YTELD COMPONENT COMPENSATION IN MIXTURES OF OATS (Avena sativa L.) Thesis for the Degree of M. S. MICE-NOAH STATE UNWERSTTY ABUBAKER M. MR 1972 «in '3 t“ v. MICHIGAN SSSSSSSSSSSSSSSSSSS IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIILIIIIIIII 3 1293 0159143 LIBRARY Michigan State University “ “ am‘gms av “'5‘ "DAB 8 “NW I 1800K BIII'IFRY W I 'i ABSTRACT YIELD COMPONENT COMPENSATION IN MIXTURES OF OATS (Avena sativa L.) BY Abubaker M. Maddur Six oat varieties were compared with several mix- tures of the same varieties for yield and yield components. The mixtures were found to have affected the yield addi- tively and therefore no mixture yielded greater than the highest yielding variety in the mixture. A significant negative correlation was observed between the tiller num- ber (X) and the kernel per tiller number (Y), and negative, though insignificant, correlation between the latter com- ponent and the kernel weight (2). A remarkable disturb- ance in the tiller number has occurred in the mixtures which is believed to have resulted from some sort of com- petition between the mixed varieties. The disturbance in X components was not found to have any influence on the additive effect of the varieties on the mixtures' yield because Y and 2 that follow x in deve10pment showed a great flexibility in adjusting in a compensatory manner to changes Abubaker M. Maddur in X in a way that maintains the yield linearity. It is believed that yield component compensation was caused by intraplant competition due to stress. A positive relation was detected between the varietal differences in X and the disturbance in X caused in their mixtures. A hypothesis relating the amount of disturbance in the tiller number in the mixture to the range of that component between the mixed varieties was prOposed. YIELD COMPONENT COMPENSATION IN MIXTURES OF OATS (Avena sativa L.) BY Abubaker M. Maddur A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Crop and Soil Sciences 1972 ACKNOWLEDGEMENTS The author wishes to express deep acknowledgement to Dr. John E. Grafius who suggested and guided the current project and generously supplied encouragement and advice throughout the course of this investigation. He also wishes to extend acknowledgement to Dr. Carter M. Harrison for his appreciable advice and suggestions and for review- ing this manuscript. The author expresses great appreciation to Mr. John Barnard for his invaluable help.and advice in analyz- ing the data. Also thanks are extended to Dr. J. Clarel Denis for his fruitful suggestions. ii TABLE OF CONTENTS AC KNOWLE DGMENTS O O O O O O O O O O O O O O 0 LI ST OF TABLES O O O O O O O O O O O O O O 0 LIST OF FIGURES O O O O O O C O O O O O O O 0 INTRODUCTION . . . . . . . . . . . . . . . . LITERATURE REVIEW . . . . . . . . . . . . . . Varietal Mixtures Versus Pure Cultures . Varietal Interaction. . . . . . . . . . . Co-operation and Competition. . . . . . . Intraplant Competition and Yield Component Compensation . . . . . . . . . . . . . MTERIALS AND METHODS O O O O O O O 0 O O O 0 RESULTS 0 O O O O O O O O O O O O O O O O O 0 DISCUSSION 0 O O O O O O O O O O O O O O O O BIBLIOGRAPHY O O O O O O O O O O O O O O O 0 iii Page ii iv vii 10 12 15 47 56 Table LIST OF TABLES Yield and yield component means of four oat varieties, Ausable (A), Garry (G), Coachman (C) and Mi.60-106-78 (E) and nine mixtures. (Exp. 1) . . . . . . . . . . . . . . . . . . . Yield and yield component means of four oat varieties Coachman (C), Diana (D), Clintland 64 (L) and Mi.60-106-78 (E) and nine mix- tures. (Exp. 2) . . . . . . . . . . . . . . Yield and yield component means of four oat varieties Coachman (C), Diana (D), Clintland 64 (L) and Mi.60-l06-78 (E), and nine mix- tures. (Exp. 3) . . . . . . . . . . . . . . . Mean squares from analysis of variance tables for a randomized block design for yield (W) and its components (X, Y, Z) for the oat varieties and mixtures tested in experiment 1. Mean squares from analysis of variance tables for a randomized block design for yield (W) and its components (X, Y, Z) for the oat varieties and mixtures tested in experiment 2. Mean squares from analysis of variance tables for randomized block design for yield (W) and its components (X, Y, Z) for the oat vari- eties and mixtures tested in experiment 3. . . Means of yield and yield components of mixtures (M) compared with those of pure stands (P) in the three experiments . . . . . . . . . . . . Testing for curvilinear regression for yield (W) and yield components (X, Y, Z) of "Ausable" (A) and "Garry" (G) varieties and mixtures. (Exp. 1, graphed in Fig. l). . . . . . . . . . iv Page 16 17 18 19 19 20 21 22 LIST OF TABLES (Cont.) Table 10. ll. 12. 13. 14. 15. 16. 17. Testing for curvilinear regression for yield (W) and yield components (X, Y, Z) of "Garry" (G) and "Coachman" (C) varieties and mixtures. (Exp. 1, graphed in Fig. 2) . . . . . . . . . . Testing for curvilinear regression for yield (W) and yield components (X, Y, Z) of Coachman (C) and Mi.60-lO6-78 (E) varieties and mixtures. (Exp. 1, graphed in Fig. 3) . . . . . . . . . . Testing for curvilinear_regression for yield (W) and yield components (X, Y, Z) of Coachman (C) and "Diana" (D) varieties and mixtures. (Exp. 2, graphed in Fig. 4) . . . . . . . . . . Testing for curvilinear regression for yield (W) and yield components (X, Y, Z) of "Diana" (D) and "Clintland 64" (L) varieties and mixtures. (Exp. 2, graphed in Fig. 5) . . . . . . . . . . Testing for curvilinear regression for yield (W) and yield components (X, Y, Z) of "Clintland 64" (L) and "Mi.60-106-78" (E) and mixtures. (Exp. 2, graphed in Fig. 6) . . . . . . . . . . Testing for curvilinear regression for yield (W) and yield components (X, Y, Z) of "Diana" (D) and "Clintland 64" (L) varieties and mixtures. (Exp. 3, graphed in Fig. 7) . . . . . . . . . Testing for curvilinear regression for yield (W) and yield components (X, Y, Z) of "Clintland 64" (L) and "Mi.60-lO6-78" (E) varieties for mixtures. (Exp. 3, graphed in Fig. 8). . . . . Comparison between observed yield of mixtures and their calculated yield from the yield of their constituent varieties (Exp. 1). . . . . . . . . Comparison between observed yield of mixtures and their calculated yield from the yield of their constituent varieties (Exp. 2). . . . . . . . . Page 22 25 25 28 28 31 31 39 40 LIST OF TABLES (Cont.) Table 18. 