4400000.0000 0 0000 00000.0 00000.0 00000.00 0 00000 0 000003 .0000 0£m003 comm com mom OHOHN mp mousom mpmom .oz amm03002 .3mCHOmm pm 0000» 030 How OoumsHm>o mocHH Omen cm>0Hm 800m OHon mo mucocomeoo 030 cam OH00> chnm How 0000 OoumHoHHoocs 00m mocm0um> mo mommHmcm mo monmswm Cmoz .mH mHnt 39 .OHmN 03 00 OoEsmmm mm? 00060000 mHanOmmmH 0008 on» 20033 How mmnHm> o>HummoZQ .ucocomeoo uOoEcou0>cm an mmmuocwm ecu NW0 .mocwH ecu OCOEm mmoconMMHO OHuocmm 00 0:0 oOCmHWm> mo “soc Iomeoo Mo .mooc000MMHO Amummmv HmucmecouH>cw ou esp oOCmHum> mo newcomeoo mom . . .. . . . . . MO mHmmm mm hHhmm O mmth so NHmOO O mambo O QOOOO O n0OOOO O No mmmmH.mN vmmOH.O .. mmmom.m> mmth.v m¢O¢0.0 mom00.mm HomOm.v M0 mmmOH.H VHOON.O .. hmOOO.mH moch.O NOOB0.0 hoomm.H~ OOO0.0 W0 N w x 3 .. N .0 x 3 00000000000 mocmHHm> OoumHmHHOOCD Hmduom mumc ©0800mmcmnu ADV .mumc Hmsuom Ame .mumc mo mumm OBu ou pommmmu cuH3 OoumHmcm cam Cmchon .Bmchmm um mumm» O30 00m c3oum mocHH amen cm>mHm 00m OHme NO mucocomEoo ecu cam OHmam chHO HO mucmcomeoo oOCmHum> mo mmumEHumm .vH oHQmB 4O 0.0m Glam .... 0.0V Ola 04mm .... ..o. mHmwxn N OQNAHOCOU 0.00 0.00 .... 0.00 0.00 0.00 0.00 0.000 00000000 0.0 0.00 .... 0.00 0.0 0.00 0.00 .... 00000 N 0 x z N M x, 3 000000000 mocmwum> OmumHmHHOOCD Hmcuom 00 00000 Eoumv 0000 m0 you some £02003 00000 2000 00m mOCmHHm> Hmuou may mo unwoumm CH Omwmoumxm mucmcomeoo mocmHHm> mo mmumE0umm .mH mHQmB 41 With the exception of the seeds-per—pod component, the con- tribution of the genotype seems to be the most important factor for the expression of the traits, especially for yield and seed weight. For X there is a definite contribu- tion of environment, whereas for Y the environmental effect is as large as that of the interaction. When effects of the correlation of X with Y and of X and Y with Z are removed so that the contribution of each component may be studied freed from relationships with others, there is an increase in the contribution of the year-genotype interaction. The contri- bution of environment is unaffected in the case of Z but moderately affected in the case of Y, so most of the in- crease in the genotype by environment portion has been at the expense of a decrease in the genotypic fraction of Z and primarily in the environmental fraction of Y. The genotype by environmental interaction appears to be the main factor controlling the relationships between components, at least for W and Z. For Y, the interaction effect and the environmental fraction seems to be equally important. The genotypic by environment interaction is more important in controlling the correlation of X and Y with Z than is the environment. 42 Genetic Advance Heritability Estimates Data from the parent population grown for two years in one locality were used to estimate heritability in a sensus latus. Estimates of the components of variance are shown in Table 16. The heritability estimates (Table 16) agree in a general way with other reports. Seed weight heritability was high, 89.2%. The estimate for number of pods per plant was intermediate in value, whereas estimates of heritability for number of seeds per pod and grain yield were low. Table 16. Estimates of variance components and heritability computed for single plots for grain yield and components of yield for the parental bean lines grown for two years at Saginaw, Michigan . 2 2 2 Trait CG OGY OE Her. Yield 4.20861 0.00000a 25.95912 14.0 No. pods/plant 35.20481 0.00000a 46.62720 43.0 No. seeds/pod 0.04093 0.07229 0.07247 21. Weight of 100 seeds 4.17285 0.06910 0.43660 89.2 aNegative values for which the most reasonable estimate was assumed to be zero. 43 Heritability estimates in the narrow sense were obtained from the regression of F1 means on the small- seeded parents and F means on the mid-parents (Table 20). 2 In general, estimates for seed size were high and seeds per pod were intermediate. Yield and number of pods per plant registered low estimates although some inconsistencies were noted when the estimates from two different years were com— pared for these two traits; namely, a negative heritability value for X and a large discrepancy in the values for W for 1968 and 1969. Although heritability estimates cannot be given an unrestrictive use without considering the environmental conditions and the genetic material, our estimates support at least the reported high values of heritability of Z in comparison with values of heritability for yield and the other components of yield. Table 17 shows the values used to calculate the realized heritability for the character seed weight in each of the crosses where selection for seed size proved to be effective. The corresponding "t" values for the differences between the selected portions and the population means for the BCl's and their selfed generations are presented. Whereas the selected BC1 plants were all significantly different from the mean of the pOpulation from which they were extracted, only eight of the twenty sets of crosses Studied showed significance when the selfed generations were 44 .onEmm ucmHthH m :0 Ommmm .00>00 x0 000 00 0000000000044 Q .onEmm quHmImN 0 co commmm .00>00.x0 000 00 000000000004 4HH.v OOh.OH 00m.0H 04mO.OH OO0.0H mmm.OH mOvO 0mm.m mho.mH mm0.mH 000m.mH Omm.ON mmm.0H boHO 40¢.N OO0.0H OOm.0H 40HH.NH OmH.Om mm0.0H OOmO 4on.m Omm.0H mom.0H 400m.m OON.OH OOm.0H OONO 00©.~ 0mm.0H H00.0H 44mm.OH OOO.mH 000.0H OOHO *Hm.m Omh.OH NHN.0H 00mO.m OOm.mH OmH.OH momo OO.N NHH.0H OOm.0H 440~.m Omm.mH OOH.0H OHMO mm.H NO0.0H www.mH 40OO.OH Omn.mH m0N.0H OOHO mm.O mHm.OH 000.0H 440m.m OO0.0H mmH.mH OOVO Hv.H Oom.OH mm0.0H 44OO.NH 00m.bH mho.mH mOvO mH.H NH0.0H mw0.0H 04NN.HH Omv.OH www.mH HHVO NO.H www.mH www.mH 0400.0 OOH.HN mm0.hH OONO 04Hm.m OO0.0H mm~.OH 00mm.OH oom.mH m0m.mH HHmO 040m.m mm0.0H mme.OH .0400.~H OOh.mH mum.vH OHmO 0emm.m mmm.0H OON.OH 440m.OH OOm.0H OOO.vH mOmO eeem.m 00m.0H 000.0H 40H0.OH Omm.mH Omm.mH homo eeoo.m NHv.mH OOh.0H 04mo.m OO¢.0H mhm.mH OOmO 400m.o OO0.0~ 00H.H~ 04mm.m OOm.Hm m00.HN mHmo 000m.m 0mm.mm mmv.Hm «40m.m OON.mm OOO.- mHNO 00mH.m OOm.0N www.mH 0000.NH Omm.mm mNH.mH NHHO mmsHm> 00:00 Hum coHuchmom mmmsHm> mmcHH coHuMHsmom 00000 0 0 00000000 000 0 00000000 00000 00000 00 000s 000 000 00 000: mammn mo mmc0H cmcmmmlmmHMH pcmnHHmEm mo 0000000 no 0000 wucm3u CH .OOHumumcom OmuHmm o>HuommmoH 00050 new COHuHom OouomHmm 000 .cOHuMHsmom Hum 0 How 00000 0N0m Ommm 030 no name: .0H oHnt 45 compared. These crosses were the only ones where selection for high seed size was considered effective. Realized heritability was calculated for these populations (Table 18)° These heritability estimates ranged from 14.8 to 64.3. Table 18. Realized heritability estimates for seed size based on actual response from selection practiced in a first backcross generation in a set of crosses between small- and large-seeded bean lines 1 l Cross Heritability 0112 64.3 0213 62.6 0313 59.2 0506 43.8 0507 25.7 0509 42.2 0510 14.8 0511 21.3 Heritability estimates were calculated also for W, Y, and Z freed from the variation attributable to correla- tions. The variance components method was used with the parental data. Table 19 includes the estimates of the variance components and heritability for grain yield and its components. W, X, and Z showed heritability values around 40%.while Y values were half this amount. Estimates derived from the different methods for calculating heritability are compared in Table 20. 46 Table 19. .Estimates of variance components and heritability for single plots for grain yield and components of yield, with effects of correlations removed . 