On our best behavior: optimality models in human behavioral ecology

This paper discusses problems associated with the use of optimality models in human behavioral ecology. Optimality models are used in both human and non-human animal behavioral ecology to test hypotheses about the conditions generating and maintaining behavioral strategies in populations via natural selection. The way optimality models are currently used in behavioral ecology faces significant problems, which are exacerbated by employing the so-called ‘phenotypic gambit’: that is, the bet that the psychological and inheritance mechanisms responsible for behavioral strategies will be straightforward. I argue that each of several different possible ways we might interpret how optimality models are being used for humans face similar and additional problems. I suggest some ways in which human behavioral ecologists might adjust how they employ optimality models; in particular, I urge the abandonment of the phenotypic gambit in the human case.     

Integrating Evolution into Ecological Modelling: Accommodating Phenotypic Changes in Agent Based Models

Evolutionary change is a characteristic of living organisms and forms one of the ways in which species adapt to changed conditions. However, most ecological models do not incorporate this ubiquitous phenomenon. We have developed a model that takes a ‘phenotypic gambit’ approach and focuses on changes in the frequency of phenotypes (which differ in timing of breeding and fecundity) within a population, using, as an example, seasonal breeding. Fitness per phenotype calculated as the individual’s contribution to population growth on an annual basis coincide with the population dynamics per phenotype. Simplified model variants were explored to examine whether the complexity included in the model is justified. Outputs from the spatially implicit model underestimated the number of individuals across all phenotypes. When no phenotype transitions are included (i.e. offspring always inherit their parent’s phenotype) numbers of all individuals are always underestimated. We conclude that by using a phenotypic gambit approach evolutionary dynamics can be incorporated into individual based models, and that all that is required is an understanding of the probability of offspring inheriting the parental phenotype.     

The long-term evolution of multilocus traits under frequency-dependent disruptive selection

Frequency-dependent disruptive selection is widely recognized as an important source of genetic variation. Its evolutionary consequences have been extensively studied using phenotypic evolutionary models, based on quantitative genetics, game theory, or adaptive dynamics. However, the genetic assumptions underlying these approaches are highly idealized and, even worse, predict different consequences of frequency-dependent disruptive selection. Population genetic models, by contrast, enable genotypic evolutionary models, but traditionally assume constant fitness values. Only a minority of these models thus addresses frequency-dependent selection, and only a few of these do so in a multilocus context. An inherent limitation of these remaining studies is that they only investigate the short-term maintenance of genetic variation. Consequently, the long-term evolution of multilocus characters under frequency-dependent disruptive selection remains poorly understood. We aim to bridge this gap between phenotypic and genotypic models by studying a multilocus version of Levene's soft-selection model. Individual-based simulations and deterministic approximations based on adaptive dynamics theory provide insights into the underlying evolutionary dynamics. Our analysis uncovers a general pattern of polymorphism formation and collapse, likely to apply to a wide variety of genetic systems: after convergence to a fitness minimum and the subsequent establishment of genetic polymorphism at multiple loci, genetic variation becomes increasingly concentrated on a few loci, until eventually only a single polymorphic locus remains. This evolutionary process combines features observed in quantitative genetics and adaptive dynamics models, and it can be explained as a consequence of changes in the selection regime that are inherent to frequency-dependent disruptive selection. Our findings demonstrate that the potential of frequency-dependent disruptive selection to maintain polygenic variation is considerably smaller than previously expected.     

A popular misapplication of evolutionary modeling to the study of human cooperation

To examine the evolutionary basis of a behavior, an established approach (known as the phenotypic gambit) is to assume that the behavior is controlled by a single allele, the fitness effects of which are derived from a consideration of how the behavior interacts, via life-history, with other ecological factors. Here we contrast successful applications of this approach with several examples of an influential and superficially similar line of research on the evolutionary basis of human cooperation. A key difference is identified: in the latter line of research the focal behavior, cooperation, is abstractly defined in terms of immediate fitness costs and benefits. Selection is then assumed to act on strategies in an iterated social context for which fitness effects can be derived by aggregation of the abstractly defined immediate fitness effects over a lifetime. This approach creates a closed theoretical loop, rendering models incapable of making predictions or providing insight into the origin of human cooperation. We conclude with a discussion of how evolutionary approaches might be appropriately used in the study of human social behavior.     