19. 20. 21. 22. 23. 24. 25. Page Comparison between observed yield of mixtures and their calculated yield from the yield of their constituent varieties (Exp. 3) . . . . . 41 Comparison between observed yield of mixtures. and the calculated yield from the yield com- ponents of their contituent varieties (Exp. 1) . . . . . . . . . . . . . . . . . . . 42 Comparison between observed yield of mixtures and the calculated yield from the yield com- ponents of their constituent varieties (Exp. 2) . . . . . . . . . . . . . . . . . . . 43 Comparison between observed yield of mixtures and the calculated yield from the yield com- ponents of their constituent varieties (Exp. 3) . . . . . . . . . . . . . . . . . . . 44 Phenotypic correlations between yield and yield components in the three eXperiments for the varieties and the mixtures tested. . . . . . . 46 Correlation between the logarithms of yield and yield components for the varieties and mix- tures in the three experiments . . . . . . . . 46 Disturbance in mixtures' X component (calculated as the mean of mixture's absolute deviation of observed from calculated in the absence of varietal interaction) as related to the range in X component between the varieties. Both variables are expressed as the percentage of the experimental grand mean. . . . . . . . . . 53 Analysis of variance of the relationship between varietal range in X and the deviation in X of the mixtures O O O O O I O O O O O O O O O O O 53 vi Figure LIST OF FIGURES Component compensation and its effect on yield of "Ausable" and "Garry" oat varieties and two mixtures among them. (Exp. 1) . . . . . Component compensation and its effect on yield of "Coachman" and "Garry" oat varieties and two mixtures. (Exp. 1). . . . . . . . . . . Component compensation and its effect on yield of "Coachman" and Mi.60-106-78" oat vari- eties and two mixtures. (Exp. 1) . . . . . Component compensation and its effect on yield of "Coachman" and "Diana" oat varieties and two mixtures. (Exp. 2). . . . . . . . . . . Component compensation and its effect on yield of "Clintland 64" and "ciana" oat varieties and two mixtures. (Exp. 2) . . . . . . . . Component compensation and its effect on yield of "Clintland 64" and "Mi.60-106-78" oat varieties and two mixtures. (Exp. 2) . . . Component compensation and its effect on yield of "Clintland 64" and "Diana" oat varieties and two mixtures. (Exp. 3). . . . . . . . . Component compensation and its effect on yield of "Clintland 64" and "Mi.60-106-78" oat varieties and two mixtures. (Exp. 3) . . . Component compensation and its effect on yield of the three 4-varietal mixtures tested in experiment 1. . . . . . . . . . . . . . . . vii Page 23 24 26 27 29 30 32 33 34 LIST OF FIGURES (Cont.) Figure 10. Component compensation and its effect on yield of the three 4-varietal mixtures tested in experiment 2. . . . . . . . . . . . . . . . . 35 11. Component compensation and its effect on yield of the three 4-varietal mixtures tested in experiment 3. . . . . . . . . . . . . . . . . 36 12. The effect of differences in the X component between oat varieties on the disturbance in the X component of mixtures . . . . . . . . . 54 viii INTRODUCTION The traditional pattern in varietal deve10pment in oats and similar crOps is characterized by the release of varieties with a high degree of homogeneity, possessing a satisfactory adaptation to the predominant environmental conditions. Yield of seed in most CrOpS, though geneti- cally controlled, is a trait highly influenced by the en- vironment, and subject to a wide variation when growth conditions change. Yield and its stability can thus be considered a measure of accommodation of the plant to the Operating natural factors of growth. Under given environmental conditions, different oat varieties may show remarkable differences in yield, probably as a result of their differences in needs for growth and deve10pment, or because of differences in capa- bility of exploiting the available environmental resources. It has been argued for a long time that hetero- geneous pOpulations might be superior to homogeneous vari- etal pepulations in their efficiency in exploiting these environmental resources, and consequently might yield more . Yield in oats is a product of several components which are sequential in time, gene regulated, and highly influenced by growth conditions. Moreover these compon- ents are interdependent in their develOpment, and known to function in a compensatory manner in expressing the ultimate grain yield. The aim of this study is to determine whether varietal mixtures would have any superiority in yield over their component varieties, by observing the behavior of yield components in their interrelated function. LITERATURE REVIEW Varietal Mixtures Versus Pure Cultures Jensen and Kent (1963) warned that the genetic homogeneity that characterizes major domestic varieties of crOps may mask a disastrous agent that cannot be ob- served under some environmental conditions and therefore a superiority expressed by a given variety under some conditions may diminish when conditions change. Their examples were the two major diseases in cats, stem rust and crown rust. With the great number of races and subraces the causal pathogens are able to produce through hybridization and mutation, it becomes very diffi- cult to develOp a single variety resistant to all those existing and to new develOping races of the pathogens. A uniline variety with resistance to one or few races is apt to lose its resistance when new races are developed or are introduced into the area. The authors suggested multiline varieties built up of several lines that are similar in appearance but different in genetic structure to supple- ment the domestic varieties. Flor (1956) similarly reported that many flax varieties, developed as rust resistant, frequently yield to new races, or to changes in the prevalence of races of the pathOgen that attacks them. He suggested that this problem can be handled by deve10ping several varieties, where each variety carries different sets of genes for resistance and then pooling these varieties into a com- posite