Non-additive Variance Research Articles

Impact of genotype-environment interactions on the inheritance of wheat yield in low-yielding environments

Complete F1 and F2 diallel crosses were used to investigate the inheritance of yield among eight Ugandan bread wheat lines grown in two low-yielding environments; one marginal because of the high incidence of yellow rust normally experienced there, the other a low-rust site. In the marginal, high-rust environment, mainly additive genetic variation was present, though in one season, when disease incidence was unusually low, non-additive variation due to dominance was also detected. Although yield was significantly higher at the low-rust site, no clear pattern of inheritance was apparent there. The results indicated that the low rust site was an intermediate environment, just below the crossover point of a crossover genotype-environment interaction. The implications of these results for wheat breeding in low-yielding and marginal environments in Uganda and elsewhere are discussed.

Genetic variation and prediction of additive and nonadditive genetic effects for six carcass traits in an Angus-Brahman multibreed herd.

Estimates of covariances and sire expected progeny differences of additive and nonadditive genetic effects for six carcass traits were obtained using records from 486 straightbred and crossbred steers from 121 sires born between 1989 and 1995 in the Angus-Brahman multibreed herd of the University of Florida. Steers were slaughtered at a similar carcass composition end point. Covariances were estimated by REML procedures, using a generalized expectation-maximization algorithm applied to multibreed populations. Straightbred and crossbred estimates of heritabilities and additive genetic correlations were within ranges found in the literature for steers slaughtered on an age- or weight-constant basis for hot carcass weight, longissimus muscle area, and shear force but equal to or less than the lower bound of these ranges for fat-related traits. Maximum values of interactibilities (i.e., ratios of nonadditive variances to phenotypic variances in the F1) and nonadditive genetic correlations were smaller than heritabilities and additive genetic correlations in straightbreds and crossbred groups. Sire additive and total direct genetic predictions for longissimus muscle area, marbling, and shear force tended to decrease with the fraction of Brahman alleles, whereas those for hot carcass weight and fat thickness over the longissimus were higher, and those for kidney fat were lower in straightbreds and F1 than in other crossbred groups. Nonadditive genetic predictions were similar across sire groups of all Angus and Brahman fractions. These results suggest that slaughtering steers on a similar carcass composition basis reduces variability of fat-related traits while retaining variability for non-fat-related traits comparable to slaughtering steers on a similar age or weight basis. Selection for carcass traits within desirable (narrow) ranges and slaughter of steers at similar compositional end point seems to be a good combination to help produce meat products of consistent quality.

POPULATION STRUCTURE OF MORPHOLOGICAL TRAITS IN CLARKIA DUDLEYANA. II. CONSTANCY OF WITHIN-POPULATION GENETIC VARIANCE.

Recent quantitative genetic studies have attempted to infer long-term selection responsible for differences in observed phenotypes. These analyses are greatly simplified by the assumption that the within-population genetic variance remains constant through time and over space, or for the multivariate case, that the matrix of additive genetic variances and covariances (G matrix) is constant. We examined differences in G matrices and the association of these differences with differences in multivariate means (Mahalanobis D2 ) among 11 populations of the California endemic annual plant, Clarkia dudleyana. Based on nine continuous morphological traits, the relationship between Mahalanobis D2 and a distance measure summarizing differences in G matrices reflected no concomitant change in (co)variances with changes in means. Based on both broad- and narrow-sense analyses, we found little evidence that G matrices differed between populations. These results suggest that both the additive and nonadditive (co)variances for traits have remained relatively constant despite changes in means.

COMBINING ABILITY ANALYSIS OVER ENVIRONMENTS IN LINSEED

Preponderance of additive gene effect was observed for days to flower, days to maturity. plant height, test weight, seed yield and oil yield. Additive genetic variation done was significant for primary branches, number of seeds per capsule, biological yield and seed oil content, whereas significant dominance genetic variation was seen for harvest index. However, none of the genetic variation was significant for number of capsules per plant. Both gca and sea were influenced by environments suggesting that to have unbiased estimate of gea and sea, the material may be tested over wide range of environments. The parental lines Chambal and Triveni were identified as a good general combiners for seed yield and oil content, earliness and other yield components. The cross combination LCK 88511 x Triveni exhibited high desired sea effects for seed yield, carliness, oil content and other yield contributing attributes. The additive and non-additive variance may be exploited following inter mating among the progenies within and between promising crosses in early segregating generations.

