When three traits make a line: evolution of phenotypic plasticity and genetic assimilation through linear reaction norms in stochastic environments

Genetic assimilation emerges from selection on phenotypic plasticity. Yet, commonly used quantitative genetics models of linear reaction norms considering intercept and slope as traits do not mimic the full process of genetic assimilation. We argue that intercept–slope reaction norm models are insufficient representations of genetic effects on linear reaction norms and that considering reaction norm intercept as a trait is unfortunate because the definition of this trait relates to a specific environmental value (zero) and confounds genetic effects on reaction norm elevation with genetic effects on environmental perception. Instead, we suggest a model with three traits representing genetic effects that, respectively, (i) are independent of the environment, (ii) alter the sensitivity of the phenotype to the environment and (iii) determine how the organism perceives the environment. The model predicts that, given sufficient additive genetic variation in environmental perception, the environmental value at which reaction norms tend to cross will respond rapidly to selection after an abrupt environmental change, and eventually becomes equal to the new mean environment. This readjustment of the zone of canalization becomes completed without changes in genetic correlations, genetic drift or imposing any fitness costs of maintaining plasticity. The asymptotic evolutionary outcome of this three‐trait linear reaction norm generally entails a lower degree of phenotypic plasticity than the two‐trait model, and maximum expected fitness does not occur at the mean trait values in the population.     

Selection on skewed characters and the paradox of stasis

Observed phenotypic responses to selection in the wild often differ from predictions based on measurements of selection and genetic variance. An overlooked hypothesis to explain this paradox of stasis is that a skewed phenotypic distribution affects natural selection and evolution. We show through mathematical modeling that, when a trait selected for an optimum phenotype has a skewed distribution, directional selection is detected even at evolutionary equilibrium, where it causes no change in the mean phenotype. When environmental effects are skewed, Lande and Arnold's (1983) directional gradient is in the direction opposite to the skew. In contrast, skewed breeding values can displace the mean phenotype from the optimum, causing directional selection in the direction of the skew. These effects can be partitioned out using alternative selection estimates based on average derivatives of individual relative fitness, or additive genetic covariances between relative fitness and trait (Robertson–Price identity). We assess the validity of these predictions using simulations of selection estimation under moderate sample sizes. Ecologically relevant traits may commonly have skewed distributions, as we here exemplify with avian laying date — repeatedly described as more evolutionarily stable than expected — so this skewness should be accounted for when investigating evolutionary dynamics in the wild.     

Evolutionary stasis of a heritable morphological trait in a wild fish population despite apparent directional selection

Comparing observed versus theoretically expected evolutionary responses is important for our understanding of the evolutionary process, and for assessing how species may cope with anthropogenic change. Here, we document directional selection for larger female size in Atlantic salmon, using pedigree‐derived estimates of lifetime reproductive success as a fitness measure. We show the trait is heritable and, thus, capable of responding to selection. The Breeder's Equation, which predicts microevolution as the product of phenotypic selection and heritability, predicted evolution of larger size. This was at odds, however, with the observed lack of either phenotypic or genetic temporal trends in body size, a so‐called “paradox of stasis.” To investigate this paradox, we estimated the additive genetic covariance between trait and fitness, which provides a prediction of evolutionary change according to Robertson's secondary theorem of selection (STS) that is unbiased by missing variables. The STS prediction was consistent with the observed stasis. Decomposition of phenotypic selection gradients into genetic and environmental components revealed a potential upward bias, implying unmeasured factors that covary with trait and fitness. These results showcase the power of pedigreed, wild population studies—which have largely been limited to birds and mammals—to study evolutionary processes on contemporary timescales.     

IS INBREEDING DEPRESSION LOWER IN MALADAPTED POPULATIONS? A QUANTITATIVE GENETICS MODEL

Despite abundant empirical evidence that inbreeding depression varies with both the environment and the genotypic context, theoretical predictions about such effects are still rare. Using a quantitative genetics model, we predict amounts of inbreeding depression for fitness emerging from Gaussian stabilizing selection on some phenotypic trait, on which, for simplicity, genetic effects are strictly additive. Given the strength of stabilizing selection, inbreeding depression then varies simply with the genetic variance for the trait under selection and the distance between the mean breeding value and the optimal phenotype. This allows us to relate the expected inbreeding depression to the degree of maladaptation of the population to its environment. We confront analytical predictions with simulations, in well-adapted populations at equilibrium, as well as in maladapted populations undergoing either a transient environmental shift, or gene swamping in heterogeneous habitats. We predict minimal inbreeding depression in situations of extreme maladaptation. Our model provides a new basis for interpreting experiments that measure inbreeding depression for the same set of genotypes in different environments, by demonstrating that the history of adaptation, in addition to environmental harshness per se, may account for differences in inbreeding depression.     

