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GENOTYPE X ENVIRONMENT INTERACTION, YIELD STABILITY AND ADAPTATION RESPONSES OF 25 SINGLE-CROSS MAIZE (Zea mays L . ) HYBRIDS GROWN IN MICHIGAN By Kingstone Mashingaidze A DISSERTATION Submitted to Michigan State University in partial fulfilment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Crop and Soil Sciences 1987 ABSTRACT G E N O T Y P E X E N V I R O N M E N T INTERACTION, YIELD STABIL I T Y AND ADAPTATION RESPONSES OF 25 SINGLE-CROSS MAIZE (Zea mays L . ) HYBRIDS GROWN IN MICHIGAN By Kingstone Mashingaidze Genotype-environment importance interaction in plant breeding. is of significant Farmers are interested in varieties that perform consistently from year-to-year, while breeders prefer widely adapted varieties. Thus, ideally, a variety should be high yielding, widely adapted and stable. Various methods have been proposed for estimating variety adaptation and stability of field crops but none of them seem to be used as routine selection tools. Twenty-five maize hybrids were evaluated in yield trials at eight locations over two seasons in Michigan. trial data were used to : (1) examine the The yield potential usefulness of adaptation and stability analyses in increasing the efficiency recommendations, yielding estimates, estimates. of selec t i o n and in making vari e t y (2) determine the associations among grain ability, ad a p t a t i o n and s t a b i l i t y p a r a m e t e r and (3) to compare different stability parameter A major proportion of the significant GE interaction was made up of genotype x location interaction emphasizing the need to replicate more over locations than years. The linear regression coefficient (b value) was used as a measure of adaptation. Similar results were obtained from the use of a dependent and independent measure of the environmental index. The b values in conjunction with mean yi e l d s across environments enabled the identification of hybrids adapted to specific types of environments. High yielding widely adapted hybrids were obtained indicating that selection for wide adaptation does not necessarily mean selecting for mediocrity. Mean square deviations from regression, stability variance measures and of coefficient relative (b value) determination were stability. were highly correlated. response of These Grain yielding used as parameter estimates ability, adaptation and stability parameter estimates not correlated suggesting that yield potential, were adaptation and stability are independent traits which should be selected for independently and that it should be possible to develop varieties with various combinations of these traits. All the hybrids used in this study had highly significant deviation mean square and stability variance values suggesting that none of them were stable. Hybrids which had b values close to unity and/or were highly correlated with the others had relatively lower deviation mean square and stability variance values. In memory of my grandfather, VaTitos MASHINGAIDZE iv To my parents and relatives in Zimbabwe v To my wife, SIPIWE, my daughter, RUMBIDZAI, and my son, RUVIMBO vi ACKNOWLEDGEMENTS I am indebted to several members of staff at Michigan State University the foremost being my major professor, C.E. Cress, for his guidance, Dr. support and encouragement throughout the period of graduate study, for his suggestions and constructive comments after perusing the early drafts of this dissertation, and for allowing me the liberty to use his computer at will. I wish to express my deepest gratitude to Dr. E.C. Rossman for providing research facilities, seed, and for his advice, help and attention throughout the course of this investigation. Appreciation is also due to Dr. T.G. Isleib for his assistance in the statistical analyses of the data. I also wish to thank the other members of my Academic Committee, Dr. Amy Iezzoni and Dr. J.D. Kelly. Special thanks and appreciation are due to Messrs Keith Dysinger and Mervin Chamberlain for their skilled technical assistance. Not least of my debts is that to Professor M.A. Schweppenhauser of the University of Zimbabwe for organizing this opportunity, and to the University of Zimbabwe and the ZIMMAN project for their generous financial assistance. expressed to my wife (Sipiwe), Deep appreciation is daughter (Rumbidzai) and son (Ruvimbo) for their assistance and willing comprehension vii throughout the period of this study, and to my parents and relatives in Zimbabwe for their moral and spiritual support. This dissertation is dedicated to my grandfather (VaTitos Mashingaidze) who passed away on May 25th, 1987. viii TABLE OF CONTENTS Page List of Tables............................................xiii List of Figures.......................................... xiv List of Appendix Tables................................. xv 1. INTRODUCTION.......................................... 1 2. LITERATURE REVIEW..................................... 5 2.1. Assessment of stability and adaptation responses.... 7 2.1.1. The estimation of variance components and coefficient 8 of variation...................................... 2.1.1.1. Components of variance.......................... 8 2.1.1.2. Coefficient of variation........................ 9 2.1.2. Linear regression techniques...................... 11 2.1.2.1. Phenotypic regression analyses................. 11 2.1.2.1.1. Yates and Cochran's (1938) regression technique 11 2.1.2.1.2. Finlay and Wilkinson's (1963) regression technique..................................... 14 2.1.2.1.3. Eberhart and Russell's (1966) regression technique..................................... 20 2.1.2.2. Genotypic stability parameters................. 31 2.1.2.2.1. Stability analysis by structural relationship. 31 2.1.2.2.2. Perkins and Jinks' (1968) regression technique 34 2.1.2.3. Limitations of the regression technique........ 36 2.1.2.3.1. Statistical limitations....................... 37 2.1.2.3.1.1. The environmental index is subject to error 37 ix Page 2.1.2.3.1.2. Heterogeneity of errorvariances............ 37 2.1.2.3.1.3. Non-independent environmentalindexes....... 38 2.1.2.3.1.3.1. Independent biological measures of the environment............................... 39 2.1.2.3.1.3.1.1. The use of a genotype(s) closely related or similar to those under test to assess the environment......................... 39 2.1.2.3.1.3.1.2. The use of extra replications of the full set of genotypes to assess the environment 40 2.1.2.3.1.3.1.3. The use of an environmental index which explicitly excludes the genotype being regressed on it......................... 41 2.1.2.3.1.3.1.4. The use of the mean of one or more standard (check) genotype(s) to assess the environment............................. 41 2.1.2.3.1.3.2. Independent physical measures of the environment............................... 44 2.1.2.3.1.3.3. The gene pool as a measure of environmental index..................................... 45 2.1.2.3.2. Biological limitations........................ 47 2.1.2.3.2.1. Cultivar response to environmental factors.. 47 2.1.2.3.2.2. Prediction of response across environments or generations.............................. 49 2.1.3. The contribution of individual varieties to interaction....................... 52 2.1.3.1. GE Mean variance component for pairwise GE interaction..................................... 53 2.1.3.2. Ecovalence...................................... 55 2.1.3.3. Stability variance.............................. 56 2.1.4. Multivariate techniques........................... 61 2.1.4.1. Principal component analysis................... 62 x Page 2.1.4.2. Pattern analysis................................ 62 2.1.4.2.1. Cluster analysis.............................. 63 2.1.4.2.2. Factor analysis............................... 66 2.1.5. Other methods................... 67 2.1.5.1. Coefficient of determination................... 67 2.1.5.2. Range Indexes................................... 68 2.1.5.3. Percentage adaptability......................... 69 2.2. Stability as a breeding objective................... 69 2.2.1. Mechanisms of yield stability.............. 69 2.2.1.1. Genetic heterogeneity........................... 70 2.2.1.2. Developmental plasticity........................ 71 2. 2.1.3. Stress resistance............................... 73 2.2.2. Inheritance of stability.......................... 73 2.2.3. Selection for stability and adaptation response... 75 2.2.3.1. Selection sites................................. 75 2.2.3.2. Selection techniques............................ 77 2.2.3.3. The different concepts of stability............ 78 2.2.3.4. Interrelationships among stability parameters... 81 2.2.4. The potential usefulness of the linear regression technique In plant breeding....................... 86 3. MATERIALS AND METHODS................................. 90 3.1. Experimental procedure.............................. 90 3.2. Statistical analyses................................ 93 4. RESULTS AND DISCUSSION................................ 97 xl Page 4.1. Adaptation responses................................ 109 4.2. Stability........................................... 124 5. CONCLUSIONS........................................... 128 6. REFERENCES............................................ 130 7. APPENDIX.............................................. 136 xii LIST OF TABLES Page Table 1. Skeleton stability analysis of variance(adapted from Eberhart and Russell, 1966)............. 21 Table 2. Site Information............................. 92 Table 3. Combined analysis of variance for grain yield of 25 maize hybrids grown at eight locations in 1985 and 1986 in Michigan.................... 98 Table 4. Site mean yields of 25 maize hybrids grown at eight locations over two years ( = 1 6 environments) in Michigan.................................. 101 Table 5. Mean grain yield across sitesand estimates of adaptation and stability parameters for grain yield of 25 maize hybrids grown at eight locations in 1985 and 1986 in Michigan...... 102 Table 6. Simple rank correlations amongproduction response andstability parameters for grain yield of 25 maize hybrids grown at eight locations in Michigan in 1985 and 1986...... 104 Table 7. Correlations among production response and stability parameters (based on actual figures) for grain yield of 25 maize hybrids grown at eight locations in Michigan during 1985 and 1986 105 Table 8. Mean grain yield across sites and estimates of adaptation and stability parameters for grain yield of 25 maize hybrids grown at eight locations in 1985 and 1986 in Michigan...... xiii 110 LIST OF FIGURES Page Fig 1. Mean yield plotted against coefficient of variation 10 (adapted from Francis and Kannenberg, 1978)...... Fig 2. A generalized interpretation of varietal adaptation (adapted from Finlay and Wilkinson, 1963)........ 17 Figs 3a and 3b. Acceptable responses to varying environments if the deviation mean square is non-significant (adapted from Eberhart, 1969)..................... 25 Fig 4. Yield responses of three maize hybrids well adapted to a range of environments........................ 113 Fig 5. Yield responses of three maize hybrids well adapted to a range of environments......... 114 Fig 6. Yield responses of two maize hybrids well adapted to a range of environments........................ 115 Fig 7. Yield responses of two maize hybrids well adapted to a range of environments........................ 116 Fig 8. Yield responses of four maize hybrids poorly adapted to a range of environments........................ 117 Fig 9. Yield responses of four maize hybrids poorly adapted to a range of environments........................ 118 Fig 10. Yield responses of two maize hybrids adapted to high-yielding environments........................ 120 Fig 11. Yield responses of two maize hybrids adapted to low-yielding environments......................... 121 Fig 12. Yield responses of three maize hybrids adapted to low-yielding environments......................... 122 xiv LIST OF APPENDIX TABLES Page Appendix Table 1. List of single-cross maize hybrids used for stability analysis.......................... 141 Appendix Table 2. Branch County site information....... 142 Appendix Table 3. Cass County (irrigated) site information..................................... 143 Appendix Table 4. Huron County site information........ 144 Appendix Table 5. Ingham County (M.S.U.) site information 145 Appendix Table 6. Kalamazoo County site information.... 146 Appendix Table 7. Monroe County site information....... 147 Appendix Table 8. Montcalm County (dryland) site information..................................... 148 Appendix Table 9. Montcalm County (irrigated) site Information..................................... 149 Appendix Table 10. Table of means for 25 maize hybrids grown at Branch County during the 1985 summer season.......................................... 150 Appendix Table 11. Table of means for 25 maize hybrids grown at Branch County during the 1986 summer season.......................................... 151 Appendix Table 12. Table of means for 25 maize hybrids grown at Cass County (irrigated trial) during the 1985 summer season.......................... 152 Appendix Table 13. Table of means for 25 maize hybrids grown at Cass County (irrigated trial) during the 1986 summer season.......................... 153 Appendix Table 14. Table of means for 25 maize hybrids grown at Huron County during the 1985 summer season.......................................... xv 154 Appendix Table 15. Table of means for 25 maize hybrids grown at Huron County during the 1986 summer season.......................................... 155 Appendix Table 16. Table of means for 25 maize hybrids grown at Ingham County (M.S.U. field plots) during the 1985 summer season.................. 156 Appendix Table 17. Table of means for 25 maize hybrids grown at Ingham County (M.S.U. field plots) during the 1986 summer season.................. 157 Appendix Table 18. Table of means for 25 maize hybrids grown at Kalamazoo County during the 1985 summer season................................... 158 Appendix Table 19. Table of means for 25 maize hybrids grown at Kalamazoo County during the 1986 summer season................................... 159 Appendix Table 20. Table of means for 25 maize hybrids grown at Monroe County during the 1985 summer season.......................................... 160 Appendix Table 21. Table of means for 25 maize hybrids grown at Monroe County during the 1986 summer season.......................................... 161 Appendix Table 22. Table of means for 25 maize hybrids grown at Montcalm County (dryland trial) during the 1985 summer season.................. 162 Appendix Table 23. Table of means for 25 maize hybrids grown at Montcalm County (dryland trial) during the 1986 summer season.................. 163 Appendix Table 24. Table of means for 25 maize hybrids grown at Montcalm County (irrigated trial) during the 1985 summer season.................. 164 Appendix Table 25. Table of means for 25 maize hybrids grown at Montcalm County (irrigated trial) during the 1986 summer season.................. 165 xvi 1. INTRODUCTION In crop breeding programmes, are usually (locations evaluated and years) over many potential a number before the of varieties env i r o n m e n t s selection and release of desirable varieties. For quantitative traits (such as yield) the relative performance of different varieties often varies from one environment to another. The changes in the relative rankings of varieties and in the magnitudes of differences among them environment is defined statistically (6E) interaction. as the genotype- This phenomenon is caused by varietal differences in physiological reactions to different environmental conditions. There is a general agreement among plant breeders that GE interactions occur with sufficient frequency and magnitude to be of notable importance in the development and evaluation of improved varieties. One impor t a n t effect of GE interactions is to reduce the correlation between phenotype and genotype with the result that valid inferences become more complicated and progress from selection is reduced. The changes in rank, which occur when varieties are evaluated over a range of environments, make it difficult for the plant breeder to decide which varieties should be selected. Often a variety's performance may be outstanding at 1 2 one or more locations in one or more years, but be variable, mediocre or performance even (e.g. substandard yield) over at other all locations. environments Mean becomes inadequate as a basis for selection because it does not fully indicate consistency of performance. Farmers are interested in high yielding varieties that give stable yields at a particular location from year to year. Breeders prefer to develop widely adapted and stable varieties. In making decisions on which varieties to select there are at least three questions to be considered:(i) How did the variety's overall performance (e.g. for yield) compare to the overall average performance of all the other (or one or more standard) varieties? (ii) Is it better adapted to one type of environment than to another? (iii) Was its mean performance performance of all the other consistent relative to the (or one or more standard) varieties? That is, a breeder will want to ascertain how the variety compared with performance Ideally other level, varieties adaptation a variety should be environments, stable and or and standard varieties stability, respectively. adapted to a wide above average in in range of yielding ability. Performance tests over a series of environments when analyzed by the conventional combined analysis of variance 3 give information on the magnitude of GE interaction but no assessment of stability individual entries. and adaptation responses of Complete answers to the above questions can be obtained from the use of statistical techniques that enable the assessment of stability and adaptation responses of the varieties from the performance data. Regression techniques are useful in characterizing genotypes as to their range of adaptation and in identifying s t a b le varieties or unusual performance at specific locations. When GE interactions are present, utilization of the adaptation and stability indexes could enhance the effectiveness of variety comparisons in making selections and variety recommendations. However, despite all the work that has been done on stability analyses in maize (Zea mays L.)and other field crops, regression techniques do not seem to be used as routine selection tools when genotypes have been evaluated environments. in yield trials In maize, the over a wide range regression technique of has been used to study the yield stability and adaptation of distinct types of maize hybrids, such as prolific vs non-prolific hybrids (Russell and Eberhart, 1968), single-cross vs doublecross maize hybrids (Eberhart, 1969), hybrids developed from improved vs unimproved germplasm (Fakorede and Mock, hybrids produced from (eGama and Hallauer, selected 1980), vs unselected inbred 1978), lines and in making comparisons of different methods used for determining stability (Prasad and 4 Singh, 1980). In the M.S.U. potential hybrids environments stability maize breeding programme are usually grown over a wide range of and, in the analyses might presence pro v i d e of GE interactions, useful additional information that will facilitate the selection process. The present study was conducted : (1) To examine the adaptation potential usefulness of stability and analyses selection and in in in c r e a s i n g the e f f i c i e n c y of making varietal recommendations, interaction is present, when GE by determining the relative yield stability and adaptation responses of 25 commercial maize hybrids grown in Michigan, which were developed without direct selection for stability and adaptation, (2) To stability determine and the associations adaptation parameter among grain estimates, yield, in order to find out whether it is necessary to select for stability and adaptation per se, and (3) To compare different stability parameter estimates. 2. LITERATURE REVIEW The existence of genotype-environment (GE) interactions has long been recognized, indeed precedes Fischer the analysis of variance, and Mackenzie responses varieties, of the earliest reference, (1923). different being that of In considering potato (Solanum which the manurial tuberosum L.) they concluded that a product formula provided a better fit to the yields of the varieties in the different manurial treatments than did an additive formula. The nature and importance of GE interactions in plant breeding have been reviewed in detail by Allard and Bradshaw (1964). As Comstock and Moll (1963) put it: "because genetic factors are inferred from observations on phenotype, because selection is based on phenotype and because there is a potential contribution of interaction effects to phenotype of all quantitative characters, GE interaction is in some way involved in most problems of quantitative genetics and many problems of plant breeding". There are two possible strategies for a plant breeder interested in developing varieties which interaction. heterogeneous The first one is the a low GE subdivision area for which the varieties 5 show of a are being bred 6 into smaller regions that a breeder feels economically in the breeding them homogeneous has a more can be programme, such environment covered that and each of its own characteristic varieties (Eberhart and Russell, 1966; Francis and Kannenberg, 1978; Horner and Frey, 1957). The second one is the development of varieties which show a high degree of stability in performance over a wide range of environmental c o n d it i o n s (Eberhart and Russell, 1966; Francis and Kannenberg, 1978). Stratification of environments is usually based on such predictable gradients, environmental length of the growing season, (Allard and Bradshaw, oat variations as temperature soil types, etc., 1964). Horner and Frey (1957) divided (Avena sativa L.) testing areas of Iowa into sub-areas within which the genotype-location interaction component of variance was substantially reduced. Abou-El-Fittouh, Rawlings and Miller (1969) used cluster analysis to define homogeneous regions of cotton (Gossypium hirsutum L.) variety trials the US Cotton Belt. However, the interaction subregion, location of in even with this stratification, varieties with locations within a and with environments encountered at the same in environmental different variations years, (because of unpredictable such as fluctuations in weather, e.g. amount and distribution of rainfall, temperature, etc.,) frequently remains too large (Eberhart and Russell, 1966). 