Comparing evolvabilities: common errors surrounding the calculation and use of coefficients of additive genetic variation

In 1992, David Houle showed that measures of additive genetic variation standardized by the trait mean, CV(A) (the coefficient of additive genetic variation) and its square (I(A) ), are suitable measures of evolvability. CV(A) has been used widely to compare patterns of genetic variation. However, the use of CV(A) s for comparative purposes relies critically on the correct calculation of this parameter. We reviewed a sample of quantitative genetic studies, focusing on sire models, and found that 45% of studies use incorrect methods for calculating CV(A) and that practices that render these coefficients meaningless are frequent. This may have important consequences for conclusions drawn from comparative studies. Our results are suggestive of a broader problem because miscalculation of the additive genetic variance from a sire model is prevalent among the studies sampled, implying that other important quantitative genetic parameters might also often be estimated incorrectly. We discuss the most prominent issues affecting the use of CV(A) and I(A) , including scale effects, data transformation, and the comparison of traits with different dimensions. Our aim is to increase awareness of the potential mistakes surrounding the calculation and use of evolvabilities, and to compile general guidelines for calculating, reporting, and interpreting these useful measures in future studies.     

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.     

NO EFFECT OF ENVIRONMENTAL HETEROGENEITY ON THE MAINTENANCE OF GENETIC VARIATION IN WING SHAPE IN DROSOPHILA MELANOGASTER

Theory suggests that heterogeneous environments should maintain more genetic variation within populations than homogeneous environments, yet experimental evidence for this effect in quantitative traits has been inconsistent. To examine the effect of heterogeneity on quantitative genetic variation, we maintained replicate populations of Drosophila melanogaster under treatments with constant temperatures, temporally variable temperature, or spatially variable temperature with either panmictic or limited migration. Despite observing differences in fitness and divergence in several wing traits between the environments, we did not find any differences in the additive genetic variance for any wing traits among any of the treatments. Although we found an effect of gene flow constraining adaptive divergence between cages in the limited migration treatment, it did not tend to increase within‐population genetic variance relative to any of the other treatments. The lack of any clear and repeatable patterns of response to heterogeneous versus homogeneous environments across several empirical studies suggests that a single general mechanism for the maintenance of standing genetic variation is unlikely; rather, the relative importance of putative mechanisms likely varies considerably from one trait and ecological context to another.     

Does habitat specialization shape the evolutionary potential of wild bird populations?

Because specialist species evolved in more temporally and spatially homogeneous environments than generalist species, they are supposed to experience less fluctuating selection. For this reason, we expect specialists to show lower overall genetic variation as compared to generalists. We also expect populations from specialist species to be smaller and more fragmented, with lower neutral genetic diversity. We tested these hypotheses by investigating patterns of genetic diversity along a habitat specialization gradient in wild birds, based on estimates of heritability, coefficients of variation of additive genetic variance, and heterozygosity available in the literature. We found no significant effect of habitat specialization on any of the quantitative genetic estimators but generalists had higher heterozygosity. This effect was mainly a consequence of the larger population size of generalists. Our results suggest that evolutionary potential does not differ at the population level between generalist and specialist species, but the trend observed in heterozygosity levels and population sizes may explain their difference in susceptibility to extinction.     

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.     

Evolutionary response when selection and genetic variation covary across environments

Although models of evolution usually assume that the strength of selection on a trait and the expression of genetic variation in that trait are independent, whenever the same ecological factor impacts both parameters, a correlation between the two may arise that accelerates trait evolution in some environments and slows it in others. Here, we address the evolutionary consequences and ecological causes of a correlation between selection and expressed genetic variation. Using a simple analytical model, we show that the correlation has a modest effect on the mean evolutionary response and a large effect on its variance, increasing among‐population or among‐generation variation in the response when positive, and diminishing variation when negative. We performed a literature review to identify the ecological factors that influence selection and expressed genetic variation across traits. We found that some factors – temperature and competition – are unlikely to generate the correlation because they affected one parameter more than the other, and identified others – most notably, environmental novelty – that merit further investigation because little is known about their impact on one of the two parameters. We argue that the correlation between selection and genetic variation deserves attention alongside other factors that promote or constrain evolution in heterogeneous landscapes.     