2 2 2 Trait 0G OGY OE Her. Yield 73.905892 64.733888 43.010056 40.7 No. pods/plant 35.204806 0.000000 46.627200 43.0 No. grains/pod 0.109940 0.337169 0.067328 21.4 Weight of 100 seeds 29.123500 38.532200 0.639400 42.6 aNontransformed data. Table 20. Estimates of the heritability of yield and its components in a bean pOpulation with Operating correlations among components Methods of Calculation F2 Variance Fl-Parent Mid-Parent Realized Trait Components Regression Regression Heritability W 14.0 31.1 0.7 X 43.0 -8.0 9.8 Y 21.2 48.2 18.4 . Z 89.2 82.8 60.6 41.7 47 Test of Additivity for Seed Size .A test for additive behavior of genes affecting seed size was performed by comparing the observed means of the first backcross generation with the expected values assuming an additive model where the mid-parental values correspond to the performance of Fl's. Results are presented in Table 21. Only 5 out of 20 of the comparisons deviated signifi- cantly from the additive scheme. Crosses involving large-seeded parents, P-06 and P-09, deviated significantly from the additive model when the recurrent parent was the small—seeded parent P-02, how- ever, no significant deviation was observed when the other small—seeded parents were involved except when P-05 and P-06 were used together. Crosses involving P-ll (e.g., 0411 and 0511) showed a differential response, BCl progenies derived from the former diverging significantly from the additive model. A particularly large and highly significant value was found for the cross 0408. Response to Selection Since the BC11 was planted in a different year than the BC the expected values for the second backcross cannot 1 be estimated using the actual BC1 data. An expected BC 1 mean value was calculated for each cross for seed size making use of the parent population data from the 1969 plantings. An additive model, that proved to be adequate according to the results from 1968, shown in Table 21, was assumed. Table 21. t-test and mean values for seed size for twenty first-generation backcrossed lines and their expected values under an additive model BCl Means Under Additive Model Cross Observeda EXpectedb t Values 0106 17.275 16.980 1.30 0107 17.525 17.760 1.02 0109 16.700 16.760 0.29 0112 18.125 19.180 1.77 0206 17.725 16.788 2.68** 0209 17.300 16.560 3.44** 0213 22.600 22.280 0.45 0306 16.625 16.160 1.60 0309 16.150 15.940 0.88 0310 17.100 16.100 0.37 0313 21.775 21.660 0.10 0406 15.125 14.940 0.81 0408 16.525 14.950 5.15** 0409 15.075 14.700 1.90 0411 15.725 14.960 2.31* 0506 15.575 14.960 2.66** 0507 15.950 15.640 1.11 0509 14.600 14.740 0.52 0510 14.875 14.900 0.08 0511 15.375 15.000 1.24 aTwenty-five plants used for each cross. *Significant at the 5% level. **Significant at the 1% level. bCalculated using the parent pOpulation planted in 1968. 49 The expected and observed values agreed very closely as indicated in Figure 2. The BCl means from the 1968 trials were compared with the values from the parental pOpu- lation grown that year. Parental seed weights from the 1969 trials were compared with the values from the parental popu- lation grown in that year. Parental seed weights from the 1969 trials were used to calculate the estimated BCl for that year based on an additive scheme. Only 3 out of 20 crosses showed a discrepancy greater than 5% when the observed and expected values were compared. The expected Bcll means assuming an additive model were calculated from the previously estimated BC1 means for the seed size trait. A maximum expected genetic gain value was set by using broad sense heritability estimates and the standardized selection differential corresponding to a selection intensity of 8%. These values, calculated for the BC11 generation, represent the estimates of the minimum and maximum expectations under the additive scheme (Table 22). The actual Bcll means and their comparisons with the small-seeded parents are given in Table 23. Eleven out of 20 backcross lines showed a significant increase in seed size with respect to their particular recurrent parent. Increases ranged from 9 to 31% and were in close agreement with the expected values. In the rest of the lines, posi- tive changes0were negligible and even slight decreases from the recurrent parent were noted. Nevertheless, the results 50 0 l 3 9 X0 0 6 O 2 .1. 9 2 O vAo 6 0 2 l 1 X0 06 07 09 Am: w>0uommmmm cans Hmumouw u m>OQ< “m2 m>auomwmmm mnu mo X unmonmm 5 1 0 0 1 l 11 09 10 5 O6 O7 0 8 85 wcaq ommm zoammv BCl means for seed size expressed in percent of the Hachured blocks midparents grown in two years. refer to observed BCl means in the 1968 trials. White blocks represent expected values calculated with the parental 1969 data assuming an additive model. Graphical representation of the deviations of the Figure 2. 51 Table 22. Expected means for two backcross generations under no selection and under 8% selection intensity on the BCl for the character seed weight Expected Means for Z Bcll BC11 From Unselected From Selected Cross BCl Populationa Population 0106 17.565 17.322 18.958 0107 18.260 17.670 19.306 0109 17.020 17.050 18.686 0112 20.098 18.589 20.224 0206 17.070 16.745 18.381 0209 16.530 16.475 18.111 0213 20.352 18.386 20.022 0306 15.900 15.375 17.011 0309 15.350 15.100 16.736 0310 15.280 15.065 16.701 0313 19.175 17.012 18.648 0406 15.630 15.065 16.701 0408 15.445 14.972 16.608 0409 15.090 14.795 16.431 0411 15.595 15.048 16.684 0506 15.900 15.375 17.011 0507 16.580 15.715 17.351 0509 15.350 15.100 16.736 0510 15.580 15.215 16.851 0511 15.860 15.355 16.991 BC = BCl + F1 11 2 bBC = (BCl + AG) + F1 11 2 52 Table 23. Actual seed size means of the BCll lines as weight of 100 seeds, under an additive model when selection is based on seed size Percent Increase of Bcll Over Small Z Parent Expected Expected Observed BCll Under No Under Cross Mean, grams Selection Selection Observed 0313 20.400 :_2.168 14.6 25.6 30.8** 0112 21.250 :_1.l66 8.8 18.4 20.4** 0506 16.875 i_0.558 3.5 14.5 18.1** 0511 16.750 :_O.223 3.4 14.4 17.3** 0509 16.400 : 0.643 5.8 16.8 14.8** 0510 16.363 :_0.346 1.7 12.7 14.5** 0507 16.075 i_0.302 5.8 16.8 12.6** 0213 20-175.i 1.249 12.0 21.9 11.8** 0309 17.200 1 0.577 1.7 12.7 10.3** 0306 17.025 : 0.423 3.5 14.5 9.2** 0310 17.037 : 0.424 1.4 12.4 9.2** 0406 16.075 : 0.583 3.9 15.1 4.1 0411 15.975 i 0.860 3.8 15.0 3.5 0408 15.937 :_0.613 3.3 14.5 3.1 0206 17.188 : 0.563 2.0 11.9 1.0 0409 15.600 i 0.519 2.0 8.9 1.0 0106 17.750 : 0.691 1.4 11.0 0.6 0107 17.625 :_O.456 3.4 13.0 -0.1 0109 17-125.1 0.678 -0.2 9.4 -2.9 0209 16.137 1 0.843 0.3 10.3 -5.2 **Significant at 1% level using Dunnett test. 53 confirmed the validity of the additive model since devia- tions from expected values under no selection were in all cases unimportant. Some exceptions were registered, as, for example, in the crosses 0306, 0309, and 0310 which showed increased seed size in the BCll according to an expectation of effective selection, but actually no response to selection had been detected in the selfed BCl generation. The cross 0406 worked in the Opposite direction: selection for seed size in the BCl generation was effective, but this pOpulation failed to show a significant increase in BCll“ and BC When the BC generations were compared with l 11 respect to variations in seed size as a result of the selec- tion practiced in the BC1{ no significant change was observed for the pOpulation where selection for large Z was effective. This observation is a valid one when the mean of all the pOpulations was considered since large differences between BC1 and BC11 may be noticed when the individual pOpulations are compared. Where selection was not successful, however, the BCll average seed size was, as expected, significantly lower than that of the BC1 (Table 24). The response of the seed number components selection had been practiced for seed size are shown in Table 25. The increases in seed number in relation to the recurrent parent ranged from 3 to 60%“ Some lines showed a decrease that in one instance was on the order of 14%. Only two of these changes, however, were significant. 54 Table 24. Differences in seed size of the BCI and Bell gen- erations of twenty bean populations, expressed as percent change over the recurrent parents % Change Over the Recurrent Parent t Population BCl BC a 11 Values POpulations Where Selection for Large Z Was Effective 0112 8.3 20.4 0213 37.2 11.8 0313 39.3 30.8 0506 11.0 18.1 0507 13.6 12.6 0509 4.0 14.8 0510 6.0 14.5 0511 9.5 17.3 Mean 16.1 17.5 0.768 ns Populations Where Selection for Large Z Was Not Effective 0106 3.3 0.6 0107 1.4 -O.1 0109 -0.2 -2.9 0206 5.9 1.0 0209 5.0 -5.2 0306 6.3 9.2 0309 3.3 10.3 0310 9.3 9.2 0406 8.0 4.1 0408 18.0 3.1 0409 7.7 1.0 0411 12.3 3.5 Mean 6.7 2.8 2.452* aCalculated after arc-sine formed on data. *Significant at 5%.leve1. transformation was per- 55 Table 25. Observed and eXpected changes on seed number and seed number components in the BC11 generation under two successive backcrosses to the small-seed parent and selection in the BCl for large-seed % Change With Reference to Recurrent Parent Seed Number Components No. Pods/Plant No. Seeds/Pod Seed Cross Number Obs. Exp. Obs. Exp. 0209 60.2** 60.8** -1.0 -1.6 -0.4 0408 38.8 22.5 -1.0 8.3* -2.0 0406 27.9 11.3 -2.9 9.3* 0.5 0411 20.6 9.4 -4.4 5.7 -0.2 0306 20.4* 16.2 -2.6 11.0* 0.7 0510 17.9 18.4 -2.8 0.5 -O.6 0206 17.3 10.9 —1.2 4.7 —0.3 0506 12.8 10.5 -2.7 2.2 0.8 0309 12.3 -2.9 -2.5 14.6** 0.6 0107 10.4 14.3 -4.8 -2.4 -1.6 0313 7.1 4.5 -6.7 1.1 -2.6 0109 7.6 8.7 -O.4 -0.7 -l.0 0213 7.1 12.2 -5.9 -5.2 —3.4 0511 6.4 —1.6 -4.3 8.4* 0.2 0106 3.4 6.6 -O.8 -2.8 -0.9 0507 -l.0 -5.7 -6.1 5.5 0.0 0310 -5.6 -10.7 -2.8 15.9** -0 6 0509 -6.4 -8.7 -2.5 3.7 0.7 0409 -6.7 -5.9 -2.7 -5.8 0.9 0112 -14.2 -1.2 -7.8 -12.8** -1.9 *Significant at 5%.level using Dunnet test. **Significant at 1% level using Dunnet test. 56 Some characteristic patterns of variation may be distinguished by examining the seed number trait and its components. Seed number increased due to a simultaneous rise of the components X and Y. Increases were also noted when a positive response in one of the components was of sufficient magnitude to offset a decrease in the other component. On the other hand, a decrease in seed number occurred due to lack of compensatory effect in the changes of the seed number components. Either X and Y decreased simultaneously or the increase of Y'was unable to compensate for the negative change of the X component. It is worth pointing out, however, that although in no case was the variation of both seed number components simultaneously significant, deviations from expected values under an additive scheme were substantial. The final outcome of the component relationship is yield. The whole picture of the variation of yield and its components with reSpect to the five recurrent parents is presented in Table 26 for each of the Bell lines. Most lines showed a numerical increase in yield over the recur- rent parent but only six lines showed as significant in- crease in yield compared with the small-seeded progenitor. Four of the six lines that did raise their grain productiv- ity appear to have reached this level through an increase in seed size. One of these lines, 0511, showed a simul- taneous positive change in the Z and Y components. The 57 Table 26. Grain yield and percent change in yield and its components with reference to the recurrent parent for twenty BC11 populations % Change Over Recurrent Parent Grain Seed Size Yield No. Pods No. Grains in Wt./1OO Cross (gms) Yield Per Plant Per Pod Seeds 0107 31.6101 9.8 14.3 -2.4 -0.1 0109 29.7830 3.4 8.7 -O.7 -2.9 0112 29.7623 3.3 -1.2 -12.8** 20.4** 0106 29.7424 3.3 6.6 2.8 0.6 P-Ol 28.8014 0.0 0.0 0.0 0.0 0209 37.6581 47.3** 60.8** -1.6 -5.2 0213 31.3544 22.6 12.2 -5.2 11.8** 0206 29.5002 15.4 10.9 4.7 1.0 P-02 25.5677 0.0 0.0 0.0 0.0 0313 42.7626 38.2* 4.5 1.1 30.8** 0309 37.8330 22.3 -2.9 l4.6** 10.3** 0306 37.1758 20.1 16.2 11.0** 9.2** 0310 34.7442 12.3 -10.7 15.9** 9.2** P-QB 30.9436 0.0 0.0 0.0 0.0 0408 32.8387 36.9* 22.5 8.3* 3.1 0406 30.4884 27.1 11.3 9.3* 4.1 0411 29.2338 21.9 9.4 5.7 3.5 0409 20.8906 -12.9 -5.9 -5.8 1.0 P-O4 23.9817 0.0 0.0 0.0 0.0 0511 38.9811 43.7* -1.6 14.6** 17.3 0510 36.5474 34.7* 18.4 0.5 14.5** 0506 36.5474 32.8* 10.5 2.2 18.1** 0507 30.4110 12.1 -5.7 5.5 12.6** 0509 29.6646 9.4 —8.7 3.7 14.8** P-05 27.1241 0.0 0.0 0.0 0.0 test. test. *Significantly different at 5% level using Dunnet **Significantly different at 1% level using Dunnet 58 remaining two lines which showed significant increases in yield attained it either through higher X level, as was the case of the cross 0209, or through significant rise in the Y component coupled with a noticeable though not a signifi— cant increase in X, as shown by cross 0408. Some significant increases in seed size were offset by significant changes in the Opposite direction in the Y component as in the lines 0112, 0306, 0309, 0310. In other cases, we did not overcome the compensatory forces by recurrent backcrossing; the high Z values, although significant, were not large enough to compensate for slight negative responses in Y (as 0213) or in X (as 0507 and 0509). In order to compare the grain productivity of the different pOpulations in the BCI and Bcll generations, the Bcll values were transformed relative to those of the BCl grown in the previous year. The adjustment was made by comparing the variation of the parental pOpulation grown in 1969 with respect to that grown in 1968. Variations on each component were expressed on a percent basis and the respec— tive change was either added to or substracted from the component values of the 1969 pOpulations according to whether there was a decrease or an increase in the values of the same parent pOpulation grown in both years. Each of the components of the parents grown in 1969 was adjusted at the 1968 parental values in this way. Bcll values were then calculated using their adjusted values according to an addi— tive model. 59 Table 27 shows the eXpected and Observed grain yields for the BCl and BC11 generations. POpulations were divided according to whether selection for seed size was effective or not, and progress of the BCl and BCll with respect to the recurrent parent values were estimated for each set. Where selection for Z was not effective no sig— nificant change in yield was observed between the BCI and BC11 generations with respect to the recurrent parent. Where selection was effective for Z there was a large in- crease in yield in the BC1 with respect to the recurrent parent and a further, though much smaller, increase in the BC 11' When selected plants in the BCl were selfed for two generations the reduction in yield as compared with the BCll generation was noticeable only in the first generation of selfing as shown in Table 28. Heterozygosis-Performance Relationship In order to elucidate any relationship between the level of heterozygosity and the performance of the BCll lines, the average values for yield and the components of yield were calculated for different levels of heterozygosity in six bean populations (Table 29). These values were plotted in Figures 3, 4, 5, and 6. In general, the average heterozygosis-performance for all the populations studied was similar, when each individual trait was taken into consideration. 60 0 0: 0mv. fim.m v~m.o um I om 0000000000 m.®0 m0m.om m.¢0 0mm.om mm0.©m 0002 0.m~ nov.mm v.m0 mm~.m~ www.mm 0000 0.0: 00¢.mm 0.00 m©0.o~ mmm.mm movo m.mm 000.0m o.mm 0mm.mm www.mm 0000 m.om om0.mm v.m0 mmv.mm Om0.0m mono N.m0 Nom.vm «.00 moo.mm O0o.om @000 0.00 ©N¢.mm v.mm Omh.om 000.0m 0000 m.h 000.Nm m.ml N00.mm O0o.om @000 0>000000m 002 003 N 0m000 000 000000000 00003 0000000sqom 00 000. 00.0 000\00 000.0 000 n 0000 0000000000 ®.Nm 00m.mm N.mm N00.vm mm0.©~ 0002 m.om moo.om m.00 000.0m mmm.hm 00mo o.mm www.mw o.o~ Omo.mm mmm.nm O0mo m.h0 www.mm 0.m0 000.0m mmm.hm momo m.m0 mum.0m v.mm 00m.vm mmm.hm homo m.vm m00.>m 0.m 0mo.om mmm.hm momo 0.0m hoo.mm b.0m www.0m 00¢.NN m0mo m.0m mom.mm 0.00 mwo.0¢ om©.¢m m0~o N.N~ mno.mm ~.©m www.0m O0O.om N000 0>00ommmm 003 N 00000 000 000000000 00053 0000000500m 0500> .m.m 00>o 000m .m.m 00>O 00m 000000 0000005000 0 0m00£U &. 000050 R 00000500m 00000 00000\00000 00000 00000005000 0000 000030 00 000000000m 000000000 000000 000 00000 000 000 0000» :000m U0>00000 .hm 00009 61 Table 28. Comparison of grain yield among the BClSl and BClSZ vs BC11 generations derived from selected BCl pOpulations Grain Yield (gms) Population Bcll % BCISl % BClS2 % 0112 29.760 100 31.612 106.2 30.882 103.8 0213 31.790 100 29.528 92.9 37.968 119.4 0313 42.490 100 31.612 74.4 32.232 75.9 0506 36.320 100 30.178 83.1 23.770 65.4 0507 30.310 100 31.442 103.7 28.305 93.4 0509 29.095 100 33.975 116.8 27.208 93.5 0510 36.815 100 30.715 83.4 28.168 76.5 0511 34.045 100 27.158 79.8 26.920 79.1 Mean 34.487 100 30.270 89.1 29.516 86.7 Generations Differences t Values BC11 - BCIS1 4.217 gms/plant 4.253** Bcll - BClS2 4.971 gms/plant 4.050** BC1S1 - BCIS2 0.754 gms/plant 0.830 **Significant at the 1%.1eve1. 62 Table 29. Means of yield and the components of yield at four levels of heterozygosity in six bean pOpulations Type of Combination and Percent Heterozygosity Inbred Lines F3 BCl F1 Character POpulation 0 25 50 100 Grain yield 0106 28.500 27.967 28.412 51.896 (grams) 0209 27.669 29.663 29.606 42.536 0408 27.729 29.031 31.578 52.913 0506 26.735 31.407 30.031 32.193 0510 23.878 24.750 33.020 35.893 0511 22.654 26.867 30.644 35.744 No. pods 0106 32.450 31.450 25.971 54.750 per plant 0209 34.050 34.900 37.587 45.450 0408 40.050 29.150 35.081 57.500 0506 39.300 41.950 37.573 38.950 0510 30.450 31.650 38.989 47.400 0511 25.850 34.600 43.250 43.250 No. seeds 0106 5.250 5.175 5.185 4.800 per pod 0209 5.000 4.700 4.504 5.275 0408 4.675 4.475 4.604 4.900 0506 4.575 4.650 4.774 4.775 0510 4.375 4.675 4.742 4.650 0511 4.625 4.475 5.071 4.975 Weight of 0106 17.075 17.600 18.052 19.425 100 seeds 0209 16.425 16.950 17.663 17.375 (grams) 0408 14.500 17.225 17.021 19.175 0506 14.850 16.000 16.541 17.625 0510 17.775 16.250 15.381 16.125 0511 18.875 16.825 17.330 16.500 63 53 .1 [0408 F / 0106 50 '/ l y o . ./ 4r / .- / O 45 .. ./ . ./ . / O . ,l 0209 0‘) a / M F o 3.4 0‘ 40 «- 'l . / B 1' ’0 .2 s U :x ./ .5 0 .’ 0510 m / I ’4 .. . ,’ 0511 (p 35 ‘ / ‘, // x—oOSOS li” ,lsk”' /’ ,x" i i 1' ‘r 0 25 50 75 100 Percent Heterozygosis Figure 3. Heterozygosis-performance relationship for yield in six bean pOpulations. 