Estimates of genetic variance in an F2 maize population

Maize (Zea mays L.) breeders have used several genetic-statistical models to study the inheritance of quantitative traits. These models provide information on the importance of additive, dominance, and epistatic genetic variance for a quantitative trait. Estimates of genetic variances are useful in understanding heterosis and determining the response to selection. The objectives of this study were to estimate additive and dominance genetic variances and the average level of dominance for an F2 population derived from the B73 x Mo17 hybrid and use weighted least squares to determine the importance of digenic epistatic variances relative to additive and dominance variances. Genetic variances were estimated using Design III and weighted least squares analyses. Both analyses determined that dominance variance was more important than additive variance for grain yield. For other traits, additive genetic variance was more important than dominance variance. The average level of dominance suggests either overdominant gene effects were present for grain yield or pseudo-overdominance because of linkage disequilibrium in the F2 population. Epistatic variances generally were not significantly different from zero and therefore were relatively less important than additive and dominance variances. For several traits estimates of additive by additive epistatic variance decreased estimates of additive genetic variance, but generally the decrease in additive genetic variance was not significant.     

Selection with Partial Selfing. I. Mass Selection

The expected responses to mass selection carried out before or after reproduction in a population whose members all have a fixed probability of self pollination (s) are formulated using covariances of relatives and their component quadratic functions for a model with arbitrary additive and dominance effects. The response measured in the first generation offspring after selection (immediate gain) can differ from that retained when the population has regained equilibrium (permanent gain). The population mean behaves in a predictable manner during the return to equilibrium, and its value at any time can be predicted from earlier generations. The permanent gain from selection after reproduction is always (1 + s)/2 times as large as that from selection before reproduction, but the relationship of the immediate gains depends on the genetic model assumed. Numerical analysis applied to a model with two alleles per locus and varying allele frequencies, dominance ratios and numbers of loci showed that the proportion of the immediate gain retained at equilibrium was reduced with the large inbreeding depression associated with increasing dominance levels and numbers of loci and was generally lower for selection after reproduction than before. In the absence of information as to the magnitude of genetic variances and inbreeding depression in species reproducing by partial selfing, the importance of this phenomenon is unknown.     

Combined genetic analysis of partial blast resistance in an upland rice population and recurrent selection for line and hybrid values

The CNA-IRAT 5 upland rice population has been improved for 4 years by recurrent selection for blast resistance in Brazil. In order to predict the efficiency of recurrent selection in different test systems and to compare the relative advantage of hybrids versus pure line breeding, a combined genetic analysis of partial blast resistance in the CNA-IRAT 5 population was undertaken. A three-level hierarchical design in inbreeding and a factorial design were derived from the base population. Partial blast resistance of lines and hybrids was evaluated in the greenhouse and in the field by inoculation with one virulent blast isolate. The means and genetic variances of the hybrids and lines were estimated. Genetic advance by recurrent selection was predicted from estimates of variance components. The inheritance of partial blast resistance was mainly additive but non-additive effects were detected at both levels of means and variances. Mean heterosis ranged from 4%–8% for lesion size and lesion density to 10–12% for leaf and panicle resistance. High dominance or homozygous dominance variances relative to additive variance and negative covariance between additive and homozygous dominance effects were estimated. A low frequency of favourable alleles for partial resistance would explain the observed organisation of genetic variability in the base population. Recurrent selection will efficiently improve partial blast resistance of the CNA-IRAT 5 population. Genetic advance for line or hybrid values was expected to be higher testing doubled haploid lines than S1 lines, or than general combining ability. Two components of partial resistance assessed in the greenhouse, lesion size and lesion density, could be used as indirect selection criteria to improve field resistance. On the whole, hybrid breeding for partial blast resistance appeared to be slightly more advantageous than pure line breeding.     

