Mapping epigenetic quantitative trait loci (QTL) altering a developmental trajectory.

Genetic variation in a quantitative trait that changes with age is important to both evolutionary biologists and breeders. A traditional analysis of the dynamics of genetic variation is based on the genetic variance-covariance matrix among different ages estimated from a quantitative genetic model. Such an analysis, however, cannot reveal the mechanistic basis of the genetic variation for a growth trait during ontogeny. Age-specific genetic variance at time t conditional on the causal genetic effect at time t - 1 implies the generation of episodes of new genetic variation arising during the interval t - 1 to t. In the present paper, the conditional genetic variance estimated from Zhu's (1995) conditional model was partitioned into its underlying individual quantitative trait loci (QTL) using molecular markers in an F2 progeny of poplars (Populus trichocarpa and Populus deltoides). These QTL, defined as epigenetic QTL, govern the alterations of growth trajectory in a population. Three epigenetic QTL were detected to contribute significantly to variation in growth trajectory during the period from the establishment year to the subsequent year in the field. It is suggested that the activation and expression of epigenetic QTL are influenced by the developmental status of trees and the environment in which they are grown.     

ON THE LOW HERITABILITY OF LIFE-HISTORY TRAITS

Life-history traits such as longevity and fecundity often show low heritability. This is usually interpreted in terms of Fisher's fundamental theorem to mean that populations are near evolutionary equilibrium and genetic variance in total fitness is low. We develop the causal relationship between metric traits and life-history traits to show that a life-history trait is expected to have a low heritability whether or not the population is at equilibrium. This is because it is subject to all the environmental variation in the metric traits that affect it plus additional environmental variation. There is no simple prediction regarding levels of additive genetic variance in life-history traits, which may be high at equilibrium. Several other patterns in the inheritance of life-history traits are readily predicted from the causal model. These include the strength of genetic correlations between life-history traits, levels of nonadditive genetic variance, and the inevitability of genotype-environment interaction.     

EVOLUTION OF PHENOTYPIC VARIANCE

A cornerstone of evolutionary theory is that the phenotypic variance of a population may be partitioned into genetic and environmental (nonheritable) components. The traditional motivation for this distinction is that the rate of evolution under natural selection depends on the (relative) magnitudes of certain genetic components of variance. The components of variation are also interesting from another perspective, as illustrated here. Phenotypic variation may be selectively maintained in a population according to its components: selection may favor the maintenance of only the environmental components, only the genetic components, or be indifferent to the composition of the variance. Even when selection is shown to favor phenotypic variation regardless of its components, the possibility exists that environmental variance will evolve to displace the genetic components or vice versa. Environmental and genetic factors may thus compete to produce a given selected level of phenotypic variance. A test of some of these models is provided from the example of seed dormancy: the prediction that variation in seed germination time should be purely environmental is supported by the demonstration of low heritability of germination time in the two available studies.     

SOME POPULATION GENETIC CONSEQUENCES OF COLONY FORMATION AND EXTINCTION: GENETIC CORRELATIONS WITHIN FOUNDING GROUPS

Extinction and recolonization in an island model affects genetic differentiation among subpopulations through a combination of sampling and mixing. We investigate the balance of these forces in a general model of population founding that predicts first the genetic variance among new groups and then the effect of these new groups on the total genetic variance among all populations. We allow for a broad range of types of mixing at the time of colonization and demonstrate the significant effects on differentiation from the probability of common origin of gametes (φ). We further demonstrate that kin-structured founding and inbreeding within populations can have a significant effect on the genetic variance among groups and use these results to make predictions about lineal fission and fusion of populations. These results show that population structure is critically affected by non-equilibrium dynamics and that the properties of new populations, especially founding number, probability of common origin, and kin structure, are vital in our understanding of genetic variation.     

Constraints on evolution and postcopulatory sexual selection: trade-offs among ejaculate characteristics

