Selection for environmental variation: a statistical analysis and power calculations to detect response

Data from uterine capacity in rabbits (litter size) were analyzed to determine whether the environmental variance was partly genetically determined. The fit of a classical homogeneous variance mixed linear (HOM) model and that of a genetically structured heterogeneous variance mixed linear (HET) model were compared. Various methods to assess the quality of fit favor the HET model. The posterior mean (95% posterior interval) of the additive genetic variance affecting the environmental variance was 0.16 (0.10; 0.25) and the corresponding number for the coefficient of correlation between genes affecting mean and variance was -0.74 (-0.90;-0.52). It is argued that stronger support for the HET model than that derived from statistical analysis of data would be provided by a successful selection experiment designed to modify the environmental variance. A simple selection criterion is suggested (average squared deviation from the mean of repeated records within individuals) and its predicted response and variance under the HET model are derived. This is used to determine the appropriate size and length of a selection experiment designed to change the environmental variance. Results from the analytical expressions are compared with those obtained using simulation. There is good agreement provided selection intensity is not intense.     

Joint effect of selection, linkage and partial inbreeding on additive genetic variance in an infinite population

Under the inifinitesimal model of gene effects, selection reduces the additive genetic variance by inducing negative linkage disequilibrium among selected genes. If the selected genes are linked, the decay of linkage disequilibrium is delayed, and the reduction of additive genetic variance is enhanced. Inbreeding in an infinite population also alters the additive genetic variance through the generation of positive association among genes within a locus. In the present study, the joint effect of selection, linkage and partial inbreeding (partial selfing or partial full-sib mating) on the additive genetic variance was modeled. The recurrence relations of the additive genetic variance between successive generations and the prediction equation of the asymptotic additive genetic variance were derived. Numerical computation showed that although partially inbred populations initially maintain larger genetic variances, the accumulated effect of selection overrides the effect of inbreeding. Stochastic simulation was carried out to check the precision of prediction, showing that the obtained equations give a satisfactory prediction during initial generations. However, the predicted values always overestimate the simulated values, especially in later generations. Based on these results, possible extensions and perspectives of the assumed model were discussed.     

Genetic evaluation and selection response for growth in meat-type quail through random regression models using B-spline functions and Legendre polynomials

The objective was to estimate (co)variance functions using random regression models (RRM) with Legendre polynomials, B-spline function and multi-trait models aimed at evaluating genetic parameters of growth traits in meat-type quail. A database containing the complete pedigree information of 7000 meat-type quail was utilized. The models included the fixed effects of contemporary group and generation. Direct additive genetic and permanent environmental effects, considered as random, were modeled using B-spline functions considering quadratic and cubic polynomials for each individual segment, and Legendre polynomials for age. Residual variances were grouped in four age classes. Direct additive genetic and permanent environmental effects were modeled using 2 to 4 segments and were modeled by Legendre polynomial with orders of fit ranging from 2 to 4. The model with quadratic B-spline adjustment, using four segments for direct additive genetic and permanent environmental effects, was the most appropriate and parsimonious to describe the covariance structure of the data. The RRM using Legendre polynomials presented an underestimation of the residual variance. Lesser heritability estimates were observed for multi-trait models in comparison with RRM for the evaluated ages. In general, the genetic correlations between measures of BW from hatching to 35 days of age decreased as the range between the evaluated ages increased. Genetic trend for BW was positive and significant along the selection generations. The genetic response to selection for BW in the evaluated ages presented greater values for RRM compared with multi-trait models. In summary, RRM using B-spline functions with four residual variance classes and segments were the best fit for genetic evaluation of growth traits in meat-type quail. In conclusion, RRM should be considered in genetic evaluation of breeding programs.     

