The temporal distribution of directional gradients under selection for an optimum

Analytical results for directional and quadratic selection gradients for log-linear models of fitness functions

Log-linear models are widely used for assessing determinants of fitness in empirical studies, for example, in determining how reproductive output depends on trait values or environmental conditions. Similarly, theoretical works of fitness and natural selection employ log-linear models, often with a negative quadratic term, generating Gaussian fitness functions. However, in the specific application of regression-based analysis of natural selection, such models are rarely employed. Rather, OLS regression is the predominant means of assessing the form of natural selection. OLS regressions allow specific evolutionary quantitative parameters, selection gradients, to be estimated, and benefit from the fact that the associated statistical models are easily applied. We examine whether selection gradients can be directly expressed in terms of the coefficients of models using exponential fitness functions with linear or quadratic arguments. Such models can be easily fitted with generalized linear models (GLMs). The expressions we obtain coincide with those for Gaussian functions, but relax the major constraint that the (log) fitness function is concave (downwardly curved). Additionally these results lead to univariate and multivariate analyses of both linear and quadratic selection that potentially incorporate pragmatic and interpretable models of fitness functions, where the parameters can be related analytically to selection gradients, and that can be operationalized using widely available statistical tools.

Natural selection fluctuates at an extremely fine spatial scale inside a wild population of snapdragon plants

Spatial variation in natural selection is expected to shape phenotypic variation of wild populations and drive their evolution. Although evidence of phenotypic divergence across populations experiencing different selection regimes is abundant, investigations of intrapopulation variation in selection pressures remain rare. Fine-grained spatial environmental heterogeneity can be expected to influence selective forces within a wild population and thereby alter its fitness function by producing multiple fitness optima at a fine spatial scale. Here, we tested this hypothesis in a wild population of snapdragon plants living on an extremely small island in southern France (about 7500 m² ). We estimated the spline-based fitness function linking individuals' fitness and five morphological traits in interaction with three spatially variable ecological drivers. We found that selection acting on several traits varied both in magnitude and direction in response to environmental variables at the scale of a meter. Our findings illustrate how different phenotypes can be selected at different locations within a population in response to environmental variation. Investigating spatial variation in selection within a population, in association with ecological conditions, represents an opportunity to identify putative ecological drivers of selection in the wild.

Indirect Genetic Effects: A Cross-disciplinary Perspective on Empirical Studies

Indirect genetic effects (IGE) occur when an individual's phenotype is influenced by genetic variation in conspecifics. Opportunities for IGE are ubiquitous, and, when present, IGE have profound implications for behavioral, evolutionary, agricultural, and biomedical genetics. Despite their importance, the empirical study of IGE lags behind the development of theory. In large part, this lag can be attributed to the fact that measuring IGE, and deconvoluting them from the direct genetic effects of an individual's own genotype, is subject to many potential pitfalls. In this Perspective, we describe current challenges that empiricists across all disciplines will encounter in measuring and understanding IGE. Using ideas and examples spanning evolutionary, agricultural, and biomedical genetics, we also describe potential solutions to these challenges, focusing on opportunities provided by recent advances in genomic, monitoring, and phenotyping technologies. We hope that this cross-disciplinary assessment will advance the goal of understanding the pervasive effects of conspecific interactions in biology.

Episodes of opposing survival and reproductive selection cause strong fluctuating selection on seasonal migration versus residence

Quantifying temporal variation in sex-specific selection on key ecologically relevant traits, and quantifying how such variation arises through synergistic or opposing components of survival and reproductive selection, is central to understanding eco-evolutionary dynamics, but rarely achieved. Seasonal migration versus residence is one key trait that directly shapes spatio-seasonal population dynamics in spatially and temporally varying environments, but temporal dynamics of sex-specific selection have not been fully quantified. We fitted multi-event capture-recapture models to year-round ring resightings and breeding success data from partially migratory European shags (Phalacrocorax aristotelis) to quantify temporal variation in annual sex-specific selection on seasonal migration versus residence arising through adult survival, reproduction and the combination of both (i.e. annual fitness). We demonstrate episodes of strong and strongly fluctuating selection through annual fitness that were broadly synchronized across females and males. These overall fluctuations arose because strong reproductive selection against migration in several years contrasted with strong survival selection against residence in years with extreme climatic events. These results indicate how substantial phenotypic and genetic variation in migration versus residence could be maintained, and highlight that biologically important fluctuations in selection may not be detected unless both survival selection and reproductive selection are appropriately quantified and combined.

