T attributes heterosis to accumulated effects of loci at which the more favorable

Transcription

1 ESTIMATES OF GENETIC VARIANCES AND LEVEL OF DOMINANCE IN MAIZE1 R. H. MOLL, M. F. LINDSEY2 AND H. F. ROBINSON Department of Genetics, North Carolina State of the University of North Carolina, Raleigh Received September 13, 1963 HE dominant favorable gene hypothesis, first proposed by BRUCE (1910), T attributes heterosis to accumulated effects of loci at which the more favorable allele contributed by one parent is manifest rather than the unfavorable allele contributed by the other parent. The concepts of linkage (JONES 1917) and large number of loci (COLLINS 1921; SINGLETON 1941) make the hypothesis compatible with the observation of symmetrical F, distributions and the lack of SUperior homozygous inbred lines. The concept of heterozygote superiority was first put into the framework of Mendelian inheritance by EAST (1936) with the suggestion that if alleles had diverged slightly in function, a heterozygote might have an advantage over the homozygotes. HULL ( 1945) introduced the term overdominance to denote heterozygote superiority over either homozygote at the locus level, and proposed this as the most important genetic effect in corn populations. The two hypotheses are not mutually exclusive; i.e., the heterosis observed in crossbred corn populations might be not only due to loci with partial to complete dominance but also due to overdominant loci. Furthermore, the effects of repulsion phase linkage of favorable dominant genes tend to mimic overdominant effects, and are indistinguishable from the effects of overdominance when the frequency of recombination is near zero. Pseudo-overdominant effects, in contrast to true overdominant effects, tend to diminish with the approach to linkage equilibrium under random mating at a rate proportional to the recombination frequency between loci. Therefore, not only the relative importance of dominance versus overdominance, but also the rate of decrease of pseudo-overdominant effects with random mating, has important implications regarding the evolutionary significance of heterosis and its practical utilization in plant breeding. Several approaches to this problem have been pursued giving somewhat conflicting conclusions. CROW ( 1948) considered the theoretical relationship between heterosis and the effect of deleterious recessives maintained in the population by mutation, and concluded that observed heterosis was not entirely attributable to the dominance of favorable genes. BRIECER (1950) presents an argument in favor 1 Contribution from the Genetics Department, North Carolina Agricultural Experiment Station, Raleigh. Published with the approval of the Director of Research as Paper No of the Journal Series. The work was supported in part by a grant from the Rockefeller Foundation. 2 Present address : Department of Agronomy, University of Nebraska, Lincoln. Genetics 49: March 1964

2 412 R. H. MOLL et al. of overdominance based on the possible evolution of corn. HULL (1948, 1952) presents evidence from constant parent regression techniques which are interpreted to favor the overdominant hypothesis, and argues that experience in corn breeding is compatible with the overdominant hypothesis. Additive and dominance variances were estimated by ROBINSON, COMSTOCK, and HARVEY (1949) and GARDNER, HARVEY, COMSTOCK, and ROBINSON (1953) in F, generations of several single crosses. Ratios of these estimates were indicative of either true overdominance or pseudo-overdominance attributable to linkage effects. Later work reported by ROBINSON, COCKERHAM, and MOLL (1960) involved F, generations which had been obtained by random mating from two of the F, populations studied previously, and demonstrated that linkage effects were present in the F, estimates. However, the evidence regarding the possible importance of overdominance was inconclusive. Two similar experiments involving different samples of F, and F, generations of a Corn Belt single cross were conducted by GARDNER and LONNQUIST (1959). Results of one of the experiments indicates linkage bias in the F, estimates. Results of the other experiment were inconclusive. However, further experimentation has provided additional evidence supporting the linkage bias hypothesis and suggests that average dominance is in the range of partial dominance ( GARDNER 1963). Other evidence compatible with the favorable dominant gene hypothesis comes from work on convergent improvement (MURPHY 1942; RICHEY and SPRAGUE 1931; SPRAGUE, RUSSELL, and PENNY 1959) and from estimates of genetic variances in varieties and variety crosses (ROBINSON, COMSTOCK, and HARVEY 1955; ROBINSON, KHALIL, COMSTOCK, and COCKERHAM 1958). Further investigations have been conducted to determine the relative magnitude of additive and dominance variance, and the rate of disappearance of pseudo-overdominance through genetic recombination. The results, which are reported here, add to the evidence that overdominance is not of primary importance in determining genetic variation in corn. METHODS AND MATERIALS The experiments to be described involved F, and advanced generations derived from each of two single crosses, NC7 x C121 and NC33 x K64, both of which gave evidence of possible overdominance in the F, generations (ROBINSON et al. 1949). Advanced generations were developed by, random mating to allow genetic recombination with subsequent dissipation of possible pseudooverdominance due to linkage. The F, generations were produced by six generations of random mating starting with the F,. Similarly, the F,, of NC7 x CI2l and the F,, of NC33 x K64 result from 11 and 10 generations of random mating respectively, and were developed by continuation of random mating from the F, populations used in these studies. The technique used was hand pollination of random plant to plant crosses in a planting of 200 plants for each generation. At least 80 and usually more than 100 ears were harvested, and an equal number of seeds of each ear were bulked to produce the next generation. The progeny evaluated were produced by the mating scheme described as Experiment I11 by COMSTOCK and ROBINSON (1952). Random plants of a segregating generation were each backcrossed to the two parental inbred lines. The two backcross progeny were assigned to sets at random, with nine progeny pairs in each set. Each set was planted in a randomized block with three replicates, giving a total of 54 plots per block. Fifteen blocks of each of two generations