variety. Cournoyer, Browning and Jowett (1968) argued that oat mixtures supported less crown rust early in the season - than did the pure line varieties and that the progress of the epiphytotic was much slower in the multiline variety. In contrast Borlaug (1959) found that mixtures are not necessarily consistent in retarding the spread of diseases among pOpulations. From this point the argument of mixtures versus pure cultures was extended to investigation on other agro- nomic characters including lodging resistance, insect re- sistance and yield. A plant population made up of several genotypes differing in their environmental needs and biolOgical ac- tivities is believed to be more efficient than a pure cul- ture in eXploiting the available environmental resources to their maximum potential and therefore may produce a high and/or more consistent yield. The available information does not support absolute superiority of mixtures over the mean of pure cultures of their consitutent vari- eties under all circumstances, in either yielding ability or yield stability. Grafius (1966) mixed two oat vari- eties, "Simcoe" and "Rodney," with a third variety, "Garry" in 10% increments, and found that random mixtures are not expected to yield more than the mean yield of the vari- eties included in the mixtures. However, the superiority of the mixture 40:60% of "Rodney" and "Garry," in yield, lodging resistance, and test weight was observed. He sug- gested that the superiority of a multiline will depend on careful selection plus optimum proportions of the varieties, included in the mixture to take advantage of non-linear effects. Jensen (1965) compared oat composites with the mean of their component lines over a period of 8 years. The mixtures exceeded the average yield of the pure stands by 3.2%, and a 5-1ine oat multiline yielded 7.3% greater than the average yield of its component lines. A study on 6 oat cultivars and 57 mixtures among them by Frey and Maldonado (1967) produced several mistures yielding more than the best cultivar and the mixtures were more stable in production and showed a remarkable increased superiority when the environment became more stressed. In the meantime no association was found in this study between the number of cultivars in the mixtures and the grain yield of the mixtures. Patterson and co—workers (1963) compared for four years six varieties of oats and equal blends of the six in all combinations of two. Though the mixtures did not show any superiority in-yield, they were superior in their standing ability. On the other hand some of the literature does not support the consistent superiority of mixtures in either yield or other agronomic characters.’ A report by Clay and Allard (1969) found that barley mix- tures expressed small advantage over their component vari— eties. Moreover the mixtures were inferior in stability. Varietal Interaction Whenever a mixture of two or more lines shows a significant deviation from the sum of the proportional performances of the pure cultures of the lines included in the mixture, some sort of phenotypic interaction be- tween the lines is assumed to be involved. This type of interaction was reported by Probst (1957). In a mixture of soybean varieties, Probst observed that the latest maturing variety in a mixture matured earlier than a pure stand of the same variety. Jensen and Federer (1964) working with population mixtures of tall and short vari- eties of wheat found that the taller varieties enhanced the yield by five bushels per acre while the shorter ones reduced the yield by only 2.3 bushels per acre. Obviously, the enhancing and depressing effects did not behave in a compensatory manner, though they were additive in effect. The results shown by Grafius (1966) and Jensen (1965), also support the possibility of this kind of phenotypic interaction. Gustafsson (1953) compared the yield performance of three barley varieties, "Golden," "Maja," and "Bonus," with their paired mixtures under two levels of manuring and two sowing densities. When sowing was dense and man- ure application was low, the mixtures were superior to the mean of the component variety by 10%. When manure was increased, with the density level constant, the mixtures yield drOpped 7% below the mean yield of its component varieties. When the density tension was-relaxed and man- ure level was lowered the mixtures and the pure stands yielded the same. However,mixtures regained a remarkable superiority when the manure was increased even under sparse sowing conditions. Varietal mixtures reacted in a specific manner to the varied environments. Co—operation and Competition Whenever organisms grow in a limited space with limited environmental inputs, they may compete against each other in exploiting the environment or act in a co- operative pattern which leads to better use of the limited resources they share. Milthorpe (1961) referred to compe- tition in plants as ". . . those events leading to the retardation in growth of a plant which arise from associa- tion with other plants." Milthorpe set two conditions to be satisfied in order for competition to Operate. First, competing individuals should share similarity in needs and activities. Second, the summed needs of individuals must exceed the supply of these needs available to the indi- vidual plants, i.e. the supply of environmental inputs does not satisfy the demand for maximum level of biolog- ical activities. Mather (1961) noticed that adjacent organisms may develOp a co-operative relationship to retard the effect of a common adverse factor, while still competing for another factor. So plants may compete for one thing while co-Operating for another. The net outcome of such adverse relationships depends on the importance of the factors they co-Operate or compete for, the degree of co-operation and the severity of competition among them. Differences in competitive ability between organisms of different genera and among species of the same genus were reported by several researchers (De Wit, 1961; Mather, 1961; Sakai, 1961; and Sandfar, 1970). Sandfar (1970) in his report on competition stated that the selective value of a genotype is positively correlated to its performance in pure stands. He also expressed