64 58 0408 55 0106 50 0510 E 45 0209 (U H m 0511 31 m /4\ m /// ‘\\ 8 ./ m 40 " ‘\ I \ x \ ____ __ ————— ' 0506 L 35 ‘ 4 _ - 4P ‘rfi 1L 4% 30‘" j?- 4r I l J J I l T r O 25 50 75 100 Percent Heterozygosis Figure 4. Heterozygosis—performance relationship for number of pods per plant in six bean pOpulations. 65 5.5" V 0209 Number of Seeds per Pod J o . is 53 7% 100 ‘D Percent Heterozygosis Figure 5. Heterozygosis-performance relationship for number of seeds per pod in six bean pOpulations. 66 19.5 0106 '0408 19.0 18.5 5 18.0 17.5 17.0 Weight of 100 Seeds, 16.5 16.0 15.5 ' i i T T 0 25 50 75 100 Percent Heterozygosis Figure 6. Heterozygosis-performance relationship for seed weight in six bean populations. 67 The trends for W and its components appeared to be curvilinear. The pOpulations having P—05 as a common genetic background plateaued either at the 20 and 50%.1eve1 (as 0506) or between 0 and 25% level (as 0510 and 0511) before rising moderately at 100% heterozygosity. The response of Z and Y to levels of heterozygosis showed a decrease in performance from the 25%.to the 50% level of heterozygosis whereas the Opposite was true for the characteristic X. With the exception of X, however, the apparent curvilinear trend proved to be unimportant when a test for curvilinear regression was undertaken (Table 30). The non- significance of the curvilinear trends for W, Y, and Z must be taken cautiously, however, since the error as expressed by the interaction lines by levels of heterozygosity was possibly too high. Further partition of the interaction and study of the variation of lines within each level of hetero- zygosity might change the picture, as indicated by the graphs. The results of the regression values showed no significance in the deviations from linearity for W thus suggesting that very little epistatic gene action may be involved in grain yield in beans. Y and Z did not show significance for the differences in the levels of heterozy- gosis, however, some heterogeneity arising from the pooling of different pOpulations may have caused the lack of signif- icance of the linear trend to account for the heterozygosity- performance relationship for the Z character as suggested by 68 .Hm>ma xa mcu um quoHMHcmHm** .Hm>ma xm mnu um unmonmucmnm« vov.a oamo.o gm.mm va.am ma mam>oa x mmcwa .ucH mmn.a «mma.o Hm.om mo.m~ m mmcfla maoem oao.o mo~o.o No.m NH.N a ownso mho.o Hmoo.o «mm.ama ha.mv A oflumuomso mma.v Hmoa.o **hh.oo> **gm.mmm a ummcflq wov.a oovo.o 54mm.omm **Hm.mmm m mam>ma mcoe< AmEmHmv com Mom unmam mom AmEmHmv mo mousom unmflmz ommz mommm .oz moom .oz moamflw Camuw mmumsvm cmmz mHmHEocmaom Hmcomocuuo an Imamu wUCmEMOMHmmImanomxuoumumn .mucmcomeoo mug 0cm Gama» How manmcoflu on» no Godmmmummu Hmmcflaa>uso Mom umme .om magma 69 the slight departure from the levels of significance, and also by the results of selection. For the character, pods-per-plant, a highly signif- icant linear effect was noted accounting for much of the variation; however, a significant nonlinear effect might suggest a curvilinear relationship indicative of a possible interaction between nonallelic genes. Discrepancies between the F2 and BC1 generations, both at the same average level of heterozygosity, are evi- dent. These differences are tabulated in Table 31. The F2 exceeded the backcross generation in grain yield and number of pods per plant. The Opposite was true when the charac- ters seeds per pod and seed size were considered. It must be noticed that the prOportion heterozygous-homozygous favor- able is different in the BCI and F2 generations. Y and Z seem not to be as affected as W and X by additional incre- ments of heterozygosis. Since selection in the first backcross generation invalidated the expected degree of heterozygosis, a valid comparison was possibly only among the backcross generations deriving from the selected plants (Table 32). Theoretically, the BCll and the BClSl should have the same level of hetero- zygosis, unless, in the selection process, heterozygosis is preferred. BC11 outyielded the BCIS1 in almost all the populations studied. This higher yield resulted from a superiority in X and Y; in all the crosses the BC11 popu- lations produced more pods per plant than their respective 70 Table 31. Comparison between filial and backcross gener- ations having the same level of heterozygosis. Plus (+) or minus (-) signs used to characterize the group exceeding (or not) the other No. Pods No. Seeds Grain Yield per Plant per Pod Seed Size 0106 + - + - - + + + 0209 + — + - - + - + 0408 + - + — - + - + 0506 + - + - - + - + 0510 - + - + - + - 0511 + - - + - + + — BClS1 generation and, except in two pOpulations (0112 and 0213), the same was true for the Y component. Seed size, on the other hand, was lower in the BCI with the exception of 1’ cross 0309. No definite pattern was noticed for W, X and Y in comparing the BClSl and BClSl generations. About half of the pOpulation showed indistinctly lower or higher values for any particular component. Seed weight did show some consistency; excluding pOpulations 0213 and 0507, all the rest of the pOpulations in BClS registered higher seed 2 weight values. When the 100% level of heterozygosity was compared with the zero level, the heterotic response expressed in grain yield and its components could be appraised (Table 33). 71 omn.oa mam.na oom.oa mma.m mom.v mmo.m mnm.mm omm.om omm.am Hmm.mm omm.o~ mma.>m Hamo mom.oH mm¢.na mmo.na omn.v omo.v mm¢.¢ omm.ne oom.mm oom.ov nwm.om moa.m~ man.om oamo mno.oa mnm.oa nmm.>a mmm.v mom.v mmm.v mmn.nm om¢.mm oon.mm Hav.om mem.mm Nev.am homo mnm.ma www.ma mav.ma mmm.v mmo.v moo.v mmm.¢v omm.s~ oma.mm vmo.om one.m~ mna.om oomo oov.o~ smo.m~ oom.om omm.¢ mov.m mmm.m omm.mv mmo.mm mmo.om mos.~¢ ~m~.mm mam.am mHmo smo.na oma.ha NHH.BH ~H~.m NHH.m omo.m mnv.mm omm.~m oma.mm vv>.vm mom.m~ ono.mm oamo oo~.na moo.>a ov~.oa oma.m Nom.v mom.¢ ooa.mv mno.om mmm.mm mmm.>m mmm.am mm~.nm momo mmo.na mna.ma oom.na «Ho.m mmm.v mmm.v oon.om omv.~m oom.om osa.nm moa.mm ~m~.om oomo mna.o~ 0mm.ma nmm.mm mmv.v mmv.¢ mn¢.m oom.mm omv.mv mne.mm «mm.am mom.>m mmm.mm mamo omm.am mno.m~ oom.v~ oom.v mno.v mon.v mmo.am om>.m~ ooo.o~ www.mm mmm.om ~H6.Hm NHHo Som mmaom Hwhom jom mmaom Hwaom jom mmaom Hmaom HHom Nmaom Hmaom cenumasmom AmEmv oom\m©mmm .oz vamam\m©om .oz AmEmv 29. m3 3mm 33» 5.86 wNHm Comm new omofluomum mmB cofiuomamm muo£3 mmouoxomn umuflu m Eonm Um>flum© mcoHumuocmm mmouoxumn cmmBuwn COmflHmmEoo .Nm magma 72 Table 33. Heterotic response for grain yield and the components of yield in six bean populations (percent increase of F1 as compared with parents) Hybrid Criteria W X Y Z 0106 MP heterosisa 81.9** 72.8** -5.2 7.6 HP heterosis 81.7** 68.7** -8.6 2.3 0209 MP heterosis 59.7** 39.0* 7.4* 4.4 HP heterosis 53.7** 33.5** 5.5 3.1 0408 MP heterosis 96.0** 49.2** l4.0** 17.0** HP heterosis 90.8** 43.6** 4.8 4.9 0506 MP heterosis 16.4 11.1 1.1 4.1 HP heterosis 12.7 -0.9 -2.0 -7.3 0510 MP heterosis 41.8* 35.9* 3.9 -l.0 HP heterosis 36.6* 20.6 1.6 -9.3 0511 MP heterosis 44.7* 32.8** 8.2* —2.2 HP heterosis 33.7* 10.0 7.6 -12.6 Mean MP heterosis 56.4 40.1 4.9 5.0 HP heterosis 51.5 29.2 1.5 -3.2 aMid-parental. hHigh parent. *Significant at 5% level. **Significant at 1% level. 73 Heterosis for seed yield was high, especially for the hybrids 0106 and 0408. Only the cross 0506 registered a relatively low heterotic response. Heterosis, although high also for the X component, was less pronounced than that for yield. Again the hybrid 0506 showed a modest increment and the performance of the F1 did not quite equal the high parent. The Y and Z components showed only slight heterosis and in most cases none at all. DISCUSSION Correlation AmongiTraits The extent to which yield and its components and the components inter §§_are correlated has been studied by many workers. Our findings agree in a general way with those reported previously, i.e., the component X seems to be the one most highly correlated with W, and the components of yield are in the majority of the cases negatively correlated in their relationships with each other. Even though the coefficients were relatively small in the case of negative associations, they were statistically significant, indicat- ing a probable association between these characters. The relationship of X and Y with Z is clearly in- fluenced by the size of Z. Only in large-seeded varieties, in the present data, were these associations negative. The degree and direction of correlation can be affected by the amount of inter-plant competition as has been demonstrated elsewhere (1). Absence of