Fitness consequences of maternal and grandmaternal effects

Transgenerational effects are broader than only parental relationships. Despite mounting evidence that multigenerational effects alter phenotypic and life‐history traits, our understanding of how they combine to determine fitness is not well developed because of the added complexity necessary to study them. Here, we derive a quantitative genetic model of adaptation to an extraordinary new environment by an additive genetic component, phenotypic plasticity, maternal and grandmaternal effects. We show how, at equilibrium, negative maternal and negative grandmaternal effects maximize expected population mean fitness. We define negative transgenerational effects as those that have a negative effect on trait expression in the subsequent generation, that is, they slow, or potentially reverse, the expected evolutionary dynamic. When maternal effects are positive, negative grandmaternal effects are preferred. As expected under Mendelian inheritance, the grandmaternal effects have a lower impact on fitness than the maternal effects, but this dual inheritance model predicts a more complex relationship between maternal and grandmaternal effects to constrain phenotypic variance and so maximize expected population mean fitness in the offspring.     

The shape of selection: using alternative fitness functions to test predictions for selection on flowering time

Selection gradient analysis examines the strength and direction of phenotypic selection as well as the curvature of fitness functions, allowing predictions on and insights into the process of evolution in natural populations. However, traditional linear and quadratic selection analyses are not capable of detecting other features of fitness functions, such as asymmetry or thresholds, which may be relevant for understanding key aspects of selection on many traits. In these cases, additional analyses are needed to test specific hypotheses about fitness functions. In this study we used several approaches to analyze selection on a major life-history trait—flowering time—in the annual plant Brassica rapa subjected to experimentally abbreviated and lengthened growing seasons. We used a model that incorporated a tradeoff between the time allocated to growth versus the time allocated to reproduction in order to predict fitness function shape. The model predicted that optimal flowering time shifts to earlier and later dates as the growing season contracts and expands. It also showed the flowering time fitness function to be asymmetrical: reproductive output increases modestly between the earliest and the optimal flowering date, but then falls sharply with later dates, truncating in a ‘tail of zeros’. Our experimental results strongly supported selection for early flowering in short season and selection for late flowering in long season conditions. We also found support for the predicted asymmetry of the flowering time fitness function, including a ‘tail of zeros’ at later flowering dates. The form of the fitness function revealed here has implications for interpreting estimates of selection on flowering time in natural populations and for refining predictions on evolutionary response to climate change. More generally, this study illustrates the value of diverse statistical approaches to understanding mechanisms of natural selection.     

Sequential search and the influence of male quality on female mating decisions

 The patterns of phenotypic association between mated males and females depend on the decision rules that individuals employ during search for a mate. We generalize the sequential search rule and examine how the shape of the function that relates a male character to the benefit of a mating decision influences the threshold value of the male trait that induces females to terminate search. If the fitness function is linear the optimal threshold value of a male character increases with the slope of the function. The phenotypic threshold criterion declines, all else being equal, if the fitness function is made more concave (or less convex) by an increase of the risk of the function. The expression of the trait in females has no effect on the optimal threshold value of a male character if the fitness function is linear and phenotypic values combine additively to influence the benefit of a mating decision; the phenotypic threshold criterion is ubiquitous among females. A convex fitness function induces females with high trait values to adopt a relatively high phenotypic threshold criterion, whereas a concave fitness function induces such females to adopt a low threshold value for the male trait. Thus, linear, convex and concave fitness functions effect random, assortative and disassortative combinations of phenotypes among mated individuals, respectively. Changes of female search behavior induced by changes of the distribution of a male character similarly depend on the shape of the fitness function. A variance-preserving increase of male trait values produces a relatively small increase of the threshold criterion for the male character if the fitness function is concave, relative to conditions in which the fitness function is either linear or convex. Our results suggest that a sequential search rule can in principle induce the kinds of mating patterns observed in nature and that the phenotypic association between mated individuals is likely to depend on how a male character translates into fitness, the distribution of the trait among males and attributes of searching females. Received: 20 September 1997 / Revised version: 13 August 1998     