7 Thus, It is important to develop widely adapted stable varieties that interact less with the environment in which they are grown. A variety must not only perform well in its area of initial selection but it also must maintain a high performance area of level in many environments within its intended adaptation (Weaver, Thurlow and Patterson, 1983). Extensive testing is required to identify varieties that have minimum interaction with environments, stability. or possess greatest Among those genetic materials in a set being tested, an ideal variety would be adapted to a wide range of growing conditions in a given production area, with above average yield and below average variance across environments. This is a working definition of stability (Saeed and Francis, 1983). Yield stability is of particular importance under subsistence factors agriculture, that limit where production control is of environmental limited, resulting in considerable seasonal yield variations. 2.1. ASSESSMENT OF STABILITY AND ADAPTATION RESPONSES A large body of literature has been devoted to analytical techniques designed to clarify 6E interactions in variety trials replicated over locations and years. Excellent reviews of these techniques have been published by Freeman (1973), Gotoh and Chang (1979), Hill (1975), Lin, Binns and Lefkovitch (1986). (1986), Moll and Stuber (1974), and Westcott The types of analyses can be grouped into:- 8 (1) the estimation of variance components and coefficients of variation; (2) linear regression analysis; (3) estimation of the contribution of each variety to the overall GE interaction; (4) multivariate analysis; and (5) other minor methods. 2.1.1. The estimation of variance components and coefficients of variation 2.1.1.1. Components of variance Genotype-environment an a l ysis of environments, variance sum studies of which squ a r e s partition the (into genotype, and GE interaction sources of variation) have helped to elucidate the nature, magnitude and extent of GE interaction 1963). (1951) (Comstock and Moll, showed how variance components Sprague and Federer could be used to separate out the effects of genotypes, environments and their interaction by equating the observed mean squares in the analysis of variance to their expectations on the random model. They used variance components to compare the GE interactions of single-cross and double-cross maize hybrids. Smaller GE interactions were obtained from double-cross than from single-cross hybrids suggesting that double crosses were more stable than single-crosses. provide information concerning However, this does not individual genoty p i c 9 stability. 2.1.1.2. Coefficient of variation (CV) Francis grouping and Kannenberg technique stability of 15 which (1978) they proposed used short-season maize in a genotype- studying hybrids yield in Southern Ontario, Canada. Varieties were grouped on the basis of mean yield and consistency of performance across environments. The conventional coefficient of variation (CV) for each genotype was used as a stability measure. g e n o t y p e across environments is The mean yield of each plotted coefficient of variation over environments. against its With the grand mean and mean coefficient of variation serving as the base lines on the x- and y-axis, respectively, varieties can be classified into four groups as shown in Fig 1 below. I ----varieties with high (above average) mean yield Group and Group I I low (below average) coefficient of variation, varieties with high (above average) mean yield and high (above average) coefficient of variation, Group III — varieties with low (below average) mean yield and low (below average) coefficient of variation, and Group I V ---- varieties with low (below average) mean yield and high (above average) coefficient of variation. This value. genotype-grouping However, technique it offers a simple, has no predictive descriptive method for 10 11.0 mean CV (%) GROUP I 10.0 GROUP II 9.0 grand mean ✓ / yield mean 8.0 yield (t/ha) 7.0 6.0 GROUP III GROUP IV 5.0 4.0 TCT CV (%) 15 20 25 Fig 1. Mean yield plotted against coefficient of variation (adapted from Francis and Kannenberg, 1978) grouping a large collected over number several of varieties environments. This from is yield data particularly useful during the initial screening stages of a breeding programme, where, because of the large numbers of individuals involved, it would be more practical to characterize varieties on a group basis rather than individually (Funnah and Mak, 1980; Ntare and Aken'Ova, 1985). Mean yield and variation tolerance limits are flexible. For the breeder practicing mass variety screening, delimiting co-ordinates for mean yield and coefficient of variation can be conveniently set by check or standard varieties (Francis 11 and Kannenberg, 1978). Lin et al (1986) showed that variance and coefficient of variation (CV) are equivalent. 2.1.2. Linear regression techniques Although, in general, genetic effects are not independent of environmental effects, a number of authors (Baker, Breese, 1969; Wilkinson, Eberhart and Russell, 1966; 1969; Finlay and 1963; Perkins and Jinks, 1968; Yates and Cochran, 1938) observed that the relationship between the performance of different varieties in various environments and some measure of these environments is often linear or nearly so. From these observations, Freeman and Perkins (1971) concluded that there is strong evidence indicating a genuine underlying linear relationship between performance of specific genotypes and environmental conditions, even though this relationship does not always account for most of the interaction observed (Moll and Stuber, 1974). Because of this linear relationship, regression techniques have been used to characterize responses of genotypes in varying environmental conditions. 2.1.2.1. Phenotypic regression analyses 2.1.2.1.1. Yates and Cochran*s (1938) regression technique Yates and Cochran (1938) were the first to propose the linear regression technique for further examining the GE interaction trials term. conducted In a study of barley (Hordeum vulgare L.) over a number of environments, they recognized that the degree of association between varietal 12 differences and general fertility (as Indicated by the mean of all varieties) could be further investigated by calculating the regression of the yields of the separate varieties on the mean yields of all varieties. The object of taking the regression on the mean yield of all varieties rather than on the mean yield of the remaining varieties was to eliminate a spurious component of regression which would otherwise be introduced by experimental errors (Yates and Cochran, 1938). The observed performance (i=l,2,...,v) in the jth (Y„ ) of environment the ith variety (j=l,2,...,n) can be expressed as:- Yij = ^ + Gi + E j + (GE)ij + ®ij where, y is the grand mean over (1) all varieties and environments; G^ is the additive genetic contribution of the ith variety, calculated as the departure from of the mean of the ith variety averaged over all environments (| = 0); Ej is the additive environmental contribution of the jth environment, between and calculated as the difference the mean of the jth environment Z over all varieties (j Ej= 0); (G E )y is the GE interaction of the ith variety in 13 e» the jth environment [E. ZiGE).. = 0]; and x j ij is the error attached to the ith variety in the jth environment. To estimate the phenotypic regression coefficient (b) for a particular variety its performance ( Y ~ ) values are regressed onto the environmental means, that is constant overall and G ^ particular variety, this + E . . Since is J is by definition constant for a approach is y in effect regressing E . + (GE).. as the dependent variate against E, as the J U J independent variate (Hill, 1975). If a linear relationship is established between these two variates then; (GE) .. = b i E j + s.. (2) where b^ is the phenotypic regression coefficient of the ith £ variety (* b 4= 0); and s „ is the deviation from the fitted 1 1 U regression line of the ith variety in the jth environment. The slope of the ith variety includes additive environmental variation besides that portion of the GE interaction variation which is a linear function of Ej(Hill, 1975). Substituting (2) in equation (1) gives: Y ij = y + G Yates and i + (1 + b )E4 + s.. + e.. i j U U Cochran (1938) showed (3) that this regression accounted for a large part of the interaction in a set of barley trials. However, until their ideas were not really taken up Finlay and Wilkinson (1963) rediscovered the same 14 technique, modified and used it for an analysis of adaptation in a trial of 277 varieties of barley grown in seven environments. Modifications of the regression technique have also been proposed by Eberhart and Russell and Perkins (1966), Freeman (1971), Hardwick and Wood (1972), Mather and Caligari (1974), and Perkins and Jinks (1968). 2.1.2.1.2. Finlay and Wilkinson's (1963) regression technique Finlay and Wilkinson (1963) elaborated and extended the regression technique stability of a to describe variety using the its adaptability linear and regression coefficient. The mean yield of all varieties for each site and is u s e d se a s o n as a quantitative measure of the environment. A relatively low mean yield of all varieties at a particular environment. indicates site and season indicates a low-yielding A relatively high mean yield of all varieties a high yielding environment. In this way the average yield of a large group of varieties describe a complex natural environment is used to without the complexities of defining or analyzing interacting edaphic and seasonal factors. For a variety a linear regression of individual mean performance on the mean performance of all varieties in each environment is calculated. Because the individual variety mean performances are plotted against the mean performance of all varieties, the average response of all varieties has a 15 regression coefficient of unity (b=1.0). Thus, of varieties vary above and below 1.0. the b values The responses of individual varieties can be assessed relative to this mean response. Finlay and Wilkinson (1963) used the regression coefficient as a measure of both adaptation and stability. The varieties under test can be classified for stability into the following categories (i) a regression coefficient not significantly different from unity (b=1.0) indicates average stability. The response of a variety is parallel to the mean response of all varieties in the trial; (ii) a regression coefficient less than unity (b<1.0) than unity (b>1.0) indicates above average stability; and (iii) a regression indicates coefficient greater below average stability. Small changes in the environment produce large changes in performance. Absolute phenotypic stability would be expressed by a regression coefficient of zero (b=0). Performance environments would be the same. However, in all this would not be desirable because it is associated with low performance and the variety cannot make use of be t t e r production environments. The mean yields of the varieties over all environments together with the regression coefficients determine the 16 adaptation of the varieties, as illustrated in Fig 2 below. Varieties with average phenotypic stability (b=1.0) when accompanied by environments are considered to have good general adaptability. high On the mean yield performance other hand, over all (wide) if they show low mean performance they are classified as having poor adaptability. Varieties with above average phenotypic stability (b<1.0) are relatively not less sensitive to environmental changes, show large changes and do to their average performance. Such varieties are relatively more productive in low-productivity environments but, being insensitive to environmental changes, give low performance in more favourable environments. These are considered to be specifically adapted to low-productivity environments. stability Varieties (b>1.0) Varieties in with below average phenotypic exhibit the opposite type of adaptation. this cate g o r y are highly sensitive to environmental changes. Performance (e.g. yield) changes at a rate well above the average of the group and under the most favourable growing conditions such varieties give the highest performance and can, therefore, be described as being specifically adapted to high-productivity environments. Finlay and Wilkinson's widely adapted, in the most (1963) concept of an ideal, variety was one with maximum yield potential favourable environment, and maximum phenotypic stability (b=0). Their barley data showed that the varieties 17 above 1.0 specifically adapted to % high-yielding environment s below ^ average stability poorly adapted to average well adapted all environments stability all environments 1.0 below 1.0 above ✓ average staHH specifically * adapted to low-yielding environments low high Variety mean performance (e.g. yield) Fig 2. A generalized interpretation of varietal adaptation (adapted from Finlay and Wilkinson, 1963) with high phenotypic stability yields and were unable to (b<1.0) exploit all had low mean highly favourable environments. They concluded that the breeder must compromise between yield potential and phenotypic stability in his/her search for an ideal variety. Jowett (1972) disagreed with the contention of Finlay 18 and Wilkinson (1963) that the lowest value for the regression parameter (b = 0) Is coefficient of unity because it the most (b=1.0) i n d i cates that desirable. A regression would be the most desirable, the variety increases its productivity by an average amount as conditions improve. Smaller values imply failure to take advantage of better conditions, while larger values imply serious yield decline as conditions worsen. Keim and Kronstad (1979) suggested with adaptation to drought stress, that when dealing grain yield in the most severely stressed environment takes on major importance. conjunction with drought resistance, an average In or better response to more favourable moisture conditions would be indicative of wide adaptation. They, therefore, proposed an ideal variety as one having both the highest yield under the most severely stressed environment expected and a strong response (b>1.0) to more favourable environments. Finlay and Wilkinson (1963) used a logarithmic (log1Q) scale which induced a reasonable degree of homogeneity in experimental errors and also a high degree of linearity in the regressions. They noted that mean yields on a logarithmic scale correspond to geometric means on the natural scale. Jowett (1972) reported that if there are wide differences in the yielding abilities of entries low yielding varieties will be constrained by the additive nature of the model (model 1) to make a relatively small contribution to the interaction 19 sums of squares, and hence have low values of regression coefficients-, if the analysis is on the arithmetic scale, but not if the analysis is on the logarithmic scale. Knight (1970) cautioned on the use of transformations. The effect of logarithmic transformation is to minimize the genotypic differences at the high performance values and maximize differences at the low performance levels. Thus, a plant breeder discriminating between varieties on the basis of regression values calculated on a logarithmic scale may be laying stress selections the on differences (Knight, original and 1970). at low yields Breese and Hill logarithmic scale regression and recognized that Log^g in more homogeneous in for his/her (1973) the compared analysis of transformation resulted error variances among varieties but introduced an abstraction which complicated both the visual interpretation of the graphs and the use of the estimated parameters in predicting response. Several Fakorede authors and Mock, (Bilbro and Ray, 1976; Breese, 1969; 1978) prefer the use of the regression coefficient (b value) as a measure of adaptation rather than stability. Bilbro and Ray (1976) stressed that the regression coefficient is a measure of adaptation and that it should be of particular importance in areas where management, soil or climatic variables cause definable and distinct differences in yield levels. For example, in irrigated and dryland 20 production areas the breeder will probably prefer to develop separate varieties for dryland and irrigated conditions. Thus, a breeder would be seeking varieties with b>1.0 irrigated (high-yielding) conditions, for and varieties with b<1.0 for dryland (low-yielding) conditions. In this sense b values would be used as an indicator of adaptation rather than stability (Bilbro and Ray, 1976). 2.1.2.1.3. Eberhairt and Russell's (1966) regression technique Eberhart and Russell technique (1966) modified the regression for evaluating empirical parameters; stability (i) the by considering two slope of the regression line (b), and (ii) the mean square deviation from the regression line (S‘). These parameters can be defined with the following model: Yu = y i + biIj + where, Y.j is the mean of the (4) ith variety at the jth environment (i=l,2,...,v; j=l,2,...,n); ^ is the mean of the ith variety over all environments; b^ is the regression coefficient that measures the response of the ith variety to varying environments; s.j is the deviation from regression of the ith variety at the jth environment; and Ij is the environmental index. 21 The environmental Index Is obtained as the mean of all varieties at the jth environment minus the grand mean, I.e.; "Ei V v- V Y8 /vn ' j (SJ Ij - 0) . The environmental Index Is merely a coded deviation of each environment (Eberhart, and from 1969) Cochran the grand mean over and this modification, (1938), does not affect all environments from that of Yates the value of the regression coefficient (Easton and Clements, 1973). The appropriate analysis of variance is shown in Table 1 below: Table 1. Skeleton stability analysis of variance from Eberhart and Russell, 1966) Source of variation Total Varieties (G) Environments (E ) GE interaction E (linear) GE (linear) Pooled deviations Variety 1 (adapted d.f. nv-1 v-1 n-1 (v-l)(n-l) 1 v-1 v(n-2) n-2 • • • • • • • Variety v Pooled error n-2 n(r-1)(v-1) 22 The sums of squares for environments and GE interactions are added together and repartitioned into a linear component with one degree of freedom (1 d.f.), a linear component of the GE interaction with (v-1) degrees of freedom, and deviations from regression, the deviations being found separately for each of the v varieties with (n-2) degrees of freedom each. The trouble with this approach is that the sum of squares for the linear component between environments, which is allocated one degree of freedom, squares for (Perkins Russell is the same environments and Jinks, (1966) with 1971; pointed (n-1) Freeman, out that in as the total sum of degrees of freedom 1973). Eberhart and their approach the comparison of the linear component of the interaction against deviations from regression assumes that the deviations within the various varieties are homogeneous. The same is true in the Yates and Cochran (1938) approach. For this reason it is better to test particular the variety significance of by comparing the the b values appropriate for a sum of squares against the deviations from the regression for that variety rather than against the pooled deviation term (Freeman, 1973). The first stability parameter (linear regression coefficient, b) is estimated by regressing the variety's mean yields in the respective environments upon the environmental indices. Thus:- 23 ■ bi =ej yu ij/ A The performance of each variety can be predicted by using the estimates of the parameters, where; Ytf " xi + bixj and , is an es timate ' of the . The deviati o n s Csy = (Yy ” Y jj ^ ^ can be S(3uare^ and summed to provide an estimate of the second parameter (S 2) j- sd i = cf s« / < n - 2)1 - °.2/r where, - is -the estimate of the pooled error (or the variance of a variety mean at the jth location), and t j 1) This model = [^ Y^ - Y^ /nl - (^ Y I )2/ ^x2 Lj Yu i. ijV 7 j j * provides a means of partitioning the GE interaction of each variety into two parts; (i) the variation due to the response of the variety to varying environmental indexes (sum of squares due to regression), unexplainable de v i a t i o n s from the and (i i ) the regression on the environmental index. Eberhart and Russell (1966) defined a stable variety as one with a regression coefficient of unity (b-1.0) and mean square deviation from regression equal to zero ( = 0). This o would be obtained if the variety responds exactly the same as 24 the mean response of the population In each environment (to environmental environments changes) and does (Marquez-Sanchez, not interact with the 1973). All varieties with other combinations of values of b and (i.e. b=1.0 and 2 9 d Sd £ 0; or tytl.O and = 0; or b/^1.0 and S ^ 0) would all be unstable. In addition to these two parameters (b and S? ), a d breeder usually wants a variety with a high mean performance (greater than the grand mean) over a wide range of environments. Thus, an ideal variety would be one with a high mean performance over a wide range of environments, response to environments average (b=1.0) and minimum deviations from regression (S^ = 0). Eberhart (1969) reported other types of acceptable responses as shown in Figs 3a and 3b below. With a regression coefficient above unity (b>1.0) a variety can still give above average yields in all environments (Fig 3a). 