correlations in our studies, then, should be interpreted cautiously since the inter-plant com- petition was reduced by the lS—cm-spacing within the row in all field-grown material. The correlation between X and Y appeared to be unaffected by seed size. 74 75 A more critical examination of associations through the study of path coefficient analysis revealed that the component X is the factor exerting the greatest influence both directly and indirectly upon grain yield. Y and Z did not appear to influence yield as dramatically as X. Although the total correlation coefficient singled out Y as more closely related with yield in small-seeded populations this difference disappeared in the large-seeded lines. Actually, in large—seeded lines, the direct effect of Z exceeded that of Y. This effect was counteracted, how- ever, because Z was negatively associated with X and Y. Due to these inverse relationships the indirect effects of Z on W and Y were negative and relatively large, the consequence being a null overall effect of Z on W, despite the evidence of a rather strong direct causal relationship between these two traits. In small-seeded parents, the lesser association between components apparently did not have much effect on altering the pattern imposed by the indirect effects of each component on yield. The varieties tested showed different yield levels but at the same time many of them shared a common pattern Of relationships among their component of yield; in a broad sense they also partook similar environmental conditions. Whether a particular configuration may be considered Optimum or not for any genotype is a matter that can only be judged if similar genotypes, which disregarding environmental effects must show the same geometric configuration, differ 76 rather on their yielding ability, i.e., show different geometric configuration under the same set of environmental conditions. Differences in the geometric construct, as rep- resentation of yield, may be attributed then, to genetic and environmental factors and their interplay. According to many reports, the environment plays an important role in conditioning the relationship among components and in the eventual form Of the geometric config- uration. We may assume here that the compensatory relation- ships derived from physiological, develOpmental and environ- mental factors and which eventually will determine the geometric yield construct exert influences on the physical expression of the components only up to the levels that their genetic make-up allows. Theoretically, then, if the potential level Of expression of one of the components could be raised without affecting the potential limits of expres- sion of the other components, an increase in yield should result assuming that essentially similar environmental conditions prevailed. Correlation patterns among the components of yield might be expected to show some changes in response to the genetic changes undergone. Nevertheless, since in our back- crossing series only one of the components has been altered genotypically, the potential levels for compensatory changes have not been greatly disrupted and no drastic changes would be expected. The successive backcrosses to the small-seeded parent while selection was practiced for large seed, did 77 change the correlation pattern of the BC compared with 11 the recurrent parent for some of the component relationships. The study of more intricate relationships through path coef- ficient analysis showed slight departures of the BCll gener- ation from the tendencies expressed in the small-seeded population. We may, however, assume a simpler model as compared with that used for the path coefficient analysis where com- ponent influences on yield run parallel to each other. The alternative model considers the traits to function in series; i.e., X, the component first in the sequence, influences both Y and Z which follow in the order of develOpment, and Y influences seed weight Z. When these influences due to sequence were removed, each trait was evaluated according to its own independent contribution. The comparisons of the components, both under con- ditions of independence and under the influence of correla- tions, showed highly significant contributions of the geno— typic source of variation to yield. Contribution due to the environment or to interaction of environment by genotype was Observed in X and Y'when the effects of correlations were Operative; Z, however, showed a substantial effect due to environment and a smaller though significant effect due to interaction (year by genotype) when the trait was analyzed free of the influence Of X and Y. 78 The correlations seem to mask the real contribution of the interaction of genotype by environment. The contri- butions of the genotype in the case of the Z component and that of the environment in the case of Y were artificially exaggerated when the effect of the correlations was present. Since some of the variation in Y and Z is a consequence Of variation in X, and the source of variation in X was mainly due to the main effects of the genotype and the environment, the contribution of the genotype by environmental inter- action on Y and Z is underestimated. The removal of the effects of the correlations has a substantial effect on the expression of these two components. The situation with respect to yield is essentially the same. Whereas under the nontransformed situation the variation in yield was explained as based entirely on geno- typic effects, when correlations were removed most of the variation is eXplained as affected by the genotype and genotype-environment interaction. The actual measure, in terms of variation, of the effect of the correlations between components is given in the analysis of the differences between actual and trans— formed values. For Y and Z the genotype by environmental interaction and the environment itself are the major factors determining these correlations; the interaction is more important than the environment as such in the case of the Z component. The genotypic influence is more conspicuous in Z than in Y. The rather drastic difference observed when 79 actual and transformed values are compared would indicate a decisive influence of the component X in the eXpression of the other components. This is in agreement with the find- ings by path coefficient analysis. The contribution of the environment is substantial, also, in affecting the expres- sion of the different components. For beans, the above mentioned model has only a limited value for pointing out the masking effects of the correlations and thus clearing up why expected values based on genetic parameters calculated in the conventional way fail to correspond with the Observed values. In beans, the develOpmental pattern is such that different substructures, the nutritional units, coexist in the plant as develOpment proceeds. These units are not wholly independent of each other. Although the seed yield components develop in a sequence and we expect a pattern of influence, one over the other, to move according to the develOpmental sequence, we cannot disregard a possible influence of any one component in the sequence over any other in different nutritional units. This influence might Operate irrespective of the order of development if limitations due to unavailability of nutrients or genetic makeup become apparent. The first trait in the sequence, X, can be safely regarded as the main determinant character based on the results of the models discussed. This could mean that the influence Of the source variation on the transformed Z values may reflect a more real situation as compared with 80 the sources of variation attributable when the effects of correlations were assumed to be operating. It is doubtful, however, that the situation for X and Y might be real since any effect of Z and Y on X and of Z on Y are disregarded. The use of component analysis in breeding programs requires not only a knowledge of the type of associations among the components of yield, but a knowledge of their heritable nature, as well. In order to estimate the advance to be expected by applying selection pressure for Z in the BCI generation, heritability estimates were calculated by different methods and with the different pOpulations used in this study. Estimates derived by three of the more commonly used methods, variance components, parent-progeny regressions, and realized heritabilities, were compared. The estimates for Z were in close agreement, and whatever the method, seed size was the character showing the highest heritability value. Estimates based on variance components