The ecological genetics of conditional strategies

We develop a quantitative genetic model for conditional strategies that incorporates the ecological realism of previous strategic models. Similar to strategic models, the results show that environmental heterogeneity, cue reliability, and environment-dependent fitness trade-offs for the alternative tactics of the conditional strategy interact to determine when conditional strategies will be favored and that conditional strategies should be a common form of adaptive variation in nature. The results also show that conditional and unconditional development can be maintained in one of two ways: by frequency-dependent selection or by the maintenance of genetic variation that exceeds the threshold for induction. We then modified the model to take into account variance in exposures to the environmental cue as well as variance in response to the cue, which allows a derivation of a dose-response curve. Here the results showed that increasing the genetic variance for response both flattens and shifts the dose-response curve. Finally, we modify the model to derive the dose-response curve for a population polymorphic for a gene that blocks expression of the conditional strategy. We illustrate the utility of the model by application to predator-induced defense in an intertidal barnacle and compare the results with phenotypic models of selection.     

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.     

Sexual selection and alternative mating behaviours generate demographic stochasticity in small populations.

Recent theory predicts that environmental variation and small population size facilitate the coexistence of alternative phenotypes despite unequal mean fitness. However, traditional studies of reproductive strategies often assume that the stability of alternative mating behaviours relies on equal male fitness. We present results from field observations and experimental manipulations of thermal resources on territories demonstrating the coexistence of alternative reproductive behaviours with unequal fitness. The side-blotched lizard Uta stansburiana exhibits two alternative strategies for territoriality: "usurp" and "defend". Paternity analysis revealed significantly greater mean fitness for "usurpers" than "defenders" in our study of natural variation. Moreover, variance in fitness was significantly higher for usurpers on both experimental and natural plots, implying that "usurp" is a risky strategy with potentially large pay-offs or none at all. We show theoretically that significantly higher variance in usurper fitness can allow for coexistence with defenders despite higher mean fitness of usurpers. This coexistence is facilitated by small population size. Our results have general implications for the evolution of alternative strategies and the maintenance of genetic diversity in small populations.     

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.     

Adaptation to marginal habitats by evolution of increased phenotypic plasticity

In an island population receiving immigrants from a larger continental population, gene flow causes maladaptation, decreasing mean fitness and producing continued directional selection to restore the local mean phenotype to its optimum. We show that this causes higher plasticity to evolve on the island than on the continent at migration-selection equilibrium, assuming genetic variation of reaction norms is such that phenotypic variance is higher on the island, where phenotypes are not canalized. For a species distributed continuously in space along an environmental gradient, higher plasticity evolves at the edges of the geographic range, and in environments where phenotypes are not canalized. Constant or evolving partially adaptive plasticity also alleviates maladaptation owing to gene flow in a heterogeneous environment and produces higher mean fitness and larger population size in marginal populations, preventing them from becoming sinks and facilitating invasion of new habitats. Our results shed light on the widely observed involvement of partially adaptive plasticity in phenotypic clines, and on the mechanisms causing geographic variation in plasticity.     

Short‐term insurance versus long‐term bet‐hedging strategies as adaptations to variable environments

Understanding how organisms adapt to environmental variation is a key challenge of biology. Central to this are bet‐hedging strategies that maximize geometric mean fitness across generations, either by being conservative or diversifying phenotypes. Theoretical models have identified environmental variation across generations with multiplicative fitness effects as driving the evolution of bet‐hedging. However, behavioral ecology has revealed adaptive responses to additive fitness effects of environmental variation within lifetimes, either through insurance or risk‐sensitive strategies. Here, we explore whether the effects of adaptive insurance interact with the evolution of bet‐hedging by varying the position and skew of both arithmetic and geometric mean fitness functions. We find that insurance causes the optimal phenotype to shift from the peak to down the less steeply decreasing side of the fitness function, and that conservative bet‐hedging produces an additional shift on top of this, which decreases as adaptive phenotypic variation from diversifying bet‐hedging increases. When diversifying bet‐hedging is not an option, environmental canalization to reduce phenotypic variation is almost always favored, except where the tails of the fitness function are steeply convex and produce a novel risk‐sensitive increase in phenotypic variance akin to diversifying bet‐hedging. Importantly, using skewed fitness functions, we provide the first model that explicitly addresses how conservative and diversifying bet‐hedging strategies might coexist.     

