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.     

From stochastic environments to life histories and back

Environmental stochasticity is known to play an important role in life-history evolution, but most general theory assumes a constant environment. In this paper, we examine life-history evolution in a variable environment, by decomposing average individual fitness (measured by the long-run stochastic growth rate) into contributions from average vital rates and their temporal variation. We examine how generation time, demographic dispersion (measured by the dispersion of reproductive events across the lifespan), demographic resilience (measured by damping time), within-year variances in vital rates, within-year correlations between vital rates and between-year correlations in vital rates combine to determine average individual fitness of stylized life histories. In a fluctuating environment, we show that there is often a range of cohort generation times at which the fitness is at a maximum. Thus, we expect ‘optimal’ phenotypes in fluctuating environments to differ from optimal phenotypes in constant environments. We show that stochastic growth rates are strongly affected by demographic dispersion, even when deterministic growth rates are not, and that demographic dispersion also determines the response of life-history-specific average fitness to within- and between-year correlations. Serial correlations can have a strong effect on fitness, and, depending on the structure of the life history, may act to increase or decrease fitness. The approach we outline takes a useful first step in developing general life-history theory for non-constant environments.     

Extending the range of additivity in using inclusive fitness

Inclusive fitness is a concept widely utilized by social biologists as the quantity organisms appear designed to maximize. However, inclusive fitness theory has long been criticized on the (uncontested) grounds that other quantities, such as offspring number, predict gene frequency changes accurately in a wider range of mathematical models. Here, we articulate a set of modeling assumptions that extend the range of scenarios in which inclusive fitness can be applied. We reanalyze recent formal analyses that searched for, but did not find, inclusive fitness maximization. We show (a) that previous models have not used Hamilton''s definition of inclusive fitness, (b) a reinterpretation of Hamilton''s definition that makes it usable in this context, and (c) that under the assumption of probabilistic mixing of phenotypes, inclusive fitness is indeed maximized in these models. We also show how to understand mathematically, and at an individual level, the definition of inclusive fitness, in an explicit population genetic model in which exact additivity is not assumed. We hope that in articulating these modeling assumptions and providing formal support for inclusive fitness maximization, we help bridge the gap between empiricists and theoreticians, which in some ways has been widening, demonstrating to mathematicians why biologists are content to use inclusive fitness, and offering one way to utilize inclusive fitness in general models of social behavior.     

Estimating fluctuating selection in age-structured populations

In age-structured populations, viability and fecundity selection of varying strength may occur in different age classes. On the basis of an original idea by Fisher of weighting individuals by their reproductive value, we show that the combined effect of selection on traits at different ages acts through the individual reproductive value defined as the stochastic contribution of an individual to the total reproductive value of the population the following year. The selection differential is a weighted sum of age-specific differentials that are the covariances between the phenotype and the age-specific relative fitness defined by the individual reproductive value. This enables estimation of weak selection on a multivariate quantitative character in populations with no density regulation by combinations of age-specific linear regressions of individual reproductive values on the traits. Demographic stochasticity produces random variation in fitness components in finite samples of individuals and affects the statistical inference of the temporal average directional selection as well as the magnitude of fluctuating selection. Uncertainties in parameter estimates and test power depend strongly on the demographic stochasticity. Large demographic variance results in large uncertainties in yearly estimates of selection that complicates detection of significant fluctuating selection. The method is illustrated by an analysis of age-specific selection in house sparrows on a fitness-related two-dimensional morphological trait, tarsus length and body mass of fledglings.     