The quantitative genetics of fluctuating asymmetry

Fluctuating asymmetry (subtle departures from identical expression of a trait across an axis of symmetry) in many taxa is under stabilizing selection for reduced asymmetry. However, lack of reliable estimates of genetic parameters for asymmetry variation hampers our ability to predict the evolutionary outcome of this selection. Here we report on a study, based on analysis of variation within and between isofemale lines and of generation means (line-cross analysis), designed to dissect in detail the quantitative genetics of positional fluctuating asymmetry (PFA) in bristle number in natural populations of Drosophila falleni. PFA is defined as the difference between the two sides of the body in the placement or position of components of a meristic trait. Heritability (measured at 25 degrees C) of two related measures of PFA were 13% and 21%, both of which differed significantly from zero. In contrast, heritability estimates for fluctuating asymmetry in the total number of anterior (0.7%) and transverse (2.4%) sternopleural bristles were smaller, not significant, and in quantitative agreement with previously published estimates. Heritabilities for bristle number (trait size) were considerably greater than that for any asymmetry measure. The experimental design controlled for the potentially confounding effects of common familial environment, and repeated testing revealed that PFA differences between lines were genetically stable for up to 16 generations in the laboratory at 25 degrees C. We performed line cross analysis between strains at the extremes of the PFA distribution (highest and lowest values); parental strains, F1, F1r (reciprocal), F2, backcross, and backcross reciprocal generations were represented. The inheritance of PFA was described best by additive and dominance effects localized to the X-chromosomes, whereas autosomal dominance effects were also detected. Epistatic, maternal, and cytoplasmic effects were not detected. The inheritance of trait size was notably more complex and involved significant autosomal additive, dominance, and epistatic effects; maternal dominance effects; and additive and dominance effects localized to the X-chromosomes. The additive genetic correlation between PFA and its associated measure of trait size was negative (-0.049), but not statistically significant, indicating that the loci contributing additive genetic effects to these traits are probably different. It is suggested that PFA may be a sensitive measure of developmental instability because PFA taps the ability of an organism to integrate interconnected developmental pathways.     

Comparing Evolvability and Variability of Quantitative Traits

There are two distinct reasons for making comparisons of genetic variation for quantitative characters. The first is to compare evolvabilities, or ability to respond to selection, and the second is to make inferences about the forces that maintain genetic variability. Measures of variation that are standardized by the trait mean, such as the additive genetic coefficient of variation, are appropriate for both purposes. Variation has usually been compared as narrow sense heritabilities, but this is almost always an inappropriate comparative measure of evolvability and variability. Coefficients of variation were calculated from 842 estimates of trait means, variances and heritabilities in the literature. Traits closely related to fitness have higher additive genetic and nongenetic variability by the coefficient of variation criterion than characters under weak selection. This is the reverse of the accepted conclusion based on comparisons of heritability. The low heritability of fitness components is best explained by their high residual variation. The high additive genetic and residual variability of fitness traits might be explained by the great number of genetic and environmental events they are affected by, or by a lack of stabilizing selection to reduce their phenotypic variance. Over one-third of the quantitative genetics papers reviewed did not report trait means or variances. Researchers should always report these statistics, so that measures of variation appropriate to a variety of situations may be calculated.     