A general model for the evolution of recombination

A general representation of multilocus selection is extended to allow recombination to depend on genotype. The equations simplify if modifier alleles have small effects on recombination. The evolution of such modifiers only depends on how they alter recombination between the selected loci, and does not involve dominance in modifier effects. The net selection on modifiers can be found explicitly if epistasis is weak relative to recombination. This analysis shows that recombination can be favoured in two ways: because it impedes the response to epistasis which fluctuates in sign, or because it facilitates the response to directional selection. The first mechanism is implausible, because epistasis must change sign over periods of a few generations: faster or slower fluctuations favour reduced recombination. The second mechanism requires weak negative epistasis between favourable alleles, which may either be increasing, or held in check by mutation. The selection (si) on recombination modifiers depends on the reduction in additive variance of log(fitness) due to linkage disequilibria (v1 < O), and on non-additive variance in log(fitness) (V'2, V'3.. for epistasis between 2, 3.. loci). For unlinked loci and pairwise epistasis, si = --(v1 +4V2/3)deltar, where deltar is the average increase in recombination caused by the modifier. The approximations are checked against exact calculations for three loci, and against Charlesworth's analyses of mutation/selection balance (1990), and directional selection (1993). The analysis demonstrates a general relation between selection on recombination and observable components of fitness variation, which is open to experimental test.

458 PB 335 HERITABILITY ESTIMATES OF POWDERY MILDEW RESISTANCE IN A TWO-YEAR-OLD LILAC POPULATION

Twenty-one control-pollinated families of lilac (Syringa) were evaluated for the presence of powdery mildew (Microsphaera syringae). Because disease developed first in the lower portions of the plant and moved up, infection was scored from the lowest (1 =only on the lower quarter of the plant) to the highest quarter of the plant (4=present on all quarters of the plant). Family means for mildew score ranged from 2.3 to 3.8 and averaged 3.1, and for height ranged from 59 to 107 cm and averaged 82 cm. Narrow sense and broad sense he&amp;abilities were estimated to be 0.08 and 0.27 respectively. Since any selections will be clonal, this relatively large proportion of non-additive variance can be fully utilized. There was a significant positive correlation between family means of height and mildew score (0.58); however, the phenotypic correlation between height and mildew score was -0.11. For this population the genetic correlation between mildew infection and height was positive (the taller families on average had mildew farther up the plant), but the environmental correlation was negative.

Age Trends in Genetic Parameters for Tree Height in a Nonselected Population of Loblolly Pine

Abstract Additive variance for height of loblolly pine (Pinus taeda L.) in Georgia was very low at younger ages (1 to 8) but rapidly increased thereafter. Nonadditive variance increased from ages 1 to 10 and then remained constant through age 26. The ratio of nonadditive variance to total genetic variance increased from 17% at age 1 to a maximum of 82% at age 6, and then declined to 20% at age 26. Heritability values ranged from almost zero to approximately 0.75 with the lowest values occurring at very young ages and for within-family and individual-tree heritabilities. The largest values were associated mainly with family heritabilities and older ages. Almost all estimates of heritability exhibited similar trends; values were very low at early ages and a maximum value between ages 14 and 16. Narrow-sense heritabilities were near zero until approximately age 8, then they increased sharply through age 16 and declined at the final measurement age. Finally, the coeffident of genetic prediction for tree height between juvenile ages (1 to 16) and the final measurement age for tree height, when based on the total genetic component (CGP_G), showed a nearly linear increase from age 1 to age 16. The maximum values for this parameter were those associated with full-sib family means and ranged from 0.13 at age 1 to 0.67 at age 16. The additive (CGP_A) and nonadditive (CGP_D) components of CGP_G followed the same patterns the additive and nonadditive variances followed. FOR. SCI. 39(2):231-251.

Genetic Variance Components and Heritabilities of Several Avocado Traits

Genetic variance components for avocado (Persea americana Mill.) traits were estimated to improve avocado breeding efficiency. The additive and nonadditive genetic variance components were calculated from the variances between and within crosses. In all nine traits examined, i.e.-anise scent, fruit density, flowering intensity, fruit weight, harvest duration, inflorescence length, seed size, softening time, and tree size-a significant nonadditive genetic variance was detected. Additive genetic variance in all traits was lower and nonsignificant. The existence of major nonadditive variance was indicated also by narrow-sense and broad-sense heritability values estimated for each trait. Therefore, parental selection should not be based solely on cultivar performance. Crosses between parents of medium and perhaps even low performance should also be included in the breeding program.