3 VARIANCE AND DOMINANCE IN MAIZE 413 wx? ran lsmly assigned throughout each experimznt. Data were obtained for yield of ear corn, number of ears, ear diameter, ear length, ear height, plant height and days to tassel. The methods of measurement are given in detail in GARDNFX et al Experiments comparing the F, and F, generations, and the F2 and F,, or F,,, were conducted for two years. In most instances, limited seed production restricted the testing of progeny of a sample of each generation to a single season so that it was necessary to resample and obtain new progeny for the second year test. Sufficient seed for two years of test were obtained for the (NC7 x CI21)FI3 and the (NC33 x K64)F1, as is indicated in Table 1. Data for each year s test were analyzed separately, and an average analysis for the two years of each experiment was computed by pooling sums of squares and degrees of freedom. This procedure was followed for all four experiments so as to give comparable estimates from the standpoint of genetic-environmental interaction bias. In addition, analyses of variance of the combined two years data were computed for the (NC7 x CI21)FI3 and (NC33 x K64)F2 and F,, to estimate the importance of genetic-environmental interaction variances. Expressions giving the genetic interpretation of the components of variance in this kind of study were derived by COMSTOCK and ROBINSON (1952). In a population in linkage equilibrium with two alleles per locus and no epistasis, the male component of variance (02,) is equivalent to Zqi(l-q)iui2/2 and the male x line component (uzm2) is Zqi(l-q)iai2ui2, where ui is one half i 1 the difference between the effects of the two homozygous genotypes at the ith locus, aiui is the diff2rence between the mean of the heterozygote and the average of the two homozygotes at the ith locus, and qi is the frequency of the favorable allele at the ith locus. If gene frequency is 1/, U*, =?ui2/8, which is equivalent to 02,/4 and uzm2 =?ai2ui2/4, which is equivalent to uzd, 1 1 where uza and 0 2 represent ~ additive and dominance variance respectively. The level of domi- nance is reflected by the value of ai. If there is no dominance, ai = 0; partial dominance, 0 < ai < 1; complete dominance. ai = 1; or overdominance, ai > 1. An estimate of the average level of dominance is given by: in which is a weighted mean of ai2 s. In a population where linkage disequilibrium is likely, terms due to linkage effects must be taken into account in the interpretation of variance components. In this case, U,, is equivalent to uza/4 + B, and 0 2,~ is equivalent to uzd + B,, where B, and B, are bias terms due to linkage effects. The term B, can be expressed as Z (pt-rs)ijuiuj and B, as 2 Z lpt-rslijaiuiajuj where i<i i<i p is the frequency of gametes with the favorable allele at both the ith and jth locus (+i+j), r TABLE 1 The sample (identified by letter) of each generation whose progeny were included in each yield test Year of test Population Generation NC7 x CI2l F, A B c D F8 E F Fl, G G&H NC33 x K64 F, I J K K F8 L M Fl, N N