Evidence for genetic control of adult weight plasticity in the snail Helix aspersa

Phenotypic plasticity and canalization are important topics in quantitative genetics and evolution. Both concepts are related to environmental sensitivity. The latter can be modeled using a model with genetically structured environmental variance. This work reports the results of a genetic analysis of adult weight in the snail Helix aspersa. Several models of heterogeneous variance are fitted using a Bayesian, MCMC approach. Exploratory analyses using posterior predictive model checking and model comparisons based on the deviance information criterion favor a model postulating a genetically structured heterogeneous environmental variance. Our analysis provides a strong indication of a positive genetic correlation between additive genetic values affecting the mean and those affecting environmental variation of adult body weight. The possibility of manipulating environmental variance by selection is illustrated numerically using estimates of parameters derived from the snail data set.     

Lack of nonadditive genetic effects on early fecundity in Drosophila melanogaster

Fecundity is usually considered as a trait closely connected to fitness and is expected to exhibit substantial nonadditive genetic variation and inbreeding depression. However, two independent experiments, using populations of different geographical origin, indicate that early fecundity in Drosophila melanogaster behaves as a typical additive trait of low heritability. The first experiment involved artificial selection in inbred and non-inbred lines, all of them started from a common base population previously maintained in the laboratory for about 35 generations. The realized heritability estimate was 0.151 +/- 0.075 and the inbreeding depression was very small and nonsignificant (0.09 +/- 0.09% of the non-inbred mean per 1% increase in inbreeding coefficient). With inbreeding, the observed decrease in the within-line additive genetic variance and the corresponding increase of the between-line variance were very close to their expected values for pure additive gene action. This result is at odds with previous studies showing inbreeding depression and, therefore, directional dominance for the same trait and species. All experiments, however, used laboratory populations, and it is possible that the original genetic architecture of the trait in nature was subsequently altered by the joint action of random drift and adaptation to captivity. Thus, we carried out a second experiment, involving inbreeding without artificial selection in a population recently collected from the wild. In this case we obtained, again, a maximum-likelihood heritability estimate of 0.210 +/- 0.027 and very little nonsignificant inbreeding depression (0.06 +/- 0.12%). The results suggest that, for fitness-component traits, low levels of additive genetic variance are not necessarily associated with large inbreeding depression or high levels of nonadditive genetic variance.     

Effect of mass selection on the within-family genetic variance in finite populations

Summary The adequacy of an expression for the withinfamily genetic variance under pure random drift in an additive infinitesimal model was tested via simulation in populations undergoing mass selection. Two hundred or one thousand unlinked loci with two alleles at initial frequencies of 1/2 were considered. The size of the population was 100 (50 males and 50 females). Full-sib matings were carried out for 15 generations with only one male and one female chosen as parents each generation, either randomly or on an individual phenotypic value. In the unselected population, results obtained from 200 replicates were in agreement with predictions. With mass selection, within-family genetic variance was overpredicted by theory from the 12th and 4th generations for the 1,000 and 200 loci cases, respectively. Taking into account the observed change in gene frequencies in the algorithm led to a much better agreement with observed values. Results for the distribution of gene frequencies and the withinlocus genetic covariance are presented. It is concluded that the expression for the within-family genetic variance derived for pure random drift holds well for mass selection within the limits of an additive infinitesimal model.     

Impact of depth of pedigree and inclusion of historical data on the estimation of additive variance and breeding values in a sugarcane breeding program

Sugarcane breeders in Australia combine data across four selection programs to obtain estimates of breeding value for parents. When these data are combined with full pedigree information back to founding parents, computing limitations mean it is not possible to obtain information on all parents. Family data from one sugarcane selection program were analysed using two different genetic models to investigate how different depths of pedigree and amount of data affect the reliability of estimating breeding value of sugarcane parents. These were the parental and animal models. Additive variance components and breeding values estimated from different amounts of information were compared for both models. The accuracy of estimating additive variance components and breeding values improved as more pedigree information and historical data were included in analyses. However, adding years of data had a much larger effect on the estimation of variance components of the population, and breeding values of the parents. To accurately estimate breeding values of all sugarcane parents, a minimum of three generations of pedigree and 5 years of historical data were required, while more information (four generations of pedigree and 7 years of historical data) was required when identifying top parents to be selected for future cross pollination.     