25 / / (a) / (b) / mean grain yield (t/ha) mean grain yield (t/ha) environmental index environmental index Figs 3a and 3b. Acceptable responses to varying environments if the deviation mean square is non-significant (adapted from Eberhart, 1969) This is also true if b<1.0; however, the mean yield must be well above average in such instances (Fig 3b). Gray (1982) reported that because yields of most perennial forage grass clones, e.g. over years, orchardgrass (Dactylis glomerata L . ) decline clones with b values less than unity (b<1.0) would have less decline in yield over years. An ideal clone in this case would be one that has a regression coefficient less than unity (b<1.0), high yield and low deviation from regression. Eberhart and Russell (1966) tested the application of their model to maize yield trial data. The GE(linear) sum of squares were not a very large proportion of the GE 26 interaction. They concluded that important stability parameter. appeared to be a very As large values of were d obtained for some lines and crosses, the data were fit to a quadratic model. The reduction in the deviation mean square was negligible, however, so that large deviations were not caused by a quadratic response. and Schmidt (1975) On the other hand, Schnell found quadratic regression to be more appropriate than linear regression in a study of yield and adaptation of medium-maturing maize hybrids. Since Eberhart and Russell the deviation mean square (1966) suggested the use of 2 (S £) as a second stability parameter, great attention has been focused on it. Bilbro arid Ray (1976), Breese (1969), Langer, Frey and Bailey (1979), and Perkins and Jinks (1968) strongly advocated its use as a stability parameter and it has received wide acceptance as evidenced by numerous publications using it. When only a small portion of GE interaction is due to heterogeneity among regression coefficients, characterization of varieties by regression coefficients is not effective (Baker, 1969; Shukla, 1972). Under such conditions the deviation mean square provides additional information and may be the most appropriate stability (Baker, 1969; parameter for evaluating varietal Eberhart and Russell, 1969). Small, non-significant deviation mean square estimates (s2) indicate d linear r e s p onses to e n v i r o n m e n t s w i t h no specific 27 interactions, and hence variety response is hig h l y predictable when based on site mean yield (Keim and Kronstad, 1979). Significant deviation mean squares indicate non-linear response or specific interactions with environments (eGama and Hallauer, 1980; Joppa, Lebsock and Busch, 1971). Bilbro and Ray (1976), and Breese (1969) emphasized that the regression coefficient should be used as a measure of adaptation response rather than stability. Breese (1969) reported that the variability of any variety with respect to the environment can be subdivided into a predictable part and an unpredictable part corresponding to deviation mean square. Because the regression part can be predicted and to some extent controlled specific (by locations), selecting it specific is not useful genotypes for to consider this component of GE interaction as a measure of stability. Breese (1969) suggested that the term stability should be reserved to describe measurements of unpredictable irregularities in the response to environment as provided by the deviation from regression. However, it might be dangerous to place too much importance on the deviation from regression because it includes not only biological stability but also experimental error indespensable with biological data (Hill, 1975). Edmeades (1972), (1984), Freeman Lin et al (1986), (1973), Hardwick and Wood and Shukla (1972) questioned the validity of the deviation mean square from regression as a 28 stability parameter. Hardwick and Wood (1972) stated that in terms of the underlying model the deviations (s.^ ) are not independent of the regression on the environmental index, so that S is not a meaningful stability parameter. Edmeades (1984) indicated that the regression analysis takes no account of curvilinear relationships between yield and the environmental index. Thus, stable varieties could be rejected because of deviations from linearity. Lin et al (1986) argued that the regression model for GE interaction is a descriptive model based on the data being analyzed, and not a prediction model as Breese's (1969) argument seemed to assume. For a useful prediction model, the independent variable experiment, and then must the be measurable deviation prior mean to square the from regression may have a deterministic property that can be associated with varieties. linear regression technique, the model independent However, considered variable for the descriptive in the regression (environmental cannot be measured prior to the experiment. index) It is no more than a data based device to represent the environment so that the variety's response can be studied quantitatively. Because the model is purely empirical, the deviation mean square for it does not have a deterministic property such as may be the case for a prediction model. Essentially the deviation mean square of this model indicates no more than how good is the fit, but has no direct bearing on the variety's stability 29 2 2 or large Sj), or a heterogeneous deviation mean square should be taken as an (Lin et al.,1986). A poor fit (i.e. small r indication that the use of the linear regression model to estimate stability is not adequate and that other approaches should be investigated (Lin et al., 1986). Moll, Cockerham, Stuber and Williams (1978) noted that the regression is a function of both (i) the responsiveness of the varieties to the environment, and (ii) of the correlations of the responses of varieties in different environments. Caution is required when the correlations vary and are small. Entries whose responses are poorly correlated do not provide reliable environmental indexes for each other. The most similar varieties largely determine the values of the environmental means and understandably these varieties will show little deviation from the linear regression (small S 2). on the other hand, varieties that differ majority of varieties under consideration, from the either below or above their optimum, will show a marked deviation around the regression Thus, line and hence appear unstable (Knight, a variety with a specific desirable trait, 1970). such as disease or drought resistance, may deviate significantly from the regression at sites whose mean yield is depressed by these factors, and a desirable variety such as this may be discarded (Edmeades, 1984). Therefore, where deviations from regression are used to measure stability one must go more 30 into the underlying biological basis for any differences in stability of response which might be present (Hill, Also, because technique, of the relative nature of 1975). the regression the deviation from regression is not a specific property of the variety. Since the mean yield of all varieties is used as a standard response in each environment, the relative ranking of an entry for stability varies according to the average response of the group of entries with which it is compared. A variety is stable only with respect to the other entries in the test with no assurance that it will appear stable if assessed with another set of varieties. For example, in a set of varieties (A,B,C,D,E), A may be assessed stable and B unstable if A resembles C,D,E more closely than does B. However, in the set of varieties (A,B, F,G,H), A may be considered unstable and B stable if A is less like F,G,H than is B. Easton and Clements (1973) found that by choosing a subset of varieties it was possible to make a previously stable variety appear unstable. They concluded that the degree of departure from linearity is not an adequate measure of instability and may be misleading if used that, as a measure of stability. Lin et al (1986) concluded until such time as the environmental index can be replaced by actual environmental factors, such as temperature or rainfall, etc., (leading to a prediction model), the use of mean square deviation from regression as a stability parameter is difficult to justify. 31 2.1.2.2. Genotypic stability parameters 2.1.2.2.1. Stability analysis by structural relationship Tal (1971) outlined a method which can be regarded as a special form of that of Eberhart and Russell (1966). The GE interaction effect of the ith genotype is partitioned into two components structural ( and relationship A^) based on the principle analysis. This is of in order to overcome the limitations of regressing one set of variables onto another which is not independent of them (Hill, 1975). The parameter a^ measures the linear response of the ith variety to the environmental effects, and A^ is the deviation from the linear response in terms of the magnitude of the error variance. If the variance component for deviations from linearity of the ith variety is S?. al is a ^ , then e and the error variance s2 + 2 S di °e ai The two components parameters and are a2 e are defined related to genotypic stability the phenotypic stability statistics of Eberhart and Russell as (1966) as follows (Tai, 1971,1979):MSL ________ (b. - 1) , and MSL-MSE * 32 (vJtn-ajsJj - ^ ( ^ ---------------- = (v-1)(n-1) MSE/r where, b^ and - 1 )MSB (v-l)MSE are the phenotypic stability parameters of Eberhart and Russell (1966); MSL, MSB and MSE are the mean squa r e s due to environments, replications within environments and error deviates, respectively; v is the number of varieties, n is the number of environments, and r is the number of replications. Tai (1971) showed that b, -1 is a biased estimate of a , i being always smaller in absolute value. In practice b^-1 will be smaller than except when b^ = 1. The difference between and X can be minimized by using similar numbers of oi i varieties and environments in the experiment or when the sample of varieties and environments employed is large (Hill, 1975). Tai (1971) gave the approximate procedures for testing « b q and \*0- Tai (1971) distinguished between the linear component of interaction and the additive effects of the environments, so that the regression coefficients have a mean of zero, as do those of Perkins and Jinks (1968), rather than of 1.0 as do those of Eberhart and Russell (1966). Also, whereas Eberhart and Russell (1966) subtract a pooled error 33 estimate from the non-linear component of the interaction so that a stable variety has a S \ value of zero. Tai (1971) Cl divides the non-linear interaction term by the pooled error estimate, so that the equivalent value of his parameter ( X) is 1.0. That is ; j s.?/n-2] -CT^/r , for Eberhart and Russell (1966), and S? + X. = _ 1 where, , for Tai (1971), -5 f s .?/n-2 is the deviation from the regression mean j U square, and is an e s t i m a t e of the poo l e d 8 experimental error, a constant for all varieties in the experiment. Like Finlay and Wilkinson (1963), Tai (1971) defined as perfectly stable a variety which does not respond at all to changes in the environment, coefficient of that is, one with a regression minus one ( = -1) and a low non-linear interaction component ( ^ = 1.0). Tai (1971) concluded that perfectly stable varieties probably do not exist and plant breeders will have to be satisfied with obtainable levels of stability. A variety with average stability would be one with = 0 and X^ =1.0. 34 2.1.2.2.2. Perkins and Jinks' (1968) regression technique Perkins and Jinks (1968) proposed a method that is similar to that of Eberhart and Russell (1966) except that the observed values are adjusted for location effects before the regression. If there are v varieties and n environments, the GE interaction can be partitioned into two orthogonal terms, one measuring that portion of the GE interactions which is due to differences between the lines (heterogeneity between regression fitted regression lines) with (v-1) degrees of freedom and the other measuring the deviations of the observed values around these fitted regression lines with (v-l)(n-2) degrees of freedom. If significant GE Interactions are present, ei t h e r or both of these terms will be significant when tested against experimental error. This approach, commonly known as joint regression analysis, has been widely adopted in practice. The null hypothesis tested by the joint regression analysis is that no relationship e xists between environmental variation. the GE component Where the inte r a c t i o n s apart from and that heterogeneity the due portion additive to chance alone is significant it may be concluded that within each genotype the rate of change of the interaction does not vary with the e n v ironment. Each genotype has, therefore, its characteristic linear response to environmental change. own If, by contrast, only the residual portion is significant, either no relationship or no simple relationship exists between the 35 genotype and the environments. More often than not, however, both items prove to be significant. When this occurs the heterogeneity residual portion should be re-tested against the portion to determine whether it accounts for a significant proportion of the GE interaction variance. Perkins and Jinks (1968) employed biometrical genetics techniques to obtain a direct estimate of 3 . With reference to equation (1 ) i.e., Y .. = U + G y +E i + (GE) + e y j , (1) u their method estimates the linear regression of G ^ + (GE^. on E for each genotype. Since G^ is a constant for a particular J genotype, this is equivalent to regressing (GE).. on E . y j (Hill, 1975). Substituting $ in equation (1) gives; Y„= y + G ^+ E j + ^1 + ^ i ^ E j + s y + e ij ’ The genotypic regression coefficient Jinks (1968) and the phenotypic of Eberhart and Russell ^5 ^ ( 8 ) of Perkins and regression coefficient (b) (1966) are equivalent according to the relationship b = 0+1. Thus, 0 is the deviation of b from unit regression. The average response of all genotypes has a regression coefficient of zero ( 0 =0 ) and the responses of individual genotypes can be assessed relative to this mean response. To determine if 0 is significantly different from zero for each 36 genotype, the regression mean square is compared with deviation mean square for that genotype. the The significance of 8 can also be tested by testing the departure of (1+ B ) from unity. B A average value of zero indicates a genotype that shows sensitivity or average response to environments of varying levels of productivity. A significantly high positive value indicates a variety with greater than aver a g e sensitivity to environmental variation. A significantly high negative value indicates a variety relatively insensitive to increased environmental productivity. The ideal variety would have a high mean yield, a regression coefficient of zero and minimum deviations from regression. regression coefficient would seem Although a positive more desirable, this usually results in lower-than-average yields in unfavourable environments positive (Weaver, et al., 1983). A cultivar with a regression coefficient would be better adapted to high-yielding environments, but would lack the wide have been adaptation of the ideal genotype. 2.1.2.3. Limitations of the regression technique Limitations of discussed by Byth, the regression Eisemann technique and Delacy (1976), Easton and Clements (1973), Freeman (1973), Freeman and Perkins (1971), Hill (1975), Knight (1970), and Whittington (1971). Lin et al (1986), and Witcombe 37 2.1.2.3.1. Statistical limitations 2.1.2.3.1.1. The environmental index is subject to error S t a t i stical objections regression technique. have been raised to the In common with many other biological associations which are measured by regression or correlation, the regression technique suffers from the drawback that the environmental index, composed of the mean value of genotypes, is subject to error (Hill, 1975). The environmental index represents only an estimate of the true environmental effect, and so its variance contains an error component presumed to be uncorrelated with the dependent variable. This phenomenon is called the attenuation effect, and results in biased estimates of the regression coefficient (Tai, 1971). However, when a large number of genotypes are included in the experiment and the environmental range is such that the among environments mean square is significantly greater than the error mean square, serious in any bias which results should not prove practice. While estimated coefficients, reducing differences among it cannot disturb their ranking (Hardwick and Wood, 1972). 2.1.2.3.1.2. Heterogeneity of error variances The validity of the Joint regression analysis of variance depends chiefly upon the assumption that the errors attached to homogeneous. the individual regression coefficients are Failure of this assumption not only raises 38 questions relating to the stability response (Breese, 1969), but it also makes the analysis and interpretation of the results more difficult (Hill, 1975). The difficulties occur when comparisons are made between the errors attached to the individual genotypes, because the sum of squares for residual deviations, with (v-l)(n-2) degrees of freedom cannot be partitioned orthogonally amongst the v genotypes. To effect such a partition requires that the whole of the withingenotype variation, with v(n-l) degrees of freedom, is taken into account (see Eberhart and Russell, 1966). It must be remembered, however, that the within-genotypes sum of squares includes variation due to environmental sources besides that due to GE interactions. Since the attaching of errors to the fitted regression lines will account for v(n-2) degrees of freedom, which available for is larger residual estimates of these errors than the deviations, degrees some of bias freedom in the is to be expected, and they must, therefore, be treated with caution (Hill, 1975). Also, the estimates of the regression coefficients will have different precisions mak i n g comparisons among the regression coefficients tedious. 2.1.2.3.1.3. Non-independent environmental indexes A basic objection to many of the regression analyses is the choice of measurement of environmental effects on which the regression is made. The mean performance of all varieties 39 grown in a specific environment is usually used to assess the environment. Thus, the variety means contribute to, and hence are not statistically independent of, the environmental means on which they are regressed. This does not provide an independent measure of environmental effects and, therefore, does not satisfy the requirements of a regression analysis. This res u l t s coefficient Shukla, in biased (Freeman, 1972; Tai, estimates 1973; 1971). Freeman Freeman of the and and regression Perkins, Perkins 1971; (1973) suggested that the whole regression approach should be based on the use of an independent measure of the environment, either biological or physical. It would be even better if environmental values could be measured without error. Many ways have been suggested to provide an independent assessment of the environment. These are as follows 2.1.2.3.1.3.1. Independent biological measures of the assessing the environment Independent environment can biological methods be into gro u p e d the of f o l l owing major categories; 2.1.2.3.1.3.1.1. The use of a genotype(s) closely related or similar to those under test to assess the environment These may be Inbred lines or parental genotypes (BucioAlanis and Hill, 1966; Freeman and Perkins, 1971; Hill, 1975; 40 Tan, Tan and Watson, parents will 1979). An Index based on the Inbred provide an environment for the (Bucio-Alanis, and later, Perkins and Jinks, assessment material material Independent measure of the segregating generations 1969). The environment should be closely related to the trial as much as possible. In most practical situations where size of the experiment is often a limiting factor, the use of a few genotypes for assessing the environment would be preferable. provide a A single appropriately satisfactory measure of chosen the genotype environment can (Fripp, 1972). 