The status of the conditional evolutionarily stable strategy

The conditional evolutionarily stable strategy (ESS) has proven to be a versatile tool for understanding the production of alternative phenotypes in response to environmental cues. Hence, we would expect the theoretical basis of the conditional strategy to be robust. However, Shuster and Wade have recently criticized the conditional ESS based on Gross's 1996 proposal that most alternative reproductive tactics are conditional and have evolved by 'status-dependent selection.' We critically assess Gross's status-dependent selection model and Shuster and Wade's critique. We find shortcomings and misconceptions in both. We return to the findings of the strategic models behind the conditional ESS and demonstrate how environmental threshold models use a reaction norm approach and quantitative genetic theory to understand the evolution of conditional strategies.     

A polygenic model for the evolution and maintenance of conditional strategies

We develop a genetic model for conditional strategies which places such strategies in the context of phenotypic plasticity. The model, which treats conditional strategies as polygenic threshold traits, indicates that, given requisite genetic variation in reaction norms, conditional strategies will evolve to their optimum level and be maintained by stabilizing selection, provided environmental variation results in a fitness trade-off for the alternative conditional phenotypes. The precise value for the evolutionary optimum is found to depend primarily on the probability density function of the environmental variation that influences the production of the conditional phenotypes and the magnitude of the fitness trade-offs of the conditional phenotypes across such environmental variation. The model is tested by application to three well-studied conditional strategies. In each case the predictions of the model are in good agreement with the results of these studies.     

Assessing adaptive phenotypic plasticity by means of conditional strategies from empirical data: the latent environmental threshold model

Conditional strategies are the most common form of discrete phenotypic plasticity. In a conditional strategy, the phenotype expressed by an organism is determined by the difference between an environmental cue and a threshold, both of which may vary among individuals. The environmental threshold model (ETM) has been proposed as a mean to understand the evolution of conditional strategies, but has been surprisingly seldom applied to empirical studies. A hindrance for the application of the ETM is that often, the proximate cue triggering the phenotypic expression and the individual threshold are not measurable, and can only be assessed using a related observable cue. We describe a new statistical model that can be applied in this common situation. The Latent ETM (LETM) allows for a measurement error in the phenotypic expression of the individual environmental cue and a purely genetically determined threshold. We show that coupling our model with quantitative genetic methods allows an evolutionary approach including an estimation of the heritability of conditional strategies. We evaluate the performance of the LETM with a simulation study and illustrate its utility by applying it to empirical data on the size-dependent smolting process for stream-dwelling Atlantic salmon juveniles.     

Investigating the genetic architecture of conditional strategies using the environmental threshold model

The threshold expression of dichotomous phenotypes that are environmentally cued or induced comprise the vast majority of phenotypic dimorphisms in colour, morphology, behaviour and life history. Modelled as conditional strategies under the framework of evolutionary game theory, the quantitative genetic basis of these traits is a challenge to estimate. The challenge exists firstly because the phenotypic expression of the trait is dichotomous and secondly because the apparent environmental cue is separate from the biological signal pathway that induces the switch between phenotypes. It is the cryptic variation underlying the translation of cue to phenotype that we address here. With a ‘half-sib common environment’ and a ‘family-level split environment’ experiment, we examine the environmental and genetic influences that underlie male dimorphism in the earwig Forficula auricularia. From the conceptual framework of the latent environmental threshold (LET) model, we use pedigree information to dissect the genetic architecture of the threshold expression of forceps length. We investigate for the first time the strength of the correlation between observable and cryptic ‘proximate’ cues. Furthermore, in support of the environmental threshold model, we found no evidence for a genetic correlation between cue and the threshold between phenotypes. Our results show strong correlations between observable and proximate cues and less genetic variation for thresholds than previous studies have suggested. We discuss the importance of generating better estimates of the genetic variation for thresholds when investigating the genetic architecture and heritability of threshold traits. By investigating genetic architecture by means of the LET model, our study supports several key evolutionary ideas related to conditional strategies and improves our understanding of environmentally cued decisions.     