Something Old and Something New: Wedding Recombinant Inbred Lines with Traditional Line Cross Analysis Increases Power to Describe Gene Interactions

In this paper we present a novel approach to quantifying genetic architecture that combines recombinant inbred lines (RIL) with line cross analysis (LCA). LCA is a method of quantifying directional genetic effects (i.e. summed effects of all loci) that differentiate two parental lines. Directional genetic effects are thought to be critical components of genetic architecture for the long term response to selection and as a cause of inbreeding depression. LCA typically begins with two inbred parental lines that are crossed to produce several generations such as F1, F2, and backcrosses to each parent. When a RIL population (founded from the same P1 and P2 as was used to found the line cross population) is added to the LCA, the sampling variance of several nonadditive genetic effect estimates is greatly reduced. Specifically, estimates of directional dominance, additive x additive, and dominance x dominance epistatic effects are reduced by 92%, 94%, and 56% respectively. The RIL population can be simultaneously used for QTL identification, thus uncovering the effects of specific loci or genomic regions as elements of genetic architecture. LCA and QTL mapping with RIL provide two qualitatively different measures of genetic architecture with the potential to overcome weaknesses of each approach alone. This approach provides cross-validation of the estimates of additive and additive x additive effects, much smaller confidence intervals on dominance, additive x additive and dominance x dominance estimates, qualitatively different measures of genetic architecture, and the potential when used together to balance the weaknesses of LCA or RIL QTL analyses when used alone.     

Inbreeding depression in the competitive fertilization success of male crickets

Mating between close relatives generally results in offspring of decreased fitness. Inbreeding depression is generally greater for life-history traits than for morphological traits, and recent studies of traits subject to sexual selection suggest that these may suffer the greatest inbreeding depression. Sexual selection continues after mating in the form of sperm competition and cryptic female choice, imposing strong selection on male competitive fertilization success. Here, I examine the effects of a single generation of full-sib mating on competitive fertilization success in a cricket, Teleogryllus oceanicus. The estimated coefficient of inbreeding depression in competitive fertilization success was 0.37, higher than that for other life-history and morphological traits. Such intense inbreeding depression coupled with little or no additive genetic variance for this trait is consistent with strong directional selection on male competitive fertilization success generating high levels of dominance variance, and provides an adaptive explanation for the evolution of inbreeding avoidance found in this species.     

The effect of genetic drift on the variance/covariance components generated by multilocus additive x additive epistatic systems

The effect of population bottlenecks on the components of the genetic variance/covariance generated by n neutral independent additive x additive loci has been studied theoretically. In its simplest version, this situation can be modelled by specifying the allele frequencies and homozygous effects at each locus, and an additional factor measuring the strength of the n-th order epistatic interaction. The variance/covariance components in an infinitely large panmictic population (ancestral components) were compared with their expected values at equilibrium over replicates randomly derived from the base population, after t bottlenecks of size N (derived components). Formulae were obtained giving the derived components (and the between-line variance) as functions of the ancestral ones (alternatively, in terms of allele frequencies and effects) and the corresponding inbreeding coefficient F(t). The n-th order derived component of the genetic variance/covariance is continuously eroded by inbreeding, but the remaining components may increase initially until a critical F(t) value is attained, which is inversely related to the order of the pertinent component, and subsequently decline to zero. These changes can be assigned to the between-line variances/covariances of gene substitution and epistatic effects induced by drift. Numerical examples indicate that: (1) the derived additive variance/covariance component will generally exceed its ancestral value unless epistasis is weak; (2) the derived epistatic variance/covariance components will generally exceed their ancestral values unless allele frequencies are extreme; (3) for systems showing equal ancestral additive and total non-additive variance/covariance components, those including a smaller number of epistatic loci may generate a larger excess in additive variance/covariance after bottlenecks than others involving a larger number of loci, provided that F(t) is low. Our results indicate that it is unlikely that the rate of evolution may be significantly accelerated after population bottlenecks, in spite of occasional increments of the derived additive variance over its ancestral value.     

Refinements to the partitioning of the inbred genotypic variance

Natural gene flow is often localised because of gamete dispersal limitations, and the quantity and structure of the genotypic variance in such populations is a key to predicting the advance from selection, in both evolution and artificial breeding programmes. Earlier derivations of this variance have shown that the total dominance variance may increase with inbreeding despite the fact that heterozygosity is decreasing. This anomaly has been corrected following the de novo biometrical derivation presented in this paper. The whole population also subdivides into descendant lineages that differ in allele frequencies and means because of the dispersion caused by genetic drift and continuing localisation of gamodemes. The paper defines for the first time the among-line and within-line partitions of the dominance variance; and corrects anomalies in the total genic (additive genetic) variance, and its underlying inbred average alle-substitution effect. The revisions also clarify the connections between the Fisher-Falconer, Mather-Hayman, and Wright approaches to defining the inbred genotypic variance. Relationships are discussed between the population dispersion structure and genetic efficiency in selection.     

