How to quantify (the response to) sexual selection on traits

Natural selection operates via fitness components like mating success, fecundity, and longevity, which can be understood as intermediaries in the causal process linking traits to fitness. In particular, sexual selection occurs when traits influence mating or fertilization success, which, in turn, influences fitness. We show how to quantify both these steps in a single path analysis, leading to better estimates of the strength of sexual selection. Our model controls for confounding variables, such as body size or condition, when estimating the relationship between mating and reproductive success. Correspondingly, we define the Bateman gradient and the Jones index using partial rather than simple regressions, which better captures how they are commonly interpreted. The model can be applied both to purely phenotypic data and to quantitative genetic parameters estimated using information on relatedness. The phenotypic approach breaks down selection differentials into a sexually selected and a “remainder” component. The quantitative genetic approach decomposes the estimated evolutionary response to selection analogously. We apply our method to analyze sexual selection in male dusky pipefish, Syngnathus floridae, and in two simulated datasets. We highlight conceptual and statistical limitations of previous path‐based approaches, which can lead to substantial misestimation of sexual selection.     

Using path analysis to measure natural selection

We expand current methods for calculating selection coefficients using path analysis and demonstrate how to analyse nonlinear selection. While this incorporation is a straightforward extension of current procedures, the rules for combining these traits to calculate selection coefficients can be complex. We demonstrate our method with an analysis of selection in an experimental population of Arabidopsis thaliana consisting of 289 individuals. Multiple regression analyses found positive directional selection and positive nonlinear selection only for inflorescence height. In contrast, the path analyses also revealed positive directional selection for number of rosette leaves and positive nonlinear selection for leaf number and time of inflorescence initiation. These changes in conclusions came about because indirect selection was converted into direct selection with the change in causal structure. Path analysis has great promise for improving our understanding of natural selection but must be used with caution since coefficient estimates depend on the assumed causal structure.     

PHASE III OF WRIGHT'S SHIFTING BALANCE PROCESS AND THE VARIANCE AMONG DEMES IN MIGRATION RATE

Interdemic selection by the differential migration of individuals out from demes of high fitness and into demes of low fitness (Phase III) is one of the most controversial aspects of Wright's Shifting Balance Theory. I derive a relationship between Phase III migration and the interdemic selection differential, S, and show its potential effect on F_ST. The relationship reveals a diversifying effect of interdemic selection by Phase III migration on the genetic structure of a metapopulation. Using experimental metapopulations, I explored the effect of Phase III migration on F_ST by comparing the genetic variance among demes for two different patterns of migration: (1) island model migration and (2) Wright's Phase III migration. Although mean migration rates were the same, I found that the variance among demes in migration rate was significantly higher with Phase III than with island model migration. As a result, F_ST for the frequency of a neutral marker locus was higher with Phase III than it was with island model migration. By increasing F_ST, Phase III enhanced the genetic differentiation among demes for traits not subject to interdemic selection. This feature makes Wright's process different from individual selection which, by reducing effective population size, decreases the genetic variance within demes for all other traits. I discussed this finding in relation to the efficacy of Phase III and random migration for effecting peak shifts, and the contribution of genes with indirect effects to among‐deme variation.     

Hamilton's rule,inclusive fitness maximization,and the goal of individual behaviour in symmetric two‐player games

Hamilton's original work on inclusive fitness theory assumed additivity of costs and benefits. Recently, it has been argued that an exact version of Hamilton's rule for the spread of a pro‐social allele (rb > c) holds under nonadditive pay‐offs, so long as the cost and benefit terms are defined as partial regression coefficients rather than pay‐off parameters. This article examines whether one of the key components of Hamilton's original theory can be preserved when the rule is generalized to the nonadditive case in this way, namely that evolved organisms will behave as if trying to maximize their inclusive fitness in social encounters.     

Path analyses of selection

Identifying the targets and causal mechanisms of phenotypic selection in natural populations remains an important challenge for evolutionary biologists. Path analysis is a statistical modeling approach that may aid in meeting this challenge. We describe several types of path model that are relevant to the analysis of selection, and review some recent empirical studies that apply path models to issues in pollination biology, phenotypic integration and selection on morphometric and ontogenetic traits. Path analysis may play two roles in the analysis of selection: first, as an exploratory analysis suggesting possible targets of selection, which are then tested by direct experimentation; and second, as a means of evaluating the relative importance of different causal pathways of selection, once the likely targets of selection have been established.     