The fitness threshold model: Random environmental change alters adaptive landscapes

We used a probabilistic optimization model to explore the joint evolutionary effects of random phenotypic and environmental variation. Two forms of environmental noise were defined in which the optimal phenotype remained constant but all organisms experienced either the same proportionate or the same absolute fitness gains and losses. There was no evolutionary effect of proportionate fitness fluctuations. In contrast, the optimal genotype varied with absolute fitness fluctuations, despite the environmental effect being phenotype-independent. We refer to such phenotype-independent fluctuation in absolute fitness as the fitness threshold model, because shared fitness effects determine the zero-fitness points (i.e. the baseline) on an intrinsic fitness function. Thus, environmental effects that are unrelated to a focal trait can cause peak shifts in the genetic optimum for the trait. Changes in the fitness threshold not only changed peak locations, but also altered the slopes defining the peaks, and so should alter the rate of evolution towards optima. This model pertains to evolution in any system, unless there is no phenotypic or environmental variance, or the selection function and distribution of phenotypic error assume similar shapes. Our results have many basic and applied implications for topics such as the maintenance of genetic variation, the canalization of development and the management of natural populations.     

The distribution of fitness effects in an uncertain world

The distribution of fitness effects (DFE) among new mutations plays a critical role in adaptive evolution and the maintenance of genetic variation. Although fitness landscape models predict several key features of the DFE, most theory to date focuses on predictable environmental conditions, while ignoring stochastic environmental fluctuations that feature prominently in the ecology of many organisms. Here, we derive an extension of Fisher's geometric model that incorporates two common effects of environmental variation: (1) nonadaptive genotype‐by‐environment interactions (G × E), in which the phenotype of a given genotype varies across environmental contexts; and (2) random fluctuation of the fitness optimum, which generates fluctuating selection. We show that both factors cause a mismatch between the DFE within single generations and the distribution of geometric mean fitness effects (averaged over multiple generations) that governs long‐term evolutionary change. Such mismatches permit strong evolutionary constraints—despite an abundance of beneficial fitness variation within single environmental contexts—and to conflicting DFE estimates from direct versus indirect inference methods. Finally, our results suggest an intriguing parallel between the genetics and ecology of evolutionary constraints, with environmental fluctuations and pleiotropy placing qualitatively similar limits on the availability of adaptive genetic variation.     

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.     

EVOLUTION IN FLUCTUATING ENVIRONMENTS: DECOMPOSING SELECTION INTO ADDITIVE COMPONENTS OF THE ROBERTSON–PRICE EQUATION

We analyze the stochastic components of the Robertson–Price equation for the evolution of quantitative characters that enables decomposition of the selection differential into components due to demographic and environmental stochasticity. We show how these two types of stochasticity affect the evolution of multivariate quantitative characters by defining demographic and environmental variances as components of individual fitness. The exact covariance formula for selection is decomposed into three components, the deterministic mean value, as well as stochastic demographic and environmental components. We show that demographic and environmental stochasticity generate random genetic drift and fluctuating selection, respectively. This provides a common theoretical framework for linking ecological and evolutionary processes. Demographic stochasticity can cause random variation in selection differentials independent of fluctuating selection caused by environmental variation. We use this model of selection to illustrate that the effect on the expected selection differential of random variation in individual fitness is dependent on population size, and that the strength of fluctuating selection is affected by how environmental variation affects the covariance in Malthusian fitness between individuals with different phenotypes. Thus, our approach enables us to partition out the effects of fluctuating selection from the effects of selection due to random variation in individual fitness caused by demographic stochasticity.     

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.     