Genetic Variance Component Estimation in a Nested Mating Design with Positive Assortative Mating, and Application to Maize

Negative estimation of genetic variance components can arise in a nested mating design. This may be due to inaccurate estimates, experimental problems, sampling error, or failure of the assumptions of the genetic or statistical models. We examined the effect of assortative mating on male and female variance components (σ2M and σ2F, respectively) in a nested mating design. Two correlation coefficients were introduced to quantify the effect of assortative mating: the correlation coefficient between females mated to the same male (r) and the correlation coefficient between male and female (r′). Under positive assortative mating, additive variance is systematically overestimated and dominance variance is underestimated. If there is a correlation among females mated to a male but no correlation between male and female (r′ = 0, r ≠ 0), the additive variance is overestimated by 4 r σ2F and nonadditive variance is underestimated by 8 r σ2F. To investigate the presence of assortative mating in a nested design, expressions of correlations among parents were given as a function of the estimated components of variance and of the type of gene action. Correlations among parents were estimated utilizing experimental data for various traits in maize (Zea mays L.) from which negative estimates of dominance had been obtained. Estimates of r were positive and high for earliness traits indicating assortative mating relative to earliness, which may in part explain negative dominance variance estimates. However, correcting variance components estimates is difficult when genetic variation of the trait is not strictly additive.

Effects of partial inbreeding on fixation rates and variation of mutant genes.

Diffusion methods were used to investigate the fixation probability, average time until fixation and extinction, and cumulative heterozygosity and genetic variance for single mutant genes in finite populations with partial inbreeding. The critical parameters in the approximation are the coefficient of inbreeding due to nonrandom mating (F) and the effective population size (Ne), which also depends on F and the variance of family size. For large Ns, the fixation probability (u) is u = 2(Ne/N)s (F + h - Fh), where N is the population census, s is the coefficient of selection of the mutant homozygote and h is the coefficient of dominance. For Poisson family size (independent Poisson distributions of selfed and nonselfed offspring with partial selfing, and independent Poisson distributions of male and female numbers with partial sib mating), Ne = N/(1 + F), and the time until fixation is approximately equal to Ne/N times the time to fixation with random mating, but this relation does not hold, however, for other distributions of family size. The cumulative nonadditive variance until fixation or loss for dominant genes is reduced with increasing F while for recessive genes it is increased with intermediate values of F. The average time until extinction of deleterious mutations is reduced by increasing F. This reduction, when expressed as a proportion, is approximately independent of the initial gene frequency as well as the selective disadvantage if this is large.

Genetic variation for bacterial wilt resistance in a population of tetraploid potato

Genetic variance components and heritability were estimated for resistance to bacterial wilt in a population of tetraploid potato with resistance derived from several specific sources. Both additive and non-additive variance components were significant. Their relative magnitudes indicated the importance of non-additive gene action in the genetic control of the resistance. Narrow-sense heritability was relatively low for both disease index and % survival indicating that progress in population development would be slow. Broad-sense heritability was, however, relatively high which promises success of clonal selection in developing clonal resistant cultivars.

Genetic parameters from a clonally replicated test of black spruce (Piceamariana)

A clonally replicated field test of full-sib black spruce (Piceamariana (Mill.) B.S.P.) progeny was established at four locations in Nova Scotia. Estimated variance components for 5-year height growth and survival were interpreted according to an additive–dominance–epistasis genetic model and used to derive estimates of gain from various selection and deployment strategies. Five years after striking, 64% of the total genetic variance for height growth was due to additive variance. Virtually all of the remaining nonadditive variance was composed of epistatic variances; dominance variance was negligible. Narrow-sense heritability for 5-year height growth was low at 0.059. Substantial nonadditive variance contributed to a somewhat higher estimate of broad-sense heritability at 0.093. Family-mean heritabilities were much higher: 0.823 and 0.697 for half-sib and full-sib family means, respectively. Comparable heritabilities for survival were estimated with high standard errors and were considered unreliable. Results from this study indicate that clonal selection may provide large increases in genetic gain by capturing (i) genetic variance due to epistasis and (ii) a greater portion of the additive variance. Genetic gains for 5-year height growth in the order of 22.6% might be achieved using the best 1% of tested clones for operational planting. Clonal propagation may also be a preferred method to capture substantial genetic gain (about 11%) from selection at the family level, resulting in simplified management of breeding populations while reducing costs associated with conventional soil-based orchards.

GENOTYPE‐ENVIRONMENT INTERACTION FOR JUVENILE GROWTH IN THE HARD CLAMMERCENARIA MERCENARIA(L.)