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.     

Genotype-by-environment interactions leads to variable selection on life-history strategy in Common Evening Primrose (Oenothera biennis)

Monocarpic plant species, where reproduction is fatal, frequently exhibit variation in the length of their prereproductive period prior to flowering. If this life-history variation in flowering strategy has a genetic basis, genotype-by-environment interactions (G x E) may maintain phenotypic diversity in flowering strategy. The native monocarpic plant Common Evening Primrose (Oenothera biennis L., Onagraceae) exhibits phenotypic variation for annual vs. biennial flowering strategies. I tested whether there was a genetic basis to variation in flowering strategy in O. biennis, and whether environmental variation causes G x E that imposes variable selection on flowering strategy. In a field experiment, I randomized more than 900 plants from 14 clonal families (genotypes) into five distinct habitats that represented a natural productivity gradient. G x E strongly affected the lifetime fruit production of O. biennis, with the rank-order in relative fitness of genotypes changing substantially between habitats. I detected genetic variation in annual vs. biennial strategies in most habitats, as well as a G x E effect on flowering strategy. This variation in flowering strategy was correlated with genetic variation in relative fitness, and phenotypic and genotypic selection analyses revealed that environmental variation resulted in variable directional selection on annual vs. biennial strategies. Specifically, a biennial strategy was favoured in moderately productive environments, whereas an annual strategy was favoured in low-productivity environments. These results highlight the importance of variable selection for the maintenance of genetic variation in the life-history strategy of a monocarpic plant.     

Environmental coupling of selection and heritability limits evolution

There has recently been great interest in applying theoretical quantitative genetic models to empirical studies of evolution in wild populations. However, while classical models assume environmental constancy, most natural populations exist in variable environments. Here, we applied a novel analytical technique to a long-term study of birthweight in wild sheep and examined, for the first time, how variation in environmental quality simultaneously influences the strength of natural selection and the genetic basis of trait variability. In addition to demonstrating that selection and genetic variance vary dramatically across environments, our results show that environmental heterogeneity induces a negative correlation between these two parameters. Harsh environmental conditions were associated with strong selection for increased birthweight but low genetic variance, and vice versa. Consequently, the potential for microevolution in this population is constrained by either a lack of heritable variation (in poor environments) or by a reduced strength of selection (in good environments). More generally, environmental dependence of this nature may act to limit rates of evolution, maintain genetic variance, and favour phenotypic stasis in many natural systems. Assumptions of environmental constancy are likely to be violated in natural systems, and failure to acknowledge this may generate highly misleading expectations for phenotypic microevolution.     

Genetic and environmental heterogeneity of residual variance of weight traits in Nellore beef cattle

Background

Many studies have provided evidence of the existence of genetic heterogeneity of environmental variance, suggesting that it could be exploited to improve robustness and uniformity of livestock by selection. However, little is known about the perspectives of such a selection strategy in beef cattle.

Methods

A two-step approach was applied to study the genetic heterogeneity of residual variance of weight gain from birth to weaning and long-yearling weight in a Nellore beef cattle population. First, an animal model was fitted to the data and second, the influence of additive and environmental effects on the residual variance of these traits was investigated with different models, in which the log squared estimated residuals for each phenotypic record were analyzed using the restricted maximum likelihood method. Monte Carlo simulation was performed to assess the reliability of variance component estimates from the second step and the accuracy of estimated breeding values for residual variation.

Results

The results suggest that both genetic and environmental factors have an effect on the residual variance of weight gain from birth to weaning and long-yearling in Nellore beef cattle and that uniformity of these traits could be improved by selecting for lower residual variance, when considering a large amount of information to predict genetic merit for this criterion. Simulations suggested that using the two-step approach would lead to biased estimates of variance components, such that more adequate methods are needed to study the genetic heterogeneity of residual variance in beef cattle.     

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.     