Intraindividual variability in behavior shapes fitness landscapes

Although intraindividual variability (IIV) in behavior is fundamental to ecological dynamics, the factors that contribute to the expression of IIV are poorly understood. Using an individual‐based model, this study examined the effects of stochasticity on the evolution of IIV represented by the residual variability of behavior. The model describes a population of prey with nonoverlapping generations, in which prey take refuge upon encountering a predator. The strategy of a prey is characterized by the mean and IIV (i.e., standard deviation) of hiding duration. Prey with no IIV will spend the same duration hiding in a refuge at each predator encounter, while prey with IIV will have variable hiding durations among encounters. For the sources of stochasticity, within‐generation stochasticity (represented by random predator encounters) and between‐generation stochasticity (represented by random resource availability) were considered. Analysis of the model indicates that individuals with high levels of IIV are maintained in a population in the presence of between‐generation stochasticity even though the optimal strategy in each generation is a strategy with no IIV, regardless of the presence or absence of within‐generation stochasticity. This contradictory pattern emerges because the mean behavioral trait and IIV do not independently influence fitness (e.g., the sign of the selection gradient with respect to IIV depends on the mean trait). Consequently, even when evolution eventually leads toward a strategy with no IIV (i.e., the optimal strategy), greater IIV may be transiently selected. Between‐generation stochasticity consistently imposes such transient selection and maintain high levels of IIV in a population.     

Optimal age of maturity in fluctuating environments under r‐ and K‐selection

Optimality models for evolution of life histories have shown that increased environmental stochasticity promotes early age of maturity. Here we argue that if r‐selection for early maturation implies a tradeoff making those phenotypes more sensitive to a change in population size than phenotypes maturing at older ages, K‐selection can favor delayed onset of maturation. We analyze a general stochastic Leslie‐matrix model with a simplified density regulation affecting all survivals equally through a function of the population vector, often called the ‘critical age class’. We show that the outcome of such an age‐dependent r‐ and K‐selection is that the expected value of the ‘critical age class’ is maximized by evolution, a strategy strongly influenced by the magnitude of the environmental stochasticity. We also demonstrate that evolution caused by such density‐dependent selection influences the population dynamics, showing a possible reciprocal effect between ecology and evolution in age‐structured populations. This modeling approach reveals that changes in population size affecting the fitness of phenotypes with different age of maturity may be an important selective agent for variation in onset of reproduction in fluctuating environments. This provides a testable hypothesis for how patterns in the population dynamics should affect life history variation.     

Demographic stochasticity alters expected outcomes in experimental and simulated non‐neutral communities

Theory has shown that the effects of demographic stochasticity on communities may depend on the magnitude of fitness differences between species. In particular, it has been suggested that demographic stochasticity has the potential to significantly alter competitive outcomes when fitness differences are small (nearly neutral), but that it has negligible effects when fitness differences are large (highly non‐neutral). Here we test such theory experimentally and extend it to examine how demographic stochasticity affects exclusion frequency and mean densities of consumers in simple, but non‐neutral, consumer–resource communities. We used experimental microcosms of protists and rotifers feeding on a bacterial resource to test how varying absolute population sizes (a driver of demographic stochasticity) affected the probability of competitive exclusion of the weakest competitor. To explore whether demographic stochasticity could explain our experimental results, and to generalize beyond our experiment, we paired the experiment with a continuous‐time stochastic model of resource competition, which we simulated for 11 different fitness inequalities between competiting consumers. Consistent with theory, in both our experiments and our simulations we found that demographic stochasticity altered competitive outcomes in communities where fitness differences were small. However, we also found that demographic stochasticity alone could affect communities in other ways, even when fitness differences between competitors were large. Specifically, demographic stochasticity altered mean densities of both weak and strong competitors in experimental and simulated communities. These findings highlight how demographic stochasticity can change both competitive outcomes in non‐neutral communities and the processes underlying overall community dynamics.     

Early constraints in sexual dimorphism: survival benefits of feminized phenotypes