2.1.2.3.1.3.1.2. The use of extra replications of the full set of genotypes to assess the environment Perkins and Jinks (1973) recognized that the regression of members of one group of genotypes onto an index derived from another is likely to be biased by d i f f e rent i a l interaction of the two groups with the environment. Entries whose responses are poorly correlated do not provide reliable environmental indexes for each other. As an alternative, Perkins and Jinks (1973) used extra replicates of the full set of genotypes environmental to values assess which the environment. This gives correspond very closely average response of the trial genotypes. to the This modification has also been reported by Fripp (1972), Hill (1975), and Snoad and Arthur (1976). The use of extra replications, 41 however, does not seem to be an efficient use of limited resources. 2.1.2.3.1.3.1.3. The use of an environmental Index which explicitly excludes the genotype being regressed on it An estimate of the regression coefficient of the ith genotype may be computed by regressing the performance of the ith genotype genotypes onto an index composed (Mather and Caligari, statistical 1974). of the remaining This removes the objection and part of the correlation which occurs when using a dependent environmental index (Mather and Caligari, 1974; Moll et al., 1978; Snoad and Arthur, 1976; Wright, 1976). The advantage of this modification is that it does not require extra varieties or replicates in the experiment, though estimates so obtained will be distorted, both by error variation and by any departures from linearity on the part of the individual regressions (Hill, 1975). 2.1.2.3.1.3.1.4. The use of the mean of one or more standard (check) genotype(s) to assess the environment Standards varieties) are or checks usually (e.g. included recommended in variety commercial trials as a reference point for comparisons of performance. The mean response of one or more standard varieties can be used to assess the environment (Bilbro and Ray, Perkins and Jinks, 1973). 1976; Fripp, 1972; 42 From a practical standpoint, breeders would want to compare their material against the best available varieties or those most widely produced in the area. case, the adaptation of the standards If this is the are secondary in importance because the breeder would be interested in how the other materials performed in comparison with the standards and not how the standards performed relative to each other (Bilbro and Ray, 1976). The advantage of this approach is that the group of the standards improved. can be updated as the breeding materials are New varieties superior to the standards serve as standards for later cycles of testing. Thus, the standards would get successively better and the quality of the breeding materials would always be tested against an ever-improving set of standards. This should lead to the development of additional superior varieties (Bilbro and Ray, 1976). The disadvantage of this approach is that some of the trial varieties may not respond in the same way as the standards used to assess the environment . The environment assessment material should be closely related to the trial varieties as much as possible. decreases The linearity of response as the varieties used to assess the environment become too distantly related to the test varieties (Fripp, 1972). Although the use of these four methods provides the 43 desired independence between environmental and genetic effects, they require the division of resources available, additional experimental costs, or the discarding of some data from the interaction analyses, and are inefficient with regard to minimizing sampling errors (Moll and Stuber, 1974; Perkins and Jinks, 1973). Several authors (Bilbro and Ray, 1976; Fripp and Caten, 1971; Perkins and Jinks, 1973; Snoad and Arthur, 1976; Tan et al., 1979; Williams, 1975) reported that similar results were obtained from regression of a large number of genotypes on their environmental means and on values derived from other closely related sets of control genotypes, suggesting that the conclusions drawn from regression data were unaffectd by the choice of measure of the environment. Perkins and Jinks (1973) concluded that it was not important whether a dependent or independent measure of environmental values was used provided observations. these In fact, were based on large the increased size of num b e r s of the sampling variances resulting from the use of fewer experimental units for the independent environmental assessment would probably be more serious than the lack of independence resulting from the use of environmental all the e x p e r imental assessments. Perkins and material Jinks for (1973) the found that regressions on means derived from only a few independent genotypes were sometimes so insensitive as to give rise to problems of interpretation. 44 2 . 1 . 2 .3.1.3.2. Independent physical measures of the environment The environment can also be assessed by physical factors such as climatic measures (e.g. amount of rainfall, temperature, etc.,), soil fertility levels, etc. Regressions of yield on environmental variables have been calculated and those for individual varieties compared by various workers. Fripp (1972) compared both biological and physical measures of the environment and found that number of varieties, the analyses, gave very similar results fora large for all reasonable external measures and the environmental mean.. Similar results were reported by Fakorede and Mock (1978). In field situations many environmental factors influence growth and yield. Of these some such as temperature, rainfall (amount and distribution) they fluctuate , etc., cannot be controlled, rap i d l y and the exact environmental variables is rarely known. differ respect with to many nature of and the Locations usually environmental factors and measurement of any one physical factor will not adequately indicate the productivity of a location (Easton and Clements, 1973). Each environment represents an amalgam ofseveral factors (nutrient levels, moisture levels, light, etc.,) each of which vary continuously and independently of the others. Faced with biological this as problem, opposed to recourse has a physical been made assessment of to a the 45 environment (Hill, 1975). Thus, a suitable index of the productivity of an environment would be the mean performance of genotypes because it provides an estimate of the combined effects, on e.g. yield, of all the physical and biological components of the environment. This approach is valuable where an assessment is being made of many varieties but ultimately it will be necessary to determine the major limiting factors influencing yield (Knight, 1970). Breese (1969) stressed that:"the phenotype is the product of the genotype and its environment. Therefore, it is just as apposite to numerically grade an environment by its mean expression over a range of genotypes as it is to measure a genotype by environments. its The mean fact expression that these over a range measurements do of not specifically describe the variable factors of the environment need not deter us any more than the fact that genotypic measurements processes. do not Indeed, specify the underlying biochemical this joint measure should ultimately provide a basis for better understanding physical limits in the environment as well as physiological control by the genotype." 2.1.2.3.1.3.3. The gene pool as a measure of environmental index The most critical comparison between two varieties is obtained when both are always grown together at the same 46 environments (locations and years). Such paired comparisons allow direct comparisons of two varieties over a range of environmental conditions. However, variety trials rarely contain the same entries over sites and years. The list of entries in the trials often varies from year to year because new entries are included as they become available and those with poor performance are deleted from further consideration. The substitution of entries in a series of trials results in unbalanced designs, of balanced data and procedures for statistical analysis cannot be used (McIntosh, 1983). This greatly reduces the flexibility needed to compare advanced germplasm with current commercial varieties over a period of time. Since new entries are being introduced annually, it is fruitless to retain the poor entries, and delay testing new entries, merely to maintain balance over a series of trials. Thus, imbalance will exist in most series of germplasm evaluation trials, and statistical analyses must accommodate this challenge. Pedersen, c o n c ept of Everson a gene pool environmental indexes. sample of genes and Grafius base as (1978) developed the a means of measu r i n g They referred to a gene pool as a representative of currently acceptable or commercially grown germplasm for a specific geographic area. The mean yield of all entries grown at a location is used as an index of the environment, and the precision of the 47 experiment is increased whenever the gene pool is adapted within the area being tested. In any year or at any location, the particular entries in the sample will vary somewhat, but as long as they are representative of the population gene pool the sample (site) mean can be used as a basis for comparison. The rationale behind the gene pool concept is that it enables comparisons among varieties grown in different locations and even in different years. Thus, it removes the necessity of a constant set of entries for comparison purposes, allowing freedom and confidence in making selections and variety recommendations over a range of yield levels. Pedersen et al. (1978), working with wheat (Triticum aestivum L.) found that limited additions and deletions to the gene pool over years and sites did not affect the average reaction to the environment. The gene pool mean can be used as an assessment of the environmental index in regression analyses. 2.1.2.3.2. Biological limitations 2.1.2.3.2.1. Cultivar response to environmental factors Knight (1970) discussed problems of the biological interpretation of results from regression studies. In studies where only one factor of the environment is varied, and where that one factor is precisely controlled, it has commonly been found that the genotypic response to increased levels of an environmental factor show optima (Knight, 1970). An optimum 48 would probably occur for any factor that was varied over a sufficient range. environmental Thus, range the relationship over the complete might be curvilinear. In linear regression analysis low yields arising from sub- and super­ optimum levels of a factor are juxtaposed and the highest yields are obtained at the optimum level of the factor in question. factors This is particularly important where physical such as plant density, fertilizer levels, moisture levels, etc., are used to create different environments at a particular location. Extrapolation of genotype response to environments beyond the range of environments used in the experiment should be approached with caution. obtained covering super- optimal If the results have been environmental conditions, then extrapolation of the regression line will be misleading as it would imply yields higher than those obtained at the optimum. However, in field situations super-optimum conditions may not always be encountered and the response is confined to the sub-optimal parts of the response curve (Knight, 1970; Snoad and linear regression is then not result of experimental experimental technique situations, Arthur, 1976). Deviation from likely to be large except as a error (Knight, therefore, the 1970). In many linear regression adequately describes the behaviour of genotypes over a range of environments, and upward extrapolation of the regression line may have some meaning. The degree to 49 which any demonstrated linearity can be extrapolated to other environments can only be determined experimentally. 2.1.2.3.2.2. Prediction of response across environments or generations From a practical point of view it would be valuable if plant response to a range of environments could be predicted from existing GE interaction data. Freeman (1973) stressed that one must not fail to recognize the conditional nature of much of the inference from linear regression. Because the mean yield of all varieties is used as a measure of the environmental index, regression techniques results of stability analysis by depend upon the particular varieties and environments studied. Varieties are not stable in some absolute sense but they are merely more stable than the rest of those under test, given set of environments the tests having been conducted in a environments. are random, It and is usually this may be assumed so, that but the varieties tested rarely are. Therefore, inferences should be confined to the set of varieties used in the experiment and should not be generalized (Freeman, 1973; Lin et al., 1986). However, when very good linearity is found by regressing results from different generations of inbred lines on midparent means predictions across generations are remarkably good (Freeman, 1973; Jinks and Perkins, 1970). Environments are usually assumed to be random and so the 50 regression technique can be used for predicting performance over environments (locations and years). The use of results for prediction of response depends on how far the environments used may be regarded as a random sample of all environments to be encountered. Particular attention should be paid to those environmental factors, deliberately response of imposed, that are whether natural or likely to determine the materials to those the conditions under which they will ultimately be grown (Perkins and Jinks, 1968). For the value regression technique across environments, to have the major high predictive part of the GE interaction should be accounted for by linear regression with little or no significant deviation from linearity. The extent to which differences among linear regressions account for GE regression interactions may be tested by the analysis. orthogonally, Essentially this analysis joint partitions, the variation which can be ascribed to GE interaction effects into an item measuring heterogeneity of regressions (GE linear) and a residual item. Where only the heterogeneity appropriate mean error square item, it is is significant, possible phenotypic response of each variety, sampling error, from its environmental index (Breese, linear to against predict within the regression 1969; Gray, an the limits of on the 1982; Jinks and Perkins, 1970; Samuel, Hill, Breese and Davies, 1970). Should 51 both the heterogeneity and residual Items prove to be significant, however, then the usefulness of any predictions will depend solely upon the relative magnitude of these two mean squares. The heterogeneity Item should be re-tested against the residual Item to determine whether It accounts for a significant proportion of the GE interaction variance. If it does the linear model will retain considerable predictive value for the varieties considered, though clearly the model will not be entirely satisfactory, since a significant amount of the variation due to GE interactions remains unaccounted for. If, by contrast, only the residual item is significant it means that either no relationship or no simple relationship exists between the varieties and the environments. More often than not, however, both items prove to be significant (Hill, 1975). The conditions making for linearity of regression are very difficult to determine. One set of characters has frequently been found to give linear regressions, while other characters measured on the same set of varieties have not (Freeman, 1973). Fripp and Caten (1971) found that the selection of a subset of environments changed the relation between mean performance and both the linear and non-linear components of stability. Jinks and Perkins (1970) presented evidence that predictions of the slope parameter (regression coefficient) can be made both across environments and across generations. 52 On the other hand, Williams (1975) examined the yield of strawberries (Fragaria spp) using regression techniques and concluded that, since different regression coefficients are obtained with the same material grown in a range of locations and years, predicting responses of varieties to untried environments us i n g these "hazardous procedure". regression Earlier, te c h n i q u e s is a Witcombe and Whittington (1971) had concluded that in practice there are often wide deviations from linearity and using regression techniques to characterize response of varieties is "an over­ simplification" . 2.1.3. The contribution of individual varieties to GE interaction Several alternative statistical approaches to the analysis of GE interactions have been reported. One approach partitions the total variation due to GE interactions into components methods have (Plaisted, Wricke, assignable 1960; 1962) parameter. been The to individual proposed for making Plaisted and Peterson, and each produces contribution of varieties. a this Several partition 1959; Shukla, slightly each variety interaction is used as a measure of its stability. 1972; different to the GE 53 2.1.3.1. Mean variance component for pairwise GE Interaction Plaisted and Peterson (1959) made an early attempt to measure the stability of individual varieties. They presented a technique for estimating the relative magnitude of the contribution of each variety to the GE interaction component of variance. The portion of variety-environment component contributed by a single variety was used as a measure of variety dependability. The procedure is as follows:(i) a combined analysis of variance is computed for all varieties over environments. If the GE interaction is significant, the succeeding steps are followed; (ii) a combined analysis of variance over all environments is computed for each pair of variet i e s . If there are v varieties, there will be v(v-l)/2 analyses and each variety occurs in v-1 pairs. (iii) an estimate of variety-environment variance O is obtained for each pair of varieties. (iv) an arithmetic mean of the cf^ estimates is obtained for all pairs of varieties having one common member. There will be v-1 estimates in each mean. The mean of the estimated a ^ having variety i in common represents the rela t i v e contribution of variety i to the GE interaction and is the stability measure analysis in n for that variety. Considering such an environments and r replicates, and with two varieties i and i' , the interaction sum of squares is;- Summing this for the ith variety over all v-1 values of i, and multiplying variety i, ( <°5E>i - 2 by (2r/v), , can be expressed as:- - (1/n)YL. vu. ♦ ♦ d/»)a y Variety stability is r?' - ( 1 / V n ) £j yf ># . inversely proportional to the attributable to that variety. mean the relative contribution of The variety with the smallest value would be the one that contributed least to GE interactions and, thus, would be considered, the most stable variety in the tests. Baker stability (1969) of used hard red a similar spring approach wheat in varieties. assessing Pairwise analysis of locations has been used by other investigators to estimate the contribution of individual locations to GE interactions (Shorter, Byth and Mungomery, 1977). The problem with Plaisted and Peterson’s (1959) approach is that it is very cumbersome. If a large number of varieties are tested this would call for a large number, v(v-l)/2 , of analyses. However, nowadays large numbers of analyses can be handled by the use of computers. Plaisted (1960) presented an alternative procedure in 55 which one variety is deleted from the entire set of data and the GE interaction variance from this subset is the stability index of that variety. The larger the contribution of variety i to the GE interaction, the smaller will be the estimate of the subset interaction component of variance. Plaisted (1960) found that this method produced the same results as that of Plaisted and Peterson (1959) but with less computational effort. 2.1.3.2. Ecovalence Wricke (1962) proposed that the relative contribution of a variety to the GE interaction sum of squares be used as a measure of parameter, its stability. termed The \ ecovalence' value of the stability (W^) for the ith variety is calculated according to the formula:-* W.»E. Y 2 - (2/v) i j 1J Y j Y U + (1/v2) -j Y2 j - (1/n)(Y .j - Y i. /v) 2 •• where, Y .. is the performance of the ith variety in the ith y — — environment (i=l,2,...,v; j=l,2,...,n); Y it is the sum of the ith variety over all n environments; Y . is the sum of the jth environment over all v •J varieties; and Y . . is the grand total. The summation of this equation over all varieties gives the total GE interaction sum of squares. This expression can be re-written as:- 56 W = J [(Y„ - Y ./v)2- l/n(Y., > i j UJ •5 1 - Y /v)2 ] •• , z [Y.. - (Y /V - Y /vn) - (Y. /n - Y /vn) - Y /vn]2 3 U •J •• •• •• u j In terms of model (1),i .e . variety over all environments. The stability of a variety is inversely proportional to the GE sum of squares (ecovalence) which is attributed to that variety. The parameter of Wricke (1962), ecovalence, is related to the parameters of Eberhart and Russell (1966), but as a single (Jowett, parameter 1972; appears Luthra potentially and Singh, less 1974). informative In reality the approach of Wricke (1962) assigns an index to a variety on the basis of its deviations from a regression line of unity; i.e., ecovalence is the sum of deviations due to a variety's regression being different from unity plus deviations from its own regression (Langer et al., 1979). 