Genomic mating in outbred species: predicting cross usefulness with additive and total genetic covariance matrices

Diverse crops are both outbred and clonally propagated. Breeders typically use truncation selection of parents and invest significant time, land, and money evaluating the progeny of crosses to find exceptional genotypes. We developed and tested genomic mate selection criteria suitable for organisms of arbitrary homozygosity level where the full-sibling progeny are of direct interest as future parents and/or cultivars. We extended cross variance and covariance variance prediction to include dominance effects and predicted the multivariate selection index genetic variance of crosses based on haplotypes of proposed parents, marker effects, and recombination frequencies. We combined the predicted mean and variance into usefulness criteria for parent and variety development. We present an empirical study of cassava (Manihot esculenta), a staple tropical root crop. We assessed the potential to predict the multivariate genetic distribution (means, variances, and trait covariances) of 462 cassava families in terms of additive and total value using cross-validation. Most variance (89%) and covariance (70%) prediction accuracy estimates were greater than zero. The usefulness of crosses was accurately predicted with good correspondence between the predicted and the actual mean performance of family members breeders selected for advancement as new parents and candidate varieties. We also used a directional dominance model to quantify significant inbreeding depression for most traits. We predicted 47,083 possible crosses of 306 parents and contrasted them to those previously tested to show how mate selection can reveal the new potential within the germplasm. We enable breeders to consider the potential of crosses to produce future parents (progeny with top breeding values) and varieties (progeny with top own performance).     

Potential bias in inbreeding depression estimates when using pedigree relationships to assess the degree of homozygosity for loci under selection

A potential bias in estimation of inbreeding depression when using pedigree relationships to assess the degree of homozygosity for loci under selection is indicated. A comparison of inbreeding coefficients based on either pedigree or genotypic frequencies indicated that, as a result of selection, the inbreeding coefficient based on pedigree might not correspond with the random drift of allelic frequencies. Apparent differences in average levels of both inbreeding coefficients were obtained depending on the genetic model (additive versus dominance, initial allelic frequencies, heritability) and the selection system assumed (no versus mass selection). In the absence of selection, allelic frequencies within a small population change over generations due to random drift, and the pedigree-based inbreeding coefficient gives a proper assessment of the accompanying probability of increased homozygosity within a replicate by indicating the variance of allelic frequencies over replicates. With selection, in addition to random drift, directional change in allelic frequencies is not accounted for by the pedigree-based inbreeding coefficient. This result implies that estimation of inbreeding depression for traits under either direct or indirect selection, estimated by a regression of performance on pedigree-based coefficients, should be carefully interpreted.Deceased     

Prediction of additive and dominance effects in selected or unselected populations with inbreeding

Summary A genetic model with either 64 or 1,600 unlinked biallelic loci and complete dominance was used to study prediction of additive and dominance effects in selected or unselected populations with inbreeding. For each locus the initial frequency of the favourable allele was 0.2, 0.5, or 0.8 in different alternatives, while the initial narrow-sense heritability was fixed at 0.30. A population of size 40 (20 males and 20 females) was simulated 1,000 times for five generations. In each generation 5 males and 10 or 20 females were mated, with each mating producing four or two offspring, respectively. Breeding individuals were selected randomly, on own phenotypic performance or such yielding increased inbreeding levels in subsequent generations. A statistical model containing individual additive and dominance effects but ignoring changes in mean and genetic covariances associated with dominance due to inbreeding resulted in significantly biased predictions of both effects in generations with inbreeding. Bias, assessed as the average difference between predicted and simulated genetic effects in each generation, increased almost linearly with the inbreeding coefficient. In a second statistical model the average effect of inbreeding on the mean was accounted for by a regression of phenotypic value on the inbreeding coefficient. The total dominance effect of an individual in that case was the sum of the average effect of inbreeding and an individual effect of dominance. Despite a high mean inbreeding coefficient (up to 0.35), predictions of additive and dominance effects obtained with this model were empirically unbiased for each initial frequency in the absence of selection and 64 unlinked loci. With phenotypic selection of 5 males and only 10 females in each generation and 64 loci, however, predictions of additive and dominance effects were significantly biased. Observed biases disappeared with 1,600 loci for allelic frequencies at 0.2 and 0.5. Bias was due to a considerable change in allelic frequency with phenotypic selection. Ignoring both the covariance between additive and dominance effects with inbreeding and the change in dominance variance due to inbreeding did not significantly bias prediction of additive and dominance effects in selected or unselected populations with inbreeding.     