THE EVOLUTION OF CANALIZATION AND THE BREAKING OF VON BAER'S LAWS: MODELING THE EVOLUTION OF DEVELOPMENT WITH EPISTASIS

Evolution can change the developmental processes underlying a character without changing the average expression of the character itself. This sort of change must occur in both the evolution of canalization, in which a character becomes increasingly buffered against genetic or developmental variation, and in the phenomenon of closely related species that show similar adult phenotypes but different underlying developmental patterns. To study such phenomena, I develop a model that follows evolution on a surface representing adult phenotype as a function of underlying developmental characters. A contour on such a “phenotype landscape” is a set of states of developmental characters that produce the same adult phenotype. Epistasis induces curvature of this surface, and degree of canalization is represented by the slope along a contour. I first discuss the geometric properties of phenotype landscapes, relating epistasis to canalization. I then impose a fitness function on the phenotype and model evolution of developmental characters as a function of the fitness function and the local geometry of the surface. This model shows how canalization evolves as a population approaches an optimum phenotype. It further shows that under some circumstances, “decanalization” can occur, in which the expression of adult phenotype becomes increasingly sensitive to developmental variation. This process can cause very similar populations to diverge from one another developmentally even when their adult phenotypes experience identical selection regimes.     

The stationary distribution of a continuously varying strategy in a class-structured population under mutation-selection-drift balance

Many traits and/or strategies expressed by organisms are quantitative phenotypes. Because populations are of finite size and genomes are subject to mutations, these continuously varying phenotypes are under the joint pressure of mutation, natural selection and random genetic drift. This article derives the stationary distribution for such a phenotype under a mutation-selection-drift balance in a class-structured population allowing for demographically varying class sizes and/or changing environmental conditions. The salient feature of the stationary distribution is that it can be entirely characterized in terms of the average size of the gene pool and Hamilton's inclusive fitness effect. The exploration of the phenotypic space varies exponentially with the cumulative inclusive fitness effect over state space, which determines an adaptive landscape. The peaks of the landscapes are those phenotypes that are candidate evolutionary stable strategies and can be determined by standard phenotypic selection gradient methods (e.g. evolutionary game theory, kin selection theory, adaptive dynamics). The curvature of the stationary distribution provides a measure of the stability by convergence of candidate evolutionary stable strategies, and it is evaluated explicitly for two biological scenarios: first, a coordination game, which illustrates that, for a multipeaked adaptive landscape, stochastically stable strategies can be singled out by letting the size of the gene pool grow large; second, a sex-allocation game for diploids and haplo-diploids, which suggests that the equilibrium sex ratio follows a Beta distribution with parameters depending on the features of the genetic system.     

Evolutionary Stability for Interactions among Kin under Quantitative Inheritance

The theory of evolutionarily stable strategies (ESS) predicts the long-term evolutionary outcome of frequency-dependent selection by making a number of simplifying assumptions about the genetic basis of inheritance. I use a symmetrized multilocus model of quantitative inheritance without mutation to analyze the results of interactions between pairs of related individuals and compare the equilibria to those found by ESS analysis. It is assumed that the fitness changes due to interactions can be approximated by the exponential of a quadratic surface. The major results are the following. (1) The evolutionarily stable phenotypes found by ESS analysis are always equilibria of the model studied here. (2) When relatives interact, one of the two conditions for stability of equilibria differs between the two models; this can be accounted for by positing that the inclusive fitness function for quantitative characters is slightly different from the inclusive fitness function for characters determined by a single locus. (3) The inclusion of environmental variance will in general change the equilibrium phenotype, but the equilibria of ESS analysis are changed to the same extent by environmental variance. (4) A class of genetically polymorphic equilibria occur, which in the present model are always unstable. These results expand the range of conditions under which one can validly predict the evolution of pairwise interactions using ESS analysis.     

Multivariate selection shapes environment-dependent variation in the clonal morphology of a red seaweed

