E!!! 3 uh limit! /I (D d (3 ~13 This is to certify that the thesis entitled GENOTYPE-ENVIRONMENT EFFECTS IN OATS presented by John Barnard has been accepted towards fulfillment of the requirements for FL D degree in @247 0—7639 ABSTRACT GENOTYPE-ENVIRONMENT EFFECTS IN OATS BY John Barnard The genotype-environment effects in the yield compon- ents of oats were investigated. The yield components of oats; panicle number, seeds per panicle, and seed weight, develop sequentially. Consideration of the developmental sequence led to the analysis of each component after adjust- ment for the effects of preceding components in the se- quence. Analysis demonstrated the importance of prior yield components in determining the variability of a given component. In the case of the component seeds per panicle, adjustment for panicle number resulted in no residual environmental effect. In the case of seed weight, adjust- ment for prior components enhanced both genotypic and environmental effects when these were compared with unad- justed values. In no case was genotype by environment interaction modified by the adjusted analysis. GENOTYPE-ENVIRONMENT EFFECTS IN OATS BY John Barnard A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Crop and Soil Science 1978 ACKNOWLEDGMENTS The author expresses his deepest appreciation to Dr. Grafius, his advisor for the duration of his graduate study. Thanks are also due Professors Adams, Cress, Magee, Harrison and D. Smith who formed the author's examining committee. ii TABLE OF CONTENTS INTRODUCTION. . . . . . . . . . . . . LITERATURE REVIEW 0 O O O O O O O O 0 Analysis of Genotype-Environment Experiments. . . . . . . . . . Environment and Yield Components MATERIALS AND METHODS . . . . . . . . RESULTS . . . . . . . . . . . . . . . DISCUSSION. . . . . . . . . . . . . . LITERATURE CITED 0 O O O O O O O O I I iii Page 10 15 20 28 31 Table 10 ll 12 l3 14 LIST OF TABLES GE analysis of variance following model [1]. . GE analysis of variance partitioning total within genotype variation by regression on environment. . . . . . . . . . . . . . . . . . GE analysis of variance partitioning GE interaction. . . . . . . . . . . . . . . . . . GE analysis of variance assuming an inde- pendent estimate of environment. . . . . . . . Analysis of variance for seed yield, W(log gms m‘z) . . . . . . . . . . . . . . . . Analysis of variance for tiller number, X(log) . . . . . . . . . . . . . . . . . . . . Analysis of variance for seeds per panicle, Y(log) o o o o o o o o o o o o o o o o o o o 0 Analysis of variance for seed weight, Z(log mg). . . . . . . . . . . . . . . . . . . Adjusted analysis of variance for seeds per panicle, Y, eliminating the linear effect of X within environments. . . . . . . . . . . . . Adjusted analysis of variance for seed weight, Z, eliminating the linear effects of X and Y within environments . . . . . . . . Analysis of variance for seed yield, W(log gms m‘z) . . . . . . . . . . . . . . . . Analysis of variance for seed number, XY(log m‘z). . . . . . . . . . . . . . . . . . Analysis of variance for seed weight, Z(log mg). . . . . . . . . . . . . . . . . . . Adjusted analysis of variance for seed weight, Z, eliminating the linear effect of XY within environments . . . . . . . . . . . . . . . . . iv Page 11 23 23 24 24 25 25 26 26 27 27 INTRODUCTION Genotype by environment analyses are of considerable importance in determining ranges of adaptation and in detecting the success of selection over a range of environ- ments. Much interest is centered on the genotype-environment interaction which is defined as the failure of a set of genotypes to maintain the same relative performance when grown in different environments. A consideration of the genotype-environment interaction in plant breeding leads to a choice of producing (i) widely adapted varieties giving acceptable performance in several environments, or (ii) varieties which are more particularly adapted to specific environments (Frankel, 1958). The two approaches are not mutually exclusive and their relative merits will depend on the specifics of the crop in question. The influence of environment on the yield component sequence appears to be complex. Yield components are not independent of each other but comprise a multivariate system. Observations on one component contain information that is often, if not always, to an extent confounded with that of previous events in the sequence. It is of