2.1.3.3. Stability variance Shukla (1972) felt that the characterization of genotypic response on the basis of regression coefficients may not be very effective when only a small proportion of the GE interaction sum of squares can be attributed to 57 heterogeneity method of among estimating corresponding genotype to each stability. Plaisted the regressions. and contribution component genotype as of a GE better interaction measure of This approach is similar to that of Peterson of a Thus he proposed a (1959) individual and Wricke genotypes to the (1962). overall The GE interaction is measured and the variance of the interaction deviations, stability variance ( o^), is used as a measure of s genotypic stability. In the general model (1), Y„ = y + G, + E U i j + (GE). y + e .. , y the stability variance of genotype i (a^.) is defined as the si variance over environments of (GE)y + e - . This can be expressed as:°si = v Ej s ij/(v-l)(n-l). For v genotypes in n environments, the stability variance for the unbiased estimate of 2 the ith g e n o t y p e ( os £ is calculated as follows (Shukla, 1972):1 [v(v-1)Ej (Y - v - v + v )2 in the (n-1)(v-1)(v-2) where, Yy is the mean of the ith genotype j th 58 environment, and the remaining terms are the corresponding means defined by the dot-sum notation. The significance of the stability variance is determined by approximate F-tests using the pooled error term from the combined analysis of variance, i.e., F« si o with (v-1) and vn(r-l) degrees of freedom, and o^is the pooled error mean square and r is the number of replicates in a trial can be applied for testing (Shukla, 1972). This method the homogeneity of all the variances or any pair of them. Shukla defined a genotype as stable if its 2 stability variance ( asi) is not significantly different from 2 w i t h i n e n v i r o n m e n t a l v a r i a n c e ( a‘ ) . S h u k l a ' s ( 1972) definition (1972) of stability coincides with Tai's (1971) definition of average stability ( a^=0;X^=l). This definition implies that the performance of a genotype is the sum of additive genotypic effect, additive environmental effect and random error without any GE interaction. The stability variance is a function of two genotypespecific parameters. High stability variance arises from failure of the genotype’s performance to have a regression slope of unity relative to the environmental index and/or from poor fit of the linear regression (high deviations from regression). Moll et al (1978) found that high stability variance could be attributed to high environmental variance 59 associated with a genotype or to a low average degree of correlation of the genotype with the others tested. Any genotype exhibiting perfect correlation with the others would n be associated with the minimal value of a . Conversely, those s genotypes that fail to conform to the predominating pattern of values across environments would have low average correlation to the overall GE variance. Thus, the most stable types are those which exhibit a consistent advantage or disadvantage types, when relative to the environmental subjected to regression analysis, index. These have slopes near one (b=l) and small deviations of observed values from those predicted by the sum of the environmental index and the average main effect of the genotype. Any genotype exhibiting larger than average environmental variance or failing to perform unstable. in proportion Isleib to the others (1986 - personal will appear communication) to be found the average degree of correlation to be the primary determinant of stability variance in a set of 15 soybean [Glycine max (L.) Merr.] breeding lines. The main advantage regression techniques, of this method is that, unlike there is no need for large numbers of environments and hence it can be used to handle large numbers of genotypes. correlations It also takes between genotypes into account pairwise and the large numbers of individual analyses can be handled with the use of computers. 60 Lin et al.# (1986) showed that the statistics of Plaisted (1960), Plaisted and Peterson (1959), Shukla (1972), and Wricke (1962) statistics are are equivalent. merely index However, while the other 2 numbers, aZ8 is an unbiased estimate of the variance of genotype i. Some of the problems of using a genotype's contribution to the total GE interaction as a measure of its stability are that:(i) the contribution of a genotype to GE interaction does not necessarily bear desirability. This is particularly true group set. In characteristics any fact, (e.g. relationship genotypes drought to its agronomic in a heterogeneous that resistance, possess etc.,) special maybe the largest contributers to GE interaction in a set of genotypes deficient for such a characteristic (Francis and Kannenberg, 1978); (ii) the magnitude of the individual variety's GE interaction does not provide information on the response pattern over the range of test environments, information that is vital for making variety recommendations; (iii) it is difficult to have low GE interactions if varieties are tested over a wide range of environments; and (iv) a low GE interaction is not desirable in practice because it is often associated with low performance in good environments. 61 2.1.4. Multivariate techniques Lin et al (1986) recommended a multivariate approach on the argument that the different stability parameters estimate different types of stability and it is difficult to reconcile the different stability parameters into a unified conclusion. They concluded that the basic reason for this difficulty is that yet a genotype’s response to environments is multivariate the parametric approach tries to transform it to a univariate problem via a stability index. Multivariate techniques are essentially an extension of the univariate technique. They have been suggested and applied as potential tools for studies on 6E interactions and genotypic adaptation (Freeman, 1973; Hill, 1975; Lin et al., 1986). the purpose Hill (1975) summarized of multivariate analysis in terms of the analysis of GE interactions as follows: first, to assess the simultaneous effects of a number of environmental factors when these can be measured and rank them in order of importance by determining how much of the observed variation is accounted for by each Individual factor, or composite factor derived therefrom, and secondly, to maximize differences between varieties (or environments) relative to differences within environments (or varieties). According to Seal (1964) the end-result is the "parsimonious summarization of a mass of observations". Some of the multivariate techniques that have been used in studies of GE interactions are as follows:- 62 2.1.4.1. Principal component analysis (PCA) Principal component analysis (PCA) was used by Goodchlld and Boyd (1975), Okuno, Kikuchi, Kumagai, Okuno, Shiyomi and Tabuchi (1971), Suzuki (1968), and Suzuki and Kikuchi (1975) in studying variety adaptability. Freeman and Oowker (1973) applied two-way PCA to data recorded from a series of yield trials in carrots (Daucus carota) after the joint regression analysis had been only partially successful in explaining the observed GE interactions. As a result they were able to demonstrate the importance of site x year and density effects upon the yield differences between varietal groups. But they concluded that, partition treatment information variance. from a in beyond Perkins this experiment, effects that had the use supplied obtained from no the of PCA to additional analysis of (1972) gave a somewhat similar conclusion PCA of GE interactions in Nicotiana rustics. They compared PCA with linear regression and got similar results. 2.1.4.2. Pattern analysis Mungomery, Shorter and Byth (1974) showed that pattern analysis methods were a useful alternative means of studying the performance of large sets of varieties over environments, using soybean data. Pattern analysis is a general term encompassing the use of both cluster analysis and ordination to examine data structure (Byth et al., 1976). 63 2.1.4.2.1. Cluster analysis In clu s t e r analysis an att e m p t Is made to find similarities between clusters on the basis of measurements on the individuals of a cluster. was The first attempt to do this by Abou-El-Fittouh et al (1969) who used cotton data to identify regions of similar genotypic adaptation (minimal GE interaction). Mungomery et al (1974) used cluster analysis to group genotypes on the basis of similarity. Similarity was defined as euclidian distance between genotype in the space whose co-ordinate axes were environments and whose origin was zero. Genotypes can also be grouped according responses (Chuang-Sheng Lin and Thompson, Everson and Cress, 1980; Hanson, 1970; to stability 1975; Ghaderi, Lin et al., 1986). Hanson (1970) proposed that relative stability be measured as the euclidian distance (D ) of a variety from the linear response of an ideal stable variety in a stability space whose co-ordinate axes are environments and whose origin is the genotypic mean. The linear response of the stable ideal was defined derived, as an arbitrary, or experimentally fraction of the average linear response of all varieties, Hanson simply i.e., (1970) as a fraction of the environmental index. also proposed that comparative stability between varieties (an indication of similarity of stability responses) be measured as euclidian distance between 64 varieties in the same space as defined for the determination of relative stability. Relative relative stability magnitude information on of gives full variation similarity. information among Comparative on varieties stability the but no provides full information on similarity of response but no information on mean differences or magnitude of variation. Hanson's (1970) stability measure is similar to Wricke's (1962) but takes into account regression. parameters of model (1), In terms of the the ecovalence of the ith variety (W ) is £ (GE) 2 ( while Hanson's (1970) parameter is D., i j »j 1 where and is not the same as Tai's (1971), being defined as the minimum observed value of (1+ $^). parameter a value of a =1.0 makes the the same as Wricke's (1962). Johnson (1977) proposed a model which gives information on varietal similarity in terms of mean differences, relative stability and comparative stability. There are various methods of calculating similarities, and these may affect the clusters obtained. The unicriterion methods distance of measuring (Abou-El-Fittouh Johnson, 1977; distance similarity Mungomery et et al., include (i) 1969; al., 1974), (ii) (Abou-El-Fittouh et al., 1969; euclidian Hanson, 1970; standardized Fox and Rosielle, 65 1982), (±11) Thompson, dissimilarity 1975), index (Lin, 1982, Lin and and (iv) correlation coefficient (Guitard, 1960; Habgood, 1977). In contrast to unicriterion clustering, the multicriterion procedure developed by Lefkovitch (1985) uses a cluster algorithm that permits more than one measure of pairwise relationship. Lefkovitch (1985) dissimilarity of genotypes by three measures: defined (i) the mean over environments, (ii) the variance across environments, and (iii) among environments pattern distance. Lin et al (1986) stated that the advantage of cluster analysis is that although genotypes are grouped based on a specific data set, the relative relationship among genotypes can be independent of any specific set of data analysed. This avoids the inferential limitation of regression techniques. In whatever way it is done, clustering allows subsets of genotypes to be described by the characteristics of the separate groups, although not directly in terms of stability (Lin et al., the test, 1986). it If a well known variety is included can be used as a paradigm for the in other varieties in the same subset. These varieties may be regarded as having the overall characteristics of this variety and extrapolation for them to a much wider range of environments than those tested may be possible (Lin and Binns, However, similarity clus t e r but no analysis gives information on full 1985). Information varietal on stability. 66 Clustering would that reveal stability) involves only similarities whereas the in clustering regression stability that includes coefficients (comparative means reveals similarities including both average performance and stability (genotypic similarity) [Johnson, 1977]. 2.1.4.2.2. Factor analysis Grafius and Kiesling (1966) used factor analysis methods to construct orthogonal effects, vectors representing and thus predict genotypic responses environmental in terms of these vectors. Multivariate techniques have not been widely used in plant breeding and in the analysis of GE interactions. This is mainly because, unlike univariate and regression methods, they lack simplicity and biological relevance (Hill, 1975). Often, multivariate methods yield answers giving insight into particularly complex situations, and this may well happen in the study of GE However, there interactions is (Freeman, the very real 1973; danger Hill, 1975). that biological relevance will be sacrificed for statistical pedantry (Hill, 1975). Thus univariate and regression techniques will continue to be important in studies of GE interactions, variety adaptation and stability. 67 2.1.5. Other methods 2.1.5.1. Coefficient of determination ( ) Pinthus (1973) proposed the use of the coefficient of determination 2 ( r fc), which measures variety's production variation that linear regression, as the proportion of a is attributable to an index of production stability to environments. Bilbro and Ray (1976) stressed that a logical parameter for stability is one which measures the dispersion of performance is, (e.g. therefore, yield) related around the regression line and to the predictability and repeatability of performance within environments. The mean 2 square deviations from regression (S *) and coefficient of 2 determination (r ) are well suited for this purpose (Bilbro and Ray, Nguyen, 1976; Fakorede and Mock, 1978; Langer et al., 1979; Sleper and Hunt, 1980). Bilbro and Ray (1976) and Langer et al (1979) favoured the use of r ^ instead of s2 , d as a measure of stability on the basis that it not only provides a measure of variation but it is easily calculated, independent of units of measure, easily interpreted and differences between r *■ values can be statistically tested. High r^ line, values indicate a good fit of the linear regression and hence high predictability and repeatability of performance. However, since the environmental sum of squares contributes regression to the analysis, regression sum of coefficients of squares in linear determination large and misleading (Moll, et al., 1978) may be 68 2.1.5.2. Range Indexes For practical plant breeding purposes It would be desirable to have a simpler method than regression analysis for evaluating the response characteristics of large numbers of genotypes Langer, et in preliminary trials. al As simpler methods, (1979) proposed two indexes related to the ranges in productivity of varieties as crude measures of production response. The first (denoted R^ ), is the difference between the minimum and maximum (extreme) yields of a variety in a series of environments. The second (denoted R 2 )> is the difference between the yields of a variety in the lowest and best production environments. In (1979) a study of yield variation in oats, obtained correlations values) and very between high linear R ^ (r=0.90), indicated that varieties and highly regression and R2 could be Langer, et significant, coefficients (r=0.76) screened al values. (b This for regression response indexes simply by utilizing the ranges in variety means. R^ would be somewhat more utilitarian than because, to estimate the former, only two fairly extreme environments would be required. This would be particularly useful in preliminary trials where there are often large numbers of varieties to be tested and consequently only few locations can be used. 69 2.1.5.3. Percentage adaptability St-Pierre, Klinck and Gauthier (1967) proposed the use of 'percentage adaptability' as a measure of wide adaptation. They defined the 'percentage adaptability' of a variety to be the number of environments in which its performance is better than the mean performance of all varieties, expressed as a percentage of the number of environments in which it is tested. On the other hand, Campbell and Lafever (1977) suggested that the proportion of environments in which a variety does not differ significantly from the highest yielding variety in that environment provides an easily calculated measure of variety potential. 2.2. Stability as a breeding objective 2.2.1. Mechanisms of yield stability Stability of performance is a breeding objective difficult to achieve. The causes of yield stability are often unclear, and physiological, mechanisms that impart Francis and Eastin, morphological and phonological stability are diverse 1983). (Heinrich, It is important for the plant breeder to recognize the traits that confer wide or specific adaptation and stability, so that selection procedures can be tailored to meet the breeding objectives. It is equally important to understand the interactions between plant traits related to adaptability environmental conditions. and the prevailing range of Where such interactions are in 70 favourable directions, stability In production can also be realized (Gotoh and Chang, 1979). Mechanisms of yield stability fall Into three general categories: (1) genetic heterogeneity, (11) developmental plasticity, and (111) stress resistance. 2.2.1.1. Genetic heterogeneity Allard and Bradshaw (1964) suggested that heterozygous and heterogeneous populations offer the best opportunity to produce varieties which show small GE interactions. They equated stability with the term 'well-buffered' two types of buffering, namely, and defined Individual buffering and population buffering. Individual buffering is a property of a single genotype and denotes the ability of that genotype to produce an acceptable phenotype over a wide range of environmental conditions. Population buffering is a property of the population and derives from the possession by a genetically diverse population, a sufficient number of different genotypes each adapted to a somewhat different range of en v i ronments. homozygous) achieve A homogeneous variety (heterozygous or must depend largely on individual buffering to stability over a range of environments, whereas a heterogeneous variety may use both individual and population buffering for this purpose. The use of genetic mixtures (e.g. three-way or double-cross hybrids, synthetics, composites, 71 multilines, etc.,) rather than homogeneous (e.g. pure lines, single-cross hybrids, etc.,) varieties has been suggested as a means to reduce GE Interactions. Russell (1966), (1964), and Sprague heterogeneous hybrids) Funk and Anderson and populations In maize, (1964), Federer Rowe (1951) (three-way Eberhart and and Andrew reported and that double-cross tended to have better yield stability (less GE interactions) than homogeneous (single-cross hybrids) populations. However, Eberhart and Russell (1969), and Lynch, Hunter and Kannenberg (1973) found that some single-crosses were just as stable for yield as the best double-crosses, and that the stability seemed to be mainly a property of the inbred parents. Thus high yielding stable single-cross maize hybrids can be developed by appropriate selection techniques, including recurrent selection for yield and prolificacy in the parental populations (Eberhart, 1969). 2.2.1.2. Developmental plasticity Mechanisms which contribute to developmental plasticity i n c l ude rapid progressive phenological flowering development, tillering, associated with the indeterminate growth habit and prolificacy. Prolificacy has been found to be associated with yield stability in maize. Russell and Eberhart (1968) found that test-cross maize hybrids developed from a group of prolific inbreds had lower deviations from regression (higher stability) than an analogous group 72 developed from non-prolific Inbreds. Similarly, Cross (1977), and Prior and Russell (1975) reported that prolific hybrids grown at different population densities were more consistent in yielding ability than single-eared hybrids. Yield component compensation can be a major mechanism of yield stability. A reduction in one yield component may be compensated, to varying degrees, by increases in other yield components, and depending on temporal development of stress, there is a tendency to stabilize yield (Heinrich et al., 1983). Some components of yield are mutually compensatory and may be so for their stability also. Saeed and Francis the yield component, stability in (1983) reported that stability for, seed number was crucial grain sorghum [Sorghum bicolor (L.) for yield Moench]. Morishima and Oka (1975) reported that stability of panicle length was strongly and positively correlated with yield stability in rice stability during (Oryza panicle sativa). This development suggested results in that yield stability. Thus, stability for yield components such as seed number, seed weight, etc., is equally important and should be considered in breeding quality characteristics, stable varieties. Stability such as protein quality, for etc., should also be of Important consideration in field crops. 73 2.2.1.3. Stress resistance Stress resistance (e.g. to drought, etc.,) is important for yield stability, subsistence agriculture. To the farmer, pests, diseases, particularly in strong demand for a variety may depend more upon minimization of performance problems in stress or low productivity environments than upon wide adaptability (Gotoh and Chang, 1979). Joppa et al (1971) suggested that large deviations from regression were due to specific instabilities such as disease susceptibility in particular environments. They found many cases of interactions between genotypes and specific pathogens in wheat. Photoperiod insensitivity is one of the important factors responsible for wide adaptability of Mexican wheats. 