Genetic variation and the potential response to selection on leaf traits after habitat degradation in a long-lived cycad

Rapid evolution may be common in human-dominated landscapes where environmental changes are severe. We used phenotypic selection analyses and a marker-based method to estimate genetic variances and covariances to predict the potential response to selection in populations of a long-lived cycad recently exposed to drastic environmental changes. Patterns of selection in adult fecundity showed that different traits were under directional selection in subpopulations from native-undisturbed habitats and the novel degraded-forest habitat. Plants from a native-habitat subpopulation tend to maximize fitness through larger leaf area or smaller specific leaf area (SLA). In contrast, larger leaf production increased fitness in a degraded-habitat subpopulation, and canopy openness appears to be a major agent of selection for this trait. Leaf production and SLA showed significant additive genetic variance and no genetic trade-offs with examined traits, suggesting that these traits can respond to selection. Directional selection coefficients and heritability values were large, therefore significant phenotypic changes between subpopulations in few generations are possible. These results suggest that recent environmental change can result in strong directional selection in subpopulations of this cycad, and that these subpopulations have the potential to diverge at the genetic level in leaf traits after anthropogenic habitat degradation.     

Natural selection on the genetical component of variance in body condition in a wild bird population

Although there is substantial evidence that skeletal measures of body size are heritable in wild animal populations, it is frequently assumed that the nonskeletal component of body weight (or ‘condition’) is determined primarily by environmental factors, in particular nutritional state. We tested this assumption by quantifying the genetic and environmental components of variance in fledgling body condition index (=relative body weight) in a natural population of collared flycatchers (Ficedula albicollis), and compared the strength of natural selection on individual breeding values with that on phenotypic values. A mixed model analysis of the components of variance, based on an ‘animal model’ and using 18 years of data on 17 717 nestlings, revealed a significant additive genetic component of variance in body condition, which corresponded to a narrow sense heritability (h²) of 0.30 (SE=0.03). Nongenetic contributions to variation in body condition were large, but there was no evidence of dominance variance nor of contributions from early maternal or common environment effects (pre‐manipulation environment) in condition at fledging. Comparison of pre‐ and post‐selection samples revealed virtually identical h² of body condition index, despite the fact that there was a significant decrease (35%) in the levels of additive genetic variance from fledging to breeding. The similar h² in the two samples occurred because the environmental component of variance was also reduced by selection, suggesting that natural selection was acting on both genotypic and environmental variation. The effects of selection on genetic variance were confirmed by calculation of the selection differentials for both phenotypic values and best linear unbiased predictor (BLUP) estimates of breeding values: there was positive directional selection on condition index both at the phenotypic and the genotypic level. The significant h² of body condition index is consistent with data from human and rodent populations showing significant additive genetic variance in relative body mass and adiposity, but contrasts with the common assumption in ecology that body condition reflects an individual’s nongenetic nutritional state. Furthermore, the substantial reduction in the additive genetic component of variance in body condition index suggests that selection on environmental deviations cannot alone explain the maintenance of additive genetic variation in heritable traits, but that other mechanisms are needed to explain the moderate to high heritabilities of traits under consistent and strong directional selection.     