the view that gen- erally the frequency of high-yielding genotypes in mix- tures is expected to increase in the course of time but sometimes the results come out to prove the opposite. But the author obviously ignored the role of selection for seed size. Under natural selection in mixtures of annual seed bearing crops, weed-like types will produce relatively more seeds, and consequently more viable off- spring. Sakai (1961) found that competitive ability in plants is an inherited trait conditioned by polygenes and characterized by a very low heritability. Harper (1961), however believes that the success of one species in a mixture at the expense of other species may be a function of the differences in embryonic capital avail- able in the seeds of the two Species or due to other differences in agronomic features such as growth rate, growth form, or still to other differences that function in the life cycle of the species. Most if not all of these authors ignore the fact that weeds have small seeds and that natural selection will not produce high yields of seed in annual crOps. 10 Intraplant Competition and Yie omponent Compensation Grafius (1965) explained that the grain yield per unit area in oats can be represented geometrically by a volume (W) of a rectangular parallelepiped with di- mensions X, Y, and Z, representing the number of panicles per unit area, the average number of kernels per panicle, and the average kernel weight respectively, so that W = XYZ. In order to keep the yield stable, any change in one axis has to be counterbalanced by change in another. This is a general characteristic of well-adapted varieties which exhibit a nearly constant mean yield under the dominant environmental conditions in the area. The yield components were reported by several workers to exhibit a negative re- lationship among them (Adams 1967, Adams and Grafius 1971, Dewey and Lu 1959, Rasmusson and Cannell 1970). In an experiment on soybean, an artificial de- crease of component (X) was found by McAlister and Krober (1958) to result in increasing in component (Z). Adams (1967) in a review of yield component compensation in crop plants eXplained that these negative relationships among yield components are develOpmental in nature. Adams believes that under severe conditions of interplant compe- tition, available essential resources becomes inadequate to support the needs of individual plants. In consequence, 11 there ensues intraplant competition involving the fitness components for those environmental inputs essential in the development of reproductive structures which finally compel the yield components to vary in a compensatory manner. MATERIALS AND METHODS Six varieties of oats (Avena sativa L.) were selected for study in three experiments. In each ex- periment, four oat varieties and nine mixtures among them were tested in a randomized block design with six replications. The mistures were made by mechanical mixing of the number of seeds from each variety equiva- lent to its desired prOportion in a Specific mixture to form a total of 1000 seeds (or nearly 30 grams) per plot. The plots were four rows each. Rows were eight feet long and one foot apart. The middle two rows in every plot were used for data collection and the outer two rows served as borders. Experiment 1 The four varieties included in this experiment were "Ausable" (A), "Garry" (G), "Coachman" (C), and "Mi.-60-106-78" (E). The mixtures among them were 70%A:30%G, 30%A:70%G, 70%G:30%C, 30%C:70%C, 70%C:30%E, 30%C:70%E; 25%A:25%G:25%C:25%E; 10%A:10%G:40%C:40%E; and 40%A:40%G:10%C:10%E. 12 13 Experiment 2 In this experiment, "Diana" (D), and "Clintland 64" (L) varieties in addition to "Coachman" (C) and "Mi.- 60-106-78" (E) were studied with their following mixtures: 70%C:30%D; 30%C:70%D; 70%D:30%L; 30%D:70%L; 70%L:30%E; 30%L:70%E; 25%C:25%D:25%L:25%E; 10%C:10%D:40%L:40%E; and 40%C:40%D:10%L:10%E. Experiments 1 and 2 were carried out at the Michigan State University CrOp Science Research Farm. The oats for both experiments were sown in the second week of April, 1971. Experiment 3 This experiment was performed on a farm in Lenawee County, Michigan, and the seeds were sown 5 days earlier than experiments 1 and 2. The same varieties and mixtures tested in experiment 2 were tested in this experiment. However, because of an error during the time of sowing, data from Coachman plots in all replications were excluded. For that reason, this experiment was analyzed and handled separately. The major interest of the study was the grain yield and its morphological components. Data on these characters were collected in a similar way in the three experiments as follows: 14 Yield (W) The inner two rows in each plot were harvested the last week of July, and the seeds were dried and weighed and then the average yield per square foot was calculated. Yield Components (X,Y,Z) 1. Number of tillers (X) Twelve days prior to harvesting the tillers in 30 inches from each of the two middle rows were counted and the average number of tillers per square foot was obtained. 2. Average Kernel Weight (Z) The number of grains contained in a random sample of three grams of grain was counted using an electrical counter and the average kernel weight calculated. 3. Number of Kernels per Tiller (Y) Kernels per tiller (Y) were calculated by dividing the average yield per square foot (W) by the product of the number of tillers per square foot (X) and the average kernel weight (2). RESULTS The mean yield (W) and its components (X,Y,Z) of the thirteen entries included in each experiment are sum-v marized in Tables 1, 2, and 3. The mean squares for the four varieties taken from analysis of variance tables are presented in Tables 4, 5, and 6. It is obvious from Tables 1, 2, and 3, that in no case did the yield of any mixture exceed the yield of its highest yielding component variety. Sets of each two varieties with the two mixtures of each were separately tested for curvilinear regression for yield and its components (Tables 8 through 15). The pattern of yield and components were further traced graph- ically (Figures 1 through 8). Figures 9, 10, and 11 illu- strate the responses of yield and components of those mix- tures in each experiment where the four varieties were in- cluded. Tables 8 through 15 clearly show that only linear reSponses occurred for yield which demonstrates how the yield components have developed a compensatory adjustment to keep the linearity of yield. 