Ejaculates function as an integrated unit to ensure male fertility and paternity, can have a complex structure, and can experience multiple episodes of selection. Current studies on the evolution of ejaculates typically focus on phenotypic variation in sperm number, size, or related traits such as testes size as adaptations to postcopulatory male-male competition. However, the evolution of the integrated nature of ejaculate structure and function depends on genetic variation in and covariation between the component parts. Here we report a quantitative genetic study of the components of the ejaculate of the cockroach Nauphoeta cinerea, including those we know to experience postcopulatory sexual selection, in the context of functional integration of ejaculate characters. We use the patterns of genetic variation and covariation to infer how the integration of the functions of the ejaculate constrain and shape its evolution. Ejaculate components were highly variable, showed significant additive genetic variance, and moderate to high evolvability. The level of genetic variation in these characters, despite strong directional or truncating selection, may reflect the integration of multiple episodes of selection that occur in N. cinerea. There were few significant phenotypic correlations, but all the genetic correlations among ejaculate characters were significantly different from zero. The patterns of genetic variation and covariation suggest that there are important trade-offs among individual traits of the ejaculate and that evolution of ejaculate characteristics will not proceed unconstrained. Fully describing the genetic relationships among traits that perform as an integrated unit helps us understand how functional relationships constrain or facilitate the evolution of the complex structure that is the ejaculate.     

Age-dependent genetic variance in a life-history trait in the mute swan

Genetic variance in characters under natural selection in natural populations determines the way those populations respond to that selection. Whether populations show temporal and/or spatial constancy in patterns of genetic variance and covariance is regularly considered, as this will determine whether selection responses are constant over space and time. Much less often considered is whether characters show differing amounts of genetic variance over the life-history of individuals. Such age-specific variation, if present, has important potential consequences for the force of natural selection and for understanding the causes of variation in quantitative characters. Using data from a long-term study of the mute swan Cygnus olor, we report the partitioning of phenotypic variance in timing of breeding (subject to strong natural selection) into component parts over 12 different age classes. We show that the additive genetic variance and heritability of this trait are strongly age-dependent, with higher additive genetic variance present in young and, particularly, old birds, but little evidence of any genetic variance for birds of intermediate ages. These results demonstrate that age can have a very important influence on the components of variation of characters in natural populations, and consequently that separate age classes cannot be assumed to be equivalent, either with respect to their evolutionary potential or response.     

ECOLOGICAL HISTORY AND EVOLUTION IN A NOVEL ENVIRONMENT: HABITAT HETEROGENEITY AND INSECT ADAPTATION TO A NEW HOST PLANT

Environmental heterogeneity has often been implicated in the maintenance of genetic variation. However, previous research has not considered how environmental heterogeneity might affect the rate of adaptation to a novel environment. In this study, I used an insect-plant system to test the hypothesis that heterogeneous environments maintain more genetic variation in fitness components in a novel environment than do uniform environments. To manipulate recent ecological history, replicate populations of the dipteran leafminer Liriomyza trifolii were maintained for 20 generations in one of three treatments: a heterogeneous environment that contained five species of host plant, and two uniform environments that contained either a susceptible chrysanthemum or tomato. The hypothesis that greater genetic variance for survivorship and developmental time on a new host plant (a leafminer-resistant chrysanthemum) would be maintained in the heterogeneous treatment relative to the uniform environments was then tested with a sib-analysis and a natural selection experiment. Populations from the heterogeneous host plant treatment had no greater genetic variance in either larval survivorship or developmental time on the new host than did populations from either of the other treatments. Moreover, the rate of adaptation to the new host did not differ between the ecological history treatments, although the populations from the uniform chrysanthemum treatment had higher mean survivorship throughout the selection experiment. The estimates of the heritability of larval survivorship from the sib-analysis and selection experiment were quite similar. These results imply that ecologically realistic levels of environmental heterogeneity will not necessarily maintain more genetic variance than uniform environments when traits expressed in a particular novel environment are considered.     

Data and theory point to mainly additive genetic variance for complex traits

The relative proportion of additive and non-additive variation for complex traits is important in evolutionary biology, medicine, and agriculture. We address a long-standing controversy and paradox about the contribution of non-additive genetic variation, namely that knowledge about biological pathways and gene networks imply that epistasis is important. Yet empirical data across a range of traits and species imply that most genetic variance is additive. We evaluate the evidence from empirical studies of genetic variance components and find that additive variance typically accounts for over half, and often close to 100%, of the total genetic variance. We present new theoretical results, based upon the distribution of allele frequencies under neutral and other population genetic models, that show why this is the case even if there are non-additive effects at the level of gene action. We conclude that interactions at the level of genes are not likely to generate much interaction at the level of variance.     