4 414 R. H. MOLL et al. is the frequency of f-i-j gametes, s is the frequency of -i+i, and t is the frequency of -i-i gametes in the F, gametic array. The bias associated with uza; i.e., B,, is positive if coupling phase linkages predominate and negative if repulsion phase linkages predominate. The bias B,, which is associated with uzd, is positive regardless of the predominant linkage phase. Linkage disequilibrium will contribute to an overestimate of the ratio, Zai*uiz/Xui2, and thus to an over- - 2 estimate of a if repulsion and coupling effects are equal, if repulsion predominates, or if coupling predominates and ( U Z ~ / U ~ < ~ (B,/4B,). ) In the advancement of the populations from the F, to later generations by random mating, the amount of disequilibrium will be reduced in each generation by an amount proportional to the average recombination value. Experiments of the kind described above with later generations which have descended from the F, by random mating should give estimates of uza and uzd with less bias due to linkage. Estimates of in advanced generations are expected to be smaller than estimates in the F, regardless of whether repulsion or coupling linkages predominate. Estimates of ~2~ in advanced generations may be larger or smaller than in the F, depending on whether coupling or repulsion linkages predominate. If the two linkage phases are of equal importance, the estimates of ~2~~ in later generations will be no different from estimates in the F,. Tests of significance of differences between variance components estimated in F, and F, generations are F-tests computed as ratios of appropriate mean squares. Tests for differences between male mean squares are two-tailed tests whereas tests for differences between male x line interaction mean squares are one-tailed. The ratio of the male x line mean square to the male mean square provides a test of the hypothesis that 3 > 1.0 if gene frequency is.5 and loci are in linkage equilibrium; i.e., if B, = B, = 0. It will also hold if B,/B, = U Z ~ / ~ U ~ ~. RESULTS Estimates of the male component of variance (az,), given in Table 2, show no consistent directional change from F, to later generations and few of the differences observed are significant. The male component of variance for yield and ear diameter in the NC33 x K64 population appears to have decreased in later generations, whereas the male component for days to tassel for both populations appears to have increased. TABLE 2 Estimatesf of U,, (male component of uariance) in F, and advanced generations of two single crosses Ear Ear Ear Plant Yield Ear diameter length height height Days to Population Years Generation (Wplant) number (inches) (inches) (inches) (inches) tassel NC7xCI F, FE F, Fl, NC33XK F, F E F, F,,, WO8.oO07.o *.mi0.oO07* DO96, , of , * ,046 1.MO.w7.M9,0647.of * W o** + Estimates computed from analyses of variance p led over years. *, ** Significantly different from the corresponding F2 estimate at 5 percent and 1 percent probability level, respectively.

5 VARIANCE AND DOMINANCE IN MAIZE 41 5 Estimates of the male x line variance component ( uzml), shown in Table 3, are in general smaller for the advanced generations than for the F, generation in both hybrid populations. Significant reductions in uzmt from F, to the later generations occurred in both populations for yield and for two of the three characters generally associated with yield, viz. ear length and ear diameter. The average degree of dominance estimates, given in Table 4, are generally smaller for advanced generations than for the F,, and as expected, follow a pattern similar to that for the male x line interaction component. Estimates for yield in the F, generations of both populations are greater than 1.0, and therefore in the overdominant range. The estimates for yield in (NC7 x CI21)F, are significantly greater than 1.0, whereas the estimates for (NC33 x K64)F2 are not. TABLE 3 Estimatesf of 02,~ (male x line interaction component) in F, und advanced generations of two single crosses Ear Ear Ear Plant Yield Ear diameter length height Days to Population Years Generation (lb/plant) number (inches) (inches) $$%E) (inches) tassel NC7xCI F,.0019.OM F,.0009** *.0296* F,.W3, F,,.0017**.0083**.0012**.0343** * ** NC33XK F, Om F,.0003** **.0280** 1.117** 2.8%** F, , F,,.0008**.0048**.0009**.0472** 1.654* 4.372**.5029 *, ** Significantly different from the corresponding F, estimate at 5 percent and 1 percent probability level, respectively. + Estimates computed from analyses of variance pooled over years. TABLE 4 Estimated of a (uuerage leuel of dominance) in F, and advanced generations of two single crosses of corn Ear Ear Ear Ear Plant Days to Population Years Generation Yield number diameter length height height tassel NC7~C F, F, F, F,, NC33XK64 1%7-58 F, P, F, F,, t Estimates computed from analyses of variance pooled over years.