Sexual dimorphism (SD) has evolved in response to selection pressures that differ between sexes. Since such pressures change across an individual's life, SD may vary within age classes. Yet, little is known about how selection on early phenotypes may drive the final SD observed in adults. In many dimorphic species, juveniles resemble adult females rather than adult males, meaning that out of the selective pressures established by sexual selection feminized phenotypes may be adaptive. If true, fitness benefits of early female‐like phenotypes may constrain the expression of male phenotypes in adulthood. Using the common kestrel Falco tinnunculus as a study model, we evaluated the fitness advantages of expressing more feminized phenotypes at youth. Although more similar to adult females than to adult males, common kestrel fledglings are still sexually dimorphic in size and coloration. Integrating morphological and chromatic variables, we analysed the phenotypic divergence between sexes as a measure of how much each individual looks like the sex to which it belongs (phenotypic sexual resemblance, PSR). We then tested the fitness benefits associated with PSR by means of the probability of recruitment in the population. We found a significant interaction between PSR and sex, showing that in both sexes more feminized phenotypes recruited more into the population than less feminized phenotypes. Moreover, males showed lower PSR than females and a higher proportion of incorrect sex classifications. These findings suggest that the mechanisms in males devoted to resembling female phenotypes in youth, due to a trend to increase fitness through more feminized phenotypes, may provide a mechanism to constrain the SD in adulthood.     

Evolution and population dynamics in stochastic environments

Inter-generational temporal variability of the environment is important in the evolution and adaptation of phenotypic traits. We discuss a population-dynamic approach which plays a central role in the analysis of evolutionary processes. The basic principle is that the phenotypes with the greatest long-term average growth rate will dominate the entire population. The calculation of longterm average growth rates for populations under temporal stochasticity can be highly cumbersome. However, for a discrete non-overlapping population, it is identical to the geometric mean of the growth rates (geometric mean fitness), which is usually different from the simple arithmetic mean of growth rates. Evolutionary outcomes based on geometric mean fitness are often very different from the predictions based on the usual arithmetic mean fitness. In this paper we illustrate the concept of geometric mean fitness in a few simple models. We discuss its implications for the adaptive evolution of phenotypes, e.g. foraging under predation risks and clutch size. Next, we present an application: the risk-spreading egg-laying behaviour of the cabbage white butterfly, and develop a two-patch population dynamic model to show how the optimal solution diverges from the ssual arithmetic mean approach. The dynamics of these stochastic models cannot be predicted from the dynamics of simple deterministic models. Thus the inclusion of stochastic factors in the analyses of populations is essential to the understanding of not only population dynamics, but also their evolutionary dynamics.     

Social phenotype extended to communities: Expanded multilevel social selection analysis reveals fitness consequences of interspecific interactions

In social species, fitness consequences are associated with both individual and social phenotypes. Social selection analysis has quantified the contribution of conspecific social traits to individual fitness. There has been no attempt, however, to apply a social selection approach to quantify the fitness implications of heterospecific social phenotypes. Here, we propose a novel social selection based approach integrating the role of all social interactions at the community level. We extended multilevel selection analysis by including a term accounting for the group phenotype of heterospecifics. We analyzed nest activity as a model social trait common to two species, the lesser kestrel (Falco naumanni) and jackdaw (Corvus monedula), nesting in either single‐ or mixed‐species colonies. By recording reproductive outcome as a measure of relative fitness, our results reveal an asymmetric system wherein only jackdaw breeding performance was affected by the activity phenotypes of both conspecific and heterospecific neighbors. Our model incorporating heterospecific social phenotypes is applicable to animal communities where interacting species share a common social trait, thus allowing an assessment of the selection pressure imposed by interspecific interactions in nature. Finally, we discuss the potential role of ecological limitations accounting for random or preferential assortments among interspecific social phenotypes, and the implications of such processes to community evolution.     

Asymmetrical Damage Partitioning in Bacteria: A Model for the Evolution of Stochasticity,Determinism, and Genetic Assimilation