VARIATION IN SEED CHARACTERS IN NEMOPHILA MENZIESII: EVIDENCE OF A GENETIC BASIS FOR MATERNAL EFFECT

A growing body of evidence indicates that phenotypic selection on juvenile traits of both plants and animals may be considerable. Because juvenile traits are typically subject to maternal effects and often have low heritabilities, adaptive responses to natural selection on these traits may seem unlikely. To determine the potential for evolutionary response to selection on juvenile traits of Nemophila menziesii (Hydrophyllaceae), we conducted two quantitative genetic studies. A reciprocal factorial cross, involving 16 parents and 1960 progeny, demonstrated a significant maternal component of variance in seed mass and additive genetic component of variance in germination time. This experiment also suggested that interaction between parents, though small, provides highly significant contributions to the variance of both traits. Such a parental interaction could arise by diverse mechanisms, including dependence of nuclear gene expression on cytoplasmic genotype, but the design of this experiment could not distinguish this from other possible causes, such as effects on progeny phenotype of interaction between the environmental conditions of both parents. The second experiment, spanning three generations with over 11,000 observations, was designed for investigation of the additive genetic variance in maternal effect, assessment of paternal effects, as well as further partitioning of the parental interaction identified in the reciprocal factorial experiment. It yielded no consistent evidence of paternal effects on seed mass, nor of parental interactions. Our inference of such interaction effects from the first experiment was evidently an artifact of failing to account for the substantial variance among fruits within crosses. The maternal effect was found to have a large additive genetic component, accounting for at least 20% of the variation in individual seed mass. This result suggests that there is appreciable potential for response to selection on seed mass through evolution of the maternal effect. We discuss aspects that may nevertheless limit response to individual selection on seed mass, including trade-offs between the size of individual seeds and germination time and between the number of seeds a maternal plant can mature and their mean size.     

Stabilizing Selection for Pupa Weight in TRIBOLIUM CASTANEUM

Ninety-five generations of stabilizing selection for pupa weight in Tribolium castaneum resulted in a significant decrease in phenotypic variance, moderate reductions in additive genetic variance, but only slight changes in heritability for the trait. Sterility was significantly lower and the average number of live progeny per fertile mating was significantly higher in populations where stabilizing selection was practiced as compared with random selected populations. The results indicate that more genetic variability is being maintained than would be expected unless a fraction of the genes have a heterozygote advantage on the fitness scale. The reduction in phenotypic variance indicated that the populations with stablizing selection became somewhat more buffered against environmental sources of variation over the course of the experiment.     

Change in Genetic Variance under Selection in a Self-Fertilizing Population

In this study we show how the genetic variance of a quantitative trait changes in a self-fertilizing population under repeated cycles of truncation selection, with the analysis based on the infinitesimal model in which it is assumed that the trait is determined by an infinite number of unlinked loci without epistasis. The genetic variance is reduced not as a consequence of the genotypic frequency change but due to the build-up of linkage disequilibrium under truncation selection in this model. We assume that the order of the genotypic contribution from each locus is n(-1/2), where n is the number of loci involved, and investigate the change in linkage disequilibrium resulting from selection and self-fertilization using genotypic frequency dynamics in order to analyze the change in the genetic variance. Our analysis gives recurrence relations of genetic variance among the succeeding generations for the three cases of gene action, i.e., purely additive action, pure dominance without additive effect and the presence of both additive effect and dominance, respectively. Numerical examples are also given as a check on the recurrence formulas.     

Analysis of response to 20 generations of selection for body composition in mice: fit to infinitesimal model assumptions

Data were analysed from a divergent selection experiment for an indicator of body composition in the mouse, the ratio of gonadal fat pad to body weight (GFPR). Lines were selected for 20 generations for fat (F), lean (L) or were unselected (C), with three replicates of each. Selection was within full-sib families, 16 families per replicate for the first seven generations, eight subsequently. At generation 20, GFPR in the F lines was twice and in the L lines half that of C. A log transformation removed both asymmetry of response and heterogeneity of variance among lines, and so was used throughout. Estimates of genetic variance and heritability (approximately 50%) obtained using REML with an animal model were very similar, whether estimated from the first few generations of selection, or from all 20 generations, or from late generations having fitted pedigree. The estimates were also similar when estimated from selected or control lines. Estimates from REML also agreed with estimates of realised heritability. The results all accord with expectations under the infinitesimal model, despite the four-fold changes in mean. Relaxed selection lines, derived from generation 20, showed little regression in fatness after 40 generations without selection.     