6 ~~ - ~~ 41 6 R. H. MOLL et al. Estimates for yield in (NC7 x C121)F8 and (NC7 x C121)F1, are not significantly greater than 1.0. Reduction in estimates of the average degree of dominance occurred in 26 of the 28 comparisons obtained. The experiments involving the F, and F,, generations of NC33 x K64 included the same progenies in the two years of the experiment ( ) and a combined analysis of variance was computed to estimate the genotype x environmental interaction variances. Therefore, the estimates of uzwl, u',l and 2 presented in Table 5 are unbiased whereas estimates presented in previous tables contain possible genotype x environmental interaction bias. It is important to note that removal of genotype x environmental interaction bias does not influence the con- clusion that estimates of azwt1 and Z are smaller in advanced generations, and essentially the same estimate of a is obtained from either biased or unbiased variance components. However, a similar analysis computed for the (NC7 X CI21)Fl, population (Table 6) gives a larger estimate of a for yield and ear length than do the biased estimates (Table 4). It is inferred from the comparisons of the variance components and estimates of average degree of dominance for F, and the later generations that the general pattern of differences observed is due to genetic recombination and the approach to linkage equilibrium. This assumes that the gene frequencies in the populations have not changed as a result of natural selection or drift as the populations were advanced by random mating. Some evidence bearing on this is given in Table 7, which lists the means for each character and each generation. None of the differences between F, and F, generations for yield, ear number, or ear height are statistically significant. However, in seven of the eight comparisons the advanced generation was slightly higher in yield than the F,. Similarly, date of flower was earlier for the advanced generations in seven of the eight comparisons. TABLE 5 Estimates of rrariance components and average level of dominance from an analysis of uariance combined over two years for F, and F,, generations of NC33 X K64 Parameter Ear Ear Ear Ear Plant Days to estimated Generation Yield nuniber diameter length height height tassel (I2,?, F,.0008, , Fl,, , ** fj2?ny F2.0001,0012,0000, ,1328 F12, ,1618 n27n 2 F o(F65.0( ,5113 Fl,.0007**.002O**.0010**.0349** **,2708 U2?nZZl 'F2.0004, F12.OaOl*.0028.OOOO, a F p , *, ** Significantly different from the corresponding F, estimate at 5 percent and 1 percent probability level, respectirely. Tests of significant differences for azml are one-tailed; tests for asw, azvrly, and ( ~ 2 are, two-tailed. ~ ~ ~

7 VARIANCE AND DOMINANCE IN MAIZE 41 7 TABLE 6 Estimates of uariance components and average leuel of dominance from an analysis of variance combined ouer two years for the F,, generation of NC7 X C121 Parameter Ear Ear Ear Ear Plant Days to estimated Yield number diameter length height height tassel u27n ,6581 u2my.ooo ow MI7 u21n 1, , u2mlv WO , a TABLE 7 Mean performance of backcross progenies of F, and aduanced generations of two single crosses Ear Ear Ear Plant Recurrent Yield Ear diameter length height height Date of Population parent Generation (Ib/plant) number (inches) (inches) (inches) (inches) flower NC7xCI21 NC7 F F * 6.0* 48.2 F, F,, CI21 F, F * 6.0* 46.3 F, F,, NC33XKW NC33 F, F, F VIZ KW F, F* * 36.6 FZ F,, ** ** * % IlO.2** 137** *, ** Significantly different from the corresponding F, estimate at 5 percent and 1 percent probability level, respectively. DISCUSSION Nonsignificant differences between estimates of uzm for F, and advanced generations for most traits suggests that coupling and repulsion effects approximately cancel each other. However, there is evidence that coupling phase linkages predominate for yield and ear diameter in the (NC33 x K64) F,, and that repulsion phase linkages predominate for days to tassel in both F, populations. Estimates of average level of dominance for yield in the F, generation of both populations are greater than 1.0 and in the overdominant range. Estimates of both u2,1 and a obtained for the F, and F,, or F1, generations are smaller than those for the F,, which suggests that linkage bias may be considerable in the E',