Non-genetic phenotypic variation is common in biological organisms. The variation is potentially beneficial if the environment is changing. If the benefit is large, selection can favor the evolution of genetic assimilation, the process by which the expression of a trait is transferred from environmental to genetic control. Genetic assimilation is an important evolutionary transition, but it is poorly understood because the fitness costs and benefits of variation are often unknown. Here we show that the partitioning of damage by a mother bacterium to its two daughters can evolve through genetic assimilation. Bacterial phenotypes are also highly variable. Because gene-regulating elements can have low copy numbers, the variation is attributed to stochastic sampling. Extant Escherichia coli partition asymmetrically and deterministically more damage to the old daughter, the one receiving the mother’s old pole. By modeling in silico damage partitioning in a population, we show that deterministic asymmetry is advantageous because it increases fitness variance and hence the efficiency of natural selection. However, we find that symmetrical but stochastic partitioning can be similarly beneficial. To examine why bacteria evolved deterministic asymmetry, we modeled the effect of damage anchored to the mother’s old pole. While anchored damage strengthens selection for asymmetry by creating additional fitness variance, it has the opposite effect on symmetry. The difference results because anchored damage reinforces the polarization of partitioning in asymmetric bacteria. In symmetric bacteria, it dilutes the polarization. Thus, stochasticity alone may have protected early bacteria from damage, but deterministic asymmetry has evolved to be equally important in extant bacteria. We estimate that 47% of damage partitioning is deterministic in E. coli. We suggest that the evolution of deterministic asymmetry from stochasticity offers an example of Waddington’s genetic assimilation. Our model is able to quantify the evolution of the assimilation because it characterizes the fitness consequences of variation.     

COGA phenotypes and linkages on chromosome 2

An initial linkage analysis of the alcoholism phenotype as defined by DSM-III-R criteria and alcoholism defined by DSM-IV criteria showed many, sometimes striking, inconsistencies. These inconsistencies are greatly reduced by making the definition of alcoholism more specific. We defined new phenotypes combining the alcoholism definitions and the latent variables, defining an individual as affected if that individual is alcoholic under one of the definitions (either DSM-III-R or DSM-IV), and indicated having a symptom defined by one of the latent variables. This was done for each of the two alcoholism definitions and five latent variables, selected from a canonical discriminant analyses indicating they formed significant groupings using the electrophysiological variables. We found that linkage analyses utilizing these latent variables were much more robust and consistent than the linkage results based on DSM-III-R or DSM-IV criteria for definition of alcoholism. We also performed linkage analyses on two first principal components derived phenotypes, one derived from the electrophysiological variables, and the other derived from the latent variables. A region on chromosome 2 at 250 cM was found to be linked to both of these derived phenotypes. Further examination of the SNPs in this region identified several haplotypes strongly associated with these derived phenotypes.     

Fitness consequences of centrality in mutualistic individual-based networks

The relationships among the members of a population can be visualized using individual networks, where each individual is a node connected to each other by means of links describing the interactions. The centrality of a given node captures its importance within the network. We hypothesize that in mutualistic networks, the centrality of a node should benefit its fitness. We test this idea studying eight individual-based networks originated from the interaction between Erysimum mediohispanicum and its flower visitors. In these networks, each plant was considered a node and was connected to conspecifics sharing flower visitors. Centrality indicates how well connected is a given E. mediohispanicum individual with the rest of the co-occurring conspecifics because of sharing flower visitors. The centrality was estimated by three network metrics: betweenness, closeness and degree. The complex relationship between centrality, phenotype and fitness was explored by structural equation modelling. We found that the centrality of a plant was related to its fitness, with plants occupying central positions having higher fitness than those occupying peripheral positions. The structural equation models (SEMs) indicated that the centrality effect on fitness was not merely an effect of the abundance of visits and the species richness of visitors. Centrality has an effect even when simultaneously accounting for these predictors. The SEMs also indicated that the centrality effect on fitness was because of the specific phenotype of each plant, with attractive plants occupying central positions in networks, in relation to the distribution of conspecific phenotypes. This finding suggests that centrality, owing to its dependence on social interactions, may be an appropriate surrogate for the interacting phenotype of individuals.     