EVOLUTIONARY GAMES IN WRIGHT'S ISLAND MODEL: KIN SELECTION MEETS EVOLUTIONARY GAME THEORY

This article studies evolutionary game dynamics in Wright's infinite island model. I study a general n×n matrix game and derive a basic equation that describes the change in frequency of strategies. A close observation of this equation reveals that three distinct effects are at work: direct benefit to a focal individual, kin‐selected indirect benefit to the focal individual via its relatives, and the cost caused by increased kin competition in the focal individual's natal deme. Crucial parameters are the coefficient of relatedness between two individuals and its analogue for three individuals. I provide a number of examples and show when the traditional inclusive fitness measure is recovered and when not. Results demonstrate how evolutionary game theory fits into the framework of kin selection.     

REGRESSION ANALYSIS OF NATURAL SELECTION: STATISTICAL INFERENCE AND BIOLOGICAL INTERPRETATION

Recent theoretical work in quantitative genetics has fueled interest in measuring natural selection in the wild. We discuss statistical and biological issues that may arise in applications of Lande and Arnold's (1983) multiple-regression approach to measuring selection. We review assumptions involved in estimation and hypothesis testing in regression problems, and we note difficulties that frequently arise as a result of violation of these assumptions. In particular, multicollinearity (extreme intercorrelation of characters) and extrinsic, unmeasured factors affecting fitness may seriously complicate inference regarding selection. Further, violation of the assumption that residuals are normally distributed vitiates tests of significance. For this situation, we suggest applications of recently developed jackknife tests of significance. While fitness regression permits direct assessment of selection in a form suitable for predicting selection response, we suggest that the aim of inferring causal relationships about the effects of phenotypic characters on fitness is greatly facilitated by manipulative experiments. Finally, we discuss alternative definitions of stabilizing and disruptive selection.     

Natural selection. VI. Partitioning the information in fitness and characters by path analysis

Three steps aid in the analysis of selection. First, describe phenotypes by their component causes. Components include genes, maternal effects, symbionts and any other predictors of phenotype that are of interest. Second, describe fitness by its component causes, such as an individual's phenotype, its neighbours’ phenotypes, resource availability and so on. Third, put the predictors of phenotype and fitness into an exact equation for evolutionary change, providing a complete expression of selection and other evolutionary processes. The complete expression separates the distinct causal roles of the various hypothesized components of phenotypes and fitness. Traditionally, those components are given by the covariance, variance and regression terms of evolutionary models. I show how to interpret those statistical expressions with respect to information theory. The resulting interpretation allows one to read the fundamental equations of selection and evolution as sentences that express how various causes lead to the accumulation of information by selection and the decay of information by other evolutionary processes. The interpretation in terms of information leads to a deeper understanding of selection and heritability, and a clearer sense of how to formulate causal hypotheses about evolutionary process. Kin selection appears as a particular type of causal analysis that partitions social effects into meaningful components.     

Alternative forms for genomic clines

Understanding factors regulating hybrid fitness and gene exchange is a major research challenge for evolutionary biology. Genomic cline analysis has been used to evaluate alternative patterns of introgression, but only two models have been used widely and the approach has generally lacked a hypothesis testing framework for distinguishing effects of selection and drift. I propose two alternative cline models, implement multivariate outlier detection to identify markers associated with hybrid fitness, and simulate hybrid zone dynamics to evaluate the signatures of different modes of selection. Analysis of simulated data shows that previous approaches are prone to false positives (multinomial regression) or relatively insensitive to outlier loci affected by selection (Barton's concordance). The new, theory‐based logit‐logistic cline model is generally best at detecting loci affecting hybrid fitness. Although some generalizations can be made about different modes of selection, there is no one‐to‐one correspondence between pattern and process. These new methods will enhance our ability to extract important information about the genetics of reproductive isolation and hybrid fitness. However, much remains to be done to relate statistical patterns to particular evolutionary processes. The methods described here are implemented in a freely available package “HIest” for the R statistical software (CRAN; http://cran.r-project.org/ ).     

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.     

PERSPECTIVE: A CRITIQUE OF SEWALL WRIGHT'S SHIFTING BALANCE THEORY OF EVOLUTION

We evaluate Sewall Wright's three-phase “shifting balance” theory of evolution, examining both the theoretical issues and the relevant data from nature and the laboratory. We conclude that while phases I and II of Wright's theory (the movement of populations from one “adaptive peak” to another via drift and selection) can occur under some conditions, genetic drift is often unnecessary for movement between peaks. Phase III of the shifting balance, in which adaptations spread from particular populations to the entire species, faces two major theoretical obstacles: (1) unlike adaptations favored by simple directional selection, adaptations whose fixation requires some genetic drift are often prevented from spreading by barriers to gene flow; and (2) it is difficult to assemble complex adaptations whose constituent parts arise via peak shifts in different demes. Our review of the data from nature shows that although there is some evidence for individual phases of the shifting balance process, there are few empirical observations explained better by Wright's three-phase mechanism than by simple mass selection. Similarly, artificial selection experiments fail to show that selection in subdivided populations produces greater response than does mass selection in large populations. The complexity of the shifting balance process and the difficulty of establishing that adaptive valleys have been crossed by genetic drift make it impossible to test Wright's claim that adaptations commonly originate by this process. In view of these problems, it seems unreasonable to consider the shifting balance process as an important explanation for the evolution of adaptations.     