A MARKER-BASED METHOD FOR INFERENCES ABOUT QUANTITATIVE INHERITANCE IN NATURAL POPULATIONS

A marker-based method for studying quantitative genetic characters in natural populations is presented and evaluated. The method involves regressing quantitative trait similarity on marker-estimated relatedness between individuals. A procedure is first given for estimating the narrow sense heritability and additive genetic correlations among traits, incorporating shared environments. Estimation of the actual variance of relatedness is required for heritability, but not for genetic correlations. The approach is then extended to include isolation by distance of environments, dominance, and shared levels of inbreeding. Investigations of statistical properties show that good estimates do not require great marker polymorphism, but rather require significant variation of actual relatedness; optimal allocation generally favors sampling many individuals at the expense of assaying fewer marker loci; when relatedness declines with physical distance, it is optimal to restrict comparisons to within a certain distance; the power to estimate shared environments and inbreeding effects is reasonable, but estimates of dominance variance may be difficult under certain patterns of relationship; and any linkage of markers to quantitative trait loci does not cause significant problems. This marker-based method makes possible studies with long-lived organisms or with organisms difficult to culture, and opens the possibility that quantitative trait expression in natural environments can be analyzed in an unmanipulative way.     

Evolution of quantitative traits in the wild: mind the ecology

Recent advances in the quantitative genetics of traits in wild animal populations have created new interest in whether natural selection, and genetic response to it, can be detected within long-term ecological studies. However, such studies have re-emphasized the fact that ecological heterogeneity can confound our ability to infer selection on genetic variation and detect a population''s response to selection by conventional quantitative genetics approaches. Here, I highlight three manifestations of this issue: counter gradient variation, environmentally induced covariance between traits and the correlated effects of a fluctuating environment. These effects are symptomatic of the oversimplifications and strong assumptions of the breeder''s equation when it is applied to natural populations. In addition, methods to assay genetic change in quantitative traits have overestimated the precision with which change can be measured. In the future, a more conservative approach to inferring quantitative genetic response to selection, or genomic approaches allowing the estimation of selection intensity and responses to selection at known quantitative trait loci, will provide a more precise view of evolution in ecological time.     

The genetic architecture of a niche: variation and covariation in host use traits in the Colorado potato beetle

The genetic basis of host plant use by phytophagous insects can provide insight into the evolution of ecological niches, especially phenomena such as specialization and phylogenetic conservatism. We carried out a quantitative genetic analysis of multiple host use traits, estimated on five species of host plants, in the Colorado potato beetle, Leptinotarsa decemlineata (Coleoptera: Chrysomelidae). Mean values of all characters varied among host plants, providing evidence that adaptation to plants may require evolution of both behavioral (preference) and post-ingestive physiological (performance) characteristics. Significant additive genetic variation was detected for several characters on several hosts, but not in the capacity to use the two major hosts, a pattern that might be caused by directional selection. No negative genetic correlations across hosts were detected for any 'performance' traits, i.e. we found no evidence of trade-offs in fitness on different plants. Larval consumption was positively genetically correlated across host plants, suggesting that diet generalization might evolve as a distinct trait, rather than by independent evolution of feeding responses to each plant species, but several other traits did not show this pattern. We explored genetic correlations among traits expressed on a given plant species, in a first effort to shed light on the number of independent traits that may evolve in response to selection for host-plant utilization. Most traits were not correlated with each other, implying that adaptation to a novel potential host could be a complex, multidimensional 'character' that might constrain adaptation and contribute to the pronounced ecological specialization and the phylogenetic niche conservatism that characterize many clades of phytophagous insects.     

The Genetic Architecture of Quantitative Traits Cannot Be Inferred from Variance Component Analysis

Classical quantitative genetic analyses estimate additive and non-additive genetic and environmental components of variance from phenotypes of related individuals without knowing the identities of quantitative trait loci (QTLs). Many studies have found a large proportion of quantitative trait variation can be attributed to the additive genetic variance (V_A), providing the basis for claims that non-additive gene actions are unimportant. In this study, we show that arbitrarily defined parameterizations of genetic effects seemingly consistent with non-additive gene actions can also capture the majority of genetic variation. This reveals a logical flaw in using the relative magnitudes of variance components to indicate the relative importance of additive and non-additive gene actions. We discuss the implications and propose that variance component analyses should not be used to infer the genetic architecture of quantitative traits.     