were rela- tively high which was not unexpected considering that esti— mates were made on a plot basis and considering, also, that some nonadditive genetic portion was presumably present. This broad-sense estimate was used in calculating the maxi- mum selection progress predicted for seed weight. When the effects of correlations were removed there was a substantial change in the heritability estimate of seed size, it being then reduced to less than half its 81 original value. The estimate for yield also changed drastically in a downward direction. It is difficult to rationalize the kind of genetic control for Z suggested by the results obtained when corre- lations were removed, with the successful outcome that has generally accompanied selection for Z. Although the results seem to indicate that much of the genetic variance shown by Z is rather a reflection of the hereditary control experted by X, the outcome from the selection process tends to sup- port the view of a more direct genetic control of the Z component. It is rational on the following hypothesis: some .portion, or possibly all, of the genes which make for more pods per plant, make for, through the compensatory system, less weight per seed. And genes that reduce the number Of pods cause increased seed weight, again on account of the compensatory process. Thus the genetic variance in X is also reflected in genetic variance in Z, although there may be additional genes affecting the level of Z that have little to do with X. There would, on this assumption, be substantial negative "genetic" covariance between X and Z, which when removed mathematically, would lower the variance in Z. Nevertheless, for selection purposes, all of the genetic variance in Z, both that which is common to X, and that which is independent of X, is available. 82 If one wishes, this co-response pattern in X and Z, due to genes and the compensatory effects, can be ascribed to pleitropism. But it is pleitropism that is based on a develOpmental effect, and not pleitropism that flows inde- pendently from the primary effects of the genes. Environmentally-induced shifts in X should also be manifested to some extent in the succeeding components, Y and Z. In addition, there is expected some environmental effect unique to Z. But of course, it is the ratio of genetic to nongenetic variances that is chiefly responsible for differential levels of heritability. In the final outcome, it is understandable that a given component (Z) should show both a high calculated and a high realized heritability, even as the X component shows a different and generally much lower heritability. It should be noticed that progress of selection as measured by the estimates of the realized heritability for Z would have been closely predicted by the heritability values Obtained for the seed size component when the effects of correlations were removed. It may well be true that in the process Of backcrossing we have driven the variance of X closer to zero while "exposing" the actual "unique" variance for Z and thus the results of the selection process reflect more accurately the portion of the genetic variance of Z that is independent of X. 83 Z Trait Responses to Selection The effectiveness of selection for Z may be seen by examining the values of the realized heritability (Table 18). The portion selected from the BC1 generation was highly sig- nificant from the mean of the population from which it was extracted, in the 20 pOpulations studied (Table 17). The selfed generations, however, showed only eight populations where the mean of the selected BClSl plants outnumbered significantly in seed size the mean of the unselected BClS1 population. Either much of the variation in Z was nongenetic, the nonadditive portion of the genetic variance was sub— stantial, or the genetic base was narrow and hence little response could have been expected anyway. We are inclined to think that the latter possibility is more in accordance with the facts at least in some crosses. The very close agreement with eXpected progress found with lines where selection was successful and the high values of the real- ized heritability would rule out the suggestion of a dis- prOportionate amount of nonadditive genetic variance. A test for additive behavior of seed size was made with the 20 BC1 pOpulations and this showed only five pOpu- lations deviating significantly from the additive scheme (Table 21). The lack of consistency between the results from the selected plants and their selfed progenies in certain 84 crosses when compared with the mean of the respective pOpulations from.which they were extracted could be due to the narrow genetic base. The variability in these crosses, the statistic that reflects the total response that might be realized from a cross, was small. The starting material covered a wide range of seed sizes, nevertheless many crosses involved lines differing only slightly in this trait. Significantly, the pOpulations derived from the widest crosses were the ones that responded best to selection. For the BCll generation the lower and upper limits for estimating the degree of advance with respect to the recurrent parent were fixed considering the expected values assuming no selection, i.e., the regression to the recurrent parent based strictly on an additive scheme, and the expec- tations under selection using the broad sense heritability values and an intensity of selection of 8%. All the pOpulations where selection for seed size was effective surpassed the respective recurrent parent in seed size in the proportions eXpected, assuming an additive model and actual genetic advance by selection in the BCI. Considering that the expected values were calculated using a high heritability value, 89.2%, the observed increases, which ranged from 10 to 31%, provide good evidence of the feasibility of raising the levels of expression of Z through selection and backcrossing without interference due to nega- tive associations with other components. The other pOpula- tions, those where selection for Z was less effective, 85 agreed remarkably with the expected values set up for these conditions (Table 23). The results obtained from the progenies of the selected lines in backcrosses suggest that selection may have succeeded in isolating the heterozygous genotypes. Selection of the homozygote would have been likely to result in little more than the recovery Of the parental genotype. With the information at hand, however, we cannot determine the number of effective factors in the presumably complex genetic system responsible for the heritable differences in seed size. Our results indicate that selection in certain crosses of the BC1 generation successfully isolated a genetic portion more closely associated with mid-parental levels than with those of the recurrent parents, thus rais- ing the mean value of the subsequent Bcll generations over the expected values based solely on an increase equivalent to one-half of the remaining difference between the back- cross and the recurrent parent means in each succeeding generation. Further support for this hypothesis may be found in a comparison of the percent increase in seed size of the BCI and BC with respect to the recurrent parent (Table 24). 11 Both values were very similar, thus indicating that through the process of selection we accumulated some plus genes for large seed size even as heterozygosity was declining. Where selection was not effective we expected the percent increase 86 of the BC over the recurrent parent to be less than that of 11 the BCl over the same parent, and that actually did happen. Stability of the Seed Number Components The successive backcrosses to the small-seeded parent were intended to maintain stability, in the genetic context, of the seed number components. To a considerable degree this aim was accomplished since only two of the 20 pOpulations tested departed significantly from the expected values in total seed number. The situation changed slightly when the seed number components were examined. One—third of the tested populations showed significant changes in seeds per pod with respect to the recurrent parent; only one out- numbered significantly the recurrent parent in pods per plant (Table 25). The possibility that genes for high Z were linked with genes for high X and Y and that therefore selection for the first character dragged along seed-number genes, seems unlikely, at least as the only or main explanation, in view of the fact that only two cases of significant changes in X and Y occurred in pOpulations where selection for high Z was effective and also since original