THE ACTION OF STABILIZING SELECTION,MUTATION, AND DRIFT ON EPISTATIC QUANTITATIVE TRAITS

For a quantitative trait under stabilizing selection, the effect of epistasis on its genetic architecture and on the changes of genetic variance caused by bottlenecking were investigated using theory and simulation. Assuming empirical estimates of the rate and effects of mutations and the intensity of selection, we assessed the impact of two‐locus epistasis (synergistic/antagonistic) among linked or unlinked loci on the distribution of effects and frequencies of segregating loci in populations at the mutation‐selection‐drift balance. Strong pervasive epistasis did not modify substantially the genetic properties of the trait and, therefore, the most likely explanation for the low amount of variation usually accounted by the loci detected in genome‐wide association analyses is that many causal loci will pass undetected. We investigated the impact of epistasis on the changes in genetic variance components when large populations were subjected to successive bottlenecks of different sizes, considering the action of genetic drift, operating singly (D), or jointly with mutation (MD) and selection (MSD). An initial increase of the different components of the genetic variance, as well as a dramatic acceleration of the between‐line divergence, were always associated with synergistic epistasis but were strongly constrained by selection.     

Gene action,genetic variation,and GWAS: A user-friendly web tool

Fisher’s partitioning of genotypic values and genetic variance is highly relevant in the current era of genome-wide association studies (GWASs). However, despite being more than a century old, a number of persistent misconceptions related to nonadditive genetic effects remain. We developed a user-friendly web tool, the Falconer ShinyApp, to show how the combination of gene action and allele frequencies at causal loci translate to genetic variance and genetic variance components for a complex trait. The app can be used to demonstrate the relationship between a SNP effect size estimated from GWAS and the variation the SNP generates in the population, i.e., how locus-specific effects lead to individual differences in traits. In addition, it can also be used to demonstrate how within and between locus interactions (dominance and epistasis, respectively) usually do not lead to a large amount of nonadditive variance relative to additive variance, and therefore, that these interactions usually do not explain individual differences in a population.     

Quantitative genetic variation in an ecological setting

The machinery was developed to investigate the behavior of quantitative genetic variation in an ecological model of a finite number of islands of finite size, with migration rate m and extinction rate e, for a quantitative genetic model general for numbers of alleles and loci and additive, dominance, and additive by additive epistatic effects. It was necessary to reckon with seven quadratic genetic components, whose coefficients in the genotypic variance components within demes, sigma Gw2, between demes within populations, sigma s2, and between replicate populations, sigma r2, are given by descent measures. The descent measures at any time are calculated with the use of transition equations which are determined by the parameters of the ecological model. Numerical results were obtained for the coefficients of the quadratic genetic components in each of the three genotypic variance components in the early phase of differentiation. The general effect of extinction is to speed up the time course leading to fixation, to increase sigma r2, and to decrease sigma s2 (with a few exceptions) in comparison with no extinction. The general effect of migration is to slow down the time course leading to fixation, to increase sigma Gw2, at least in the later generations, and to decrease sigma s2 (with a few exceptions) in comparison with no migration. Except for these, the effects of migration and extinction on the variance components are complex, depending on the genetic model, and sometimes involve interaction of migration and extinction. Sufficient details are given for an investigator to evaluate numerically the results for variations in the quantitative genetic and ecological models.     

Rapid evolution of larval development time during mass-rearing in the melon fly, Bactrocera cucurbitae

A quantitative genetic analysis of rapid evolution of a life history trait has been conducted on the first 24 generations of mass-rearing in the melon fly Bactrocera cucurbitae (Coquillett) (Diptera: Tephritidae). The phenotypic variance of larval development time in each generation was divided into genetic and residual components. Mean and phenotypic coefficients of variation of larval development time decreased gradually as generations proceeded as a result of artificial selection for shorter larval period in the mass-rearing procedure. There was a trend that additive genetic coefficients of variation in larval development time decreased with generations. These changes are entirely attributed to genetic responses to laboratory selection under the mass-rearing environment because the population was maintained at a very large size so as to exclude random genetic drift and inbreeding depression, which would be other factors responsible for the observed genetic changes. The residual coefficients of variation in larval development time did not change with generations. Realized heritability of larval development time was low. The heritabilities for larval development time estimated from parent–offspring regression at generations 60 and 70, when the evolutionary plateau was asymptotically reached, were not significantly larger than 0. Received: April 22, 1999 / Accepted: September 20, 1999     