15 16 mv.av moomo. mm.av vo.mm cam: mm.~v mmomo. mm.vv hm.om wwoauowoauwwoeudmov mm.Hv mmmmo. mm.a¢ o~.vm umov"0movuowoau¢woa hh.av mmamo. mv.vm m~.mm Mmmmuowmmuwwmmugmmm Ne.mq mamas. mm.mv >5.Hm Hmooa mm.oe mwomo. 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Hm.om mm.Hm wwooa mm.mm ommmo. on.h¢ mN.Nm wwoanmom Hm.mm «mmmo. mm.m¢ om.mm HwomquOB vm.mm Hmmmo. vm.hm mm.mm Awooa mh.mm mmnmo. Hm.mm mm.¢m nachuawom hm.nm mmmmo. no.mm om.mm Awomuowon mo.mm Hmnmo. hm.hm mm.mm Qwooa nh.hm evomo. wh.vm mm.mm QthuUwom mm.mm mwomo. ma.hm mm.¢m Qwomuowoh I I I I Uwooa ANV macaw va Hmaafla “mm Axv mum “mm xzv imam as usmsmz mascumm mo mumaaua mo mom mamuuv chnmm wmmum>¢ Hmnfidz wmmum>¢ Hmnfisz mmmum>¢ mmfluucm mama» momum>¢ musmsomfioo pawwm Am .mxmv .mmunuxus was: was .xmv maumoauom.us can .Aqv em canauauao .iom cacao .AUV smficomoo mmflumwum> umo Hsom mo Hmcmmfi uswsomaoo pawfim cam camflwII.m mqmda 19 TABLE 4.--Mean squares from analysis of variance tables for a randomized block design for yield (W) and its components (X, Y, Z) for the oat varieties and mixtures tested in experiment 1. Source of X Y Z ‘ W Variation M.S. M.S. M.S. M.S. Replications 5 19.420 182.930** .00000183 l46.l85** Entries 12 41.474* 214.034* .00001345** 38.734** Remaining error 60 14.177 24.555 .00000252 5.477 *, ** = Significance at 5% and 1% level respectively. TABLE 5.--Mean squares from analysis of variance tables for a randomized block design for yield (W) and its components (X, Y, Z) for the oat varieties and mixtures tested in experiment 2. Source of X Y z W' Variation M.S. M.S. M.S. M.S. Replications 5 33.714 267.957** .00000269 198.767** Entries 12 29.078 132.162** .00002245** 49.265** Remaining error 60 25.776 20.584 .00000271 15.374 ** = Significance at 1% level. 20 TABLE 6.--M.ean.squares1 from analysis of variance tables for randomized block design for yield (W) and its components (X, Y, & Z) for the oat varieties and mixtures tested in experiment 3. Source of X Y Z W Variation ° ‘ I Replications 5 54.083** 322.353** .00000379 162.415** Entries 11 l7.865** 132.505** .00001412** 12.920 Remaining 53 6 355 20 730 00000197 7 545 error ' ' ° ' ** = Significance at 1% level. 1Note that in an unbalanced experiment the adjusted source sums of squares will not, in general, add to give exactly the (unadjusted) total sums of squares. 21 .Hm>ma wa um ucmuwMMHp haucmoHMHsmHm mum mousuxwa cam mccmum musm u «I vm.mm on.mm «gmmmmo. mmmmo. mo.ov va.mv mm.em vo.mm m .mxm mm.mm mv.nm «Nome. mmmmo. mm.mm mm.mm va.vm mm.mm m .mxm oe.ae mm.av mmomo. mmomo. Hm.ae vm.ae ma.mm mm.mm H .dxm z m 2 m 2 m 2 m Awe ABC macaw ANV nomads Hmcumm umHHHB\mHmsumx Axv mumaafle ucweflummxm Mo Honesz mo umnEsz mo mmonu :uH3 cmummEoo sz .musmaflummxw mmucu wau Ga Amy mpsmum whom mousuxfia mo mucmcomaoo Gamma can macaw mo mamszI.> mqmda 22 TABLE 8.--Testing for curvilinear regression for yield (W) and yield components (X, Y, Z) of "Ausable" (A) and "Garry" (G) varieties and mixtures. (Exp. 1, graphed in Fig. 1) Source of Components 0 I DOF. W Var1at1on M.S. X Y Z M.S. M.S. M.S. Replications 5 8.042 63.813* .00000121 34.907** Trends 3 22.619 78.753* .00000387 16.633 Linear 1 11.189 20.504 .00000420 48.424* Quadratic 1 38.001* 161.244* .00000643 .423 Cubic 1 18.668 54.512 .00000097 1.051 Error 15 8.201 20.663 .00000196 7.190 *, ** = Significance at 5% and 1% level respectively. TABLE 9.--Testing for curvilinear regression for yield (W) and yield components (X, Y, Z) of "Garry" (G) and "Coachman” (C) varieties and mixtures. (Exp. 1, graphed in Fig. 2) Source of D F Components W Variation ° ' , M.S. X Y Z M.S. M.S. M.S. Replications 5 19.946 30.826 .00000017 69.624** Trends 3 4.402 26l.726** .00002660** 98.271** Linear l .387 698.183** .00006319** 287.510** Quadratic 1 10.401 64.478 .00000656 .315 Cubic 1 2.417 22.517 .00001005 6.988 Error 15 21.663 21.575 .00000269 2.591 ** = Significance at 1% level. 23 ISO - E In E IZOI- Q 5; 0: Q: I l0 - k 2 Lu In l X I44 m 90— S ‘0. o L“ 80 '- _2 0 x Tillers ft. IS y Kernels tiller" .3 z Kernel weight 3:) 7° " w Yield ft.‘2 '4.) 0. 60 l l l J °loAusoble IOO 70 30 O %Garry O 30 70 IOO ENTRIES FIG. I.--Component compensation and its effect on yield of "Ausable" and "Garry" oat varieties and two mixtures among them. (Exp. I) 24 I30” 3 lg .20 _. Q 3 % HO“- S '4.) 3 I00- F: '44 3; ll.) 90*- 3 ‘t X x Tillers n“2 K. ’ . -| o 80- ,’ y Kernels tIller lu (/ Z Kernel weight 3 w Yield rI-Z Fe E 70*- E '4.) 0. 6C) 1 I l I °/. Coachman IOO 7O 30 O % Garry O 30 70 I00 ENTRIES FIG. 2.--Component compensation and its effect on yield of "Coachman" and "Garry" oat varieties and two mixtures. (Exp. 1) 25 TABLE 10.--Testing for curvilinear regression for yield (W) and yield components (X, Y, Z) of Coachman (C) and Mi.60-lO6-78 (E) varieties and mixtures. (Exp. 1, graphed in Fig. 3) Source of D F Components W Variation ' ° M.S. X Y Z M.S. M.S. M.S. Replications 5 17.158 165.041** .00000106 75.307** Trends 3 37.331* 419.973** .00003123** 69.258** Linear 1 39.471 1199.327** .00008807** 207.644** Quadratic 1 14.415 43.585 .00000006 .000 Cubic 1 58.106* 17.008 .00000555 .131 Error 15 11.308 14.394 .00000167 5.756 *, ** = Significance at 5% and 1% level respectively. TABLE ll.-—Testing for curvilinear regression for yield (W) and yield components (X, Y, Z) of Coachman (C) and "Diana" (D) varieties and mixtures. (Exp. 2, graphed in Fig. 4) Source of D F Components W Variation ' ' M.S. X Y Z M.S. M.S. M.S. Replications 5 30.031 146.916** .00000455 123.812** Trends 3 12.667 5.775 .00001823* 4.185 Linear 1 18.947 4.493 .00003642* .006 Quadratic l .106 12.808 .00000035 10.834 Cubic 1 18.947 0.025 .00001792 1.716 Error 15 24.884 24.970 .00000539 11.499 *, ** = Significance at 5% and 1% level respectively. 26 I30 - 2 '1 In 3 I20 - Q I‘ Y 2 l q / E / F~ IIC>- .\~. I, 2 \. l/ “J "\‘ UV SE "‘U—...__.__. " 3: I00 -- ' '“; Q / \ . X :3 / \, / \ z o 90 — / 5 / O I, 2 LL. . .- 80 ._ X TIIlers f1. 3 ”’J y Kernels tiller" l~ 0"” '42.: z Kernel weight - -2 U P w YIeld ft. 0: 70 In 0. 6‘) I l l J % Coachman I00 70 30 O % Mi.60- O 30 7O IOO l06-78 ENTRIES FIG. 3.