8 41 8 R. H. MOLL et al. estimates. None of the other traits show evidence of overdominant effects in the F,, and yet estimates of U,? and a in the advanced generations were smaller, in most instances, than those obtained in the F,. It is desirable at this point to consider whether or not the amounts of decrease in estimates of c2,l obtained from F, and F, comparisons, and from F2 and F,, or F,, comparisons are compatible with the expected decrease due to recombination of linked loci with no epistasis. Consider a homologous pair of chromosomes with N segregating loci that are equally spaced with u the recombination frequency between adjacent loci. This chromosome can be thought of as made up of a number of segments, each of which bears n loci where n can vary from 2 to N. Let R, be the chance of an odd number of exchanges occurring between loci at the extremes of a segment bearing n loci; that is, R, is the recombination frequency of loci that are v(n-1) units apart. With no interference, the value of R, will be the sum of the terms representing an odd number of recombinations in the expansion of [ (1-0) + vln-l, and may be expressed as R,= [ 1 -(l-2u),-l] /2. With complete interference, R, reduces to u (n-1 ). The value of (pt-rs), which has been defined for any pair of loci in the gametic array produced by the F,, can be shown to be ( 1-2R,) /4. Let B,, be the expected bias, B2, in the F, generation so that the expected value of u~~~(f,) = uz3, + B2,. If it is assumed that the a s and U S of different loci have the same value, then for the gth generation material: u~,~(f,) = a2u2[n/4 + 2 B Ip t - r s l 1 < J where p t r and s are the corresponding frequencies in the g-1 gametic array, which reduces to: = a2u2[n/4 + 2 X I pt - rs (l-r,,)g- ] 1 < 3 where R,, is the recombination frequency between the ith and jth locus. This can also be expressed as A ui,(f,) a2uz[n/4 + Z(N-nfl) (1-2R,) (1-R,),-2/2]. Let A, be the ratio of u:~~~ of the F, generation to uz,~, of the F,. That is, n=2 v N f 2 Z(N-nfl) (1-2R,) (l-r,),- n=z A, = N N f 2 B(N-nS1) (1-2R,) n=z Although this development is based on a single pair of chromosomes, it can be shown to hold for any number of chromosome pairs that have N segregating loci with gene frequency of one half. Values of A, have been tabulated for A,, A,, and A, for selected values of N and u assuming no interference and complete interference (Table 8). The values selected represent map lengths between 80 and 120, which would appear to en-

9 VARIANCE AND DOMINANCE IN MAIZE 419 compass the average map length for corn (Rhoades 1955). The A, values are included to demonstrate the closeness of approach to the equilibrium value under the different models. Estimates of A, values for each trait measured are given in Table 9. The majority of the A, estimates fall within the range of reasonable theoretical values. Although exceptions occur, they are divided between too large and too small as though they are a result of sampling errors. Furthermore, the theoretical values were computed from an idealized genetic model, and discrepancies are likely when compared to values representing a real situation. The theoretical values were computed assuming that the a s and U S of different loci were the same, and assuming equal spacing of effective loci along the chromosomes. The first assump- TABLE 8 Theoretical value of Ag+ for selected combinations of the number of loci per chromosome (N) and the recombination frequency of adiacent loci (v) with no interference and complete interference No interference Complete interference U N A, A,, Am A8 AI, Am IO I I I IO t% eE I2.12.I t A,=oZmz (Fg)/ozmz(Fz). TABLE 9 Estimates of Ag+ for NC7 x CI21 and NC33 X K64 populations Population A, Yield Ear number Ear diameter Ear length Ear height Plant height Days to tassel NC7 x C121 A, Q NC33XK64 A,.I I A,,

10 420 R. H. MOLL et al. tion would tend to make the theoretical values too small since a:uf + afu: > 2uzuzalu3 if a,ul # a3uj, whereas the assumption of equal spacing might introduce a bias in either direction depending on whether the more widely spaced loci tend to be more important or less important than the more closely spaced loci. In this light, the comparisons of the observed and theoretical ratios are interpreted as further evidence that linkage is an important source of bias in early generation estimates of average dominance, and that the decrease observed in later generations is due to recombination of linked loci. The relative magnitudes of genetic-environmental interaction variances and their respective genetic variances bear directly upon the interpretations of estimates obtained by averaging single-year experiments as was done here. The estimate of particular interest is that of a, which is the square root of U~,~/~U,~~. AS Comstock ( 1955) has pointed out, if the genetic-environmental interaction variances are proportional to the genetic variances, more efficient estimates (in terms of effort and precision) of the ratio would be obtained from the biased estimates. This would not be true if different alleles become favorable in different environments with partial dominance always in the favorable direction such as proposed by LEVINE (1953) and discussed by COMSTOCK (1960) in relation to estimates of genetic variances. Data presented by MATZINGER, SPRAGUE, and COCK- ERHAM (1959) and ROJAS and SPRAGUE (1952) indicate that the variances are not proportional, but the reports do not agree as to which kind of interaction is largest. Data reported by ROBINSON and MOLL (1959) show some discrepancy from proportionality, but it is not great. In the (NC33 x K64) F, and F,, experiment, estimates of genetic-environmental interaction variances and their respective genetic variances are nearly proportional so that the biased and unbiased estimates lead to the same general conclusion concerning linkage and level of dominance. In the (NC7 x C121)F1,, however, the estimate of the male x year interaction variance for yield is the same size as the variance among males, whereas the male x line x year interaction variance is estimated to be much smaller than ;he male x line variance This kind of nonproportionality leads to a much larger estimate of afrom the unbiased estimates than from the biased estimates. Detailed exemination of the data reveals that extremely large interactions occurred in only one of the blocks. Elimiiation of this block from the combined analysis resulted in an estimate of ;of The concentration of large interaction effects in a single Hock may be due to sampling errors rather than to chance accumulation of overdominance effects. although the possibility of the latter caniiot be ruled out. More critical data bearing on genotype x environmental interactions and level of dominance are needed. Substantial evidence for the presence of overdominant loci in corn seems to be lacking. Nevertheless, there remains the possibility that a relatively small proportion of loci show overdominent effects which experiments to date have failed to detect. Evidence that mutations occur in Drosophila which result in heterozygote superiority have been reported by WALLACE (1960), and if they occur in Drosophila it is not unreasonable to presume they occur in corm, also. If so, then