A test of quantitative genetic theory using Drosophila- effects of inbreeding and rate of inbreeding on heritabilities and variance components

Inbreeding is expected to decrease the heritability within populations. However, results from empirical studies are inconclusive. In this study, we investigated the effects of three breeding treatments (fast and slow rate of inbreeding - inbred to the same absolute level - and a control) on heritability, phenotypic, genetic and environmental variances of sternopleural bristle number in Drosophila melanogaster. Heritability, and phenotypic, genetic and environmental variances were estimated in 10 replicate lines within each of the three treatments. Standard least squares regression models and Bayesian methods were used to analyse the data. Heritability and additive genetic variance within lines were higher in the control compared with both inbreeding treatments. Heritabilities and additive genetic variances within lines were higher in slow compared with fast inbred lines, indicating that slow inbred lines retain more evolutionary potential despite the same expected absolute level of inbreeding. The between line variance was larger with inbreeding and more than twice as large in the fast than in the slow inbred lines. The different pattern of redistribution of genetic variance within and between lines in the two inbred treatments cannot be explained invoking the standard model based on selective neutrality and additive gene action. Environmental variances were higher with inbreeding, and more so with fast inbreeding, indicating that inbreeding and the rate of inbreeding affect environmental sensitivity. The phenotypic variance decreased with inbreeding, but was not affected by the rate of inbreeding. No inbreeding depression for mean sternopleural bristle number was observed in this study. Considerable variance between lines in additive genetic variance within lines was observed, illustrating between line variation in evolutionary potential.     

Severe outbreeding and inbreeding depression maintain mating system differentiation in Epipactis (Orchidaceae)

In hermaphroditic plants, theory for mating system evolution predicts that populations will evolve to either complete autonomous selfing (AS) or complete outcrossing, depending on the balance between automatic selection favouring self‐fertilization and costs resulting from inbreeding depression (ID). Theory also predicts that selection for selfing can occur rapidly and is driven by purging of genetic load and the loss of ID. Therefore, selfing species are predicted to have low levels of ID or even to suffer from outbreeding depression (OD), whereas predominantly outcrossing species are expected to have high levels of ID. To test these predictions, we related the capacity of AS to the magnitude of early‐acting inbreeding or OD in both allogamous and autogamous species of the orchid genus Epipactis. For each species, the level of AS was assessed under controlled greenhouse conditions, whereas hand‐pollinations were performed to quantify early costs of inbreeding or OD acting at the level of fruit and seed production. In the autogamous species, the capacity of AS was high (> 0.72), whereas in the allogamous species AS was virtually absent (< 0.10). Consistent with our hypothesis, allogamous Epipactis species had significantly higher total ID (average: 0.46) than autogamous species, which showed severe costs of OD (average: ?0.45). Overall, our findings indicate that strong early‐acting ID represents an important mechanism that contributes to allogamy in Epipactis, whereas OD may maintain selfing in species that have evolved to complete selfing.     

Allele frequency changes due to hitch-hiking in genomic selection programs

Background

Genomic selection makes it possible to reduce pedigree-based inbreeding over best linear unbiased prediction (BLUP) by increasing emphasis on own rather than family information. However, pedigree inbreeding might not accurately reflect loss of genetic variation and the true level of inbreeding due to changes in allele frequencies and hitch-hiking. This study aimed at understanding the impact of using long-term genomic selection on changes in allele frequencies, genetic variation and level of inbreeding.