ADAPTIVE GENETIC VARIATION IN GROWTH AND DEVELOPMENT OF TADPOLES OF THE HYBRIDOGENETIC RANA ESCULENTA COMPLEX

The distribution and proportion of the sexual species Rana lessonae to the hemiclonal hybrid R. esculenta among natural habitats suggests that these anurans may differ in adaptive abilities. I used a half-sib design to partition phenotypic and quantitative genetic variation in tadpole responses at two food levels into causal variance components. Rana lessonae displays strong phenotypic variation across food levels. Growth rate is strictly determined by environmental factors and includes weak maternal effects. Larval period and body size at metamorphosis both contain moderate levels of additive genetic variance. The sire x food interactions and the lack of environmental correlations indicate that adaptive phenotypic plasticity is present in both of these traits. In contrast, R. esculenta displays less phenotypic variation across food levels, especially for larval period. Variation in body size at metamorphosis is underlain by genetic variation as shown by high levels of additive genetic variance, yet growth rate and larval period are not. Significant environmental correlations between larval period at high food level and growth, larval period, and body size at low food, indicate phenotypic plasticity is absent. A positive phenotypic correlation between body size at metamorphosis and larval period for R. lessonae at both food levels suggests a trade-off between growing large and metamorphosing quickly to escape predation or pond drying. The lack of a similar correlation for R. esculenta at the high food level suggests it may be less constrained. Different levels of adaptive genetic variation among larval traits suggest that the sexual species and the hybridogenetic hemiclone differ in their abilities to cope with temporally and spatially heterogeneous environments.     

Multifactorial genetic models for quantitative traits in humans.

Quantitative traits measured in human families can be analyzed to partition the total population variance into genetic and environmental components, or to elucidate the genetic mechanism involved. We review the estimation of variance components directly from human pedigree data, or in the form of path coefficients from correlations between pairs of relatives. To elucidate genetic mechanisms, a mixed model that allows for segregation at a major locus, a polygenic effect and a sibling environmental correlation is described for nuclear families. In each case appropriate likelihoods are derived as a basis, using numerical maximum likelihood methods, for parameter estimation and hypothesis testing. A general model is then described that allows for several familial sources of environmental variation, assortative mating, and both major gene and polygenic effects; and an algorithm for calculating the likelihood of a pedigree under this model is indicated. Finally, some of the remaining problems in this area of biometric analysis are pointed out.     

Comparing environmental and genetic variance as adaptive response to fluctuating selection

Phenotypic variation within populations has two sources: genetic variation and environmental variation. Here, we investigate the coevolution of these two components under fluctuating selection. Our analysis is based on the lottery model in which genetic polymorphism can be maintained by negative frequency-dependent selection, whereas environmental variation can be favored due to bet-hedging. In our model, phenotypes are characterized by a quantitative trait under stabilizing selection with the optimal phenotype fluctuating in time. Genotypes are characterized by their phenotypic offspring distribution, which is assumed to be Gaussian with heritable variation for its mean and variance. Polymorphism in the mean corresponds to genetic variance while the width of the offspring distribution corresponds to environmental variance. We show that increased environmental variance is favored whenever fluctuations in the selective optima are sufficiently strong. Given the environmental variance has evolved to its optimum, genetic polymorphism can still emerge if the distribution of selective optima is sufficiently asymmetric or leptokurtic. Polymorphism evolves in a diagonal direction in trait space: one type becomes a canalized specialist for the more common ecological conditions and the other type a de-canalized bet-hedger thriving on the less-common conditions. All results are based on analytical approximations, complemented by individual-based simulations.     

Good genes and sexual selection in dung beetles (Onthophagus taurus): genetic variance in egg-to-adult and adult viability

Whether species exhibit significant heritable variation in fitness is central for sexual selection. According to good genes models there must be genetic variation in males leading to variation in offspring fitness if females are to obtain genetic benefits from exercising mate preferences, or by mating multiply. However, sexual selection based on genetic benefits is controversial, and there is limited unambiguous support for the notion that choosy or polyandrous females can increase the chances of producing offspring with high viability. Here we examine the levels of additive genetic variance in two fitness components in the dung beetle Onthophagus taurus. We found significant sire effects on egg-to-adult viability and on son, but not daughter, survival to sexual maturity, as well as moderate coefficients of additive variance in these traits. Moreover, we do not find evidence for sexual antagonism influencing genetic variation for fitness. Our results are consistent with good genes sexual selection, and suggest that both pre- and postcopulatory mate choice, and male competition could provide indirect benefits to females.     