Evolution of competitive ability: an adaptation speed vs. accuracy tradeoff rooted in gene network size

Ecologists have increasingly come to understand that evolutionary change on short time-scales can alter ecological dynamics (and vice-versa), and this idea is being incorporated into community ecology research programs. Previous research has suggested that the size and topology of the gene network underlying a quantitative trait should constrain or facilitate adaptation and thereby alter population dynamics. Here, I consider a scenario in which two species with different genetic architectures compete and evolve in fluctuating environments. An important trade-off emerges between adaptive accuracy and adaptive speed, driven by the size of the gene network underlying the ecologically-critical trait and the rate of environmental change. Smaller, scale-free networks confer a competitive advantage in rapidly-changing environments, but larger networks permit increased adaptive accuracy when environmental change is sufficiently slow to allow a species time to adapt. As the differences in network characteristics increase, the time-to-resolution of competition decreases. These results augment and refine previous conclusions about the ecological implications of the genetic architecture of quantitative traits, emphasizing a role of adaptive accuracy. Along with previous work, in particular that considering the role of gene network connectivity, these results provide a set of expectations for what we may observe as the field of ecological genomics develops.     

Genotype-environment interaction for quantitative trait loci affecting life span in Drosophila melanogaster

The nature of genetic variation for Drosophila longevity in a population of recombinant inbred lines was investigated by estimating quantitative genetic parameters and mapping quantitative trait loci (QTL) for adult life span in five environments: standard culture conditions, high and low temperature, and heat-shock and starvation stress. There was highly significant genetic variation for life span within each sex and environment. In the analysis of variance of life span pooled over sexes and environments, however, the significant genetic variation appeared in the genotype x sex and genotype x environment interaction terms. The genetic correlation of longevity across the sexes and environments was not significantly different from zero in these lines. We estimated map positions and effects of QTL affecting life span by linkage to highly polymorphic roo transposable element markers, using a multiple-trait composite interval mapping procedure. A minimum of 17 QTL were detected; all were sex and/or environment-specific. Ten of the QTL had sexually antagonistic or antagonistic pleiotropic effects in different environments. These data provide support for the pleiotropy theory of senescence and the hypothesis that variation for longevity might be maintained by opposing selection pressures in males and females and variable environments. Further work is necessary to assess the generality of these results, using different strains, to determine heterozygous effects and to map the life span QTL to the level of genetic loci.     

Rapid changes in genetic architecture of behavioural syndromes following colonization of a novel environment

Behavioural syndromes, that is correlated behaviours, may be a result from adaptive correlational selection, but in a new environmental setting, the trait correlation might act as an evolutionary constraint. However, knowledge about the quantitative genetic basis of behavioural syndromes, and the stability and evolvability of genetic correlations under different ecological conditions, is limited. We investigated the quantitative genetic basis of correlated behaviours in the freshwater isopod Asellus aquaticus. In some Swedish lakes, A. aquaticus has recently colonized a novel habitat and diverged into two ecotypes, presumably due to habitat‐specific selection from predation. Using a common garden approach and animal model analyses, we estimated quantitative genetic parameters for behavioural traits and compared the genetic architecture between the ecotypes. We report that the genetic covariance structure of the behavioural traits has been altered in the novel ecotype, demonstrating divergence in behavioural correlations. Thus, our study confirms that genetic correlations behind behaviours can change rapidly in response to novel selective environments.     

GENETICS OF FLUCTUATING ASYMMETRY: A DEVELOPMENTAL MODEL OF DEVELOPMENTAL INSTABILITY

Although numerous studies have found that fluctuating asymmetry (FA) can have a heritable component, the genetic and developmental basis of FA is poorly understood. We used a developmental model of a trait, according to a diffusion-threshold process, whose parameters are under genetic control. We added a small amount of random variation to the parameter values of this model to simulate developmental noise. As a result of the nonlinearity of the model, different genotypes differed in their sensitivity to developmental noise, even though the noise is completely random and independent of the genotype. The heritable component of FA can thus be understood as genetically modulated expression of variation that is itself entirely nongenetic. The loci responsible for this genetic variation of FA are the same that affect the left/right mean of the trait, showing that genetic variation for FA does not require genes that specifically control FA. Furthermore, the model offers alternative explanations for phenomena widely discussed in the literature on FA, for instance, the correlations between FA and heterozygosity and between FA and trait size. The model underscores the importance of dominance and epistasis, and therefore unites the study of FA with the classical theory of quantitative genetics.     