ESTIMATING AND VISUALIZING FITNESS SURFACES USING MARK–RECAPTURE DATA

Understanding how selection operates on a set of phenotypic traits is central to evolutionary biology. Often, it requires estimating survival (or other fitness‐related life‐history traits) which can be difficult to obtain for natural populations because individuals cannot be exhaustively followed. To cope with this issue of imperfect detection, we advocate the use of mark‐recapture data and we provide a general framework for both the estimation of linear and nonlinear selection gradients and the visualization of fitness surfaces. To quantify the strength of selection, the standard second‐order polynomial regression method is integrated in mark‐recapture models. To visualize the form of selection, we use splines to display selection acting on multivariate phenotypes in the most flexible way. We employ Markov chain Monte Carlo sampling in a Bayesian framework to estimate model parameters, assessing traits relevance and calculating the optimal amount of smoothing. We illustrate our approach using data from a wild population of Common blackbirds (Turdus merula) to investigate survival in relation to morphological traits, and provide evidence for correlational selection using the new methodology. Overall, the framework we propose will help in exploring the full potential of mark‐recapture data to study natural selection.     

Natural selection on body size is mediated by multiple interacting factors: a comparison of beetle populations varying naturally and experimentally in body size

Body size varies considerably among species and among populations within species, exhibiting many repeatable patterns. However, which sources of selection generate geographic patterns, and which components of fitness mediate evolution of body size, are not well understood. For many animals, resource quality and intraspecific competition may mediate selection on body size producing large-scale geographic patterns. In two sequential experiments, we examine how variation in larval competition and resource quality (seed size) affects the fitness consequences of variation in body size in a scramble-competing seed-feeding beetle, Stator limbatus. Specifically, we compared fitness components among three natural populations of S. limbatus that vary in body size, and then among three lineages of beetles derived from a single base population artificially selected to vary in size, all reared on three sizes of seeds at variable larval density. The effects of larval competition and seed size on larval survival and development time were similar for larger versus smaller beetles. However, larger-bodied beetles suffered a greater reduction in adult body mass with decreasing seed size and increasing larval density; the relative advantage of being large decreased with decreasing seed size and increasing larval density. There were highly significant interactions between the effects of seed size and larval density on body size, and a significant three-way interaction (population-by-density-by-seed size), indicating that environmental effects on the fitness consequences of being large are nonadditive. Our study demonstrates how multiple ecological variables (resource availability and resource competition) interact to affect organismal fitness components, and that such interactions can mediate natural selection on body size. Studying individual factors influencing selection on body size may lead to misleading results given the potential for nonlinear interactions among selective agents.     

The MIAmaxent R package: Variable transformation and model selection for species distribution models

The widely used “Maxent” software for modeling species distributions from presence‐only data (Phillips et al., Ecological Modelling, 190, 2006, 231) tends to produce models with high‐predictive performance but low‐ecological interpretability, and implications of Maxent's statistical approach to variable transformation, model fitting, and model selection remain underappreciated. In particular, Maxent's approach to model selection through lasso regularization has been shown to give less parsimonious distribution models—that is, models which are more complex but not necessarily predictively better—than subset selection. In this paper, we introduce the MIAmaxent R package, which provides a statistical approach to modeling species distributions similar to Maxent's, but with subset selection instead of lasso regularization. The simpler models typically produced by subset selection are ecologically more interpretable, and making distribution models more grounded in ecological theory is a fundamental motivation for using MIAmaxent. To that end, the package executes variable transformation based on expected occurrence–environment relationships and contains tools for exploring data and interrogating models in light of knowledge of the modeled system. Additionally, MIAmaxent implements two different kinds of model fitting: maximum entropy fitting for presence‐only data and logistic regression (GLM) for presence–absence data. Unlike Maxent, MIAmaxent decouples variable transformation, model fitting, and model selection, which facilitates methodological comparisons and gives the modeler greater flexibility when choosing a statistical approach to a given distribution modeling problem.     