11 VARIANCE AND DOMINANCE IN MAIZE 42 1 why is overdominance not more prevalent in corn? HULL S (1945) arguments in support of the overdominant hypothesis suggest that the past selection in corn populations has accentuated variation due to overdominant effects by tending to reduce genetic variability at non-overdominant loci. Since segregation at overdominant loci tend to lower population performance, it seems reasonable that past selection may also have had a tendency to minimize the effects of overdominance. It has been suggested that overdominance may be a transitory phenomenon in evolutionary development (CROW DOBZHANSKY and PALOV- SKY 1960). That is, if a mutation occurs that results in a superior heterozygote, selection will favor any subsequent mutation that results in a homozygote of equal value. Therefore, if overdominant loci have arisen in corn, the fact that their effects have not become important enough to be detected is compatible with possible selective forces affecting the evolution of corn. Estimates of additive genetic variance are large enough to indicate that family selection within populations of this kind should be effective in concentrating genes with superior general combining ability. However, practical utilization of this material will be in the form of inbred lines in combination with lines of another source, so at some point, tests must be made involving crosses with the other source. Furthermore, overdominance is possible and pseudo-overdominance is likely in crosses of divergent material. Therefore, some emphasis must eventually be directed toward isolating specific combinations. Recurrent selection for specific combining ability as proposed by HULL (1945) is a possible solution, but it is not effective for loci with partial dominance. The data in this report suggest the presence of partially dominant loci. This is especially so in the NC33 X K64 populations, where for later generations are definitely in the partially dominant range. Values of 2i for the NC7 X C121 populations are all greater than 1.O, but partially dominant loci in repulsion linkage will account for the results in view of the rate of decrease in linkage bias with random mating. Therefore, it is concluded that recurrent selection for specific combining ability could not be relied upon to isolate the best genotypes. Reciprocal recurrent selection is expected to be effective regardless of level of dominance ( COMSTOCK, ROBINSON and HARVEY 1949). Even though the weight of evidence is in favor of the dominance hypothesis, the fact that overdominance cannot be ruled out and pseudo-overdominance due to linkage is very likely strongly suggests that this is the most reasonable procedure to choose. SUMMARY Four experiments were conducted to estimate the average level of dominance and the effects of linkage bias in estimation of genetic variances. The populations studied were F, generations of two single crosses and advanced generations derived by random mating each of the two populations. Seven quantitative traits were measured. Reduction in estimates of dominance variance and average level of dominance were noted following random mating, indicating that linkage effects cause an upward bias in estimates obtained from F, populations. Estimates of average