parents were high Z, low XY or low Z, high XY and therefore we would not expect link- age of high Z with high XY. With a sufficient number Of backcrosses we are vir- tually assured of recovering the recurrent parent genotype. In the second backcross the average expected percentage of 87 germplasm contributed by the recurrent parent should be 87.5%» so we may expect our results to be influenced to some small extent by this residual heterozygosis. Nevertheless, although heterosis was reported, if we would have to ascribe the deviations in the values for the seed number components, with respect to their expected values, to heterosis we would have to assume it affected one component but not the other in some cases, or it affected the components in Opposite directions in other cases--a rather unlikely situation. Other causes may be invoked as more plausible to account for the deviations of the seed number component from its eXpected value. Assuming additivity, we may expect the means to regress by one-half of the difference per genera- tion. It is unlikely, however, that the additive scheme would be the only genetic system Operating, nor that all the assumptions on which the backcross theory is based would prevail. For example, the study of the relationship of per- formance with heterozygosity showed that as increments of plus genes were added to a genotype the expression of hybrid vigor for X, one of the seed number components, did not fol- low a linear trend. This curvilinear relationship, then, could suggest the presence of dominance, overdominance, or interaction among nonallelic genes. Of course, a conclusive assertion based only on the study of heterozygosity is not possible in our data. 88 Lastly, the fact that total number of seeds remained almost unchanged but the components for seed number did vary could suggest an Operative mechanism such as the one de- scribed by Adams (1) to explain the basis of yield component compensation in beans, i.e., these changes are only conse- quence of compensatory relationships derived from develOp- mental process in the plant. A further look at the components of yield through and F would lead one to conclude that the l 2 gene action involved in the expression of the components Y study of the F and Z is mostly additive. This is indicated by the infre- quent manifestations of heterosis for these components. The X component, on the other hand, showed a most conspicuous heterotic effect. Even transgressive segregation was ob- served for this character. This may indicate that there are epistatic genetic factors conditioning the number of pods per plant or other conditions that can produce heterosis. Since maximum heterozygosity is achieved in the F1 the transgressive segregation in the F2 may result from comple- mentary effects brought together by recombination. Genetic Advance in Yield The components of yield interact in the expression of a yield phenotype. As a result of a plan based strictly on the components-of-yield approach, alterations in grain yield ranging from a decrease of 12% to an increase of 47% with respect to the recurrent parent, were Obtained. 89 Increase in seed size as a result of selection did not neces- sarily result in an increase in yield and in two cases an increase in the mean value of a component other than Z resulted in a significant increment in yield (Table 26). POpulations formed by crosses 0107, 0109, 0106, 0206, 0406, 0411, and 0409, where no increases in yield were Obtained, represent the pOpulations where no reSponses for selection for high Z were Obtained. Presumably this outcome resulted from the failure to isolate genetically distinct genotypes due to insufficient genetic variability. Neither were the seed number components altered. For each partic- ular pOpulation there are plus or minus variations of the components with reference to their respective counterparts in the recurrent parent. This variation we interpret more as random fluctuations of the develOpmental process in the plant rather than as evidence of component compensation. Granted, the components compete for the same total amount of metabolic substrate produced by the plant and the values shown may very well be a reflection of the compromise that the level of the components have to reach to attain the max- imum grain yield under such circumstances. In the absence, however, of significance in the differences, relatively low fluctuation values, and absence of a characteristic pattern, no inferences from these populations can be made. Populations derived from the crosses, 0112, 0213, 0306, 0309, 0310, 0406, 0507, and 0509 showed significant increases either in X, in Y, and some also in Z, but no 90 significant increase in yield was noticed. Insufficient genetic variability may not explain the whole situation because of pOpulations such as 0213 and 0112 which showed a wide range of variability. Genetic advance for character Z was attained in these pOpulations: decreases in the Y component, however, may have offset the gains in Z, the final result being no change in yield. Since in the selection and backcross pro- gram planned, the theoretical expectations called for no change in the components X and Y, the fact that component Y was altered by the selection pressure placed on Z suggests that physiological controls over the components still Oper- ate in spite Of genetic control. Other crosses, however, showed a positive association in Y and Z, which, if ex- plained on the basis of competitional alternatives of plant develOpment alone, would imply biological significance to an otherwise nonsignificant statistical variation in X. Population 0209 showed a significant increase in grain yield due exclusively to a substantial rise in X. Both original parents have equal numbers of pods per plant; it may have happened that as a result of selection for Z, different plus genes for X could have been brought together thus producing a new genotype capable of giving expression to high X. A similar case may have occurred with population 0408 where only the Y component was significantly above the values of the recurrent parent, nevertheless, increased 91 yield resulted. This outcome, however, should not be attributed solely to the higher Y. An increase in yield on the order of 37% is hardly explained by increasing Y only 8%“ Similar increases of Y in pOpulations with the same genetic background, as in 0409, did not result in a signif- icant increase in yield. Undoubtedly, the parallel rise in the X component made this increment possible. With the information at hand it is not possible categorically to assign to indirect selection the cause of variation in components X and Y. Since backcrossing and selfing lead rapidly to homozygosis it could be possible that the detected variation may have resulted from the recombination of entire or large segments of chromosomes. New gene combinations for X and Y, some favorable and others unfavorable, could have been brought about as a consequence of these processes. Of course, there is also some residual heterozygosis which could explain part of the discrepancies from the expected values. A comparison of the BC1 and the F gener- 2 ations may throw some light on the effect of heterozygosity. Both generations have identical distributions of heterozy- gous and homozygous phases. Although the distribution of homoqygous alleles is different, the distribution of hetero- zygous pairs is identical. Since we observed differences between the BC1 and the F2 (Table 26) heterozygosis cannot be the cause of the difference between these two generations; it may therefore be due to the differences in the homozygous 92 portion AA versus 1/2 AA + 1/2 aa or aa versus 1/2 AA + 1/2 aa. With less heterozygosis present it is doubtful that it may account for the differences. On the other hand, this unexpected response of X and Y was observed only in a few of the 20 populations examined whereas all have the same amount of residual heterozygosis present. We cannot discard the possibility of random varia- tion. Expectations under the backcross theory are based on infinite populations; the possibility that our sample could have been divergent from the infinite population cannot be ruled out. One final explanation of the joint variation of selected and nonselected components may be the competition taking place at the level of the metabolic develOpmental processes in the plant. The different components of yield follow a succession of develOpment during the course of which a competition for environmental resources occurs. Although the components are subject to genetic control, the final outcome, yield, depends