How does the strength of selection influence genetic correlations?

Genetic correlations between traits can strongly impact evolutionary responses to selection, and may thus impose constraints on adaptation. Theoretical and empirical work has made it clear that without strong linkage and with random mating, genetic correlations at evolutionary equilibrium result from an interplay of correlated pleiotropic effects of mutations, and correlational selection favoring combinations of trait values. However, it is not entirely clear how change in the overall strength of stabilizing selection across traits (breadth of the fitness peak, given its shape) influences this compromise between mutation and selection effects on genetic correlation. Here, we show that the answer to this question crucially depends on the intensity of genetic drift. In large, effectively infinite populations, genetic correlations are unaffected by the strength of selection, regardless of whether the genetic architecture involves common small-effect mutations (Gaussian regime), or rare large-effect mutations (House-of-Cards regime). In contrast in finite populations, the strength of selection does affect genetic correlations, by shifting the balance from drift-dominated to selection-dominated evolutionary dynamics. The transition between these domains depends on mutation parameters to some extent, but with a similar dependence of genetic correlation on the strength of selection. Our results are particularly relevant for understanding how senescence shapes patterns of genetic correlations across ages, and genetic constraints on adaptation during colonization of novel habitats.

Fluctuating optimum and temporally variable selection on breeding date in birds and mammals

Temporal variation in natural selection is predicted to strongly impact the evolution and demography of natural populations, with consequences for the rate of adaptation, evolution of plasticity, and extinction risk. Most of the theory underlying these predictions assumes a moving optimum phenotype, with predictions expressed in terms of the temporal variance and autocorrelation of this optimum. However, empirical studies seldom estimate patterns of fluctuations of an optimum phenotype, precluding further progress in connecting theory with observations. To bridge this gap, we assess the evidence for temporal variation in selection on breeding date by modeling a fitness function with a fluctuating optimum, across 39 populations of 21 wild animals, one of the largest compilations of long-term datasets with individual measurements of trait and fitness components. We find compelling evidence for fluctuations in the fitness function, causing temporal variation in the magnitude, but not the direction of selection. However, fluctuations of the optimum phenotype need not directly translate into variation in selection gradients, because their impact can be buffered by partial tracking of the optimum by the mean phenotype. Analyzing individuals that reproduce in consecutive years, we find that plastic changes track movements of the optimum phenotype across years, especially in bird species, reducing temporal variation in directional selection. This suggests that phenological plasticity has evolved to cope with fluctuations in the optimum, despite their currently modest contribution to variation in selection.

Fluctuations in lifetime selection in an autocorrelated environment

Most natural environments vary stochastically and are temporally autocorrelated. Previous theory investigating the effects of environmental autocorrelation on evolution mostly assumed that total fitness resulted from a single selection episode. Yet organisms are likely to experience selection repeatedly along their life, in response to possibly different environmental states. We model the evolution of a quantitative trait in organisms with non-overlapping generations undergoing several episodes of selection in a randomly fluctuating and autocorrelated environment. We show that the evolutionary dynamics depends not directly on fluctuations of the environment, but instead on those of an effective phenotypic optimum that integrates the effects of all selection episodes within each generation. The variance and autocorrelation of the integrated optimum shape the variance and predictability of selection, with substantial qualitative and quantitative deviations from previous predictions considering a single selection episode per generation. We also investigate the consequence of multiple selection episodes per generation on population load. In particular, we identify a new load resulting from within-generation fluctuating selection, generating the death of individuals without significance for the evolutionary dynamics. Our study emphasizes how taking into account fluctuating selection within lifetime unravels new properties of evolutionary dynamics, with crucial implications notably with respect to responses to global changes.