A rare model limits the distribution of its more common mimic: a twist on frequency-dependent Batesian mimicry

Batesian mimics are predicted to lose their fitness advantage not only in the absence of an unpalatable model, but also when the mimic becomes relatively abundant. The phenotypic hybrid zone between mimetic and nonmimetic admiral butterflies, comprising the polytypic Limenitis arthemis species complex, offers an ideal opportunity to test these predictions because the position of the hybrid zone is hypothesized to be controlled by the geographic range of Battus philenor , the chemically defended model. We used 29 years of observational field data from a continental-scale butterfly monitoring program, the 4th of July Butterfly Counts, to show that (1) the advantage of mimicry does not extend beyond the range of the model, (2) in contrast to expectations, the mimicry complex is maintained even where the model is rare and (3) the sharp phenotypic transition between mimetic and nonmimetic admiral populations occurs over a very narrow spatial scale corresponding to the limit of the model's range. These results suggest that, even at very low densities, there is selection for Batesian mimicry and it maintains the geographic position of this hybrid zone. Our findings highlight the value of large-scale, long-term citizen science monitoring programs for answering basic ecological and evolutionary questions.     

Evolution of temperature optimum in <Emphasis Type="Italic">Thermotogaceae</Emphasis> and the prediction of trait values of uncultured organisms

Quantitative characterization of the mode and rate of phenotypic evolution is rarely applied to prokaryotes. Here, we present an analysis of temperature optimum (T _opt) evolution in the thermophilic family Thermotogaceae, which has a large number of cultured representatives. We use log-rate-interval analysis to show that T _opt evolution in Thermotogaceae is consistent with a Brownian motion (BM) evolutionary model. The properties of the BM model are used to a establish confidence intervals on the unknown phenotypic trait value of an uncultured organism, given its distance to a close relative with known trait value. Cross-validation by bootstrapping indicates that the predictions are robust.     

Flowering time plasticity in Arabidopsis thaliana: a reanalysis of Westerman & Lawrence (1970)

Environmental variation in temperature can have dramatic effects on plant morphology, phenology, and fitness, and for this reason it is important to understand the evolutionary dynamics of phenotypic plasticity in response to temperature. We investigated constraints on the evolution of phenotypic plasticity in response to a temperature gradient in the model plant Arabidopsis thaliana by applying modern analytical tools to the classic data of Westerman & Lawrence (1970). We found significant evidence for two types of constraints. First, we detected numerous significant genetic correlations between plastic responses to temperature and the mean value of a trait across all environments, which differed qualitatively in pattern between the set of ecotypes and the set of mutant lines in the original sample. Secondly, we detected significant costs of flowering time plasticity in two of the three experimental environments, and a net pattern of selection against flowering time plasticity in the experiment overall. Thus, when explored with contemporary methods, the prescient work of Westerman & Lawrence (1970) provides new insights about evolutionary constraints on the evolution of plasticity.     

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 adaptive dynamics of niche constructing traits in spatially subdivided populations: evolving posthumous extended phenotypes

Niche construction, by which organisms modify the environment in which they live, has been proposed to affect the evolution of many phenotypic traits. But what about the evolution of a niche constructing trait itself, whose expression changes the pattern of natural selection to which the trait is exposed in subsequent generations? This article provides an inclusive fitness analysis of selection on niche constructing phenotypes, which can affect their environment from local to global scales in arbitrarily spatially subdivided populations. The model shows that phenotypic effects of genes extending far beyond the life span of the actor can be affected by natural selection, provided they modify the fitness of those individuals living in the future that are likely to have inherited the niche construction lineage of the actor. Present benefits of behaviors are thus traded off against future indirect costs. The future costs will generally result from a complicated interplay of phenotypic effects, population demography and environmental dynamics. To illustrate these points, I derive the adaptive dynamics of a trait involved in the consumption of an abiotic resource, where resource abundance in future generations feeds back to the evolutionary dynamics of the trait.     