Darwin's ‘one special difficulty’: celebrating Darwin 200

Darwin identified eusocial evolution, especially of complex insect societies, as a particular challenge to his theory of natural selection. A century later, Hamilton provided a framework for selection on inclusive fitness. Hamilton''s rule is robust and fertile, having generated multiple subdisciplines over the past 45 years. His suggestion that eusociality can be explained via kin selection, however, remains contentious. I review the continuing debate on the role of kin selection in eusocial evolution and suggest some lines of research that should resolve that debate.     

Reducing environmental bias when measuring natural selection

Abstract.— Crucial to understanding the process of natural selection is characterizing phenotypic selection. Measures of phenotypic selection can be biased by environmental variation among individuals that causes a spurious correlation between a trait and fitness. One solution is analyzing genotypic data, rather than phenotypic data. Genotypic data, however, are difficult to gather, can be gathered from few species, and typically have low statistical power. Environmental correlations may act through traits other than through fitness itself. A path analytic framework, which includes measures of such traits, may reduce environmental bias in estimates of selection coefficients. We tested the efficacy of path analysis to reduce bias by re-analyzing three experiments where both phenotypic and genotypic data were available. All three consisted of plant species (Impatiens capensis, Arabidopsis thaliana , and Raphanus sativus) grown in experimental plots or the greenhouse. We found that selection coefficients estimated by path analysis using phenotypic data were highly correlated with those based on genotypic data with little systematic bias in estimating the strength of selection. Although not a panacea, using path analysis can substantially reduce environmental biases in estimates of selection coefficients. Such confidence in phenotypic selection estimates is critical for progress in the study of natural selection.     

THE GENETICS OF CENTRAL AND MARGINAL POPULATIONS OF DROSOPHILA SERRATA. II. HYBRID BREAKDOWN IN FITNESS COMPONENTS AS A CORRELATED RESPONSE TO SELECTION FOR DESICCATION RESISTANCE

Multiple-peak epistasis is one of the four premises that underlie Wright's shifting-balance theory of evolution. A selection experiment was conducted in an attempt to push different geographic populations to different fitness peaks as a correlated response to selection for an additively controlled character (desiccation resistance). Four populations of Drosophila serrata, sampled from central and marginal areas of its distribution along a 3000-km stretch of Australia's east coast, underwent selection for desiccation resistance for 14 generations. After selection had ceased, control lines from each of the populations were crossed to determine the amount of hybrid breakdown that existed before selection and selected lines were crossed to determine the amount of hybrid breakdown after selection. Hybrid breakdown was measured in three fitness traits: developmental time, viability, and fecundity. When the individual crosses were examined, virtually no evidence was found for hybrid breakdown between these populations. However, the level of hybrid breakdown in development time in the control lines increased as the distance between the populations in the field increased. This relationship was lost in the selected lines. Therefore, selection for desiccation resistance influenced the level of hybrid breakdown in a fitness trait, although selection may need to be maintained for longer than 14 generations if a new relationship between hybrid breakdown and distance is to be formed.     

PAIRWISE VERSUS DIFFUSE NATURAL SELECTION AND THE MULTIPLE HERBIVORES OF SCARLET GILIA,IPOMOPSIS AGGREGATA

Recent theoretical studies have argued that plant-herbivore coevolution proceeds in a diffuse rather than a pairwise manner in multispecies interactions when at least one of two conditions are met: (1) genetic correlations exist between plant resistances to different herbivore species; and (2) ecological interactions between herbivores sharing a host plant cause nonadditive impacts of herbivory on plant fitness. We present results from manipulative field experiments investigating the single and interactive fitness effects of three types of herbivory on scarlet gilia (Ipomopsis aggregata) over two years of study. We utilize these data to test whether selection imposed by herbivore attack on date of first flowering is pairwise (independent) or diffuse (dependent) in nature. Our results reveal complex patterns of the fitness effect of herbivores. Simulated early season browsing had a strong negative fitness effect on plants and also reduced subsequent insect attack. Surprisingly, this ecological interaction did not translate into significant interactions between clipping and insect manipulations on plant fitness. However, we detected a significant interaction between seed fly and caterpillar herbivory on plant fitness, with the negative effect of either insect being greatest when occurring alone. These results suggest that herbivore-imposed selection may have pairwise and diffuse components. In our selection analysis of flowering phenology, we discovered significant pairwise linear selection imposed by clipping, diffuse linear selection imposed by insects, and diffuse nonlinear selection imposed by clipping and insect attack acting simultaneously. Our results reveal that the evolution of flowering phenology in scarlet gilia may be in response to diffuse and pairwise natural selection imposed by multiple herbivores. We discuss the evolution of resistance characters in light of diffuse versus pairwise forms of linear and nonlinear selection and stress the complexity of selection imposed by suites of interacting species.