2.2.2. Inheritance of stability Genotype-environment interactions are as much a function of the genotype as they are of the environment and so are partly heritable (Hill, Eberhart and Russell 1975). In a diallel experiment, (1966) found genetic differences among single-cross maize hybrids for stability. The variation among single-crosses in the average performance suggested additive gene action for the regression coefficients and to a lesser extend in the deviation mean squares. Stability seemed to be partly a property of the inbred parent lines. s h o w ed that yield stability in m a i z e Scott (1967) is g e n e t i c a l l y controlled and that selection can be effective. Reich (1968) 74 also reported genetic differences stability parameters in sorghum. among single-crosses By using appropriate male parents on the same male-sterile female parents, possible to squares. Bucio-Alanis (1968) also choose hybrids with limited et al (1969), demonstrated that for it was deviation mean and Perkins and production Jinks stability is heritable in crop plants. In a later study, Eberhart and Russell (1969) found that stability in maize, as measured by deviation mean square, appeared to involve all types of gene action. They concluded that stability, as measured by the deviation from regression on the environmental index, seems to be inherited in a more complex fashion and hence, it will have to be determined for each genotype in extensive evaluation trials over a wide range of environmental conditions. Estimates of the less important regression coefficient would require fewer but widely differing environments. Thus potentially useful genotypes must be grown in an adequate number of environments covering a wide range of possible environments occurring in the region selected for the breeding programme in order to identify stable, high yielding genotypes by regression techniques (Eberhart, 1969; Russell and Prior, 1975). eGama and Hallauer (1980) compared the relative stability of grain yield among maize hybrids produced from selected and unselected lines. Yields of selected hybrids 75 were significantly greater than yields of unselected hybrids, but both groups hybrids when of hybrids had equal the stability numbers of stable parameters b and were considered. Selection based on yield did not seem to enhance stability for yield. They concluded that selection of hybrids for mean yield across environments should be emphasized first, over and then the relative stability of the elite hybrids environments been different determined. if previous However, results might have selection had been based on stability rather than on yield alone. 2.2.3. Selection for stability and adaptation response 2.2.3.1. Selection sites The site of early generation selection plays a major role in determining the range of adaptation (Johnson, 1977). The adaptability and stability of crop plants is generally assessed at the advanced testing stage without any previous directed selection for wide adaptation or stability. Material previously screened at one or two environments is evaluated over a number of environments (locations and years) during the advanced testing stages. would be and/or facilitated if selection for wide adaptability stability However, Progress in yield improvement could be conducted in early generations. in early generations of a breeding programme there are often large numbers of genotypes to test and consequently only few locations can be used. Testing for stability using 76 regression techniques is, therefore, not feasible. Varieties with wide adaptation should come from a selection programme which permits the best expression of genes for wide adaptation (St-Pierre et al., 1967). It seems logical to assume that a variety selected under environments which favour optimum expression of genes for adaptation should possess the morphological and physiological plasticity required for wide adaptation. The generally accepted theory of selection for wide adaptation is that selection should be made under the environmental conditions where the variety is expected to be grown. conducted under Selection and evaluation should be a wide range of conditions to ensure wide adaptation of the genotypes (Bilbro and Ray, 1976). If the number of testing sites must be limited (as is almost always the case), that one should choose sites, for making selections, are highly correlated with other sites in the region where the varieties are to be grown. Site similarity can be determined by cluster analysis or by calculating the correlation coefficients of the variety mean yield at each location with the corresponding mean yields at each of the other locations. A high correlation indicates that a site is representative of the others. Specific adaptation may be desirable yield for representative stabilizing of the region in at general locations (Campbell not and Lafever, 1977). Where rainfall (both amount and distribution) is a major 77 environmental factor, early and late dates of planting can often be used to obtain extra environments at each location (Eberhart and Russell, 1966). Similarly, management factors primarily responsible for differences in performance, such as plant densities, fertilizer application rates, etc., can be used to increase the number of environments possible from a fixed number of locations, greater range Clements, Mock, of 1973; 1978; and at the same time provide a environmental conditions Eberhart and Russell, Heinrich et al., (Easton and 1966; Fakorede and 1983; Luthra and Singh, 1974; Snoad and Arthur, 1976). 2.2.3.2. Selection techniques It is possible to select for yield adaptation using two contrasting environments seasons). Oka (1967) called this stability and (locations or 'disruptive seasonal selection'. The wide adaptation of Mexican wheat varieties (which do well in Canada and Aslan countries) is attributable to an aggregate of characters including insensitivity to photoperiod, stiff straw, resistance to many rusts, high response to nitrogen, etc. According to Borlaug (1965), at CIMMYT (Mexico), two generations of segregating materials were grown and selected each year to accelerate the breeding programme. The plants were grown in a winter nursery at sea level in north-west Mexico at latitude 27° N and in a summer nursery at 2 800m altitude near Mexico city at latitude 18°N. 78 Selection for the best material at each of the test sites in turn resulted in a gene pool of high-yielding and widely adapted lines for final selection. This approach (also known as 'shut-tle breeding') is an example of disruptive seasonal selection. 2.2.3.3. The different concepts of stability Plant breeders generally agree on the importance of good phenotypic stability, but there is much less accord on the most appropriate definition of stability and on a statistical measure of stability in variety trials. As the review of literature indicates, the concept of stability has been defined in a variety of ways, each dependent on the method used to estimate it. Plaisted (1960), Plaisted and Peterson (1959), Shukla (1972), and Wricke (1962) based their measure of stability upon the contribution of a genotype to the total GE interaction sum of squares. defined stability coefficient composite so l e l y (b values), measure of in Finlay and Wilkinson (1963) terms of the regression whereas Hanson (1970) stabi l i t y which devised a combi n e s the contribution of the ith genotype to the GE interaction sum of squares with its response (Eberhart and Russell, 1971) opt regression for two to environmental 1966; separate coefficient (b) change. Perkins and Jinks, stability values Others 1968; Tai, parameters, the being considered in conjunction with a measure of the scatter of points about 79 this fitted regression line (mean square deviations from regression). By contrast, Bilbro and Ray (1976), and Breese (1969) argued against coefficient values instead reserve to the into the incorporation of measures term of for the regression stability, those preferring measurements of unpredictable irregularities in the response to environments 2 as provided by the deviations from regression (S £ ) and 2 coefficient of determination (r ). They interpreted the regression coefficient (b) reflecting the response, as an additional parameter adaptation or sensitivity of a genotype to the level of productivity of the environments. In addition to the stability parameters considered above, more simple methods have been proposed, such as the use of the differences between the maximum and minimum yields of a variety over a range of environments (Langer, 1979), comparisons of et al., the ranks of a variety in different environments (Thomson and Cunningham, 1979), or relating the yields to the highest yielding variety (Sepahi, 1974; Jensen, 1976), etc. These methods may be worthy of attention for practical plant breeding and much more information on their efficiency argued is desirable. that the approaches are regression Others (Lin et technique inadequate and al., 1986) have and other parametric proposed the use of multivariate techniques in studies of GE interactions. Hill (1975) cautioned on the use of multivariate techniques, and 80 most of them are measures of similarity rather than stability or adaptability and hence have not been widely used. Becker (1981a,b) phenotypic stability. distinguished two basic concepts of He used the term 'biological concept' of stability to characterize a genotype which has a constant performance in all environments. Such a genotype has minimal variance over different environments. This type of stability is in agreement with the concept of homeostasis and is equivalent to what Finlay and Wilkinson (1963) referred to as maximum phenotypic stability (b=0). Lin et al (1986) referred to it as Type 1 stability. This type of stability is not desirable because the variety does not respond to improved growing conditions. Researchers and farmers prefer varieties which always realize the yield expected at the level of production of the respective environment, i.e., varieties with GE interactions as small as possible. Becker (1981a,b) referred to this as an 'agronomic concept' of stability, and is equivalent to Lin et al's (1986) Type 2 stability. When the biological concept of stability is applied, the variance of performance over environments is usually used as a statistical measure. been proposed stability. regarded The as a for Different assessing widely used combination concepts of stability, statistical the agronomic regression of measures have concept technique biological and of may be agronomic since the regression coefficient is strongly associated with variance (Becker, 1981a,b). The mean 81 square deviation from regression Indicates the phenotypic stability according to the agronomic concept of stability and should be as small as possible in a variety. The regression coefficient measures the response of the variety based on the biological concept of stability. Its desired value depends upon the special situation and the breeder's objectives (Becker, However, 1981a). Lin et al (1986) considered the regression coefficient to be a measure of Type 1 stability or the biological concept of stability only if its desired value is zero (b=0). All other values of the regression coefficient (b<1.0 or b>1.0) measure Type 2 stability or the agronomic concept of stability. Also, Lin et al (1986) considered the deviation mean square to be a measure of a different type of stability (Type 3 stability) which is not equivalent to the agronomic concept of stability. They considered Type 3 stability to be the least attractive. However, the deviation mean square provides useful additional information when used in conjunction with the regression coefficient. Many reports are available which indicate that the deviation mean square is highly correlated with the parameters which measure Type 2 or the agronomic concept of stability. 2.2.3.4. Interrelationships among stability parameters The regression coefficient is a suitable measure of production response in the performance of a genotype to changes in environmental productivity. Eberhart and Russell 82 (1966) found that maize hybrids with regression coefficients less than unity (b<1.0) usually had mean yields below the grand mean suggesting a positive relationship between yield and the response Index (b ). There are many other reports on significant, high positive correlations between mean yields and regression coefficients 1976; Cross, 1977; Eagles (Baihaki, and Frey, Stucker and Lambert, 1977; Eberhart, 1969; Fatunla and Frey, 1974; Finlay and Wilkinson, 1963; GonzalezRosguel, 1976; Langer et al., 1979; Jensen and Cavalieri, 1983; Perkins and Jinks, 1968; Saeed and Francis, 1983). If the stability of a variety is assumed to be a measure of how well the observed response agrees with the expected response derived from the linear regression equation (variety predictability), dispersion of regression are Ray, 1976; then the parameters r^ and S \ that measure d p o i n t s around the best fitting linear the best measures of Breese, 1969; Langer et stability al.. (Bilbro and 1979). Several authors (Becker, 1981a,b; Campbell and Lafever, 1977; Easton and Clements, 1973; 1974; et al., Nguyen ecovalence (W), Langer et al., 1979; Luthra and Singh, 1980) found the stability coefficient of determination parameters 2 (r ), mean square deviation (S^ ), and stability variance (a^) to be d # significantly and highly correlated with one another, when large numbers of varieties are grown in a sufficiently broad environmental range. This suggests that any of them should be 83 a satisfactory parameter for measuring stability. On the other hand, low or no significant correlations have been reported between either the response parameter (b) or mean productivity (e.g. mean yield) with the various parameters 2 (W, r , 2 2 S ^ or cr8) that measure stability of production (Becker, 1981a,b; Easton and Clements, 1973; Gray, 1982? Langer suggests et al., 1979; Nguyen et al., that production stability indexes 1980). This and production response indexes (b and/or mean performance) can be selected independently. varieties with Thus, it should be possible any combination of production production stability and, hence, to obtain response and it should be possible to accomplish breeding for high yield, high response (b>1.0) and stability (Langer et al., 1979). Becker (1973), (1981a,b), and Easton and Clements Marguez-Sanchez (1973) (1973), Freeman discussed the interrelationships among the different stability parameters. Becker (1981b) discussed the existence of strong correlations between (i) ecovalence (W) and mean square deviation (S2 ), 2 2 2 (ii) r fcand W, (iii) r and S ^ , and (iv)variance andthe regression coefficient (b). The strong correlation between ecovalence (W) and S 2 can d be understood if W is partitioned in order to distinguish between the relative importance of various components. ecovalence can be partitioned into two components, The (1) a o 2 component which is a function of linear regression [(b-1 )* 0.90) and significant correlations between mean yield and regression coefficients in oat lines. The positive sign of the non-significant correlation is in agreement with the findings of Eberhart (1969), and Eberhart and Russell (1966) who reported that maize hybrids with a regression coefficient less than unity usually had mean yields below the grand mean. The rank correlations between mean yield and stability parameter estimates (S j a , 5 2 a* and r ) s 107 were all that very low selection and non-signifleant (Table 6) Indicating based on yield might not enhance yield stability. The rank correlations for the regression coefficients (b ) with mean square deviations from regression (S ^ ), and b with stability variances ( o were both near zero (r= 0.05 s and r=0.02, respectively). This suggests that it should be possible to obtain maize hybrids with any combination of b and S \ or b and cr2 values. Similar results were obtained for d s yield in maize (Becker, 1981a, b), oat (Langer et al.. 1979), orchard grass (Gray, 1982), tall fescue (Festuca arundinacea Schreb.), and wheat (Easton and Clements, 1973). 2 2 The rank correlation between and was very high (r=0.92) and highly significant (Table 6) indicating that the rankings of entries by these two parameters are similar and that there is close similarity between the two parameters. Thus any one of them can be used in place of the other as a 2 measure of stability. High stability variance (a 9 _) can arise from (i) failure of a genotype to have a regression slope of unity to the environmental index, the linear regression Hybrids 20, 21 or (ii) from poor fit of (high deviation from regression). and 25 which had b values significantly 2 different from unity had high values of o which were also of much higher magnitudes than d b values close to unity had magnitude. values. All hybrids which had 2 2 and a* values of similar Thus when the b value is close to unity the 108 magnitude of the stability variance depends chiefly on the 2 2 magnitude of the deviation mean square and hence and are highly correlated. Lin et al (1986) suggested that if the data does not fit linear regression or if residual mean square is significant then ecovalence or stability variance should be used and deviation mean square is not recommended. 2 2 However, since S^ and ag are highly correlated Lin et al's (1986) suggestion does not seem to be valid in these data. As expected, correlations there were highly significant negative 2 2 2 2 between S d with r (r= -0.71) and r with a ‘ (r = - 0.68). The coefficient of determination is a measure of goodness of fit of the linear regression line and hence, as expected, a small r ^ value translates into large Sy and 2 oZ2 s values. In this way r values can be used as a measure of 2 stability, and high r values would be more desirable. There was no significant correlation between mean yield across sites and mean correlations among varieties (Tables 6 and 7). The correlations between regression coefficients and 2 r with the mean variety correlations were highly significant indicating that the varieties that were highly correlated with the others or followed the general pattern of response 2 had higher b and r values. The highly significant negative — 2 2 correlations between r with Sy (r= -0.72) and ag (r= -0.72) indicate that the varieties that were less correlated with the others and hence did not follow the general pattern 2 2 closely had higher values of Sy and a g . These would be 109 considered the most unstable while those that were highly and o2 values d s (Table 8). Thus it is important to find out the underlying correlated with the others had lower biological basis for any differences in stability of response so that varieties with specific desirable traits are not discarded on the basis of failure to follow the general pattern, However, which might not necessarily be the desirable one. on average, the varieties were all highly and significantly correlated with each other and so the parameter 2 2 estimates S* and a- should provide valid measures of relative stability. In this study, an entry with significantly high d and o 2 values would still be considered desirable if its high s s2 and a 2 values are a result of d e s i r a b l e atypical d s behaviour. 4.1. Adaptation responses The regression coefficient measure (b value) was used as a of adaptation response. The 25 hybrids used in this study responded differently to environments of varying levels of productivity. The regression coefficients ranged from 0.69 (for hybrid 21) to 1.37 (for hybrid 25). Two hybrids (20 and 21) had b values significantly less than unity (Table 8), indicating a environments. lower than average Only one hybrid respo n s e to vary i n g (hybrid 25) had a b value significantly greater than unity (b=1.37), indicating an above average response to varying environments. All the other 110 Table 8. Mean grain yield across sites and estimates of adaptation and stability parameters for grain yield of 25 maize hybrids grown at eight locations in 1985 and 1986 in Michigan hybrid number 14 11 15 4 10 7 3 20 6 24 23 1 19 8 13 2 16 25 12 9 17 21 22 5 18 mean yield (t/ha) 12.06a* 11.58b 11.41 be 11.33 be 11.29 be 11.16 c 10.84 d 10.84 d 10.66 de 10.66 de 10.54 def 10.48 def 10.35 efg 10.34 efg 10.32 efg 10.22 fgh 10.07 gh 10.02 gh 9.90 hi 9.88 hi 9.67 i 9.66 i 9.56 ij 9.34 jk 9.13 k b 0.99 1.09 1.02 1.06 1.02 1.02 1.12 0.75* 1.00 1.06 1.12 0.96 0.82 1.01 0.96 0.98 0.82 1.37** 1.16 1.17 0.94 0.69* 1.16 0.89 0.82 r2 0.86 0.89 0.88 0.85 0.89 0.88 0.89 0.80 0.87 0.83 0.88 0.72 0.77 0.65 0.86 0.83 0.73 0.92 0.82 0.89 0.89 0.59 0.87 0.75 0.91 S2 d 0.32** 0.29** 0.29** 0.42** 0.27** 0.30** 0.33** 0.28** 0.30** 0.51** 0.37** 0.78** 0.43** 1.20** 0.30** 0.41** 0.53** 0.48** 0.62** 0.36** 0.22** 0.72** 0.43** 0.57** 0.11** 2 °s 0.33** 0.32** 0.30** 0.44** 0.29** 0.32** 0.38** 0.44** 0.32** 0.53** 0.42** 0.80** 0.52** 1.23** 0.31** 0.42** 0.63** 0.80** 0.70** 0.44** 0.25** 0.96** 0.50** 0.61** 0.20** r 0.92** 0.94** 0.93** 0.92** 0.94** 0.93** 0.94** 0.89** 0.93** 0.90** 0.93** 0.83** 0.87** 0.81** 0.92** 0.90** 0.84** 0.94** 0.90** 0.94** 0.94** 0.75** 0.92** 0.85** 0.95** grand mean yield = 10.45 *,** b significantly different from 1.0 for the regression coefficients, from the pooled error mean square for the deviation from regression mean square and stability variance, and from zero for the mean correlation coefficients, at the 0.05 and 0.01 probability levels, respectively. ^means followed by the same letter not significantly different based on SNK multiple range test at the 0.05 probability level. b = regression coefficient based on a non-independent r 2 = coefficient of determination based on a non-independent Ij Table 8 (continued) mean square deviation from regression; stability variance; and mean correlation coefficients among entries. 