upon a complex interaction of genetic and environmental processes as a result of which a particular geometric construct is obtained. A high level of genetic control was exerted over Z, the component subject to selection, as indicated by the genetic gains in seed weight. Unexpected changes in the other components, however, might be an indication that physiologic adjustments within the plant maintain their preeminence in adjusting the geometric configuration whenever limitations of any order threaten the 93 potential efficiency of the plant. This point of view is not incompatible with that which contemplates the possibil- ity that the components not subject to selection might have been modified in their genetic make-up since the above men- tioned develOpmental or physiological adjustments might take place also in response to a new broader genetic potential for the expression of the components. A good measure of the rate Of progress in yield as a result of the selection pressure put on Z is the compar- ison of the different backcross generations since the BCI pOpulations were not derived from selected material. The pOpulations are grouped in Table 27 according to whether selection for Z was effective or not. An increase in yield over the recurrent parent well above that expected assuming an additive model were noted for both groups in the BC1 generation. Since selection had not been practiced at this stage in either of the populations, the difference in magni- tude between the two groups (28.2% vs 14.5%) is a mere con- sequence of the genetic diversity in the parental material in the sets. On the other hand, the difference of either set with respect to their expected values could be explained on the basis of some heterotic effect. The heterosis observed for seed yield when the F1 was studied (Table 29) suggests that other kinds of gene action other than additive may also be operative. The fact that the F2 populations yielded less than their corresponding 94 mid-parents and F1 hybrids may indicate the presence of epistatic gene action or of adverse component interaction. The marked difference in progress for yield in the BCI generation between populations where selection for seed size was effective may indicate that the success in selec- tion for high seed size was indeed linked to the wider genetic base of certain crosses. In the BCll generation there was a gain in yield over the recurrent parent as com- pared with the BC generation. Whereas the BC generation 1 l exceeded the recurrent parent by 14.5%.in yield the BC11 did it only by 16.8% in pOpulations where selection for Z was not effective. Where selection for seed size was effective, however, yield increased from 28.2% over the recurrent par— ent in the BC to 32.6% in the BC 1 11' The increase in yield from one backcross generation to the other was not spectacular in many crosses, but neither was the reduction experienced when the selected BC pOpulations were selfed. l The idea behind this thesis proved to be effective since improvement in yield was achieved through effective manipulation of the components of yield based on their differential heritable value and taking advantage of the negative correlations among them. The yield-dampening effect of these negative associations was overcome by hold- ing constant the genetic complex for seed number while increasing the seed size component. Penetrance of the 95 large-seed-size genes was not affected by either introducing them into an alien background or because of environmental conditions as evidenced by the recovery of the expected genotypes in spite of the persistence of negative corre- lations among the components of yield. Where increased yield was not achieved, the causes could be traced to either a narrow genetic base among the parent pOpulation or the inability to isolate the truly large—seeded genotypes in the process of selection. These limitations, however, might be surmounted by choosing par— ents such as to give a wider genetic base, growing large pOpulations in which selection is to be practiced and select- ing on basis Of a progeny test. SUMMARY AND CONCLUSIONS This study confirms the findings of previous works with respect to gene action and heritability of the com- ponents Of yield. The relationships between each of the components of yield as well as the type of association among the components themselves, conform to results of a majority of previously reported studies. The component Z appeared to have the highest heri- tability. Pods-per-plant, however, was found to be of over- riding importance in determining yield levels either in a direct or indirect way. Negative correlations among compo- nents were evident through the fact that none of the high yielding lines showed a high mean value for all three compo— nents in the parent pOpulation. Yield seemed to be related more to an harmonious balance of the levels of the different components. The possibility that the effect of the correlations might bias the estimation of the true genetic contribution of the components involved was examined by removing the effects of correlation in a unidirectional and sequential model. The study of the character when isolated from the one preceding it in the sequence revealed differences in 96 97 the degree with which genotypic and environmental sources of variation affect the expression of the character as compared with those acting when correlations were present. Differences in the heritable contributions of the components late in the sequence were also detected. Based on the re- sults of selection as denoted by the realized heritability estimates, it was suggested that the heritability values for seed size obtained after correlations were removed may have been closer to the true genetic situation. The unidirec- tional model of influence based on the sequential origin of correlated characters was considered to explain only par- tially the develOpmental sequence of events in beans, being accurate inasmuch as it explains the processes taking place at the level of the nutritional unit. Considering the whole integrated biological system, however, interpretations de- rived from this model should be taken cautiously, especially for the components X and Y. Through recurrent backcrossing it was possible to exercise genetic control over the most heritable component and to raise its mean value to a desired level by exerting selection pressure. Seed size values for the BCl and BCll generations were similar. It is postulated that through selection we succeeded in accumulating plus genes for large seed size while retaining some heterozygosis. The expected regression toward the mean values of the recurrent parents for the seed number components was not 98 attained uniformly. In some cases, the value of only one of the components corresponded with the expected rate of regression; in none Of the cases did this happen with the two components simultaneously. The total seed number, how— ever, did remain stable, according well with expectations. Aside from explanations derived from nonfulfillment of some basic assumptions underlying the backcross theory, the lack of a consistent approach towards their expected values by the seed number components examined separately, may indicate that despite the genetic control exerted the environmental or physiological influences prevail when stress develOps. The fact that negative correlations per— sisted and that departures from the expected values in the seed number components were observed even in the populations where selection for Z was not effective, may be an indication that an explanation based on component compensation would be very plausible. A significant increase in yield was obtained in six of the twenty pOpulations studied. Five other pOpulations outyielded the recurrent parent although the differences were not significant. It is postulated that new levels of yield can be attained by increasing the level of expression of one of the components of yield while maintaining the others constant. Component compensation, though present, would not necessarily be incompatible with higher levels of productivity under this approach. 99 One of the basic requirements for a successful back- cross breeding program is to have a satisfactory recurrent parent. Among all the small-seeded parents studied, P-03 and P-05 were the only ones meeting these requirements on a seed number basis. Significantly, the populations where significant genetic gain in yield was reported as a result of changes in Z, were populations involving these particular parents. 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