Evolutionary rescue under demographic and environmental stochasticity

Populations suffer two types of stochasticity: demographic stochasticity, from sampling error in offspring number, and environmental stochasticity, from temporal variation in the growth rate. By modelling evolution through phenotypic selection following an abrupt environmental change, we investigate how genetic and demographic dynamics, as well as effects on population survival of the genetic variance and of the strength of stabilizing selection, differ under the two types of stochasticity. We show that population survival probability declines sharply with stronger stabilizing selection under demographic stochasticity, but declines more continuously when environmental stochasticity is strengthened. However, the genetic variance that confers the highest population survival probability differs little under demographic and environmental stochasticity. Since the influence of demographic stochasticity is stronger when population size is smaller, a slow initial decline of genetic variance, which allows quicker evolution, is important for population persistence. In contrast, the influence of environmental stochasticity is population-size-independent, so higher initial fitness becomes important for survival under strong environmental stochasticity. The two types of stochasticity interact in a more than multiplicative way in reducing the population survival probability. Our work suggests the importance of explicitly distinguishing and measuring the forms of stochasticity during evolutionary rescue.     

Spatially heterogeneous stochasticity and the adaptive diversification of dormancy

Diversified bet‐hedging, a strategy that leads several individuals with the same genotype to express distinct phenotypes in a given generation, is now well established as a common evolutionary response to environmental stochasticity. Life‐history traits defined as diversified bet‐hedging (e.g. germination or diapause strategies) display marked differences between populations in spatial proximity. In order to find out whether such differences can be explained by local adaptations to spatially heterogeneous environmental stochasticity, we explored the evolution of bet‐hedging dormancy strategies in a metapopulation using a two‐patch model with patch differences in stochastic juvenile survival. We found that spatial differences in the level of environmental stochasticity, restricted dispersal, increased fragmentation and intermediate survival during dormancy all favour the adaptive diversification of bet‐hedging dormancy strategies. Density dependency also plays a major role in the diversification of dormancy strategies because: (i) it may interact locally with environmental stochasticity and amplify its effects; however, (ii) it can also generate chaotic population dynamics that may impede diversification. Our work proposes new hypotheses to explain the spatial patterns of bet‐hedging strategies that we hope will encourage new empirical studies of this topic.     

Evolution of alternative insect life histories in stochastic seasonal environments

Deterministic seasonality can explain the evolution of alternative life history phenotypes (i.e., life history polyphenism) expressed in different generations emerging within the same year. However, the influence of stochastic variation on the expression of such life history polyphenisms in seasonal environments is insufficiently understood. Here, we use insects as a model and explore (1) the effects of stochastic variation in seasonality and (2) the life cycle on the degree of life history differentiation among the alternative developmental pathways of direct development and diapause (overwintering), and (3) the evolution of phenology. With numerical simulation, we determine the values of development (growth) time, growth rate, body size, reproductive effort, adult life span, and fecundity in both the overwintering and directly developing generations that maximize geometric mean fitness. The results suggest that natural selection favors the expression of alternative life histories in the alternative developmental pathways even when there is stochastic variation in seasonality, but that trait differentiation is affected by the developmental stage that overwinters. Increasing environmental unpredictability induced a switch to a bet‐hedging type of life history strategy, which is consistent with general life history theory. Bet‐hedging appeared in our study system as reduced expression of the direct development phenotype, with associated changes in life history phenotypes, because the fitness value of direct development is highly variable in uncertain environments. Our main result is that seasonality itself is a key factor promoting the evolution of seasonally polyphenic life histories but that environmental stochasticity may modulate the expression of life history phenotypes.     

Indirect effects on fitness between individuals that have never met via an extended phenotype

Interactions between organisms are ubiquitous and have important consequences for phenotypes and fitness. Individuals can even influence those they never meet, if they have extended phenotypes that alter the environments others experience. North American red squirrels (Tamiasciurus hudsonicus) guard food hoards, an extended phenotype that typically outlives the individual and is usually subsequently acquired by non‐relatives. Hoarding by previous owners can, therefore, influence subsequent owners. We found that red squirrels breed earlier and had higher lifetime fitness if the previous hoard owner was a male. This was driven by hoarding behaviour, as males and mid‐aged squirrels had the largest hoards, and these effects persisted across owners, such that if the previous owner was male or died in mid‐age, subsequent occupants had larger hoards. Individuals can, therefore, influence each other's resource‐dependent traits and fitness without ever meeting, such that the past can influence contemporary population dynamics through extended phenotypes.     