Offspring from half-sib and full-sib families of the hard clam, Mercenaria mercenaria were reared in five locations along the Atlantic Coast to test for the presence of genotype-environment interaction for juvenile growth rate. Location effects upon growth rate variation were prevalent; of the genetic effects, the additive genetic by location variance was predominant with the nonadditive genetic by location component contributing to a lesser degree to the interaction variance. The additive and nonadditive variation over all environments was negligible. Genotype-environment interaction was found to be at least partially due to a change in the amount of genetic variation expressed at each location; with significant additive variation detected at Charleston and Georgetown, SC sites and significant nonadditive variation at Millsboro, DE. Genetic covariance/correlation analysis indicated that reversals in relative family performance across locations were prevalent, implying the possibility of habitat specialization among genotypes. In addition, graphical analysis produced no evidence of a ubiquitously superior genotype. These analyses suggest that genotype-environment interaction should act to constrain the evolution of juvenile growth rate in Mercenaria, preserve any heritable variation associated with this trait and may lead to the development of phenotypic plasticity for growth.

Genetics of Seed Yield and Its Components in Common Beans (Phaseolus vulgaris L.) of Andean Origin

AbstractAdditive genetic variance in large‐seeded common beans (Phaseolus vulgaris L.), mostly of Andean South American origin, was higher than nonadditive variance for all traits. Heritability was 0.43 ± 0.19 for yield, 0.49 ± 0.20 for pods/m2, 0.63 ± 0.21 for seeds/m2, 0.76 ± 0.23 for 100‐seed weight, and 0.55 ± 0.22 for days to maturity. Expected gain from selection (expressed in percentage of the population mean) was 9.2 for yield, 12.8 for pods/m2, 21.0 for seeds/m2, 17.6 for 100‐seed weight, and 4.6 for days to maturity.

Combining Ability for Test Weight and Agronomic Traits of Oat

The relative importance of additive and nonadditive variation for agronomic traits provides guidelines for setting breeding strategies for cultivar development. To estimate the relative importance of general and specific combining ability (GCA and SCA) for five traits of oat (Avena sativa L.), 24 oat genotypes were mated according to a Design II scheme. The 24 parents were a sample from elite germplasm available for cultivar development at Iowa State University and in various regions of the USA. Test weight, grain yield, harvest index, date of heading, and plant height were measured for 10 random F2‐derived F3 lines from each of 95 crosses. The oat lines were evaluated in 1988 in four replicates at each of three locations in Iowa. Both GCA and SCA were significant (P ≤ 0.01) for all traits; GCA, however, accounted for 75% of the variability among crosses for test weight, 85% for grain yield, 82% for harvest index, 72% for date of heading, and 85% for plant height. We speculate that additive ✕ additive epistasis was primarily responsible for the observed significant SCA because the estimate of SCA represents 1/4 σ2D + 1/2 σ2AA, and in our experiment σ2D seemed small (based on contrasts of parent vs. offspring means). We suggest that breeders use mild selection intensities in early generations of inbreeding to avoid discarding lines before favorable epistatic combinations form. In regard to parent selection, our results indicate that most parents could be used as male or female in a cross without affecting segregation for these five traits; however, midparent values alone do not adequately predict which crosses produce the most outstanding lines.

Quantitative genetics of disease incidence in Ustilago hordei controlled by virulence and aggressiveness genes

Biometric analyses of variability in the disease incidence phenotype were performed using three F2 dikaryotic populations of the smut fungus Ustilago hordei (Pers.) Lagerh. on barley cultivars 'Trebi' (partially resistant) and 'Odessa' (universal suscept). The variance component involving interactions between segregating genes of U. hordei and environmental factors made the largest contribution towards the disease incidence on both cultivars. Additive and nonadditive (dominant and epistatic) gene effects contributed significantly to total disease incidence variation on both 'Trebi' and 'Odessa'. Heritability (additive genetic variance) was 2.5 times higher on 'Trebi' than on 'Odessa', and nonadditive variance effects were higher on 'Odessa' than on 'Trebi' by a factor of 1.5. Five effective factors were estimated to be segregating in the F2 populations; the virulence gene and four agressiveness factors. It is hypothesized that certain aggressiveness polygenes interact either with at least one other aggressiveness polygene or with the virulence gene. Analysis of variance–covariance provided supporting evidence for the epistatic activity of some genes and weak evidence for possible previous selection for intermediate optimal rather than maximal expression of the disease incidence phenotype. Key words: Ustilago hordei, aggressiveness, polygenes, disease incidence, smut.