Where is the optimum? Predicting the variation of selection along climatic gradients and the adaptive value of plasticity. A case study on tree phenology

Many theoretical models predict when genetic evolution and phenotypic plasticity allow adaptation to changing environmental conditions. These models generally assume stabilizing selection around some optimal phenotype. We however often ignore how optimal phenotypes change with the environment, which limit our understanding of the adaptive value of phenotypic plasticity. Here, we propose an approach based on our knowledge of the causal relationships between climate, adaptive traits, and fitness to further these questions. This approach relies on a sensitivity analysis of the process‐based model phenofit, which mathematically formalizes these causal relationships, to predict fitness landscapes and optimal budburst dates along elevation gradients in three major European tree species. Variation in the overall shape of the fitness landscape and resulting directional selection gradients were found to be mainly driven by temperature variation. The optimal budburst date was delayed with elevation, while the range of dates allowing high fitness narrowed and the maximal fitness at the optimum decreased. We also found that the plasticity of the budburst date should allow tracking the spatial variation in the optimal date, but with variable mismatch depending on the species, ranging from negligible mismatch in fir, moderate in beech, to large in oak. Phenotypic plasticity would therefore be more adaptive in fir and beech than in oak. In all species, we predicted stronger directional selection for earlier budburst date at higher elevation. The weak selection on budburst date in fir should result in the evolution of negligible genetic divergence, while beech and oak would evolve counter‐gradient variation, where genetic and environmental effects are in opposite directions. Our study suggests that theoretical models should consider how whole fitness landscapes change with the environment. The approach introduced here has the potential to be developed for other traits and species to explore how populations will adapt to climate change.

Selective Sweep at a QTL in a Randomly Fluctuating Environment

Adaptation is mediated by phenotypic traits that are often near continuous, and undergo selective pressures that may change with the environment. The dynamics of allelic frequencies at underlying quantitative trait loci (QTL) depend on their own phenotypic effects, but also possibly on other polymorphic loci affecting the same trait, and on environmental change driving phenotypic selection. Most environments include a substantial component of random noise, characterized both by its magnitude and its temporal autocorrelation, which sets the timescale of environmental predictability. I investigate the dynamics of a mutation affecting a quantitative trait in an autocorrelated stochastic environment that causes random fluctuations of an optimum phenotype. The trait under selection may also exhibit background polygenic variance caused by many polymorphic loci of small effects elsewhere in the genome. In addition, the mutation at the QTL may affect phenotypic plasticity, the phenotypic response of given genotype to its environment of development or expression. Stochastic environmental fluctuations increase the variance of the evolutionary process, with consequences for the probability of a complete sweep at the QTL. Background polygenic variation critically alters this process, by setting an upper limit to stochastic variance of population genetics at the QTL. For a plasticity QTL, stochastic fluctuations also influences the expected selection coefficient, and alleles with the same expected trajectory can have very different stochastic variances. Finally, a mutation may be favored through its effect on plasticity despite causing a systematic mismatch with optimum, which is compensated by evolution of the mean background phenotype.

Quantification and decomposition of environment-selection relationships

In nature, selection varies across time in most environments, but we lack an understanding of how specific ecological changes drive this variation. Ecological factors can alter phenotypic selection coefficients through changes in trait distributions or individual mean fitness, even when the trait-absolute fitness relationship remains constant. We apply and extend a regression-based approach in a population of Soay sheep (Ovis aries) and suggest metrics of environment-selection relationships that can be compared across studies. We then introduce a novel method that constructs an environmentally structured fitness function. This allows calculation of full (as in existing approaches) and partial (acting separately through the absolute fitness function slope, mean fitness, and phenotype distribution) sensitivities of selection to an ecological variable. Both approaches show positive overall effects of density on viability selection of lamb mass. However, the second approach demonstrates that this relationship is largely driven by effects of density on mean fitness, rather than on the trait-fitness relationship slope. If such mechanisms of environmental dependence of selection are common, this could have important implications regarding the frequency of fluctuating selection, and how previous selection inferences relate to longer term evolutionary dynamics.