12 422 R. H. MOLL et al. level of dominance in advanced generations were not significantly different from 1.0, the value for complete dominance. From this it is concluded that overdominance is not a prevalent kind of gene action in these populations. BRIEGER, G. F., 1950 BRUCE, A. B., : COLLINS, G. N., LITERATURE CITED The genetic basis of heterosis in maize. Genetics 35: The Mendelian theory of heredity and the augmentation of vigor. Science Dominance and the vigor of first generation hybrids. Am. Naturalist 55: COMSTOCK, R. E., 1955 Theory of quantitative genetics: synthesis. Cold Spring Harbor Symp. Quant. Biol. 20: Dominance, genotype-environment interaction, and homeostasis. pp Biometrical Genetics. Edited by 0. KEMPTHORNE. Pergamon Press, New York. COMSTOCK, R. E., and H. F. ROBINSON, 1952 Estimation of average degree of dominance. pp Heterosis. Edited by J. W. GOWEN. Iowa State College Press, Ames. COMSTOCK, R. E., H. F. ROBINSON, and P. H. HARVEY, 1949 A breeding procedure designed to make maximum use of both general and specific combining ability. Agronomy J. 41 : CROW, J. F., 1948 Alternative hypotheses of hybrid vigor. Genetics 33: Population genetics. Am. J. Human Genet. 13: DOBZHANSKY, TH., and 0. PAVLOVSKY, 1960 How stable is balanced polymorphism? Proc. Natl. Acad. Sci. U. S. 46: EAST, E. M., 1936 Heterosis. Genetics 21: GARDNER, C. O., 1963 Estimates of genetic parameters in cross-fertilizing plants and their implications in plant breeding. pp Statistical Genetics and Plant Breeding. Natl. Acad. Sci.-Natl. Res. Council Publ GARDNER, C. O., and J. H. LONNQUIST, 1959 Linkage and the degree of dominance of genes controlling quantitative characters in maize. Agronomy J. 51 : GARDNER, C. O., P. H. HARVEY, R. E. COMSTOCK, and H. F. ROBINSON, 1953 Dominance of genes controlling quantitative characters in maize. Agronomy J. 45 : HULL, F. H., 1945 Recurrent selection for specific combining ability in corn. J. Am. Soc. Agron. 37: Evidence of overdominance in yield of corn. Genetics 33:llO Recurrent selection and overdominance. pp Heterosis. Edited by J. W. GOWEN. Iowa State College Press, Ames. JONES, D. F., 1917 Dominance of linked factors as a means of accounting for heterosis. Genetics 2 : LEVINE, H., 1953 Genetic equilibrium when more than one ecological niche is available. Am. Naturalist 87: MATZINGER, D. F., G. F. SPRAGUE, and C. C. COCKERHAM, 1959 Diallel crosses of maize in experiments repeated over locations and years. Agronomy J. 51 : MURPHY, R. P., 1942 Convergent improvement with four inbred lines of corn. J. Am. Soc. Agron. 34: RICHEY, F. D., and G. F. SPRAGUE, 1931 Experiments on hybrid vigor and convergent improvement in corn. U. S. Dept. Agr. Tech. Bull RHOADES, M. M., 1955 The cytogenetics of maize. Chapter IV. Corn and Corn Improuement. Edited by G. F. SPRAGUE. Academic Press, New York.

13 VARIANCE AND DOMINANCE IN MAIZE 423 ROBINSON, H. F., R. E. COMSTOCK, and P. H. HARVEY, 1949 Estimates of heritability and the degree of dominance in corn. Agronomy J. 41 : Genetic variances in open-pollinated varieties of corn. Genetics 40: ROBINSON, H. F., C. C. COCKERHAM, and R. H. MOLL, 1960 Studies on estimates of dominance variance and effects of linkage bias. pp Biometrical Genetics. Edited by 0. KEMP- THORNE. Pergamon Press, New York. ROBINSON, H. F., A. KHALIL, R. E. COMSTOCK, and C. C. COCKERHAM, 1958 Joint interpretation of heterosis and genetic variances in two open-pollinated varieties of corn and their cross. Genetics 43: ROBINSON, H. F., and R. H. MOLL, 1959 Implications of environmental effects on genotypes in relation to breeding. pp Proc. 14.th Hybrid Corn Ind. Conf. American Seed Trade Association, Chicago, Illinois. ROJAS, B. A., and G. F. SPRAGUE, 1952 A comparison of variance components in corn yield trials General and specific combining ability and their interactions with locations and years. Agronomy J. 44: SINGLETON, W. R., 1941 Hybrid vigor and its utilization in sweet corn breeding. Am. Naturalist 75: SPRAGUE, G. F., W. A. RUSSELL, and L. H. PENNY, 1959 Further studies on convergent improvement in corn. Genetics 44: WALLACE, B Heterotic mutations. pp Molecular Genetics and Human Disease. Edited by L. I. GARDNER, et al. Thomas, Springfield, Illinois.