Field heritability of a plant adaptation to fire in heterogeneous landscapes

The strong association observed between fire regimes and variation in plant adaptations to fire suggests a rapid response to fire as an agent of selection. It also suggests that fire‐related traits are heritable, a precondition for evolutionary change. One example is serotiny, the accumulation of seeds in unopened fruits or cones until the next fire, an important strategy for plant population persistence in fire‐prone ecosystems. Here, we evaluate the potential of this trait to respond to natural selection in its natural setting. For this, we use a SNP marker approach to estimate genetic variance and heritability of serotiny directly in the field for two Mediterranean pine species. Study populations were large and heterogeneous in climatic conditions and fire regime. We first estimated the realized relatedness among trees from genotypes, and then partitioned the phenotypic variance in serotiny using Bayesian animal models that incorporated environmental predictors. As expected, field heritability was smaller (around 0.10 for both species) than previous estimates under common garden conditions (0.20). An estimate on a subset of stands with more homogeneous environmental conditions was not different from that in the complete set of stands, suggesting that our models correctly captured the environmental variation at the spatial scale of the study. Our results highlight the importance of measuring quantitative genetic parameters in natural populations, where environmental heterogeneity is a critical aspect. The heritability of serotiny, although not high, combined with high phenotypic variance within populations, confirms the potential of this fire‐related trait for evolutionary change in the wild.     

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.     

Environmental variance in male mating success modulates the positive versus negative impacts of sexual selection on genetic load

Sexual selection on males is predicted to increase population fitness, and delay population extinction, when mating success negatively covaries with genetic load across individuals. However, such benefits of sexual selection could be counteracted by simultaneous increases in genome-wide drift resulting from reduced effective population size caused by increased variance in fitness. Resulting fixation of deleterious mutations could be greatest in small populations, and when environmental variation in mating traits partially decouples sexual selection from underlying genetic variation. The net consequences of sexual selection for genetic load and population persistence are therefore likely to be context dependent, but such variation has not been examined. We use a genetically explicit individual-based model to show that weak sexual selection can increase population persistence time compared to random mating. However, for stronger sexual selection such positive effects can be overturned by the detrimental effects of increased genome-wide drift. Furthermore, the relative strengths of mutation-purging and drift critically depend on the environmental variance in the male mating trait. Specifically, increasing environmental variance caused stronger sexual selection to elevate deleterious mutation fixation rate and mean selection coefficient, driving rapid accumulation of drift load and decreasing population persistence times. These results highlight an intricate balance between conflicting positive and negative consequences of sexual selection on genetic load, even in the absence of sexually antagonistic selection. They imply that environmental variances in key mating traits, and intrinsic genetic drift, should be properly factored into future theoretical and empirical studies of the evolution of population fitness under sexual selection.     

Linear and threshold analysis of direct and maternal genetic effects for secondary sex ratio in Iranian buffaloes

The objective of this study was to estimate variance components and genetic parameters for secondary sex ratio (SSR) in Iranian buffaloes. Calving records from April 1995 to June 2010 comprising 15,207 calving events from the first three lactations of 1066 buffalo herds of Iran were analyzed using linear and threshold animal models to estimate variance components, heritabilities and genetic correlations between direct and maternal genetic effects for SSR. Linear and threshold animal models included direct and maternal genetic effects with covariance between them and maternal permanent environmental effects were implemented by Gibbs sampling methodology. Posterior means of direct and maternal heritabilities and repeatability for SSR obtained from linear animal model were 0.15, 0.10, and 0.17, respectively. Threshold estimates of direct and maternal heritabilities and repeatability for SSR were 0.48, 0.27, and 0.52, respectively. The results showed that the correlations between direct and maternal genetic effects of SSR were negative and high in both models. In addition, the ratios of maternal permanent environmental variance were low. Exploitable genetic variation in SSR can take advantage of sexual dimorphism for economically important traits which may facilitate greater selection intensity and thus greater response to selection, as well as reducing the replacement costs. Threshold animal model may be applied in selection programs where animals are to be genetically ranked for female rate.     