Measuring the contribution of evolution to community trait structure in freshwater zooplankton

There are currently few predictions about when evolutionary processes are likely to play an important role in structuring community features. Determining predictors that indicate when evolution is expected to impact ecological processes in natural landscapes can help researchers identify eco-evolutionary ‘hotspots', where eco-evolutionary interactions are more likely to occur. Using data collected from a survey in freshwater cladoceran communities, landscape population genetic data and phenotypic trait data measured in a common garden, we applied a Bayesian linear model to assess whether the impact of local trait evolution in the keystone species Daphnia magna on cladoceran community trait values could be predicted by population genetic properties (within-population genetic diversity, genetic distance among populations), ecological properties (Simpson's diversity, phenotypic divergence) or environmental divergence. We found that the impact of local trait evolution varied among communities. Moreover, community diversity and phenotypic divergence were found to be better predictors of the contribution of evolution to community trait values than environmental features or genetic properties of the evolving species. Our results thus indicate the importance of ecological context for the impact of evolution on community features. Our study also demonstrates one way to detect signatures of eco-evolutionary interactions in communities inhabiting heterogeneous landscapes using survey data of contemporary ecological and evolutionary structure.     

Evolutionarily unstable fitness maxima and stable fitness minima of continuous traits

Summary We present models of adaptive change in continuous traits for the following situations: (1) adaptation of a single trait within a single population in which the fitness of a given individual depends on the population's mean trait value as well as its own trait value; (2) adaptation of two (or more) traits within a single population; (3) adaptation in two or more interacting species. We analyse a dynamic model of these adaptive scenarios in which the rate of change of the mean trait value is an increasing function of the fitness gradient (i.e. the rate of increase of individual fitness with the individual's trait value). Such models have been employed in evolutionary game theory and are often appropriate both for the evolution of quantitative genetic traits and for the behavioural adjustment of phenotypically plastic traits. The dynamics of the adaptation of several different ecologically important traits can result in characters that minimize individual fitness and can preclude evolution towards characters that maximize individual fitness. We discuss biological circumstances that are likely to produce such adaptive failures for situations involving foraging, predator avoidance, competition and coevolution. The results argue for greater attention to dynamical stability in models of the evolution of continuous traits.     

Evolutionary potential of morphological traits across different life‐history stages

Despite accumulating examples of selection acting on heritable traits in the wild, predicted evolutionary responses are often different from observed phenotypic trends. Various explanations have been suggested for these mismatches. These include within‐individual changes across lifespan that can create important variation in genetic architecture of traits and selection acting on them, but also potential problems with the methodological approach used to predict evolutionary responses of traits. Here, we used an 8‐year data set on tree swallow (Tachycineta bicolor) to first assess the effects of differences among three nestling life‐history stages on the genetic (co)variances of two morphological traits (body mass and primary feather length) and the selection acting on them over three generations. We then estimated the evolutionary potential of these traits by predicting their evolutionary responses using the breeder's equation and the secondary theorem of selection approaches. Our results showed variation in strength and direction of selection and slight changes in trait variance across ages. Predicted evolutionary responses differed importantly between both approaches for half of the trait–age combinations we studied, suggesting the presence of environmentally induced correlations between focal traits and fitness possibly biasing breeder's equation predictions. Our results emphasize that predictions of evolutionary potential for morphological traits are likely to be highly variable, both in strength and direction, depending on the life stage and method used, thus mitigating our capacity to predict adaptation and persistence of wild populations.     

The phenotypic gambit: selective pressures and ESS methodology in evolutionary game theory

The ‘phenotypic gambit,’ the assumption that we can ignore genetics and look at the fitness of phenotypes to determine the expected evolutionary dynamics of a population, is often used in evolutionary game theory. However, as this paper will show, an overlooked genotype to phenotype map can qualitatively affect evolution in ways the phenotypic approach cannot predict or explain. This gives us reason to believe that, even in the long-term, correspondences between phenotypic predictions and dynamical outcomes are not robust for all plausible assumptions regarding the underlying genetics of traits. This paper shows important ways in which the phenotypic gambit can fail and how to proceed with evolutionary game theoretic modeling when it does.     