112 22 hybrids sh o w e d an average response to varying environments, with regression coefficients not significantly different from unity (Table 8). The mean grain yields across environments ranged from 9.13 t/ha (for hybrid 18) to 12.06 t/ha (for hybrid 14), with a grand mean of 10.45 t/ha (Table 8 ). On the basis of both mean yield across environments and b values the 25 hybrids can be classified for adaptation into four distinct classes. Ten hybrids (1,3,4,6,7,10,11,14,15 and 24) were well adapted to the whole range of environments used in this study. They had b values not significantly different from unity and above average mean yields across environments. Their expected relative yield responses above average throughout the whole (Figs 4 to 7) range are of environments. Nine of these were among the top 10 hybrids in this study, on the basis of mean yield across environments. (4,7,10,11,14 and 15) had mean yield across Six of these environments significantly higher than the grand mean (Table 8). These ten hybrids would be selected if selection is based on two-year mean yields across eight sites. Eight hybrids (2, 5, 8, 9, 12, 17, 18 and 22) were poorly adapted to all environments (Figs 8 and 9). They had b values not significantly different from unity and all but two (2 and 8) had across-environments mean yields significantly lower than the grand mean (Table 8). Thus on the basis of the 113 15.0 14.0 13.0 12.0 hybrid mean yield (t/ha) 10.0 9.0 8.0 hybrid no. hybrid no. hybrid no. population 7.0 14 11 4 mean 6.0 5.0 7.0 8.0 9.0 10.0 11.0 12.0 Environmental index (t/ha) 13.0 Fig 4. Yield responses of three maize hybrids well adapted to a range of environments 114 15.0 13.0 12.0 hybrid mean yield (t/ha) .0 10.0 9.0 8.0 7.0 hybrid no. hybrid no. hybrid no. population 6.0 15 10 7 mean 5.0 7.0 8.0 9.0 10.0 11.Q 12.0 Environmental index (t/ha) Fig 5. Yield responses of three maize hybrids well adapted to a range of environments 13.0 115 15.0 14.0 13.0 12.0 hybrid mean yield (t/ha) 11.0 iQsQ 9.0 8.0 7.0 papulation mean hybrid no. 24 hybrid no. 1 6.0 5.0 7.0 8.0 9.0 10.0 11.0 12.0 Environmental index (t/ha) Fig 6. Yield responses of two maize hybrids well adapted to a range of environments 13.0 116 15.0 14*0 13.0 12. 0 hybrid mean yield (t/ha) 10.0 9.0 8.0 hybrid no. 3 hybrid no. 6 population mean 7.0 6.0 5.0 7.0 8.0 9.0 10.0 11.0 12.0 Environmental index (t/ha) 13. Fig 7. Yield responses of two maize hybrids well adapted to a range of environments 117 15.0 14.0 13.0 12.0 hybrid mean yield (t/ha) 0 10.0 9.0 8.0 7.0 hybrid no* 2 6*0 hybrid no* hybrid no* hybrid no* population 9 17 5 mean 5.0 7.0 8*0 9*0 10.0 11*0 12*0 13.0 Environmental index (t/ha) Fig 8. Yield responses of four maize hybrids poorly adapted to a range of environments 118 15.0 14.0 13*0 12.0 hybrid mean yield (t/ha) 10.0 9.0 8.0 7.0 hybrid no. 22 hybrid no. hybrid no. hybrid no. population 6.0 12 18 8 mean 5.0 7.0 9.0 10.0 8.0 11.0 12.0 Environmental index (t/ha) 13. Fig 9. Yield responses of four maize hybrids poorly adaptsd to a range of environments 119 across-environments mean yield they could possibly be discarded. Two hybrids (23 and 25) were poorly adapted to lowyielding environments but well environments. Their adapted to high-yielding expected relative response is to give below average mean yields in low-yielding environments and above-average yield response in high-yielding environments (Fig 10). Hybrid 23 with a b value of 1.12 had the capacity to utilize environments with a yield potential of about 10.0 t/ha and above (Fig 10) resulting in its above average mean yield across sites. On the basis of across sites mean yield alone, hybrid 23 could be selected. The unusually large and highly significant b value of hybrid 25 (b = 1.37) was primarily related to its low yield under low yielding environments and its ability to catch up with other entries in increasingly favourable environments. Its superiority was beyond a yield potential level of about 11.5 t/ha (Fig 10). It yielded below average for most of the environmental range resulting in below average mean yield across environments and on the basis of mean yield it would be discarded. Five hybrids (13, 16, 19, 20 and 21) were specifically adapted to low-yielding environments (Fig 11 and 12). Of these, three hybrids (13,16 and 21) had mean yields below average for most of the yield range (above 8 t/ha) resulting in low mean yields across sites. Their yield performance in the low-yielding environments is inferior to that of the best 120 15*0 14.0 13.0 12.0 hybrid mean yield (t/ha) •0 10.0 9.0 8.0 7.0 hybrid no. 23 hybrid no. 25 population mean 6.0 5.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 Environmental index (t/ha) Fig 10. Yield responses of two maize hybrids adapted to high-yielding environments 1 21 15.0 14*0 13.0 12.0 hybrid mean yield (t/ha) 11*0 10.0 9.0 8.0 hybrid no. 19 . . . hybrid no. 21 7.0 ■ population mean 6.0 5.0 7.0 Environmental index (t/ha) Fig 11. Yield reaponses of two maize hybrids adapted to low-yielding environments 122 15.0 14.0 13.0 12.0 hybrid mean yield (t/ha) 11.0 1Q^0 9.0 8.0 hybrid no. hybrid no. hybrid no. population 7.0 20 16 13 mean 6.0 5.0 7.0 8.0 9.0 10.0 11.0 12.0 Environmental index (t/ha) 13. Fig 12. Yield responses of three maize hybrids adapted to low-yielding environments 123 well-adapted hybrids and hence seem to be undesirable even In the low-yielding environments. Hybrid 20 had mean yields above average throughout most of the yield range resulting In Its above average mean yield across environments (Table 8). Its regression coefficient was significantly less than unity (b=0.75) Indicating its inability to exploit highly favourable environments, beyond 12.0 t/ha. Hybrid 19 is well adapted to low-yielding environments below 10.0 t/ha but lacks the ability to exploit highly favourable environments (with b = 0.82) resulting in a lower than average mean yield across environments. The results of this study show that the regression technique is a valuable tool for identifying varieties specifically adapted to specific types of environments and would be a valuable tool in making variety recommendations. Such varieties cannot be easily identified and could even be discarded if selection were on the basis of mean yield across sites. Selection for specific adaptation would be particularly Important in breeding for stress resistance (e.g. drought resistance).To be useful for making selections b values should be used in conjunction with mean yields across environments. particularly Graphing of the regression lines is effective in emphasizing performance to a range of environments. the trend of Selection based on mean yield across sites is adequate for selecting widely adapted varieties but does not identify varieties with 124 specific possible adaptation. The results also to develop high-yielding widely show that it is adapted varieties that are superior to specifically adapted varieties, in their areas of adaptation. 4.2. Stability If the stability of a variety is assumed to be a measure of how well the observed response agrees with the expected response derived from the linear equation, then the parameter 2 2 2 estimates (r , and ) that measure the dispersion of points around the best fitting linear regression are the best measures of stability (Bilbro and Ray, 1976; Breese, 1969.; Langer et al., 1979). High r^ values and low values of and 2 crj indicate that the variety response is highly predictable when based on site mean yield and b values. An entry was considered stable if its deviation from regression mean square or stability variance was not significantly different 2 from the pooled error mean square or if its r value was close to unity. On the basis of the stability parameter 2 2 estimates and os all hybrids used in this study were 2 2 unstable. All had S ^ and aa values significantly different 2 from the pooled error mean square (Table 8). The and 2 os values ranged from 0.11 and 0.20 to 1.20 and 1.23, respectively (Table 8). Significant deviation from regression mean squares indi c a t e non-linear response, specific interactions with environments or lack of stability. The 125 2 coefficient of determination (r ) is a measure of goodness of fit of the linear response and is a m e a s u r e of the 2 reliability of the linear response. The r values for some of 2 the entries in this study were rather low. The r values ranged from 0.59 (for hybrid 21) to 0.92 (for hybrid 25). The distribution of observed means were not close to the expected relative varietal responses (Figs 4 to 12), indicating a poor fit of the linear regression lines. Varieties with the smallest values of mean varietal _ 2 correlations (r) also had the smallest values of r and, 2 2 consequently, had the largest values of S £ and a* (Table 8). Thus part of the instability was a result of failure to follow the general pattern of response closely. However, 2 varieties with relatively high r and r values (e.g. hybrids 3, 9, 10, 11, 17, 18 and 25) also had highly significant ando^ values suggesting that the highly s a significant o d and values were not only a result of a poor fit of the linear regression and/or poor average entries with the others correlations of individual (failure to follow the dominant pattern) but also a result of lack of stability. All the hybrids used in this study were developed by private seed companies (in or outside Michigan), so the initial selection and evaluation of these hybrids were conducted in environments other than those in which the stability trials were conducted, possibly without direct selection for 126 stability. Thus, It Is not surprising that none of these hybrids were stable. However, other workers (Beaver and Johnson, 1981; Walker and Fehr, 1978; Weaver et al., 1983) reported that varieties demonstrate often undesirable stability parameter estimates even when tested In the area where they were Initially developed. This emphasizes the relative nature of stability and/or the need to do direct selection for stability. There was no association between maturity and stability. There was an equal distribution of early and late maturing hybrids with relatively higher and lower values stability parameter estimates. In sorghum, Saeed and of the Francis (1983) reported that late maturing varieties were more stable than early maturing varieties. Eberhart and Russell (1966) proposed that an ideal variety would be one which has the highest yield over a wide range of environments, average response (b = 1.0) and a deviation mean square of zero. Such a variety was not found in this study. Hybrids 4, desirable and widely 10, adapted. 11, 14 and 15 were the most Despite their significantly high deviations from regression mean squares and stability variances, they had regression coefficients (b values) close to unity, significantly high mean yields across environments and their observed mean yields were superior at all yield levels, being consistently at or above the site mean yields throughout the whole range of environments used in this 127 study. Hybrid unstable and environments. number 7 would also be yielding below average desirable at two of though the 16 5. Conclusions The results of this study lead to the following conclusions: 1. The combined analysis of variance showed that a major portion of attributed the to highly genotype significant x location 6E interaction interaction suggesting the need to replicate more over years, was effects, locations than if the two years were representative of year-to-year variance in Michigan. 2.The use of the mean of all varieties as a (non-independent) measure of the environment does not satisfy the requirements of a regression reliable analysis estimates of but it provides sufficiently adaptation and stability parameters, particularly if the entries are highly correlated. 3. Mean yield, adaptation and stability parameter estimates were relatively independent of one another, thus; (i) it appears possible to develop high yielding varieties 2 2 with various combinations of b and Sj d or o s values. (ii) selection stability on the basis ofyield for yield. This alone will not might explain enhance why none of the hybrids used in this study were stable. (iii) selection for yield adaptation and stability should be 128 129 done Independently and simultaneously with selection for yield. 4. the parameter estimates r 2 2 , S ^ and 2 o are highly and 8 significantly correlated indicating that any of them should be a satisfactory parameter for measuring stability. However, caution should be exercised in describing as unstable those genotypes with high values of S j* and or low values of r^ if a s the v a r i e t i e s are not h i g h l y c o r r e l a t e d and/or the correlations are heterogeneous. 5. It is possible to develop high yielding and widely adapted hybrids that are superior to those with specific adaptation. 6. Variety adaptation and stability should be considered JLn developing varieties and in making variety recommendations. 7. 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APPENDIX 141 7. APPENDIX Appendix Table 1. List of single-cross maize hybrids used for stability analysis Hybrid number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Brand name and hybrid designation Callahan 754 Cargill 842 Cargill 859 Dairyland 1107 Dairyland 1001 DeKalb-Pfizer DK484 DeKalb-Pfizer DK524 Funk G-4312 Funk G-4342 Garno S-100X Glenn & Garno GX1007 Golden Harvest H-2480 Great Lakes GL-540 Great Lakes 5922 King K5574 MFI 1834 Northrup King PX9345 Payco SX620 Pioneer 3737 Pioneer 3744 Pioneer 3901 Renk RK66 Rupp XR1639 Stauffer S5340 Stauffer S5650 Source Callahan Seeds, IN 46074 Cargill Seeds, MN 55440 Cargill Seeds, MN 55440 Dairyland Seed Co., WI 53095 Dairyland Seed Co., WI 53095 DeKalb-Pfizer Genetics, IL DeKalb-Pfizer Genetics, IL Funk Seeds International, IL Funk Seeds International, IL Garno Seed Co., MI 49268 Garno Seed Co., MI 49268 Sommer Bros. Seed Co., IL Great Lakes Hybrids, Inc., MI Great Lakes Hybrids, Inc., Ml King Grain Ltd., Canada MFI Seeds, MI 49072 Northrup King Co., MN 55440 Payco Seeds, Inc., MN 55325 Pioneer Hi-Bred Int. IN 46072 Pioneer Hi-Bred Int. IN 46072 Pioneer Hi-Bred Int. IN 4607 Renk Seed Co., WI 53590 Rupp Seeds, Inc., OH 43567 Stauffer Seeds, Inc., WI 53711 Stauffer Seeds, Inc., Wi 53711 142 Appendix Table 2. Branch County site information 1985 1986 Planted April 29 May 8 Harvested October 24 October 29 Soil type Gilford sandy loam Gilford sandy loam Previous crop maize maize Row spacing 75cm (30 inches) 75cm Fertilizer rates 209-74-0 36-92-120 Soil test:pH 6.5 5.6 P 240 (very high) 350 (very high) K 200 (medium) 211 (medium) Farm cooperator: David Labar, Union City. 143 Appendix Table 3. Cass County (Irrigated) site Information 1985 1986 Planted April 29 May 2 Harvested October 23 October 8 Soil type Oshtemo sandy loam Oshtemo sandy loam Previous crop maize maize Row spacing 75cm (30 inches) 75cm Fertilizer rates 343-44-131 248-44-131 Irrigation 200mm (8 inches) 125mm (5 inches) Soil test:pH 6.8 6.8 P 230 (very high) 264 (very high) K 440 (very high) 392 (very high) Farm cooperator: Dave Crlpe, Cassopolls. 144 Appendix Table 4. Huron County site Information 1985 1986 Planted May 2 May 1 Harvested October 29 November 6 Soil type Kilmanagh loam Kilmanagh loam Previous crop maize maize Row spacing 75cm (30 inches) 75cm Fertilizer rates 197-63-129 148-62-99 Soil test:pH 7.6 7.7 P 85 (high) 81 (high) K 180 (medium) 160 (medium) Farm cooperator: William McCrea, Bad Axe. 145 Appendix Table 5. Ingham County (M.S.U.) site information 1985 1986 Planted April 26 April 24 Harvested October 17 October 11 Soil type Capac loam Capac loam Previous crop maize maize Row spacing 90cm (36 inches) 90cm Fertilizer rates 165-50-50 165-50-50 Soil test:pH 6.1 5.9 P 155 (very high) 186 (very high) K 235 (high) 215 (high) Farm cooperator: M.S.U., East Lansing. 146 Appendix Table 6. Kalamazoo County site information 1985 1986 Planted April 30 May 3 Harvested October 24 October 30 Soil type Kalamazoo loam Kalamazoo loam Previous crop maize maize Rows spacing 75cm (30 inches) 75cm Fertilizer rates 125-48-24 112-48-24 Soil test:pH 5.9 5.7 P 162 (very high) 161 (very high) K 364 (very high) 286 (high) Farm cooperator: Richard van Vrancken, Climax. 147 Appendix Table 7. Monroe County site information 1985 1986 Planted May 5 May 5 Harvested October 26 October 28 Soil type Brookston loam Brookston loam Previous crop wheat-clover sod wheat Row spacing 75cm (30 inches) 75cm Fertilizer rates 220-72-240 170-68-90 Soil test:pH 6.3 6.8 P 218 (very high) 97 (high) K 435 (very high) 128 (low) Farm cooperator: Gerald Heath, Milan. NB All fertilizer rates represent actual amounts of NPK applied in lbs/acre. 14 8 Appendix Table 8. Montcalm County (dryland) site Information 1985 1986 Planted May 1 April 30 Harvested October 30 November 3 Montcalm-McBride sandy loam Soil type Previous crop alfalfa Sudan grass Row spacing 75cm (30 inches) 75cm Fertilizer rates 253-135-135 253-135-135 Soil test:pH 5.6 6.1 P 505 (very high) 576 (very high) K 184 (medium) 337 (very high) Montcalm Research Comden). Farm, Farm cooperator: Lakeview (Theron 149 A p p e n d i x Table information 9. Montcalm County (irrigated) 1985 1986 Planted May 1 April 30 Harvested October 30 November 3 site Montcalm-McBride sandy loam Soil type Previous crop alfalfa Sudan grass Row spacing 75cm (30 inches) 75cm Fertilizer rates 253-135-135 253-135-135 Irrigation 150mm (6 inches) 131.25mm (5.25 inches) Soil test:pH 5.6 6.1 P 505 (very high) 576 (very high) K 184 (medium) 337 (very high) Montcalm Research Comden). Farm, Farm cooperator: Lakeview (Theron 150 Appendix Table 10. Table of means for 25 maize hybrids grown at Branch County during the 1985 summer season hybrid number grain yield (bu/acre) grain yield (t/ha) 4 10 14 23 11 7 3 15 24 6 25 22 16 13 20 1 17 19 12 9 2 21 18 5 8 13.25 12.88 12.71 12.65 12.61 12.56 12.39 12.25 12.15 11.82 11.63 10.74 10.68 10.48 10.36 10.18 10.16 10.16 10.02 9.89 9.87 9.81 9.60 9.50 9.38 site mean CV(%) LSD(0.05) LSD(0.01) F-test RE( %) 11.11 3.76 0.59 0.79 ** 104 a* ab abc abc abc abc abed bed bed cd d e e ef efg efg efg efg efg efg efg efg fg fg g 204.34 198.66 196.06 195.12 194.40 193.64 191.04 188.97 187.40 182.19 179.26 165.67 164.62 161.61 159.71 156.92 156.64 156.63 154.52 152.57 152.14 151.21 147.96 146.51 144.59 171.29 3.76 9.12 12.14 ** 104 a* ab abc abc abc abc abed bed bed cd d e e ef efg efg efg efg efg efg efg efg fg fg g stalk lodging (%) root lodging (%) 2.32 1.68 1.14 0.84 3.12 1.30 4.26 3.67 3.51 1.44 3.06 1.24 2.45 3.18 0.85 2.18 1.06 1.33 1.28 3.67 2.68 3.98 1.76 4.39 3.67 1.61 0.53 0.00 2.08 1.53 0.00 0.50 1.54 1.04 1.52 0.51 0.00 1.10 0.00 0.00 2.62 0.00 3.77 0.00 1.06 2.10 1.09 0.53 1.51 1.16 2.40 107.86 3.67 4.89 ns 113 1.03 165.17 2.41 3.21 ns —— — ** F-test significant at the 0.01 probability level, and ns = F-test not significant at the 0.05 probability level; RE(%) = relative efficiency of the Simple Lattice Design over the Randomized Block Design, (--- = no efficiency). + **■ means followed by the same letter are not significantly different based on SNK's multiple range test at the 0.05 probability level. 151 Appendix Table 11. Table of means for 25 maize hybrids grown ab Branch County during the 1986 summer season hybrid number grain yield (t/ha) 14 11 10 4 15 23 7 12 20 1 22 6 2 24 19 3 9 25 13 17 16 8 5 21 18 13.33 13.20 12.84 12.65 12.39 12.37 12.10 11.71 11.34 11.04 10.97 10.93 10.72 10.66 10.58 10.41 10.25 10.07 9.99 9.96 9.81 9.44 9.38 9.36 8.96 site mean CV(%) LSD(0.05) LSD(0.01) F-test RE( %) 10.98 4.50 0.70 0.93 ** ** F-test — _ mm_ grain yield (bu/acre) a* a ab abc abc abc bed cde def efg efgh efgh efgh efgh fgh fghi fghi ghi ghij ghid hij ij id id d 205.51 203.62 197.98 195.09 190.99 190.76 186.58 180.53 174.92 170.30 169.15 168.49 165.38 164.46 163.10 160.52 158.07 155.35 154.04 153.66 151.31 145.51 144.72 144.35 138.10 a* a ab abc abc abc bed cde def efg efgh efgh efgh efgh fgh fghi fghi ghi ghid ghid hid id id id d 169.30 4.50 10.78 14.35 ** 110 significant at the 0.01 stalk lodging (%) root lodging (%) 4.47 3.50 3.06 3.38 6.38 5.38 5.79 5.13 2.94 5.67 4.96 8.24 7.42 3.16 7.13 7.18 9.06 7.42 9.12 1.98 2.76 7.14 13.60 6.53 7.82 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 5.97 55.16 4.66 6.21 ** 0.00 ------------- ™ ™“• probability level; RE(%) = relative efficiency of the Simple Lattice Design over the Randomized Block Design, (--- = no efficiency) t m e a n s followed by the same letter are not significantly different based on SNK's multiple range test at the 0.05 probability level. 