Partitioning of genetic variation across the genome using multimarker methods in a wild bird population

The underlying basis of genetic variation in quantitative traits, in terms of the number of causal variants and the size of their effects, is largely unknown in natural populations. The expectation is that complex quantitative trait variation is attributable to many, possibly interacting, causal variants, whose effects may depend upon the sex, age and the environment in which they are expressed. A recently developed methodology in animal breeding derives a value of relatedness among individuals from high‐density genomic marker data, to estimate additive genetic variance within livestock populations. Here, we adapt and test the effectiveness of these methods to partition genetic variation for complex traits across genomic regions within ecological study populations where individuals have varying degrees of relatedness. We then apply this approach for the first time to a natural population and demonstrate that genetic variation in wing length in the great tit (Parus major) reflects contributions from multiple genomic regions. We show that a polygenic additive mode of gene action best describes the patterns observed, and we find no evidence of dosage compensation for the sex chromosome. Our results suggest that most of the genomic regions that influence wing length have the same effects in both sexes. We found a limited amount of genetic variance in males that is attributed to regions that have no effects in females, which could facilitate the sexual dimorphism observed for this trait. Although this exploratory work focuses on one complex trait, the methodology is generally applicable to any trait for any laboratory or wild population, paving the way for investigating sex‐, age‐ and environment‐specific genetic effects and thus the underlying genetic architecture of phenotype in biological study systems.     

Heritability of seed weight in Maritime pine,a relevant trait in the transmission of environmental maternal effects

Quantitative seed provisioning is an important life-history trait with strong effects on offspring phenotype and fitness. As for any other trait, heritability estimates are vital for understanding its evolutionary dynamics. However, being a trait in between two generations, estimating additive genetic variation of seed provisioning requires complex quantitative genetic approaches for distinguishing between true genetic and environmental maternal effects. Here, using Maritime pine as a long-lived plant model, we quantified additive genetic variation of cone and seed weight (SW) mean and SW within-individual variation. We used a powerful approach combining both half-sib analysis and parent–offspring regression using several common garden tests established in contrasting environments to separate G, E and G × E effects. Both cone weight and SW mean showed significant genetic variation but were also influenced by the maternal environment. Most of the large variation in SW mean was attributable to additive genetic effects (h²=0.55–0.74). SW showed no apparent G × E interaction, particularly when accounting for cone weight covariation, suggesting that the maternal genotypes actively control the SW mean irrespective of the amount of resources allocated to cones. Within-individual variation in SW was low (12%) relative to between-individual variation (88%), and showed no genetic variation but was largely affected by the maternal environment, with greater variation in the less favourable sites for pine growth. In summary, results were very consistent between the parental and the offspring common garden tests, and clearly indicated heritable genetic variation for SW mean but not for within-individual variation in SW.     

Environmental fluctuations restrict eco-evolutionary dynamics in predator–prey system

Environmental fluctuations, species interactions and rapid evolution are all predicted to affect community structure and their temporal dynamics. Although the effects of the abiotic environment and prey evolution on ecological community dynamics have been studied separately, these factors can also have interactive effects. Here we used bacteria–ciliate microcosm experiments to test for eco-evolutionary dynamics in fluctuating environments. Specifically, we followed population dynamics and a prey defence trait over time when populations were exposed to regular changes of bottom-up or top-down stressors, or combinations of these. We found that the rate of evolution of a defence trait was significantly lower in fluctuating compared with stable environments, and that the defence trait evolved to lower levels when two environmental stressors changed recurrently. The latter suggests that top-down and bottom-up changes can have additive effects constraining evolutionary response within populations. The differences in evolutionary trajectories are explained by fluctuations in population sizes of the prey and the predator, which continuously alter the supply of mutations in the prey and strength of selection through predation. Thus, it may be necessary to adopt an eco-evolutionary perspective on studies concerning the evolution of traits mediating species interactions.