Improving the efficiency of artificial selection: more selection pressure with less inbreeding

The use of population genetic variability in present-day selection schemes can be improved to reduce inbreeding rate and inbreeding depression without impairing genetic progress. We performed an experiment with Drosophila melanogaster to test mate selection, an optimizing method that uses linear programming to maximize the selection differential applied while at the same time respecting a restriction on the increase in inbreeding expected in the next generation. Previous studies about mate selection used computer simulation on simple additive genetic models, and no experiment with a real character in a real population had been carried out. After six selection generations, the optimized lines showed an increase in cumulated phenotypic selection differential of 10.76%, and at the same time, a reduction of 19.91 and 60.47% in inbreeding coefficient mean and variance, respectively. The increased selection pressure would bring greater selection response, and in fact, the observed change in the selected trait was on average 31.03% greater in the optimized lines. These improvements in the selection scheme were not made at the expense of the long-term expectations of genetic variability in the population, as these expectations were very similar for both mate selection and conventionally selected lines in our experiment.     

Maintenance of genetic variation in quantitative traits of a woodland rodent during generations of captive breeding

Breeding programs to conserve diversity are predicated on the assumption that genetic variation in adaptively important traits will be lost in parallel to the loss of variation at neutral loci. To test this assumption, we monitored quantitative traits across 18 generations of Peromyscus leucopus mice propagated with protocols that mirror breeding programs for threatened species. Ears, hind feet, and tails became shorter, but changes were reversible by outcrossing and therefore were due to accumulated inbreeding. Heritability of ear length decreased, because of an increase in phenotypic variance rather than the expected decrease in additive genetic variance. Additive genetic variance in hind foot length increased. This trait initially had low heritability but large dominance or common environmental variance contributing to resemblance among full-sibs. The increase in the additive component indicates that there was conversion of interaction variances to additive variance. For no trait did additive genetic variation decrease significantly across generations. These findings indicate that the restructuring of genetic variance that occurs with genetic drift and novel selection in captivity can prevent or delay the loss of phenotypic and heritable variation, providing variation on which selection can act to adapt populations to captivity and perhaps later to readapt to more natural habitats after release. Therefore, the importance of minimizing loss of gene diversity from conservation breeding programs for threatened wildlife species might lie in preventing immediate reduction in individual fitness due to inbreeding and protecting allelic diversity for long-term evolutionary change, more so than in protecting variation in quantitative traits for rapid re-adaptation to wild environments.     

Genetic parameters related to environmental variability of weight traits in a selection experiment for weight gain in mice; signs of correlated canalised response

Data from an experimental mice population selected from 18 generations to increase weight gain were used to estimate the genetic parameters associated with environmental variability. The analysis involved three traits: weight at 21 days, weight at 42 days and weight gain between 21 and 42 days. A dataset of 5273 records for males was studied. Data were analysed using Bayesian procedures by comparing the Deviance Information Criterion (DIC) value of two different models: one assuming homogeneous environmental variances and another assuming them as heterogeneous. The model assuming heterogeneity was better in all cases and also showed higher additive genetic variances and lower common environmental variances. The heterogeneity of residual variance was associated with systematic and additive genetic effects thus making reduction by selection possible. Genetic correlations between the additive genetic effects on mean and environmental variance of the traits analysed were always negative, ranging from -0.19 to -0.38. An increase in the heritability of the traits was found when considering the genetic determination of the environmental variability. A suggested correlated canalised response was found in terms of coefficient of variation but it could be insufficient to compensate for the scale effect associated with an increase of the mean.     