Among‐individual heterogeneity in maternal behaviour and physiology affects reproductive allocation and offspring life‐history traits in the garter snake Thamnophis elegans

Accumulating evidence suggests that within‐individual plasticity of behavioural and physiological traits is limited, resulting in stable among‐individual differences in these aspects of the phenotype. Furthermore, these traits often covary within individuals, resulting in a continuum of correlated phenotypic variation among individuals within populations and species. This heterogeneity, in turn, affects individual fitness and can have cross‐generational effects. Patterns of trait covariation, among‐individual differences, and subsequent fitness consequences have long been recognized in reptiles. Here, we provide a test of patterns of among‐individual heterogeneity in behaviour and physiology and subsequent effects on reproduction and offspring fitness in the garter snake Thamnophis elegans. We find that measures of activity levels vary among individuals and are consistent within individuals in reproductive female snakes, indicating stable behavioural phenotypes. Blood hormone and glucose concentrations are not as stable within individuals, indicating that these traits do not describe consistent physiological phenotypes. Nonetheless, the major axes of variation in maternal traits describe behavioural and physiological phenotypes that interact to predict offspring body condition and mass at birth. This differential allocation of energy to offspring, in turn, strongly influences subsequent offspring growth and survival. This pattern suggests the potential for strong selection on phenotypes defined by behaviour–physiology interactions.     

Evolutionarily stable sex ratios and sex allocations

The paternal fitness of a sexual individual is equated with the fitness of those eggs of its potential mates which it is able to fertilize. This property enables the total sexual fitness of individuals to be expressed in terms of female gamete contributions in separate equations for a cosex (an individual in a population composed of a single sexual class which combines male and female functions) and for parents in a dioecious population. The general equations are used in phenotypic models of selection which examine conditions maximizing the fitness advantage of one phenotype over another with a different sex ratio or allocation. As an example, it is shown that finite population size confers full stability on the sexual allocations in a cosexual population and on the sex ratio in a dioecious population.The use of fitness advantages provides the outcome of selection for all frequencies of contrasted phenotypes. It is therefore possible to redefine an ESS to allow for persistent variability in a population. A phenotype is an ESS in a population if, from any initial frequency, it is protected from loss by its fitness advantage. The conditions for a rare mutant to spread invariably coincide with those for its fixation only if an individual of any phenotype affects the fitness of other individuals of all phenotypes in identical ways.     

Phenotypic differentiation is associated with gender plasticity and its responsive delay to environmental changes in Alternanthera philoxeroides--phenotypic differentiation in alligator weed

Phenotypic plasticity is common in many taxa, and it may increase an organism's fitness in heterogeneous environments. However, in some cases, the frequency of environmental changes can be faster than the ability of the individual to produce new adaptive phenotypes. The importance of such a time delay in terms of individual fitness and species adaptability has not been well studied. Here, we studied gender plasticity of Alternanthera philoxeroides to address this issue through a reciprocal transplant experiment. We observed that the genders of A. philoxeroides were plastic and reversible between monoclinous and pistillody depending on habitats, the offspring maintained the maternal genders in the first year but changed from year 2 to 5, and there was a cubic relationship between the rate of population gender changes and environmental variations. This relationship indicates that the species must overcome a threshold of environmental variations to switch its developmental path ways between the two genders. This threshold and the maternal gender stability cause a significant delay of gender changes in new environments. At the same time, they result in and maintain the two distinct habitat dependent gender phenotypes. We also observed that there was a significant and adaptive life-history differentiation between monoclinous and pistillody individuals and the gender phenotypes were developmentally linked with the life-history traits. Therefore, the gender phenotypes are adaptive. Low seed production, seed germination failure and matching phenotypes to habitats by gender plasticity indicate that the adaptive phenotypic diversity in A. philoxeroides may not be the result of ecological selection, but of gender plasticity. The delay of the adaptive gender phenotype realization in changing environments can maintain the differentiation between gender systems and their associated life-history traits, which may be an important component in evolution of novel traits and taxonomic diversity.