The danger of applying the breeder's equation in observational studies of natural populations

The breeder's equation, which predicts evolutionary change when a phenotypic covariance exists between a heritable trait and fitness, has provided a key conceptual framework for studies of adaptive microevolution in nature. However, its application requires strong assumptions to be made about the causation of fitness variation. In its univariate form, the breeder's equation assumes that the trait of interest is not correlated with other traits having causal effects on fitness. In its multivariate form, the validity of predicted change rests on the assumption that all such correlated traits have been measured and incorporated into the analysis. Here, we (i) highlight why these assumptions are likely to be seriously violated in studies of natural, rather than artificial, selection and (ii) advocate wider use of the Robertson–Price identity as a more robust, and less assumption‐laden, alternative to the breeder's equation for applications in evolutionary ecology.     

Evolution in a changing environment: a case study with great tit fledging mass

Heritable phenotypic traits under significant and consistent directional selection often fail to show the expected evolutionary response. A potential explanation for this contradiction is that because environmental conditions change constantly, environmental change can mask an evolutionary response to selection. We combined an "animal model" analysis with 36 years of data from a long-term study of great tits (Parus major) to explore selection on and evolution of a morphological trait: body mass at fledging. We found significant heritability of this trait, but despite consistent positive directional selection on both the phenotypic and the additive genetic component of body mass, the population mean phenotypic value declined rather than increased over time. However, the mean breeding value for body mass at fledging increased over time, presumably in response to selection. We show that the divergence between the response to selection observed at the levels of genotype and phenotype can be explained by a change in environmental conditions over time, that is, related both to increased spring temperature before breeding and elevated population density. Our results support the suggestion that measuring phenotypes may not always give a reliable impression of evolutionary trajectories and that understanding patterns of phenotypic evolution in nature requires an understanding of how the environment has itself changed.     

Evolution and maintenance of the environmental component of the phenotypic variance: benefit of plastic traits under changing environments

How environmental variances in quantitative traits are influenced by variable environments is an important problem in evolutionary biology. In this study, the evolution and maintenance of phenotypic variance in a plastic trait under stabilizing selection are investigated. The mapping from genotypic value to phenotypic value of the quantitative trait is approximated by a linear reaction norm, with genotypic effects on its phenotypic mean and sensitivity to environment. The environmental deviation is assumed to be decomposed into environmental quality, which interacts with genotypic value, and residual developmental noise, which is independent of genotype. Environmental quality and the optimal phenotype of stabilizing selection are allowed to randomly fluctuate in both space and time, and individuals migrate equally before development and reproduction among different niches. Analyses show that phenotypic plasticity is adaptive within variable environments if correlations have become established between the optimal phenotype and environmental quality in space and/or time. The evolved plasticity increases with variances in optimal phenotypes and correlations between optimal phenotype and environmental quality; this further induces increases in mean fitness and the environmental variance in the trait. Under certain circumstances, however, the environmental variance may decrease with increase in variation in environmental quality.     

Natural genetic variation in Arabidopsis: tools, traits and prospects for evolutionary ecology

BACKGROUND: The model plant Arabidopsis thaliana (Arabidopsis) shows a wide range of genetic and trait variation among wild accessions. Because of its unparalleled biological and genomic resources, the potential of Arabidopsis for molecular genetic analysis of this natural variation has increased dramatically in recent years. SCOPE: Advanced genomics has accelerated molecular phylogenetic analysis and gene identification by quantitative trait loci (QTL) mapping and/or association mapping in Arabidopsis. In particular, QTL mapping utilizing natural accessions is now becoming a major strategy of gene isolation, offering an alternative to artificial mutant lines. Furthermore, the genomic information is used by researchers to uncover the signature of natural selection acting on the genes that contribute to phenotypic variation. The evolutionary significance of such genes has been evaluated in traits such as disease resistance and flowering time. However, although molecular hallmarks of selection have been found for the genes in question, a corresponding ecological scenario of adaptive evolution has been difficult to prove. Ecological strategies, including reciprocal transplant experiments and competition experiments, and utilizing near-isogenic lines of alleles of interest will be a powerful tool to measure the relative fitness of phenotypic and/or allelic variants. CONCLUSIONS: As the plant model organism, Arabidopsis provides a wealth of molecular background information for evolutionary genetics. Because genetic diversity between and within Arabidopsis populations is much higher than anticipated, combining this background information with ecological approaches might well establish Arabidopsis as a model organism for plant evolutionary ecology.