152 Appendix Table 12. Table of means for 25 maize hybrids grown at; Cass County (Irrigated trial) during the 1985 summer season hybrid number grain yield (t/ha) 8 4 14 1 10 7 24 11 15 23 19 3 2 20 9 6 25 13 16 12 17 5 22 18 21 13.89 13.33 13.17 13.13 12.93 12.90 12.83 12.74 12.63 12.38 12.07 11.98 11.69 11.65 11.63 11.58 11.57 11.40 11.02 10.83 10.42 10.26 10.20 10.12 9.65 site mean CV(%) LSD(0.05) LSD(0.01) F-test RE(%) 11.82 2.69 0.45 0.60 ** 102 grain yield (bu/acre) + a ab ab ab abc abc abc abc be cd de de ef ef ef ef ef ef fg gh hi i i i j 206.44 205.53 203.11 202.44 199.43 198.85 197.88 196.43 194.75 190.84 186.14 184.78 180.24 179.68 179.29 178.62 178.37 175.86 169.99 167.07 160.75 158.22 157.30 156.11 148.85 182.28 2.69 6.93 9.23 ** 102 + a ab ab ab abc abc abc abc be cd de de ef ef e ef ef ef fg gh hi i i i J stalk lodging (%) root lodging (%) 3.45 1.00 1.16 1.11 3.22 1.14 3.87 2.14 2.87 1.61 3.29 2.06 2.57 3.22 3.67 7.52 0.52 5.76 1.60 1.71 3.08 9.27 1.66 3.27 1.16 3.35 2.06 0.00 1.67 2.11 0.00 0.52 1.10 1.63 1.09 3.70 3.17 2.09 0.00 1.25 3.22 0.00 0.00 2.10 0.00 0.00 4.40 0.00 6.75 1.06 2.88 104.27 4.25 5.65 * 1.65 189.58 4.43 5.90 ns — * ** p test significant at the 0.05 and 0.01 probability level, respectively, and ns = F-test not significant at the 0.05 probability level; _ RE(%) = relative efficiency of the Simple Lattice Design over the Randomized Block Design, (--- = no efficiency). % e a n s followed by the same letter are not significantly different based on SNK's multiple range test at the 0.05 probability level. 153 Appendix Table 13. Table of means for 25 maize hybrids grown at Cass County (Irrigated trial) during the 1986 summer season hybrid number grain yield (t/ha) 14 4 11 15 7 1 10 3 6 23 9 16 20 13 24 25 8 22 19 2 12 17 18 5 21 13.24 12.67 12.65 12.62 12.01 11.91 11.70 11.51 11.38 11.28 11.21 11.04 11.04 11.01 10.67 10.65 10.56 10.55 10.45 10.42 10.19 9.99 9.70 9.70 9.62 site mean CV(%) LSD(0.05) LSD(0.01) F-test RE(%) 11.11 3.93 0.62 0.82 ** •“* a * ab ab ab be be c cd cde cde cdef cdef cdef cdef defg defg defg defg efg efg fg g g g g grain yield (bu/acre) stalk lodging (%) root lodging (%) 204.21 195.33 195.09 194.59 185.25 183.66 180.36 177.53 175.41 173.94 172.93 170.25 170.23 169.71 164.51 164.30 162.88 162.66 161.14 160.70 157.11 154.10 149.59 149.54 148.42 2.89 3.80 1.88 5.84 1.16 1.64 3.90 4.21 1.03 3.48 8.66 1.37 0.39 1.51 1.91 4.45 3.21 3.34 0.78 2.95 3.45 1.77 3.51 3.48 1.79 2.51 2.62 2.50 2.50 2.08 4.83 2.00 0.53 1.70 3.62 1.50 2.00 1.09 0.50 1.75 3.26 1.60 2.02 1.50 0.53 2.01 1.50 7.50 1.00 0.00 2.90 106.37 4.37 5.81 ns 102 2.11 128.43 3.83 5.10 ns 171.34 3.93 9.50 12.64 ** “••“ .* ab ab ab be be c cd cde cde cdef cdef cdef cdef defg defg defg defg efg efg fg g g g g « _ m m mm ** F-test significant at the 0.01 probability level, and ns = F-test not significant at the 0.05 probability level; RE(%) = relative efficiency of the Simple Lattice Design over the Randomized Block Design, (--- = no efficiency). $means followed by the same letter are not significantly different based on SNK's multiple range test at the 0.05 probability level. 154 Appendix Table 14. Table of means for 25 maize hybrids grown at Huron County during the 1985 summer season hybrid number grain yield (t/ha) 7 8 14 20 5 17 19 11 15 10 3 21 1 4 16 6 13 23 9 2 18 12 24 25 22 10.98 10.98 10.97 10.77 10.71 10.54 10.49 10.46 10.36 10.16 10.16 10.02 9.96 9.94 9.93 9.89 9.70 9.67 9.49 9.38 9.04 8.79 8.78 8.48 8.42 site mean CV(%) LSD(0.05) LSD(0.01) F - test RE( %) 9.92 5.30 0.74 0.99 ** 101 grain yield (bu/acre) a* a a ab abc abc abc abc abc abed abed abede abede abede abede abede abede abede bedef cdef def ef ef f f 169.31 169.26 169.10 166.02 165.22 162.49 161.71 161.34 159.70 156.68 156.62 154.56 153.64 153.21 153.19 152.45 149.61 149.07 146.27 144.59 139.35 135.60 135.33 130.82 129.92 153.00 5.30 11.48 15.28 ** 101 a* a a ab abc abc abc abc abc abed abed abede abede abede abede abede abede abede bedef cdef def ef ef f f stalk lodging (%) root lodging (%) 0.00 1.68 1.05 0.51 1.61 1.16 1.52 1.62 1.54 0.00 1.59 1.05 2.13 0.00 0.00 0.52 2.18 1.74 2.83 0.00 3.33 2.15 0.00 0.57 2.13 0.00 0.00 0.52 1.02 2.11 0.51 1.56 0.54 1.55 1.04 3.76 6.20 0.00 0.52 2.06 1.06 1.67 0.50 4.26 3.02 0.60 0.00 1.02 0.00 3.80 1.24 143.04 2.51 3.33 ns 1.49 175.52 3.71 4.94 ns **F-test significant at the 0.01 probability level; ns = F-test not significant at the 0.05 probability level; RE(%) = relative efficiency of the Simple Lattice design over a Randomized Block Design, ( --- represents no efficiency). Cleans followed by the same letter are not significantly different based on SNK's multiple range test at the 0.05 probability level. 155 Appendix Table 15. Table of means for 25 maize hybrids grown at Huron County during the 1986 summer season hybrid number grain yield (t/ha) grain yield (bu/acre) stalk lodging <%) 14 24 20 2 7 19 13 4 15 11 16 10 25 6 21 12 3 23 17 1 5 8 18 9 22 9.64 8.80 8.78 8.75 8.66 8.62 8.49 8.45 8.37 8.35 8.31 7.99 7.80 7.80 7.66 7.65 7.50 7.50 7.39 7.19 6.66 6.65 6.51 6.42 5.82 148.72 135.73 135.45 134.92 133.58 132.89 130.94 130.26 129.13 128.79 128.17 123.28 120.27 120.23 118.13 117.95 115.71 115.68 114.00 110.85 102.67 102.58 100.37 98.99 89.75 0.00 0.51 3.64 1.04 5.58 2.86 2.55 0.52 3.08 0.50 0.53 1.02 1.52 4.58 2.56 3.66 4.13 2.59 4.13 2.08 3.09 4.58 1.75 4.60 3.61 1.17 0.50 0.14 0.38 3.36 0.58 0.69 4.73 5.97 4.08 1.53 4.17 0.09 9.04 1.88 6.93 13.33 6.31 0.40 0.00 0.10 2.18 2.20 1.00 1.84 site mean CV(%) LSD(0.05) LSD(0.01) F -test RE( %) 7.83 2.74 0.30 0.40 ** 103 2.59 95.47 3.50 4.66 * — “ 2.90 123.98 5.09 6.78 ** 101 a* b b b b b b b be be be cd de de de de ef ef ef f g g g g h 120.76 2.74 4.69 6.24 ** 103 a* b b b b b b b be be be cd de de de de ef ef ef f g g g g h root lodging (%) *,** F-test significant at the 0.05 and 0.01 probability levels, respectively; RE(%) = relative efficiency of the Simple Lattice design over the Randomized Block Design, (--- = no efficiency). ^neans followed by the same letter are not significantly different based on SNK's multiple range test at the 0.05 probability level. 156 Appendix Table 16. Table of means for 25 maize hybrids grown at: Ingham County (M.S.U. field plots) during the 1985 summer season grain hybrid yield number (t/ha) 15 6 4 1 14 24 10 11 16 7 2 23 20 13 8 3 5 17 9 22 19 21 25 18 12 11.43 11.42 11.22 11.17 11.06 11.06 10.92 10.81 10.80 10.69 10.62 10.48 10.40 10.40 10.27 10.22 10.18 9.94 9.61 9.60 9.54 9.23 9.05 8.92 8.90 site mean 10.32 CV(%) 2.81 LSD(.05) 0.41 LSD(.01) 0.55 ** F-test RE( %) 125 a* a ab ab abc abc abed abede abede bede bede cdef cdef cdef def ef ef fg gh gh gh hi hi i 1 grain yield (bu/acre) stalk root ear lodging lodging height (cm) (%) (%) plant ht (cm) 176.18 a* 176.10 a 173.05 ab 172.25 ab 170.58 abc 170.57 abc 168.38 abed 166.64abcde 166.54abcde 164.91 bede 163.78 bede 161.67 cdef 160.40 cdef 160.30 cdef 158.34 def 157.55 ef 156.96 ef 153.23 fg 148.19 gh 148.10 gh 147.05 gh 142.28 hi 139.52 hi 137.54 i 137.31 i 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.56 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.58 0.00 0.00 0.00 0.00 0.00 0.63 1.58 3.37 1.56 0.58 2.19 2.72 3.10 2.02 0.51 0.00 1.12 0.53 0.00 2.15 4.56 1.58 2.13 1.16 0.00 1.85 1.04 1.21 1.22 0.56 101.8 87.2 103.1 99.4 88.3 99.8 107.1 99.9 99.4 102.0 98.2 105.0 77.9 74.6 84.5 78.2 61.3 86.3 86.6 90.8 77.4 85.7 103.7 82.5 88.5 232.1 220.3 224.8 221.6 235.9 227.1 235.0 234.2 221.4 245.5 229.9 230.3 220.8 227.7 232.2 210.5 200.7 222.4 221.7 235.9 221.0 220.6 242.3 218.1 243.5 0.05 765.85 0.49 0.66 ns 1.49 120.89 5.09 6.78 ns »«••_ 90.8 3.1 4.7 6.3 ** 365 227.0 3.1 11.8 15.8 ** 231 159.10 2.81 6.33 8.42 ** 125 ** F-test significant at the 0.01 probability level, and ns = F-test not significant at the 0.05 probability level; RE(%) = the relative efficiency of the Simple Lattice Design ^over the Randomized Block Design, (--- = no efficiency). means followed by the same letter are not significantly different based on SNK's multiple range test at the 0.05 probability level. 157 Appendix Table 17. Table of means for 25 maize hybrids grown at: Ingham County (M.S.U. field plots) during the 1986 summer season grain hybrid yield number (t/ha) 14 15 10 11 24 4 6 1 20 3 16 7 8 23 2 19 9 22 17 13 21 25 12 5 18 12.06 11.39 11.37 11.22 10.90 10.74 10.59. 10.59 10.47 10.35 10.08 10.00 9.90 9.83 9.67 9.63 9.41 9.41 9.40 9.19 8.89 8.74 8.37 8.35 8.27 site mean 9.95 CV(%) 2.27 LSD(.05) 0.32 LSD(.01) 0.43 ** F-test RE( %) 108 grain stalk root ear plant yield lodging lodging ht ht (bu/acre) (%) (%) (c m ) (cm) a* b b b c cd cd cd cd de ef ef f fg fg fgh gh gh gh hi ij j k k k 185.99 175.59 175.30 173.00 168.04 165.58 163.36 163.32 161.44 159.54 155.38 154.13 152.69 151.58 149.12 148.51 145.17 145.13 145.02 141.65 137.03 134.77 129.06 128.70 127.50 14.35 9.68 15.60 22.86 10.15 9.82 14.95 14.12 5.45 10.05 11.58 8.06 11.60 11.47 6.23 4.64 9.15 11.37 3.28 5.57 10.52 9.48 16.31 6.14 10.18 0.00 0.00 0.00 0.00 3.18 4.23 0.00 5.05 0.00 0.50 0.52 0.00 0.00 3.00 2.66 0.00 0.00 0.52 0.00 0.00 0.00 0.00 1.00 0.00 1.02 153.46 2.27 4.94 6.58 ** 108 10.50 53.48 7.96 10.59 ** 105 0.87 287.55 3.53 4.7 ns “"*•“ of cobs per 100 plants 91.3 102.2 99.2 100.8 103.3 103.7 81.0 106.3 75.4 87.9 96.8 92.5 73.4 99.5 103.7 77.2 82.6 101.7 84.6 70.6 82.0 99.2 94.4 60.5 83.7 245.2 248.0 238.5 237.8 236.8 239.7 222.0 240.8 233.7 226.8 242.9 240.8 238.4 236.1 246.4 232.6 230.5 248.6 237.9 230.0 226.2 247.7 253.5 215.8 231.2 98.9 111.9 106.2 108.9 113.2 108.4 105.2 113.4 103.7 105.7 111.2 102.1 98.9 108.3 100.9 107.8 98.8 97.4 105.7 101.7 99.0 97.2 99.7 108.2 99.0 90.1 5.7 7.2 9.6 ** 102 237.1 2.9 9.8 13.1 ** 108 104.5 5.2 7.7 10.2 ** ** F-test significant at the 0.01 probability level, and ns = F-test not significant at the 0.05 probability level; RE(%) = relative efficiency of the Simple Lattice Design over the Randomized Block Design, (--- * no efficiency). Cleans followed by the same letter are not significantly different based on SNK's multiple range test at the 0.05 probability level. 158 Appendix Table 18. Table of means for 25 maize hybrids grown at Kalamazoo County during the 1985 summer season hybrid number grain yield (t/ha) grain yield (bu/acre) stalk lodging (%) root lodging (%) 14 20 4 10 15 11 1 19 21 7 3 16 18 6 8 13 23 22 24 9 17 2 5 12 25 8.47 8.35 8.35 8.27 8.23 8.02 7.96 7.66 7.49 7.44 7.21 7.16 7.04 6.99 6.98 6.93 6.79 6.12 6.10 6.06 6.00 5.94 5.80 5.58 5.54 130.57 128.80 128.79 127.57 126.89 123.64 122.72 118.09 115.50 114.67 111.21 110.44 108.57 107.86 107.61 106.86 104.71 94.40 94.04 93.38 92.56 91.55 89.48 86.04 85.48 1.10 0.54 2.22 2.10 1.62 2.21 1.56 2.55 1.67 1.58 4.81 1.00 2.69 0.50 1.06 1.15 0.00 1.64 4.22 1.62 1.14 1.56 2.03 1.14 1.04 0.03 1.06 0.68 0.53 0.06 0.00 0.97 0.00 4.03 0.03 1.32 0.22 2.09 1.33 1.61 0.11 0.64 0.00 0.55 1.63 0.43 0.71 0.72 0.00 0.06 site mean CV(%) LSD(0.05) LSD(0.01) F - test RE( %) 7.06 6.03 0.60 0.80 ** 1.71 109.74 2.66 3.54 ns “•™™“ 0.74 221.15 2.31 3.08 ns 106 a* ab ab ab ab abc abc abed bed bed cd cd d d d d de ef ef ef ef ef f f f 108.86 6.03 9.30 12.38 ** a* ab ab ab ab abc abc abed bed bed cd cd d d d d de f ef ef ef ef f f f ** p - test significant at the 0.01 probability leve, and ns = F - test not significant at the 0.05 probability level; RE(%) = relative efficiency of the Simple Lattice design over the Randomized Block Design, (--- = no efficiency). $ means followed by the same letter are not significantly different based on SNK's multiple range test at the 0.05 probability level. 159 Appendix Table 19. Table of means for 25 maize hybrids grown at Kalamazoo County during the 1986 summer season hybrid number grain yield (t/ha) 11 14 3 20 7 10 8 2 1 4 24 19 15 6 12 23 13 16 9 22 21 25 5 17 18 11.02 10.89 10.51 10.47 10.40 10.40 10.40 10.29 10.06 9.60 9.55 9.50 9.50 9.46 9.43 9.36 9.11 9.04 8.75 8.67 8.62 8.57 8.35 8.29 8.22 site mean CV(%) LSD(0.05) LSD(0.01) F - test RE( %) 9.54 4.63 0.63 0.83 ** 109 grain yield (bu/acre) a* a ab ab abc abc abc abc abed bede bede bede bede bede bede cde def def ef ef ef ef f f f 169.90 167.93 162.07 161.52 160.40 160.38 160.37 158.69 155.08 148.03 147.23 146.52 146.49 145.88 145.34 144.35 140.40 139.33 134.94 133.64 132.94 132.13 128.76 127.80 126.80 147.08 4.63 9.64 12.83 ** 109 a* a ab ab abc abc abc abc abed bede bede bede bede bede bede cde def def ef ef ef ef f f f stalk lodging (%) root lodging (%) 2.00 1.06 1.54 1.56 3.52 3.56 2.04 5.19 4.73 5.29 2.62 2.13 4.06 2.04 6.65 3.56 3.13 1.71 3.00 0.00 2.54 2.74 4.69 0.51 3.56 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.94 88.40 3.64 4.85 ns 0.00 — — — — ------------— •— — — ** F-test significant at the 0.01 probability level, and ns = F-test not significant at thei 0.05 probability level; RE(%) = relative efficiency of the Simple Lattice design over the Randomized Block Design, (--- = no efficiency). ^ means followed by the same letter are not significantly different based on SNK's multiple range test at the 0.05 probability level. 160 Appendix Table 20. Table of means for 25 maize hybrids grown at Monroe County during the 1985 summer season hybrid number grain yield (t/ha) 14 15 3 4 8 7 11 10 6 9 1 24 2 25 20 13 19 5 16 17 23 12 18 21 22 12.94 12.82 12.70 12.65 12.54 12.44 12.42 12.41 11.98 11.57 11.53 11.42 11.07 10.93 10.75 10.72 10.70 10.55 10.48 10.31 10.29 9.97 9.74 9.64 9.23 site mean CV(%) LSD(0.05) LSD(0.01) F-test RE( %) 11.27 2.11 0.34 0.45 ** a * ab ab ab ab b b b c d d d e ef efg efg efg fg fg gh gh hi i i j grain yield (bu/acre) stalk lodging (%) root lodging (%) 199.51 197.69 195.78 195.11 193.34 191.78 191.46 191.34 184.78 178.45 177.82 176.11 170.75 168.53 165.74 165.36 164.93 162.68 161.55 158.98 158.70 153.76 150.17 148.69 142.32 3.44 1.83 8.27 3.00 3.88 1.64 2.27 1.63 3.22 2.28 1.80 5.03 4.81 1.30 3.06 5.27 5.09 7.81 3.36 1.18 0.15 3.43 2.92 6.13 7.56 1.53 5.23 1.03 4.26 2.14 0.00 5.24 2.05 0.53 0.51 4.61 1.60 5.19 1.71 0.63 1.76 2.67 1.51 1.62 1.06 2.07 1.09 1.74 2.00 4.56 3.61 110.13 5.64 7.51 ns 101 2.25 131.67 4.20 5.59 ns 173.81 2.11 5.18 6.90 ** •™ — a* ab ab ab ab b b b c d d d e ef efg efg efg fg fg gh gh hi i i j ** F-test significant at the 0.01 probability level, and ns = F-test not significant at the 0.05 probability level; RE(%) 3 relative efficiency of the Simple Lattice Design over the Randomized Block Design, (--- = no efficiency). ^neans followed by the same letter are not significantly different based on SNK's multiple range test at the 0.05 probability level. 161 Appendix Table 21. Table of means for 25 maize hybrids grown at Monroe County during the 1986 summer season hybrid number grain yield (t/ha) 14 15 11 7 8 4 10 20 6 19 9 23 24 3 25 13 12 17 5 22 16 2 1 21 18 12.87 12.76 12.20 12.18 11.66 11.61 11.33 11.28 11.19 11.11 11.10 10.96 10.82 10.76 10.21 10.18 10.16 9.94 9.93 9.91 9.86 9.83 9.81 9.73 9.45 site mean CV(%) LSD(0.05) LSD(0.01) F-test RE( %) 10.83 5.02 0.77 1.02 ** « « _ mm grain yield (bu/acre) a* a ab ab be be bed bed bed bede bede cdef cdef cdef defg defg defg efg efg efg fg fg fg fg g 198.49 196.75 188.07 187.83 179.80 179.07 174.76 173.89 172.57 171.35 171.11 169.06 166.91 165.87 157.42 157.03 156.66 153.35 153.20 152.75 152.07 151.57 151.24 150.06 145.72 167.06 5.02 11.87 15.81 ** a* a ab ab be be bed bed bed bede bede cdef cdef cdef defg defg defg efg efg efg fg fg fg fg g stalk lodging (%) root lodging (%) 3.00 9.12 5.67 6.54 6.52 6.24 6.53 5.27 8.64 8.22 6.83 6.62 6.45 4.67 6.05 5.52 6.82 3.68 9.87 5.30 3.09 5.26 5.10 5.31 11.51 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 6.31 77.65 6.94 9.24 ns 114 0.00 ------------- ** F-test significant at the 0.01 probability level, and ns = F-test not significant at the 0.05 probability level; RE(%) = relative efficiency of the Simple Lattice Design over the Randomized Block Design, (--- = no efficiency). ^means followed by the same letter are not significantly different based on SNK's multiple range test at the 0.05 probability level. 162 Appendix Table 22. Table of means for 25 maize hybrids grown at Montcalm County (dryland trial) during the 1985 summer season hybrid number grain yield (t/ha) 14 3 21 8 6 13 15 4 20 2 24 10 11 5 12 23 7 9 16 1 25 18 17 19 22 11.95 11.52 11.46 11.39 11.37 11.31 11.08 11.06 10.97 10.94 10.80 10.79 10.67 10.54 10.49 10.39 10.29 10.21 10.01 9.97 9.92 9.66 9.40 9.22 9.17 site mean CV(%) LSD(0.05) LSD(0.01) F-test RE( %) 10.58 2.86 0.43 0.57 ** a* ab abc abc abc bed bede bede bede bedef cdefg cdefg defg efgh efgh efgh fgh ghi hi hi hi ij j j j grain yield (bu/acre) stalk lodging (%) root lodging (%) 184.32 177.65 176.68 175.65 175.33 174.38 170.89 170.49 169.17 168.73 166.48 166.40 164.58 162.45 161.70 160.13 158.66 157.46 154.32 153.70 152.96 148.94 144.88 142.10 141.41 0.00 0.00 1.03 0.00 0.53 0.00 0.00 0.00 0.52 1.04 0.51 0.00 0.57 0.63 0.00 0.00 0.00 0.00 1.09 0.00 0.56 1.10 0.00 0.51 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.54 0.00 0.52 0.53 0.53 0.00 0.00 0.00 0.54 0.00 0.00 0.00 0.00 0.54 0.00 0.32 282.69 1.29 1.72 ns 0.13 421.81 0.77 1.02 ns 163.18 2.86 6.61 8.80 ** a* ab abc abc abc bed bede bede bede bedef cdefg cdefg defg efgh efgh efgh fgh ghi hi hi hi ij j j j ** F-test significant at the 0.01 probability level, and ns = F-test not significant at the 0.05 probability level; RE(%) = relative efficiency of the Simple Lattice Design over the Randomized Block Design, (--- = no efficiency). ^means followed by the same letter are not significantly different based on SNK's multiple range test at the 0.05 probability level. 163 Appendix Table 23. Table of means for 25 maize hybrids grown at Montcalm County (dryland trial) during the 1986 summer season hybrid number grain yield (t/ha) 14 11 20 24 19 15 7 10 13 12 3 21 4 6 23 25 17 22 2 8 9 18 16 1 5 12.32 11.85 11.19 11.13 11.05 10.95 10.84 10.75 10.64 10.54 10.38 10.29 10.12 10.07 9.94 9.73 9.59 9.56 9.51 8.83 9.77 8.67 8.66 8.66 8.27 site mean CV(%) LSD(0.05) LSD(0.01) F-test RE(%) 10.09 2.31 0.33 0.44 ** 101 a* b c c cd cde cdef cdefg defg efgh fghi ghi hij hij ijk jk k k k 1 1 lm lm lm m grain yield (bu/acre) stalk lodging (%) root lodging (%) 190.04 182.73 172.61 171.67 170.32 168.89 167.11 165.83 164.01 162.50 160.05 158.67 156.02 155.30 153.29 150.06 147.82 147.42 146.61 136.09 135.24 133.62 133.61 133.61 127.53 3.26 4.23 4.56 7.03 2.86 2.47 5.76 4.82 3.69 4.36 4.48 5.00 8.53 8.09 3.46 2.78 5.45 4.20 5.63 8.77 8.66 7.89 7.33 7.00 2.74 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.50 0.00 0.00 0.00 0.00 0.00 0.50 1.50 0.00 3.00 0.00 0.00 0.00 1.00 0.00 0.00 0.50 5.32 59.29 4.47 5.95 ns 110 0.28 342.09 1.34 1.78 A* 155.62 2.31 5.09 6.77 ** 101 a* b c c cd cde cdef cdefg defg efgh fghi ghi hij hij ijk jk k k k 1 1 lm lm lm m — ** F-test significant at the 0.01 probability level, and ns = F-test not significant at the 0.05 probability level; RE(%) = relative efficiency of the Simple Lattice Design over the Randomized Block Design, (--- = no efficiency). means followed by the same letter are not significantly different based on SNK's multiple range test at the 0.05 probability level. 164 Appendix Table 24. Table of means for 25 maize hybrids grown at Montcalm County (irrigated trial) during the 1985 summer season hybrid number grain yield (t/ha) 25 16 12 1 15 11 10 9 22 4 14 24 23 13 3 2 17 7 20 19 8 18 6 5 21 13.52 13.35 13.18 13.03 13.01 12.91 12.89 12.76 12.73 12.72 12.55 12.50 12.46 12.19 12.06 11.89 11.86 11.78 11.74 11.57 11.56 11.16 10.97 10.91 10.18 site mean CV(%) LSD(0.05) LSD(0.01) F-test RE( %) 12.22 1.98 0.34 0.46 ** 101 a* ab abc bed bed bed bed cd cd cd de def def efg fgh gh gh gh gh hi hi ij j j k grain yield (bu/acre) stalk lodging (%) root lodging (%) 208.55 205.90 203.19 200.88 200.56 199.13 198.73 196.69 196.31 196.19 193.49 192.68 192.08 188.02 186.01 183.34 182.88 181.68 181.02 178.47 178.32 172.03 169.14 168.29 157.02 0.56 0.54 0.54 0.52 0.00 1.09 0.54 1.60 0.53 0.00 0.00 0.00 1.14 1.11 1.09 0.53 1.16 0.00 1.14 0.56 0.00 0.60 1.11 0.00 0.51 0.00 0.00 0.00 0.99 0.00 0.00 0.21 0.26 0.00 0.80 0.05 0.59 0.44 0.00 0.14 0.68 0.00 0.16 0.00 0.56 1.32 0.00 1.10 0.19 0.21 0.59 221.44 1.85 2.46 ns 0.27 315.39 1.19 1.58 ns 128 188.42 1.98 5.29 7.04 ** 101 a^ ab abc bed bed bed bed cd cd cd de def def efg fgh gh gh gh gh hi hi ij j j k ** F-test significant at the 0.01 probability level, and ns = F-test not significant at the 0.05 probability level; RE(%) = relative efficiency of the Simple Lattice Design over the Randomized Block Design, (--- = no efficiency. ^means followed by the same letter are not significantly different based on SNK's multiple range test at the 0.05 probability level. 165 Appendix Table 25. Table of means for 25 maize hybrids grown at Montcalm County (Irrigated trial) during the 1986 summer season hybrid number grain yield (t/ha) 14 11 25 3 20 13 7 19 6 10 2 4 21 15 12 24 23 22 17 8 1 18 9 16 5 14.76 14.14 13.93 13.82 13.81 13.32 13.32 13.24 13.12 13.00 12.94 12.92 12.92 12.75 12.62 12.32 12.30 11.85 11.56 11.55 11.43 11.06 11.02 10.82 10.37 site mean CV(%) LSD(0.05) LSD(0.01) F-test RE( %) 12.60 2.45 0.44 0.58 ** ™ " a* b b be be cd cd cd d d de de de de de ef ef fg gh gh gh hi hi i j grain yield (bu/acre) stalk lodging (%) root lodging (%) 227.62 218.09 214.82 213.12 213.02 205.38 205.37 204.22 202.26 200.45 199.61 199.30 199.29 196.56 194.67 189.91 189.75 182.80 178.28 178.16 176.21 170.60 169.90 166.80 159.98 1.03 1.50 0.54 2.00 1.00 1.00 1.00 2.00 1.50 3.50 2.50 1.50 2.00 2.00 2.51 1.50 2.00 1.51 1.00 3.03 3.50 2.00 4.57 0.50 5.50 2.74 5.78 4.80 4.79 0.79 0.18 1.75 0.11 0.00 3.65 1.50 6.73 0.00 4.34 2.45 4.94 0.00 4.22 0.00 0.00 4.84 4.64 2.51 1.73 0.40 2.03 98.10 2.82 3.75 ns 2.47 121.78 4.27 5.68 ** 104 194.25 2.45 6.75 8.98 ** a* b b be be cd cd cd d d de de de de de ef ef fg gh gh gh hi hi i j ** F-test significant at the 0.01 probability level, and ns = F-test not significant at the 0.05 probability level; RE(%) = relative efficiency of the Simple Lattice Design over the Randomized Block Design, (--- = no efficiency). means followed by the same letter are not significantly different based on SNK's multiple range test at the 0.05 probability level.