interest to examine the character of a com- ponent in a sequential system in isolation from prior events in the said system. Analyses that separate 'prior' and 'present' sources of variability not only provide new in- formation on the character of the component in question but also permit an explicit assessment of the degree of influence of prior components. The present work examines the genotype-environment relationships in the yield component sequence of oats. A comparison is drawn between analyses performed when prior components in the sequence are ignored and when they are (linearly) eliminated. LITERATURE REVIEW Analysis of Genotype-Environment Experiments Statistical treatments of the genotype-environment, henceforth abbreviated as GE, interaction are based on the widely used concept of the linear model. Acceptance of the linear model allows observations on random variables to be additively partitioned into components of variation, the components being generally ascribable to known (or presumed) sources of variation. Under the circumstances of a suitably designed experi- ment the linear model permits an evaluation of the relative contributions of these components to total variation by means of the analysis of variance and related techniques. Let an experiment be constructed with t genotypes grown in s environments with ith genotype repeated r times within the jth environment; then under the assumption of a linear model the performance, with respect to some charac- teristic, of the kth replicates of the ith genotype in the jth environment may be represented by Yijk such that =u+di+ej+g..+u l] ijk [l] Yijk where u is the general mean, estimated by Y.../rst, di is the genetic effect due to the ith genotype, 3 e. is the environmental effect due to the jth environ- ment, gij is the GE effect due to the ith genotype being grown in the jth environment, uijk is the error associated with the kth replicate of the ith genotype grown in the jth environment. For the usual tests of significance the assumption is made that the u. 2 ijk N(o,o ). Analysis of variance of this simple form of GB model may follow a partition of degrees of freedom as in Table 1.1 In the GE models to be considered various subdivisions of within genotype variation are made. Rowe and Andrew (1964) and Eberhart and Russell (1966) partition within genotype variation into degrees of freedom due to regression on an estimate of the environmental com- ponent and deviations from this regression. This approach, first described by Yates and Cochran (1938) assumes a linear relationship of the form: Yij = Yi + Biej + 6ij [2] where §ij is the mean of the ith genotype grown in the jth environment, 1Throughout this discussion it will be assumed, for simplicity, that variation due to replication within environ- ments and variation due to genotype-replicate interaction within environments can be pooled to give a valid estimate of experimental error. .n n n\ .Mwww n x.wwwww Aanuvum nouns .0 oh. and .HH umn\. mw+uu\ .mww I mu\ www u u\ .wwww AeanAHIuv mo oh. umu\...mw I uu\ .Nww Him mpcmecoufl>cm AHImVu mommuocmm cflnuflz pmH\...Nw I mu\..www HID mommuocmw mmuosqm mo Edm .m.U mousom Hag Hopes mGH3OHH0m moccanm> mo mHmMHmcm mm .H canoe is the mean of the ith genotype over all environ- ments, 8. is the coefficient of regression of §ij on the estimated environmental component, ej, 5ij is the deviation from regression in the (ij)th cell. Recognizing that §i = p + di, total degrees of freedom are partition as in Table 2. In Eberhart and Russell's treatment the regression co- efficients and the deviation sum of squares for each geno- type provide 'stability' parameters. A stable genotype is defined as one with unit regression coefficient and zero deviation sum of squares. An estimate of the environmental component is taken to be the environmental mean, Y.j./rt, however, it is recognized that the non-independent nature of these quantities vitiates strict F-tests. Finlay and Wilkinson (1963) also utilize the technique of regressing individual yields on environmental means to generate stability statistics.l Genotypes with regression coefficients approaching unity demonstrate an average sta- bility over all environments (i.e. a low order of interac- tion). Genotypes with coefficients less than or exceeding 1The interaction sum of squares with (t-l) degrees of freedom appearing in Finlay and Wilkinson's table 2 is some- what confusingly called regression sum of squares. It pre- sumably is a sum of squares due to differences, or hetero— geneity, of regression coefficients. Aauuvum Houum mum u mmmuocmw mum H mmmuocmw Amlmvu mcofiDMfi>mQ n n.n..nufl Anemcflav>emufiwmm\mk.m . swvmiw any Anemceav mo me\mamm.m.wv mm H Aummcflav mucmEconfl>cm Aalmvu mommuocmm segue: Hip mommpocmw mmnmsvm mo 89m .m.