Methods

Selection was performed in simulated scenarios with a population of 400 animals for 25 consecutive generations. Six genetic models were considered with different heritabilities and numbers of QTL (quantitative trait loci) affecting the trait. Four selection criteria were used, including selection on own phenotype and on estimated breeding values (EBV) derived using phenotype-BLUP, genomic BLUP and Bayesian Lasso. Changes in allele frequencies at QTL, markers and linked neutral loci were investigated for the different selection criteria and different scenarios, along with the loss of favourable alleles and the rate of inbreeding measured by pedigree and runs of homozygosity.

Results

For each selection criterion, hitch-hiking in the vicinity of the QTL appeared more extensive when accuracy of selection was higher and the number of QTL was lower. When inbreeding was measured by pedigree information, selection on genomic BLUP EBV resulted in lower levels of inbreeding than selection on phenotype BLUP EBV, but this did not always apply when inbreeding was measured by runs of homozygosity. Compared to genomic BLUP, selection on EBV from Bayesian Lasso led to less genetic drift, reduced loss of favourable alleles and more effectively controlled the rate of both pedigree and genomic inbreeding in all simulated scenarios. In addition, selection on EBV from Bayesian Lasso showed a higher selection differential for mendelian sampling terms than selection on genomic BLUP EBV.

Conclusions

Neutral variation can be shaped to a great extent by the hitch-hiking effects associated with selection, rather than just by genetic drift. When implementing long-term genomic selection, strategies for genomic control of inbreeding are essential, due to a considerable hitch-hiking effect, regardless of the method that is used for prediction of EBV.     

Analysis of genetic control of mating behavior in screwworm (Diptera: Calliphoridae) males through diallel crosses and artificial selection

Summary The mode of genetic control of male screw-worm (Diptera: Calliphoridae) mating behavior was examined using diallel cross and artificial selection. Diallel crosses showed strong dominance effects, with hybrids being uniformly more successful in copulation than their more inbred parental strains. Weaker additive and reciprocal effects were also noted. Environmental (replicate) effects were highly significant. Regression of array variances and covariances indicated that epistatic interactions or unequal allele distribution during gametogenesis may have occurred and that high courtship propensity polygenes show dominance over low propensity genes. Artificial selection on males from outbred strains from Guatemala and Belize resulted in a decreased number of mating attempts for lines selected for reduced activity, but mating attempts in lines selected for high mating activity did not increase. A combination of inbreeding during the selection cycles as well as selection for recessive traits would explain this response. The two types of experiments were in general agreement, indicating significant dominance and environmental influence on male mating behavior with weaker additive and possible maternal effects.     

Selection theory for selfed progenies

Summary The purpose of this article was to extend the model used to predict selection response with selfed progeny from 2 alleles per locus to a model which is general for number and frequency of alleles at loci. To accomplish this, 4 areas had to be dealt with: 1) simplification of the derivation and calculation of the condensed coefficients of identity; 2) presentation of the genetic variances expressed among and within selfed progenies as linear function of 5 population parameters; 3) presentation of selection response equations for selfed progenies as functions of these 5 population parameters; and 4) to identify a set of progeny to evaluate, such that one might be able to estimate these 5 population parameters.The five population parameters used in predicting gains were the additive genetic variance, the dominance variance, the covariance of additive and homozygous dominance deviations, the variance of the homozygous dominance deviations and a squared inbreeding depression term.Contribution from the Missouri Agricultural Experiment Station. Journal Series No. 9971     

The change in quantitative genetic variation with inbreeding

Inbreeding is known to reduce heterozygosity of neutral genetic markers, but its impact on quantitative genetic variation is debated. Theory predicts a linear decline in additive genetic variance (V(A)) with increasing inbreeding coefficient (F) when loci underlying the trait act additively, but a nonlinear hump-shaped relationship when dominance and epistasis are important. Predictions for heritability (h2) are similar, although the exact shape depends on the value of h2 in the absence of inbreeding. We located 22 published studies in which the level of genetic variation in experimentally inbred populations (measured by V(A) or h2) was compared with that in outbred control populations. For life-history traits, the data strongly supported a nonlinear change in genetic variation with increasing F. V(A) and h2 were, respectively, 244% and 50% higher at F = 0.4 than in outbred populations, and dominance plus epistatic variance together exceeded additive variance by a factor of four. For nonfitness traits the decline was linear and estimates of nonadditive variance were small. These results confirm that population bottlenecks frequently increase V(A) in some traits, and imply that life-history traits are underlain by substantial dominance or epistasis. However, the importance of drift-induced genetic variation in conservation or evolutionary biology is questionable, in part because inbreeding depression usually accompanies inbreeding.     