Evolution of the environmental component of the phenotypic variance: stabilizing selection in changing environments and the cost of homogeneity

Quantitative traits show abundant genetic, environmental, and phenotypic variance, yet if they are subject to stabilizing selection for an optimal phenotype, both the genetic and environmental components are expected to decline. The mechanisms that determine the level and maintenance of phenotypic variance are not yet fully understood. While there has been extensive study of mechanisms maintaining genetic variability, it has generally been assumed that environmental variance is not dependent on the genotype and therefore not subject to change. However, accumulating data suggest that the environmental variance is under some degree of genetic control. In this study, it is assumed accordingly that both the genotypic value (i.e., mean phenotypic value) and the variance of phenotypic value given genotypic value depend on the genotype. Two models are investigated as potentially able to explain the protected maintenance of environmental variance of quantitative traits under stabilizing selection. One is varying environment among generations, such that both the optimal phenotype and the strength of the stabilizing selection vary between generations. The other is the cost of homogeneity, which is based on an assumption of an engineering cost of minimizing variability in development. It is shown that a small homogeneity cost is enough to maintain the observed levels of environmental variance, whereas a large amount of temporal variation in the optimal phenotype and the strength of selection would be necessary.     

LIMITS TO BEHAVIORAL EVOLUTION: THE QUANTITATIVE GENETICS OF A COMPLEX TRAIT UNDER DIRECTIONAL SELECTION

Replicated selection experiments provide a powerful way to study how “multiple adaptive solutions” may lead to differences in the quantitative–genetic architecture of selected traits and whether this may translate into differences in the timing at which evolutionary limits are reached. We analyze data from 31 generations (n = 17,988) of selection on voluntary wheel running in house mice. The rate of initial response, timing of selection limit, and height of the plateau varied significantly between sexes and among the four selected lines. Analyses of litter size and realized selection differentials seem to rule out counterposing natural selection as a cause of the selection limits. Animal‐model analyses showed that although the additive genetic variance was significantly lower in selected than control lines, both before and after the limits, the decrease was not sufficient to explain the limits. Moreover, directional selection promoted a negative covariance between additive and maternal genetic variance over the first 10 generations. These results stress the importance of replication in selection studies of higher‐level traits and highlight the fact that long‐term predictions of response to selection are not necessarily expected to be linear because of the variable effects of selection on additive genetic variance and maternal effects.     

Evolution of the additive genetic variance–covariance matrix under continuous directional selection on a complex behavioural phenotype

Given the pace at which human-induced environmental changes occur, a pressing challenge is to determine the speed with which selection can drive evolutionary change. A key determinant of adaptive response to multivariate phenotypic selection is the additive genetic variance–covariance matrix (G). Yet knowledge of G in a population experiencing new or altered selection is not sufficient to predict selection response because G itself evolves in ways that are poorly understood. We experimentally evaluated changes in G when closely related behavioural traits experience continuous directional selection. We applied the genetic covariance tensor approach to a large dataset (n = 17 328 individuals) from a replicated, 31-generation artificial selection experiment that bred mice for voluntary wheel running on days 5 and 6 of a 6-day test. Selection on this subset of G induced proportional changes across the matrix for all 6 days of running behaviour within the first four generations. The changes in G induced by selection resulted in a fourfold slower-than-predicted rate of response to selection. Thus, selection exacerbated constraints within G and limited future adaptive response, a phenomenon that could have profound consequences for populations facing rapid environmental change.     

Genetic variability in the diapause response of the burnet moth Zygaena trifolii (Lepidoptera: Zygaenidae)

A high degree of phenotypic variability was observed in the diapause response of the burnet moth Zygaena trifolii. In this study, we show that the observed variability is partly based on genetic differences between individuals. In a selection experiment, the larval instar at which diapause occurs was changed within six generations. Diapause instars were dependent on the time of pre-diapause development of larvae, which varied considerably between larvae. A heritability analysis indicates that a part of the variability in development time is based on additive genetic variance. The maintenance of genetic variability in the development time and the diapause response of Z. trifolii is discussed in the context of spatially and temporally changing selection pressures.