© mousom Ammma .Hammmsm cam unmcumnm “mummy ucmficoufi>cm :0 coflmmmumou an coflpmwnm> mmmuocmm cflcufl3 Hmuou mqwcowpfluumm moccaum> mo mwmwamcm mm .m magma unity demonstrate a greater or lesser than average stability respectively. Practical assessment of a particular genotype must be made, it is suggested, with reference to both the respective genotypic mean performance as well as regression coefficient. Other treatments of the GE analysis concern themselves with a partition of GE variation per se. Perkins and Jinks (1968) express the GE component, gij’ as a linear function of the environmental component gij = Bdiej + 6ij which when substituted into [1] gives a model of the form =u+di+e.+8diej+6..+u. [4] Yijk J 1] ljk Bdi being the regression coefficient for the ith genotype, Sij being the deviation from regression in the jth environ- ment. Proceeding from [4] Perkins and Jinks subdivide degrees of freedom as in Table 3. Significance of either heterogeneity or deviation mean squares indicates the presence of GE interaction. The relative magnitudes of the two mean squares indicates the reliability of the predictions made on the basis of regres- sion. Fripp and Caten (1971) point out that the parameters of [2] and the parameters of [4] are simply related. Bi is equal to l + Bdi' Table 3. GE analysis of variance partitioning GE inter- action (after Perkins and Jinks, 1968) Source d.f. Genotypes t-l Environments s-l GE (t-l)(s-l) Heterogeneity of regressions t—l Deviations (t-l)(s-2) Freeman and Perkins (1971) detail statistical objections to the use of non-independent estimates of the environmental component. They note that when non-independent estimates are in fact used the sum of squares for environment-linear in Table 2 is equal to the environment sum of squares in Table 3 with a consequent ambiguity in degrees of freedom. Free- man and Perkins propose to use independent estimates, say zj, such as control genotypes or additional replications, and suggest a model of the form: yij = p + di + sz + éj + Bdizj + 5dij in which Ezj + Sj is an expansion of the environmental com- ponent of [1] in terms of E, the coefficient of the combined regression of yij on zj, and Ej' the associated residuals. + 6 is an expansion of the GE component of [l] in Bdi terms of Bdi = B dij - E and 6dij = 6.. - 3. Although average i ij 10 stability will not necessarily be associated with a unit regression coefficient, as when environmental means replace the zj, less stable genotypes will be associated with larger coefficients and more stable genotypes will be asso- ciated with smaller coefficients. Under the circumstance that the Ej are (statistically) homogenous and B does not differ from unity than [6] reduces to [4].1 The analysis of variance procedes as in Table 4. Environment and Yield Components Grain yield in cereal crops is the product of a number of yield components (e.g. Grafius, 1965). Thus in oats the components are taken to be the morphological traits tiller number, seed number per panicle and seed weight. The com- plex trait grain yield is the numerical product of these components, is therefore completely determined by these components, and no change in yield can occur unless there are changes in one or more of these components. Yield components are not, in general, independent of each other in their expression but comprise a complex in— teracting system. The components are not formed simul- taneously but differentially in accordance with an onto- genetic sequence. Thus in the small grains tiller number is established before seed number per panicle, and the lIf environment mean is used to estimate e- then these two conditions will be fulfilled and [4] will be appropriate. ll “anuvum uouum Amumvxanuv Hmsowmmm h oh. n ohH .n H muw\muu\mA.N . MwVIH\NA.N ..>wvw_ Hip mGmemmummn mo muflmcmmoumumm Aaumvxauu. mo mum stcwmmm n n .n. .NNN\HDH\NA.N . wwva a cosmmmummu pecanEou Hum mucwscoufi>cm Hip mommuocow mmumnqm mo 85m .m.