Within-individual strategies of variation (e.g., phenotypic plasticity) are particularly relevant to modular organisms, in which ramets of the same genetic individual may encounter diverse environments imposing diverse patterns of selection. Hence, measuring selection in heterogeneous environments is essential to understanding whether environment-dependent phenotypic change enhances the fitness of modular individuals. In sublittoral marine habitats, competition for light and space among modular taxa generates extreme patchiness in resource availability. Little is known, however, of the potential for plasticity within individuals to arise from spatially-variable selection in such systems. We tested whether plasticity enhances genet-level fitness in Asparagopsis armata, a clonal seaweed in which correlated traits mediate morphological responses to variation in light. Using the capacity for rapid, clonal growth to measure fitness, we identified aspects of ramet morphology targeted by selection in two contrasting light environments and compared patterns of selection across environments. We found that directional selection on single traits, coupled with linear and nonlinear selection on multi-trait interactions, shape ramet morphology within environments and favor different phenotypes in each. Evidence of environment-dependent, multivariate selection on correlated traits is novel for any marine modular organism and demonstrates that seaweeds, such as A. armata, may potentially adapt to environmental heterogeneity via plasticity in clonal morphology.     

Phenotypic plasticity and population viability: the importance of environmental predictability

Phenotypic plasticity plays a key role in modulating how environmental variation influences population dynamics, but we have only rudimentary understanding of how plasticity interacts with the magnitude and predictability of environmental variation to affect population dynamics and persistence. We developed a stochastic individual-based model, in which phenotypes could respond to a temporally fluctuating environmental cue and fitness depended on the match between the phenotype and a randomly fluctuating trait optimum, to assess the absolute fitness and population dynamic consequences of plasticity under different levels of environmental stochasticity and cue reliability. When cue and optimum were tightly correlated, plasticity buffered absolute fitness from environmental variability, and population size remained high and relatively invariant. In contrast, when this correlation weakened and environmental variability was high, strong plasticity reduced population size, and populations with excessively strong plasticity had substantially greater extinction probability. Given that environments might become more variable and unpredictable in the future owing to anthropogenic influences, reaction norms that evolved under historic selective regimes could imperil populations in novel or changing environmental contexts. We suggest that demographic models (e.g. population viability analyses) would benefit from a more explicit consideration of how phenotypic plasticity influences population responses to environmental change.     

Adaptation and constraint in the evolution of environmental sex determination

When environments differentially influence male and female performance, environmental sex determination (ESD) might evolve. The conclusion from several previous theoretical models was that reaction norms for sex determination should have a single, sharp threshold, with only females being produced in some environments and only males in others. These reaction norms can be disadvantageous in fluctuating environments, however, because they lead to sex-ratio fluctuations. We analysed the evolution of ESD, looking for equilibrium strategies in unconstrained as well as constrained strategy spaces. We identified situations where a single-threshold reaction norm is not evolutionarily stable. In these cases, we found stable strategies in the form of complex reaction norms, showing an oscillatory pattern of sex determination with respect to variation in an environmental variable. Considering that constraints could prevent such phenotypes from being realized, we found that certain randomized reaction norms, with probabilistic sex determination for a range of environments, would achieve nearly the same fitness. We also investigated reaction norms constrained to have a single threshold and found that genetic polymorphism in the environmental threshold value could evolve, producing a similar effect as a randomized reaction norm. We argue that the appearance of genetic variation can be regarded as an alternative outcome when constraints prevent the evolution of a more complex or a randomized strategy.     

Does frequency-dependence determine male morph survival in the bulb mite Rhizoglyphus robini?

Alternative reproductive phenotypes (ARPs) represent discrete morphological variation within a single sex; as such ARPs are an excellent study system to investigate the maintenance of phenotypic variation. ARPs are traditionally modelled as a mixture of pure strategies or as a conditional strategy. Most male dimorphisms are controlled by a conditional strategy, where males develop into a particular phenotype as a result of their condition which allows them to reach a certain threshold. Individuals that are unable to reach the threshold of a conditional strategy are considered to ‘make the best of a bad job’; however, these individuals can have their own fitness merits. Given these fitness merits, condition-dependent selection alone is not sufficient to maintain a conditionally determined male dimorphism and other mechanisms, most likely frequency-dependent selection, are required. We studied in an experiment, the male dimorphic bulb mite Rhizoglyphus robini—where males are fighters that can kill other males or benign scramblers—to assess the strength of frequency-dependent survival in a high and low-quality environment. We found that male survival was frequency-dependent in the high-quality environment but not the low-quality environment. In the high-quality environment the survival curves of the two morphs crossed but the direction of frequency-dependence was opposite to what theory predicts.     

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.