--Component compensation and its effect on yield of "Coachman" and "Mi.60-I06-78" oat varieties and two mixtures. (Exp. I) 27 I30 - S ‘s I— Q IZO S 8 HO - '5 lu E 0: I00- I41 3. ll.) g, 90 P E s. . _2 o x TIllers ft '44 30 .. y Kernels tiller" 3 Z Kernel weight- : w Yield ft'2 8 70 ES 0. 60 I I I I %Coachman IOO 70 30 0 ‘7. Diana 0 30 70 IOO ENTRIES FIG. 4.--Comp0nent compensation and its effect on yield of "Coachman” and "Diana" oat varieties and two mixtures. (Exp. 2) 28 TABLE 12.--Testing for curvilinear regression for yield (W) and yield components (X, Y, Z) of "Diana" (D) and "Clintland 64" (L) varieties and mixtures. (Exp. 2, graphed in Fig. 5) Source of D F Components W Variation ' ° M.S. X Y Z M.S. M.S. M.S. Replications 5 34.822 79.918** .00000263 76.246** Trends 3 56.299 37.930 .00001860** 58.251** Linear 1 55.360 107.218* .00004264** 152.673** Quadratic 1 74.202 5.229 .00001100* 3.860 Cubic 1 39.336 1.343 .00000217 18.219 Error 15 39.221 14.771 .00000210 9.782 *, ** = Significance at 5% and 1% level respectively. TABLE 13.-~Testing for curvilinear regression for yield (W) and yield components (X, Y, Z) of "Clintland 64" (L) and "Mi.60-106-78" (E) and mixtures. (Exp. 2, graphed in Fig. 6) Source of D F Components W Variation ' ' M.S. X Y Z M.S. M.S. M.S. Replications 5 26.535 71.707 .00000093 25.085 Trends 3 91.071 360.705** .00000611** 124.684** Linear 1 173.896*1031.581** .00000397 367.131** Quadratic 1 99.226 48.496 .00001276* 5.876 Cubic 1 0.091 2.038 .00000160 1.044 Error 15 41.280 25.556 .00000180 23.956 *, ** = Significance at 5% and 1% level respectively. 29 ISO - E In E IZO - Q S 0: “'9 IIo —- L. E z 3 . ._.../ w E [00 I- .___ . ___. . ——-— x E ./ "‘a.y / -0”’ X . _, —" u-I ./ .’ ’v " .2 90 '- I 1” 1. I “a ./ g 80 b x Tillers ft’z IS y Kernels tiller" 2 z Kernel weight ° -2 3:31 70 r w YIeld ft In R 6&3 L, J, I I “A Clintland 64 IOO 70 30 O % Diana 0 30 70 IOO ENTRIES FIG. 5.--Comp0nent compensation and its effect on yield of "Clintland 64" and "Diana“ oat varieties and two mixtures. (Exp. 2) 30 130 r- 5. ,/ y In /” 3 120 r- / s / 3‘; / W / ‘9 I IO - / k / 2 / lu / a / t '00 '- I I“ / e\ g l ’ a' ’ .\ x I“ / /°"’ ,\.. z 90 - ° s '7 “5 (I g 80 .. x Tillers It."2 E y Kernels tiller" E z Kernel weight w Yield “3‘2 3:3 70 r- Lu 0. 60 I I J J °/o Clintland64 IOO 70 30 O %Mi.60- O 30 70 IOO l06-78 ENTRIES FIG. 6.--Component compensation and its effect on yield of "Clintland 64" and "Mi.60—l06-78" oat varieties and two mixtures. (Exp. 2) 31 TABLE 14.--Testing for curvilinear regression for yield (W) and yield components (X, Y, Z) of "Diana" (D) and "Clintland 64" (L) varieties and mixtures. (Exp. 3, graphed in Fig. 7) Source of D F Components W Variation ' ' M.S. X Y Z M.S. M.S. M.S. Replications 5 22.375 82.113* .00000246 53.074** Trends 3 6.529 10.187 .00000182 2.354 Linear 1 2.475 2.208 .00000257 6.655 Quadratic 1 4.743 .008 .00000195 .407 Cubic 1 12.368 28.345 .00000095 .000 Error 13 10.160 23.780 .00000189 7.550 *, ** = Significance at 5% and 1% level respectively. TABLE 15.--Testing for Curvilinear regression for yield (W) and yield components (X, Y, Z) of "Clintland 64" (L) and "Mi.60-106-78" (E) varieties for mixtures. (Exp. 3, graphed in Fig. 8) Source of D F Components W Variation ‘ ° M.S. X Y Z M.S. M.S. M.S. Replications 5 16.081* l90.915** .00000331 69.686** Trends 3 22.059* 170.408** .00000046 33.522** Linear 1 56.497** 508.440** .00000090 92.745** Quadratic 1 9.068 2.782 .00000036 4.689 Cubic 1 .611 .003 .00000004 3.131 Error 14 5.279 33.331 .00000320 5.921 *, ** = Significance at 5% and 1% level respectively. I30 IZO IIO I00 90 80 7O PERCENTAGE of the EXPERIMENT GRAND MEAN 60 96 Clintland 64 I00 “A Diana 32 __. X -— ___, ”K.‘ § 2 or” 3 + A“, 4' .fl.- av ‘~‘~“ ‘. \ ,v Y \\ ”’ v x Tillers ft'z y Kernels tiller"I z Kernel weight w Yield fix-2 1 I l J 70 30 O O 30 70 IOO ENTRIES FIG. 7.--Component compensation and its effect on yield of "Clintland 64" and ”Diana" oat varieties and two mixtures. (Exp. 3) 33 ISO- mo- ,/ IIO- IOO - 90F Tillers ft.'2 Kernels tiller"| 80 - Kernels weight Yield ft."2 £N~ Mm>ummno mmusuxflz .AH .mxmv mowuewum> usosuflumsoo Mama» mo paowm ecu scum namflm cwumHsono Hagan new mousuxwfi mo_oaww> Um>nomno somsumn consummfiooll.ma mnmde 40 .m.z mNmH. H u + mw.hm cm.mm mN.H mwoaquoauawovuowo¢ «H.l NM.hm mH.bm mwosnnwosuawoauUmoa Hm. mv.hm mm.hm mmeuflmmNqumNumeN Hm.H Hm.mm mm.c¢ MwOBunwom he. ma.mm mm.mm mwoanWOF ma.~l mm.mm 2.4m Awohunwom mm. 56m 23mm Among—won mh.Hl Hm.hm oo.wm QwohuUwom em.l Nh.hm mh.mm Qmomu0w0b +mocMWMWWHQ Gama» cMWMHsoHMU camflm ww>ummno mousuxflz .Am .mxmv mowuowuw> ucosuwumcoo Mama» mo papa» esp scum papa» kumasoamo Mama“ was monsust mo pamflm Ud>uomno somsuon GOmHHmmEooll.>H mqmda 41 TABLE 18.--Comparison between observed yield of mixtures and the calculated yield from the yield of their constituent varieties (Exp. 3). Mixturesl Observed yield Calculated yield Differencet Wo Wc Wo—Wc 70%D:30%L 37.27 37.58 -.31 30%D:70%L 36.76 36.99 -.23 70%L:30%E 36.61 38.04 —1.43 30%L:70%E 39.68 40.04 -.36 1Note that the We of the rest of the mixtures cannot be cal- culated because of lack of data on "Coachman" (C). T t = 2.0525 N.S. 42 .Hm>ma mm as unmoAMhamhm .« «who.m u u + .......................... mm.- , ma.nq mm.~e ...., ...uuoauouofluomosuaaoe Ha.- oG.H¢ mm.as mmosuoaovuomoauawoa ~e.l mm.~¢ ne.aq mammuowmmuommmnaamw NG.H- mm.~s om.os mmosuomom mH.Hl m~.mm mo.mm mmomnoaos me. Ha.mm mm.mm owchnowom oa.al mm.~s mp.av omomuosos ma.l os.ss h~.vq omcsuawcm ~m.- mo.mv . m~.~v owomuaaon +ooawwmmwhn sash» awwaasoamo cash» mm>uomno mousuxhz .AH .mxmv mofluowum> usosuwumgoo “Moan mo mucocomsoo Gama» onu sown Gama» poundsoamo mnu.p:o mousust mo pamwm om>ummno coozumn0:0maumm500ll.ma wands 43 .Hm>ma am pm unschedamhm .s omn.~ u u + ............................................ «m. mm.mm om.mm mwoaunwoaunwovuowov sv.Hl No.mm mH.hm umovuqmo¢uaw0Huowoa mm.l mm.mm mm.hm MwmmqummunmeuUmmN Ho.l mm.o¢ Nm.o¢ mwonunwom ov.l wN.mm mm.mm mwcmquOB mw.ml mm.vm mh.Hm Awohuowom mo.l mh.mm on.mm Awomuawon hm.ml mv.mm wo.mm QwOBuUwom ww.Hl N¢.mm mh.mm QwomuUmon +oocm%wm%fio oaoflm OMWMHsOHmu oaoflh MW>Homno mousuxflz .Am .mxmv mowumaum> usmsuwumsoo Mamas mo mucmsomaoo papa» on» scum papa» poumasoamo may use mousust no cash» Um>nomno coospmn GOmAHMQEOUll.om mange 44 TABLE 21.