MUTATION,SELECTION, AND THE MAINTENANCE OF LIFE-HISTORY VARIATION IN A NATURAL POPULATION

In an effort to provide insight into the role of mutation in the maintenance of genetic variance for life-history traits, we accumulated spontaneous mutations in 10 sets of clonal replicates of Daphnia pulex for approximately 30 generations and compared the variance generated by mutation with the standing level of variation in the wild population. Mutations for quantitative traits appear to arise at a fairly high rate in this species, on the order of at least 0.6 per character per generation, but have relatively small heterozygous effects, changing the phenotype by less than 2.5% of the mean. The mean persistence time of a new mutation affecting life-history/body-size traits is approximately 40 generations in the natural population, which requires an average selection coefficient against new mutations of approximately 3% in the heterozygous state. These data are consistent with the idea that the vast majority of standing genetic variance for life-history characters may be largely a consequence of the recurrent introduction of transient cohorts of mutations that are at least conditionally deleterious and raise issues about the meaning of conventional measures of standing levels of variation for fitness-related traits.     

TATES: Efficient Multivariate Genotype-Phenotype Analysis for Genome-Wide Association Studies

To date, the genome-wide association study (GWAS) is the primary tool to identify genetic variants that cause phenotypic variation. As GWAS analyses are generally univariate in nature, multivariate phenotypic information is usually reduced to a single composite score. This practice often results in loss of statistical power to detect causal variants. Multivariate genotype–phenotype methods do exist but attain maximal power only in special circumstances. Here, we present a new multivariate method that we refer to as TATES (Trait-based Association Test that uses Extended Simes procedure), inspired by the GATES procedure proposed by Li et al (2011). For each component of a multivariate trait, TATES combines p-values obtained in standard univariate GWAS to acquire one trait-based p-value, while correcting for correlations between components. Extensive simulations, probing a wide variety of genotype–phenotype models, show that TATES''s false positive rate is correct, and that TATES''s statistical power to detect causal variants explaining 0.5% of the variance can be 2.5–9 times higher than the power of univariate tests based on composite scores and 1.5–2 times higher than the power of the standard MANOVA. Unlike other multivariate methods, TATES detects both genetic variants that are common to multiple phenotypes and genetic variants that are specific to a single phenotype, i.e. TATES provides a more complete view of the genetic architecture of complex traits. As the actual causal genotype–phenotype model is usually unknown and probably phenotypically and genetically complex, TATES, available as an open source program, constitutes a powerful new multivariate strategy that allows researchers to identify novel causal variants, while the complexity of traits is no longer a limiting factor.     

Environmental and genetic sources of diversification in the timing of seed germination: implications for the evolution of bet hedging

Environmental variation that is not predictably related to cues is expected to drive the evolution of bet-hedging strategies. The high variance observed in the timing of seed germination has led to it being the most cited diversification strategy in the theoretical bet-hedging literature. Despite this theoretical focus, virtually nothing is known about the mechanisms responsible for the generation of individual-level diversification. Here we report analyses of sources of variation in timing of germination within seasons, germination fraction over two generations and three sequential seasons, and the genetic correlation structure of these traits using almost 10,000 seeds from more than 100 genotypes of the monocarpic perennial Lobelia inflata. Microenvironmental analysis of time to germination suggests that extreme sensitivity to environmental gradients, or microplasticity, even within a homogeneous growth chamber, may act as an effective individual-level diversification mechanism and explains more than 30% of variance in time to germination. The heritability of within-season timing of germination was low (h(2) = 0.07) but significant under homogeneous conditions. Consistent with individual-level diversification, this low h(2) was attributable not to low additive genetic variance, but to an unusually high coefficient of residual variation in time to germination. Despite high power to detect additive genetic variance in within-season diversification, it was low and indistinguishable from zero. Restricted maximum likelihood detected significant genetic variation for germination fraction (h(2) = 0.18) under homogeneous conditions. Unexpectedly, this heritability was positive when measured within a generation by sibling analysis and negative when measured across generations by offspring-on-parent regression. The consistency of dormancy fraction over multiple delays, a major premise of Cohen's classic model, was supported by a strong genetic correlation (r = 0.468) observed for a cohort's germination fraction over two seasons. We discuss implications of the results for the evolution of bet hedging and highlight the need for further empirical study of the causal components of diversification.     

Genetic analysis of crossfostering data with sire and dam records

A method is presented for the analysis of data from crossfostering experiments in which parts of litters are reciprocally interchanged at birth. Observed variances and covariances of differently related individuals are expressed as functions of theoretical causal components of phenotypic variance (additive direct, dominance direct, additive maternal, dominance maternal, direct-maternal covariance, and environmental). Causal components are estimated by weighted least squares analysis of this system of equations, including a ridge-regression procedure to examine consequences of correlation between observed components. Ridge regression suggests that dominance direct genetic variance is generally underestimated, but that narrow-sense heritability estimates are reliable.