Models of Quantitative Variation of Flux in Metabolic Pathways

As a model of variation in a quantitative character, enzyme activity variation segregating in a population is assumed to affect the flux in simple metabolic pathways. The genetic variation of flux is partitioned into additive and nonadditive components. An interaction component of flux variance is present because the effect of an allelic substitution is modified by other substitutions which change the concentrations of shared metabolites. In a haploid population, the the proportion of interaction variance is a function of the gene frequencies at the loci contributing to the flux variation, enzyme activities of mutant and wild type at variable loci and activities at nonvariable loci. The proportion of interaction variance is inversely related to the ratio of mutant to wild-type activities at the loci controlling the enzyme activities. The interaction component as a function of gene frequencies is at a maximum with high mutant allele frequencies. In contrast, the dominance component which would apply to a diploid population is maximal as a proportion of the total when mutant alleles are at low frequencies. Unless there are many loci with large differences in activity between the alleles, the interaction component is a small proportion of the total variance. Data on enzyme activity variation from natural and artificial populations suggest that such variation generates little nonadditive variance despite the highly interactive nature of the underlying biochemical system.

Models of quantitative variation of flux in metabolic pathways.

As a model of variation in a quantitative character, enzyme activity variation segregating in a population is assumed to affect the flux in simple metabolic pathways. The genetic variation of flux is partitioned into additive and nonadditive components. An interaction component of flux variance is present because the effect of an allelic substitution is modified by other substitutions which change the concentrations of shared metabolites. In a haploid population, the the proportion of interaction variance is a function of the gene frequencies at the loci contributing to the flux variation, enzyme activities of mutant and wild type at variable loci and activities at nonvariable loci. The proportion of interaction variance is inversely related to the ratio of mutant to wild-type activities at the loci controlling the enzyme activities. The interaction component as a function of gene frequencies is at a maximum with high mutant allele frequencies. In contrast, the dominance component which would apply to a diploid population is maximal as a proportion of the total when mutant alleles are at low frequencies. Unless there are many loci with large differences in activity between the alleles, the interaction component is a small proportion of the total variance. Data on enzyme activity variation from natural and artificial populations suggest that such variation generates little nonadditive variance despite the highly interactive nature of the underlying biochemical system.

Diallel analysis of resistance to Septoria tritici isolates in durum wheat

All crosses, except for reciprocals, were made among ten cultivars originating from crop improvement programs in North Africa and the Middle East. The entries varied widely in reaction to Septoria tritici. F1 and F2 progenies of the crosses were evaluated using eight S. tritici isolates from seven countries in the Mediterranean area. Thus, sixteen separate combining ability analyses were excecuted. General combining ability (GCA) was the major component of variation, although specific combining ability (SCA) was present in most cases. Additive variance thus appears to be of predominant importance. Nevertheless, non-additive variance may interfere when line selection in a breeding program is practiced. While differing greatly among cultivars, specific GCA effects for each cultivar separately were of similar magnitude for all isolates. Ranking statistics determined that cultivars were ranked in similar order for both means and specific GCA effects independent of the isolate used. Different isolates may therefore interact with similar or identical genetically controlled mechanisms in a particular cultivar. This could indicate the absence of differential gene-for-gene relationships and suggests that isolates vary in aggressiveness rather than in virulence.

Variance components of fitness under stabilizing selection.

SummaryVariance components of fitness under the stabilizing selection scheme of Wright (1935) for metric characters are calculated, extending his original analysis to the case with any number of alleles and multiple characters assuming additivity of gene effects. They are calculated in terms of the moments of the effects of alleles at individual loci for the metric characters. From these formulas, the variance components of fitness are evaluated at the mutation–selection equilibria predicted by the ‘Gaussian’ approximation (Lande, 1976), which is applicable if the per locus mutation rate is high, and the ‘House of Cards’ approximation (Turelli, 1984), which is applicable if the per locus mutation rate is low. It is found that the additive variance of fitness is small compared to non-additive variance in the ‘Gaussian’ case, whereas the additive variance is larger than non-additive variance in the ‘House of Cards’ case if the number of loci per character and the number of characters affected by each locus are not too large. With the assumption that a significant portion of fitness is due to this type of stabilizing selection, it is suggested that the real parameters are in the range where the ‘House of Cards’ approximation is applicable, since available data on variance components of fitness components in Drosophila show that the additive variance is far larger than the non-additive variance. It is noted that the present method does not discriminate the two approximations if the average values of the metric characters deviate from the optimum values. Other limitations of the present method are also discussed.