Fluctuating selection and its (elusive) evolutionary consequences in a wild rodent population

Temporal fluctuations in the strength and direction of selection are often proposed as a mechanism that slows down evolution, both over geological and contemporary timescales. Both the prevalence of fluctuating selection and its relevance for evolutionary dynamics remain poorly understood however, especially on contemporary timescales: unbiased empirical estimates of variation in selection are scarce, and the question of how much of the variation in selection translates into variation in genetic change has largely been ignored. Using long-term individual-based data for a wild rodent population, we quantify the magnitude of fluctuating selection on body size. Subsequently, we estimate the evolutionary dynamics of size and test for a link between fluctuating selection and evolution. We show that, over the past 11 years, phenotypic selection on body size has fluctuated significantly. However, the strength and direction of genetic change have remained largely constant over the study period; that is, the rate of genetic change was similar in years where selection favoured heavier vs. lighter individuals. This result suggests that over shorter timescales, fluctuating selection does not necessarily translate into fluctuating evolution. Importantly however, individual-based simulations show that the correlation between fluctuating selection and fluctuating evolution can be obscured by the effect of drift, and that substantially more data are required for a precise and accurate estimate of this correlation. We identify new challenges in measuring the coupling between selection and evolution, and provide methods and guidelines to overcome them.

Stochastic Evolutionary Demography under a Fluctuating Optimum Phenotype

Many natural populations exhibit temporal fluctuations in abundance that are consistent with external forcing by a randomly changing environment. As fitness emerges from an interaction between the phenotype and the environment, such demographic fluctuations probably include a substantial contribution from fluctuating phenotypic selection. We study the stochastic population dynamics of a population exposed to random (plus possibly directional) changes in the optimum phenotype for a quantitative trait that evolves in response to this moving optimum. We derive simple analytical predictions for the distribution of log population size over time both transiently and at stationarity under Gompertz density regulation. These predictions are well matched by population- and individual-based simulations. The log population size is approximately reverse gamma distributed, with a negative skew causing an excess of low relative to high population sizes, thus increasing extinction risk relative to a symmetric (e.g., normal) distribution with the same mean and variance. Our analysis reveals how the mean and variance of log population size change with the variance and autocorrelation of deviations of the evolving mean phenotype from the optimum. We apply our results to the analysis of evolutionary rescue in a stochastic environment and show that random fluctuations in the optimum can substantially increase extinction risk by both reducing the expected growth rate and increasing the variance of population size by several orders of magnitude.

Exploring the impact of multidecadal environmental changes on the population genetic structure of a marine primary producer

Many marine protists form resting stages that can remain viable in coastal sediments for several decades. Their long‐term survival offers the possibility to explore the impact of changes in environmental conditions on population dynamics over multidecadal time scales. Resting stages of the phototrophic dinoflagellate Pentapharsodinium dalei were isolated and germinated from five layers in dated sediment cores from Koljö fjord, Sweden, spanning ca. 1910–2006. This fjord has, during the last century, experienced environmental fluctuations linked to hydrographic variability mainly driven by the North Atlantic Oscillation. Population genetic analyses based on six microsatellite markers revealed high genetic diversity and suggested that samples belonged to two clusters of subpopulations that have persisted for nearly a century. We observed subpopulation shifts coinciding with changes in hydrographic conditions. The large degree of genetic diversity and the potential for both fluctuation and recovery over longer time scales documented here, may help to explain the long‐term success of aquatic protists that form resting stages.

Mediterranean blue tits as a case study of local adaptation

While the study of the origins of biological diversity across species has provided numerous examples of adaptive divergence, the realization that it can occur at microgeographic scales despite gene flow is recent, and scarcely illustrated. We review here evidence suggesting that the striking phenotypic differentiation in ecologically relevant traits exhibited by blue tits Cyanistes caeruleus in their southern range‐edge putatively reflects adaptation to the heterogeneity of the Mediterranean habitats. We first summarize the phenotypic divergence for a series of life history, morphological, behavioural, acoustic and colour ornament traits in blue tit populations of evergreen and deciduous forests. For each divergent trait, we review the evidence obtained from common garden experiments regarding a possible genetic origin of the observed phenotypic differentiation as well as evidence for heterogeneous selection. Second, we argue that most phenotypically differentiated traits display heritable variation, a fundamental requirement for evolution to occur. Third, we discuss nonrandom dispersal, selective barriers and assortative mating as processes that could reinforce local adaptation. Finally, we show how population genomics supports isolation – by – environment across landscapes. Overall, the combination of approaches converges to the conclusion that the strong phenotypic differentiation observed in Mediterranean blue tits is a fascinating case of local adaptation.

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.