Recent approaches into the genetic basis of inbreeding depression in plants

Predictions for the evolution of mating systems and genetic load vary, depending on the genetic basis of inbreeding depression (dominance versus overdominance, epistasis and the relative frequencies of genes of large and small effect). A distinction between the dominance and overdominance hypotheses is that deleterious recessive mutations should be purged in inbreeding populations. Comparative studies of populations differing in their level of inbreeding and experimental approaches that allow selection among inbred lines support this prediction. More direct biometric approaches provide strong support for the importance of partly recessive deleterious alleles. Investigators using molecular markers to study quantitative trait loci (QTL) often find support for overdominance, though pseudo-overdominance (deleterious alleles linked in repulsion) may bias this perception. QTL and biometric studies of inbred lines often find evidence for epistasis, which may also contribute to the perception of overdominance, though this may be because of the divergent lines initially crossed in QTL studies. Studies of marker segregation distortion commonly uncover genes of major effect on viability, but these have only minor contributions to inbreeding depression. Although considerable progress has been made in understanding the genetic basis of inbreeding depression, we feel that all three aspects merit more study in natural plant populations.     

Quantitative Genetics of Sperm Precedence in Drosophila Melanogaster

To assess the genetic basis of sperm competition under conditions in which it occurs, I estimated additive, dominance, homozygous and environmental variance components, the effects of inbreeding, and the weighted average dominance of segregating alleles for two measures of sperm precedence in a large, outbred laboratory population. Both first and second male precedence show significant decline on inbreeding. Second male precedence demonstrates significant dominance variance and homozygous genetic variance, but the additive variance is low and not significantly different from zero. For first male precedence, the variance among homozygous lines is again significant, and dominance variance is larger than the additive variance, but is not statistically significant. In contrast, male mating success and other fitness components in Drosophila generally exhibit significant additive variance and little or no dominance variance. Other recent experiments have shown significant genotypic variation for sperm precedence and have associated it with allelic variants of accessory-gland proteins. The contrast between sperm precedence and other male fitness traits in the structure of quantitative genetic variation suggests that different mechanisms may be responsible for the maintenance of variation in these traits. The pattern of genetic variation and inbreeding decline shown in this experiment suggests that one or a few genes with major effects on sperm precedence may be segregating in this population.     

家蝇（Musca domestica）对三氟氯氰菊酯的抗药性遗传

研究了家蝇对三氟氯氰菊酯抗性的遗传,通过对抗性品系和敏感品系杂交后代的抗性遗传分析发现家蝇对三氟氯氰菊酯的抗性受多因子控制,抗性显性率为－0．102,为不完全隐性。其对三氟氯氰菊酯的抗性现实遗传力为0．120。     

The effects of dominance, regular inbreeding and sampling design on Q(ST), an estimator of population differentiation for quantitative traits

To test whether quantitative traits are under directional or homogenizing selection, it is common practice to compare population differentiation estimates at molecular markers (F(ST)) and quantitative traits (Q(ST)). If the trait is neutral and its determinism is additive, then theory predicts that Q(ST) = F(ST), while Q(ST) > F(ST) is predicted under directional selection for different local optima, and Q(ST) < F(ST) is predicted under homogenizing selection. However, nonadditive effects can alter these predictions. Here, we investigate the influence of dominance on the relation between Q(ST) and F(ST) for neutral traits. Using analytical results and computer simulations, we show that dominance generally deflates Q(ST) relative to F(ST). Under inbreeding, the effect of dominance vanishes, and we show that for selfing species, a better estimate of Q(ST) is obtained from selfed families than from half-sib families. We also compare several sampling designs and find that it is always best to sample many populations (>20) with few families (five) rather than few populations with many families. Provided that estimates of Q(ST) are derived from individuals originating from many populations, we conclude that the pattern Q(ST) > F(ST), and hence the inference of directional selection for different local optima, is robust to the effect of nonadditive gene actions.