© wousom Aanma .mcflxumm can cmemmum Hmummv quEaOHH>Gm mo mumaflumm unoccmmmccfl so mcHESmmm mo:maum> mo mflmwamcm mw .v canoe 12 establishment of seed number per panicle precedes the determination of seed size. It may be postulated that in a finite environment, using environment, in the most general sense, there is com— petition for common resources between components within the plant with the result that negative associations would tend to be observed. Such is the case (Adams, 1967 and refer- ences). The notion of compensatory reaction in sequential components was first suggested by Adams (199. git.). Under conditions of constant but limiting environmental input it was proposed that a primary trait, say X, would utilize more or less input and a second trait, Y, would tend to use up any residual in a compensatory fashion. In a series of observations over a number of genotypes, each demonstrating a different degree of expression for X, X would then tend to be negatively correlated with Y. Under a second model of fluctuating environmental in- put, Adams explains compensation in terms of a phasing of input with the ontogeny of the plant. The interpretation of negative inter-component corre- lations as the result of environmental stresses during the growing season was made by Grafius (1969). Correlation coefficients computed on the basis of environment mean component values were used as an indication of between environment stress and as such measured the differential 13 distribution of environmental resources between environments. Correlation coefficients computed on the basis of genotype means within environments were used as a measure of within location stress. Low correlations were interpreted as a '1ess forced' developmental situation with less competition between components. Thomas gt a1. (1971 a,b,c) applied Gram-Schmidt ortho- gonalization to yield component sequences in barley and rice. Once again inter-component correlations were taken as an indication of stress existent in the genotype set within the environment where it was grown. Orthogonaliza- tion of the component data was used to adjust out the influence of correlation. A GE analysis (Thomas 22 31., 1971c) involving unadjusted and adjusted data demonstrated an enhanced role of GE interaction in determining variabil- ity in the adjusted data. A similar study undertaken by Voysest (1970) demon— strated changes in the importance of sources of variance. When the effects of prior traits were adjusted out of the yield component sequence an increase in the contribution of the GE interaction was observed. Grafius and Thomas (1971) examined the yield component sequence in oats by means of a second order recurrence equation. Convergently, divergently and continuously oscillating component sequences were considered. The l4 implication of weak 'direct' genetic control of later com- ponents in the sequence under conditions of significant oscillation was recognized. In particular it was observed that seed size was to a great extent determined by tiller number and seed number per panicle. MATERIALS AND METHODS Thirty six lines of oats were grown in three Michigan locations. At two locations measurements on tiller number per unit area (X), seed weight (Z) and grain yield per unit area (W) were taken. At the third location observa- tions on seed weight (Z) and grain yield (W) were taken. Seed number per panicle (Y) and seed number per unit area (XY) were computed from the relationships Y W / (X Z) XY W / Z Simple lattice designs with four replications were used at each location. The incomplete block structure was ig- nored for the present study. Logarithmic transformation of all data was effected prior to statistical analysis. GE relationships in the yield component sequence were examined by a comparison of source variation when the effects of the sequence were ignored and when the effects of the sequence were eliminated. Analysis ignoring sequence followed the partition in Table 1. To eliminate linear prior sequence effects model [7] was constructed. 15 16 n n m m n . " + . .. .. 13k m + d + e g1] + 1 b3 Yle + ule [7] In [7] ngk is the observation on the nth yield component of the ith genotype in the kth replicate of the jth environment, n m is the general mean of the nth yield component, d? is the genetic component due to the ith genotype for the nth yield component, e? is the environmental component due to the jth environment for the nth yield component, ggj is the GE component due to the ith genotype being grown in the jth environment, m