--Comparison between observed yield of mixtures and the calculated yield from the yield com- ponents of their constituent varieties (Exp. 3). 1 Observed yield Calculated yield Difference+ Mixtures Wo Wc. Wo-Wc 70%D:30%L 37.27. 37.94 -.67 30%D:70%L 36.76 37.34 -.54 70%L:30%E 36.61 38.88 -2.27 30%L:70%E 39.68 41.03 -l.35 1Note that the We of the rest of the mistures cannot be cal- culated because of lack of data on "Coachman" (C). + t = 3.0477 N.S. 45 From Tables 22 and 23, X and Y components are tied with a negative relationship in the three experiments, although the relationship is not significant in experiment 2. Negative, though not significant association obtains between Y and 2 components in all experiments. With the Y component being positively correlated with W (rYw = .67), it appears that the number of kernels per head was more important than any other component in determining the yield. 46 TABLE 22.--Phenotypic correlations between yield and yield components in the three experiments for the varieties and the mixtures tested. Experiment rXY rXZ rXW rYz rYW rZW Exp. 1 -.6978** .1166 -.0447 -.5469 .6395* -.2286 Exp. 2 -.4760 -.2613 .1767 —.2769 .6587* -.0452 Exp. 3 -.7381** .1977 -.2280 -.4224 .6987* .1208 *, ** = Significance at 5% and 1% level respectively. TABLE 23.-—Corre1ation between the logarithms of yield and yield components for the varieties and mixtures in the three experiments. Experiment. rXY rxz rXW rYZ rYw rzw Exp. 1 -.7079** .1262 -.0457 -.5396 .6622; -.2319 Exp. 2 -.4841 -.2522 .1449 -.2496 .7089** -.0395 Exp. 3 _ -.7547** .2010 -.2524 -.4221 .7116** .1133 Average -.660* .020 -.045 -.410 .694** -.060 *, ** = Significance at 5% and 1% levels respectively. DISCUSSION The mixtures failed to yield more than their con- stituent varieties in any experiment. Instead the yield of mixtures was prOportional to the yield and relative frequencies with which the varieties were mixed (Tables 16, 17, & 18). Differences between yield of mixtures and their yield calculated from the yield of the pure cultures of their constituent varieties were not significant, sta- tistically or biologically; however, when the yield of mixtures was calculated using yield components based on pure culture values, the differences between the actual and the approximated yield values were almost unidirectional. In nearly every case the calculated was less than the ob- served. These differences when tested were significant. The reason for this difference is both biologic and geo- metric. The failure of yield components to approximate the yield can be related to the interaction between com- petitive varieties. Under varietal interaction which the present data suggest i ? (ax A n 1 With negative correlation between x + be) will not be equal to the calculated XAB' and Y, also 1_Z (aYA + bYB) will not be equal to Y AB' n 47 48 However with the results showing that the disturbance in one component due to varietal interaction was counter- balanced by the other component(s), therefore varietal in- teraction alone does not eXplain the cause of the deviation of the observed yield of mixtures and their calculated yield from the yield components of their constituent varieties. n In the two dimentional relation between X and Y, 2 XY equals n n to 1 2X2 if and only if r equals zero. Also since the n11 XY present study shows that X and Y are negatively correlated, n n n ZXY will not-equal l zxzy. Similarly, £(aX + bx ) (aY + bY ) n11 1 A B A B will not equal 1 n n H i (aXA + bXB) i (aYA + bYB). The same argument applies to Y and Z; therefore, W # (aXA + bxB + ... + nXN) (aY AB...N + bYB + "° + “YN) A (a2 + sz + ... + nZN). A When those mistures made up of two varieties were studied separately, the compensatory trends among yield components became apparent. Figures 1 through 8 where those relations were graphically illustrated are self-explanatory. Also the 4-variety mixtures in Figures 9, 10, & 11 show the compensatory pattern of yield components. The oscillatory nature of the components X, Y, & z maintained the linearity of yield. This situation was further confirmed in Tables 8 through 15, where in not one case did yield follow a 49 non-linear course while the components were non-linear in several cases. The compensatory counterbalance relationship be- tween components is undoubtedly related to both the geno- types and to the sequential nature of develOpment of yield components. A well adapted good yielding variety of a grain crOp with high tiller number usually tends to be early, have shorter stalks, smaller Y and larger 2, while a good yielding variety with low tiller number usually tends to be late, have tall stalks, large Y and medium 2. The effects in these character combinations are determined by both genotypes of the plants and the Operating growth conditions. The compensatory requirements in the present situation are established by the gene pool and the Michigan environment which enhanced stress. Since yield components known to be independently inherited, they are expected to be also bi010gically independent in function and magnitude. Their sequential development which seem to determine the interdependent relationships among them suggests that the compensatory pattern that the components follow to determine the yield is unlikely to occur in the absence of intraplant competition due to stress factors. Under stress, mixtures are then likely to tend to modify the stress pattern of a variety by introducing competition of another variety. The degree and the sign of a component modification depends on 50 what signal it receives from the preceding component.in the sequence. The original signal is perhaps mainly genetic but the influence of genotype on a trait diminishes as its position in the developmental sequence approaches the end of the sequence (Thomas, Grafius, and Hahn 1971). Tiller number (X), being the first component to be determined in the deveIOpmentary sequence, frequently sets the stage for the behavior of the varieties in the mixtures, and any varietal interference in this stage will direct the follow- ing components' behavior according to the outcome of such interference. Component X seemed to have followed three distinct