Genetic variation underlying the expression of a polyphenism

Polyphenic traits are widespread and represent a conditional strategy sensitive to environmental cues. The environmentally cued threshold (ET) model considers the switchpoint between alternative phenotypes as a polygenic quantitative trait with normally distributed variation. However, the genetic variation for switchpoints has rarely been explored empirically. Here, we used inbred lines to investigate the genetic variation for the switchpoint in the mite Rhizoglyphus echinopus, in which males are either fighters or scramblers. The conditionality of male dimorphism varied among inbred lines, indicating that there was genetic variation for switchpoints in the base population, as predicted by the ET model. Our results also suggest a mixture between canalized and conditional strategists in R. echinopus. We propose that major genes that canalize morph expression and affect the extent to which a trait can be conditionally expressed could be a feature of the genetic architecture of threshold traits in other taxa.     

Heritability of flight and resting metabolic rates in the Glanville fritillary butterfly

Dispersal capacity is a key life‐history trait especially in species inhabiting fragmented landscapes. Evolutionary models predict that, given sufficient heritable variation, dispersal rate responds to natural selection imposed by habitat loss and fragmentation. Here, we estimate phenotypic variance components and heritability of flight and resting metabolic rates (RMRs) in an ecological model species, the Glanville fritillary butterfly, in which flight metabolic rate (FMR) is known to correlate strongly with dispersal rate. We modelled a two‐generation pedigree with the animal model to distinguish additive genetic variance from maternal and common environmental effects. The results show that FMR is significantly heritable, with additive genetic variance accounting for about 40% of total phenotypic variance; thus, FMR has the potential to respond to selection on dispersal capacity. Maternal influences on flight metabolism were negligible. Heritability of flight metabolism was context dependent, as in stressful thermal conditions, environmentally induced variation dominated over additive genetic effects. There was no heritability in RMR, which was instead strongly influenced by maternal effects. This study contributes to a mechanistic understanding of the evolution of dispersal‐related traits, a pressing question in view of the challenges posed to many species by changing climate and fragmentation of natural habitats.     

FITNESS VARIATION DUE TO SEXUAL ANTAGONISM AND LINKAGE DISEQUILIBRIUM

Extensive fitness variation for sexually antagonistic characters has been detected in nature. However, current population genetic theory suggests that sexual antagonism is unlikely to play a major role in the maintenance of variation. We present a two‐locus model of sexual antagonism that is capable of explaining greater fitness variance at equilibrium than previous single‐locus models. The second genetic locus provides additional fitness variance in two complementary ways. First, linked loci can maintain gene variants that are lost in single‐locus models of evolution, expanding the opportunity for polymorphism. Second, linkage disequilibrium results between any two sexually antagonistic genes, producing an excess of high‐ and low‐fitness haplotypes. Our results uncover a unique contribution of conflicting selection pressures to the maintenance of variation, which simpler models that neglect genetic architecture overlook.     

Indirect genetic effects and the spread of infectious disease: are we capturing the full heritable variation underlying disease prevalence?

Reducing disease prevalence through selection for host resistance offers a desirable alternative to chemical treatment. Selection for host resistance has proven difficult, however, due to low heritability estimates. These low estimates may be caused by a failure to capture all the relevant genetic variance in disease resistance, as genetic analysis currently is not taylored to estimate genetic variation in infectivity. Host infectivity is the propensity of transmitting infection upon contact with a susceptible individual, and can be regarded as an indirect effect to disease status. It may be caused by a combination of physiological and behavioural traits. Though genetic variation in infectivity is difficult to measure directly, Indirect Genetic Effect (IGE) models, also referred to as associative effects or social interaction models, allow the estimation of this variance from more readily available binary disease data (infected/non-infected). We therefore generated binary disease data from simulated populations with known amounts of variation in susceptibility and infectivity to test the adequacy of traditional and IGE models. Our results show that a conventional model fails to capture the genetic variation in infectivity inherent in populations with simulated infectivity. An IGE model, on the other hand, does capture some of the variation in infectivity. Comparison with expected genetic variance suggests that there is scope for further methodological improvement, and that potential responses to selection may be greater than values presented here. Nonetheless, selection using an index of estimated direct and indirect breeding values was shown to have a greater genetic selection differential and reduced future disease risk than traditional selection for resistance only. These findings suggest that if genetic variation in infectivity substantially contributes to disease transmission, then breeding designs which explicitly incorporate IGEs might help reduce disease prevalence.     

A POPULATION GENETIC THEORY OF CANALIZATION

Canalization is the suppression of phenotypic variation. Depending on the causes of phenotypic variation, one speaks either of genetic or environmental canalization. Genetic canalization describes insensitivity of a character to mutations, and the insensitivity to environmental factors is called environmental canalization. Genetic canalization is of interest because it influences the availability of heritable phenotypic variation to natural selection, and is thus potentially important in determining the pattern of phenotypic evolution. In this paper a number of population genetic models are considered of a quantitative character under stabilizing selection. The main purpose of this study is to define the population genetic conditions and constraints for the evolution of canalization. Environmental canalization is modeled as genotype specific environmental variance. It is shown that stabilizing selection favors genes that decrease environmental variance of quantitative characters. However, the theoretical limit of zero environmental variance has never been observed. Of the many ways to explain this fact, two are addressed by our model. It is shown that a “canalization limit” is reached if canalizing effects of mutations are correlated with direct effects on the same character. This canalization limit is predicted to be independent of the strength of stabilizing selection, which is inconsistent with recent experimental data (Sterns et al. 1995). The second model assumes that the canalizing genes have deleterious pleiotropic effects. If these deleterious effects are of the same magnitude as all the other mutations affecting fitness very strong stabilizing selection is required to allow the evolution of environmental canalization. Genetic canalization is modeled as an influence on the average effect of mutations at a locus of other genes. It is found that the selection for genetic canalization critically depends on the amount of genetic variation present in the population. The more genetic variation, the stronger the selection for canalizing effects. All factors that increase genetic variation favor the evolution of genetic canalization (large population size, high mutation rate, large number of genes). If genetic variation is maintained by mutation-selection balance, strong stabilizing selection can inhibit the evolution of genetic canalization. Strong stabilizing selection eliminates genetic variation to a level where selection for canalization does not work anymore. It is predicted that the most important characters (in terms of fitness) are not necessarily the most canalized ones, if they are under very strong stabilizing selection (k > 0.2V_e). The rate of decrease of mutational variance V_m is found to be less than 10% of the initial V_m. From this result it is concluded that characters with typical mutational variances of about 10^–3 V_e are in a metastable state where further evolution of genetic canalization is too slow to be of importance at a microevolutionary time scale. The implications for the explanation of macroevolutionary patterns are discussed.     

The population genetic theory of hidden variation and genetic robustness

One of the most solid generalizations of transmission genetics is that the phenotypic variance of populations carrying a major mutation is increased relative to the wild type. At least some part of this higher variance is genetic and due to release of previously hidden variation. Similarly, stressful environments also lead to the expression of hidden variation. These two observations have been considered as evidence that the wild type has evolved robustness against genetic variation, i.e., genetic canalization. In this article we present a general model for the interaction of a major mutation or a novel environment with the additive genetic basis of a quantitative character under stabilizing selection. We introduce an approximation to the genetic variance in mutation-selection-drift balance that includes the previously used stochastic Gaussian and house-of-cards approximations as limiting cases. We then show that the release of hidden genetic variation is a generic property of models with epistasis or genotype-environment interaction, regardless of whether the wild-type genotype is canalized or not. As a consequence, the additive genetic variance increases upon a change in the environment or the genetic background even if the mutant character state is as robust as the wild-type character. Estimates show that this predicted increase can be considerable, in particular in large populations and if there are conditionally neutral alleles at the loci underlying the trait. A brief review of the relevant literature suggests that the assumptions of this model are likely to be generic for polygenic traits. We conclude that the release of hidden genetic variance due to a major mutation or environmental stress does not demonstrate canalization of the wild-type genotype.     

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.