patterns in the mixtures (Figures 1 through 8). In two cases X dropped below either variety in the mixtures (Figures 1 and 2). In two cases, one mixture pro- duced more tillers and the other mixture produced less tillers than either one of their constituent varieties (Figures 3 and 4). The third pattern was represented in Figures 6 and 8 which show a linear reSponse in regard to the X component. The X curve in either Figures 5 or 7 was difficult to categorize in any of the previous groups. The linearity of the X component in Figures 6 and 8 indicate that intervarietal competition is not evident. The number of tillers increased as the prOportion of the high tiller- ing variety (Clintland 64) increased and decreased as the low tillering companion (Mi.60-106-78) increased in the 51 mixture. Figure 3 indicates that some sort of varietal interference occurred among the varieties forming that set. In Figure 3 the mixture with a high frequency of Coachman--the highest tillering variety in this set--in- creased the tiller number of the mixed p0pulation. In the other mixture where Mi.60-106-78 was the dominant variety the tiller number fell behind. Since Coachman matures earlier than its companion variety, it is reasonable to assume that Coachman in a mixture will tend to determine its tiller number in a shorter time than its companion variety. This would give Coachman the advantage of an earlier start and develOpment at the expense of the neigh- boring variety. As Coachman approaches heading stage and maturity, the stress of competition relaxes and conditions become more favorable for the Mi.60-106-78 variety to pro- duce a large number of tillers under less competitive con- ditions. This would increase the total tiller number of the mixed p0pulation. Because this increase in tillers occurs late in the season, most of the tillers of the de- pressed variety that were produced later will not have enough time and favorable conditions to form enough kernels. So these tillers will tend to bear few panicles, or panicles with a large portion of florets unable to set seeds. This may also explain why kernel number (Y) was low in that mix- ture where tiller number was high. 52 However, it is difficult to say very much about those mixtures where four varieties were involved (Figures 9, 10 & 11). The relationship among varieties in those mixtures is expected to reflect more complex interrelations than those Operating among two varieties. A further attempt was made to explore the dis- turbances in component X resulting from the varietal inter- action in the light of the difference between the interacting varieties. This was done by comparing the range between com- peting varieties and the deviation in the X variable of the mixtures from what was expected if the varieties are not competitive (Table 24, Figure 12). The regression analysis applied to the data shows that the relationship between the varietal difference in X and disturbance in this component when varieties grow in a mixture can be represented by a linear model (Table 25) and the fluctuation in mixtures in- creases as the range between the mixed varieties increases (Figure 12). 53 TABLE 24.--Disturbance in mixtures' X component (calculated as the mean of mixture's absolute deviation of observed from calculated in the absence of vari- etal interaction) as related to the range in X component between the varieties. Both variables are expressed as the percentage of the experi- mental grand mean. 4‘ . . X range in X Mean deviation of Varieties between varieties mixtures in X Ausable 2.63 7.63 Garry Exp. 1 ggfiggman .00 4.00 Coachman Mi.60-106-78 5'24 7'17 Coachman Diana 4.05 3.93 Exp. 2 Sigfizland 64 15.40 10.17 Clintland 64 Mi.60-106—78* 20.61 11.73 Clintland 64 Exp 3 Diana .20 3.08 ‘ Clintland 64 Mi.60-106-78. 13°32 3'80 TABLE 25.--Analysis of variance of the relationship between varietal range in X and the deviation in X of the mixtures. Source of variation D.F. S.S. M.S. F Explained--due to * linear regression 1 33-8748 38.8748 6.9324 Unexplained--error around regression line 6 35'4841 5°9140 Total 7 74.3589 *Significance at 5% level. 54 I4— I2r- IO MEAN DE VIATIONxW/X TURES from the LINEAR MODEL EXPRESSED as PERCENTAGE of the EXPERIMENT 6 2 E4 3 Q <2: 2r— E.' I 1 1L I I L, I l I YJ 41 _J 2 4 s 8 IO l2 l4 l6 l8 202224 RANGE in x EXPRESSED as a PERCENTAGE of the EXPERIMENT GRAND MEAN FIG. l2.--The effect of differences in the X component between oat varieties 0n the disturbance in the x component of mixtures. 55 Varietal difference in X reflects genetical dif- ference for this trait. If any deviation in X is assumed to be caused by varietal interaction due to competition, it is possible to conclude that competition for X resources-- under the present growth conditions will be most keen where X is genetically different in the competitive varieties. A. hypothesis that relates the deviation in the X component of mixtures to the range of their constituent varieties may be prOposed as follows: "In a mechanical mixture, the proba- bility of disturbance in Component X is greater when the constituent varietal range in X is greater. Y and 2, that follow X in the sequence, will adjust in a compensatory manner." However, this should not be understood to mean that stress conditions will necessarily function in the tillering stage. If the competing varieties started with the same tiller number (Thomas, Grafius, and Hahn 1971), or conditions for any reason tend to provoke stress in the later stages, say in the seed setting stage for example, this will eliminate X as a factor that determines the magni- tude and the direction of the compensatory pattern. The failure of the mixtures to yield greater than the pure cultures of the varieties should not close the door to further investigations on the subject. Under conditions resulting in the highest yielding variety being more suscep- tible to a given stress such as disease or lodging, mixtures may yield greater than the highest yielding variety. BIBLIOGRAPHY Adams, M. W. 1967. Basis of yield component compensation in crOp plants with special reference to the field bean, Phaseolus vulgaris. Crop. Sci. 7:505-510. Adams, M. W. and Grafius, J. E. 1971. 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