Stochastic fluctuations in frequency-dependent selection: a one-locus, two-allele and two-phenotype model

Stochastic fluctuations in a simple frequency-dependent selection model with one-locus, two-alleles and two-phenotypes are investigated. The steady-state statistics of allele frequencies for an interior stable phenotypic equilibrium are shown to be similar to the stochastic fluctuations in standard evolutionary game dynamics [Tao, Y., Cressman, R., 2007. Stochastic fluctuations through intrinsic noise in evolutionary game dynamics. Bull. Math. Biol. 69, 1377-1399]. On the other hand, for an interior stable phenotypic or genotypic equilibrium, our main results show that the deterministic model cannot be used to predict the expectation of phenotypic frequency. The variance of phenotypic frequency for an interior stable genotypic equilibrium is more sensitive to the expected population size than for an interior stable phenotypic equilibrium. Furthermore, the stochastic fluctuations of allele frequency and phenotypic frequency can be considered approximately independent of each other for these genotypic equilibria, but not for phenotypic.     

learnPopGen: An R package for population genetic simulation and numerical analysis

Here, I briefly present a new R package called learnPopGen that has been designed primarily for the purposes of teaching evolutionary biology, population genetics, and evolutionary theory. Functions of the package can be used to conduct simulations and numerical analyses of a wide range of evolutionary phenomena that would typically be covered in advanced undergraduate through graduate‐level curricula in population genetics or evolution. For instance, learnPopGen functions can be used to visualize gene frequency changes through time under multiple deterministic and stochastic processes, to compute and animate the changes in phenotypic trait values or distributions under natural selection, to numerically analyze and graph the outcome of simple game theory models, and to plot coalescence within a population experiencing genetic drift, along with a number of other things. Functions have been designed to be maximally didactic and frequently employ compelling animated visualizations. Furthermore, it is straightforward to export plots and animations from R in the form of flat or animated graphics, or as videos. For maximum flexibility, students working with the package can run functions directly in R; however, instructors may choose to guide students less adept in the R environment to one of various web interfaces that I have built for a number of the functions of the package and that are already available online.     

Darwinian adaptation,population genetics and the streetcar theory of evolution

 This paper investigates the problem of how to conceive a robust theory of phenotypic adaptation in non-trivial models of evolutionary biology. A particular effort is made to develop a foundation of this theory in the context of n-locus population genetics. Therefore, the evolution of phenotypic traits is considered that are coded for by more than one gene. The potential for epistatic gene interactions is not a priori excluded. Furthermore, emphasis is laid on the intricacies of frequency-dependent selection. It is first discussed how strongly the scope for phenotypic adaptation is restricted by the complex nature of ‘reproduction mechanics’ in sexually reproducing diploid populations. This discussion shows that one can easily lose the traces of Darwinism in n-locus models of population genetics. In order to retrieve these traces, the outline of a new theory is given that I call ‘streetcar theory of evolution’. This theory is based on the same models that geneticists have used in order to demonstrate substantial problems with the ‘adaptationist programme’. However, these models are now analyzed differently by including thoughts about the evolutionary removal of genetic constraints. This requires consideration of a sufficiently wide range of potential mutant alleles and careful examination of what to consider as a stable state of the evolutionary process. A particular notion of stability is introduced in order to describe population states that are phenotypically stable against the effects of all mutant alleles that are to be expected in the long-run. Surprisingly, a long-term stable state can be characterized at the phenotypic level as a fitness maximum, a Nash equilibrium or an ESS. The paper presents these mathematical results and discusses – at unusual length for a mathematical journal – their fundamental role in our current understanding of evolution. Received 22 April 1994; received in revised form 10 July 1995     

Generating phenotypic variation: prospects from "evo-devo" research on Bicyclus anynana wing patterns

Understanding the generation of phenotypic variation is an important challenge for modern evolutionary biology, and butterfly wing patterns are an exciting system that can shed some light on this issue. Here, we report on recent advances in the genetics of Bicyclus anynana butterflies. This system provides the potential for a fully integrated study of the evolutionary and developmental processes underlying diversity in morphology.     

Phenotypic Novelty in EvoDevo: The Distinction Between Continuous and Discontinuous Variation and Its Importance in Evolutionary Theory

The introduction of novel phenotypic structures is one of the most significant aspects of organismal evolution. Yet the concept of evolutionary novelty is used with drastically different connotations in various fields of research, and debate exists about whether novelties represent features that are distinct from standard forms of phenotypic variation. This article contrasts four separate uses for novelty in genetics, population genetics, morphology, and behavioral science, before establishing how novelties are used in evolutionary developmental biology (EvoDevo). In particular, it is detailed how an EvoDevo-specific research approach to novelty produces insight distinct from other fields, gives the concept explanatory power with predictive capacities, and brings new consequences to evolutionary theory. This includes the outlining of research strategies that draw attention to productive areas of inquiry, such as threshold dynamics in development. It is argued that an EvoDevo-based approach to novelty is inherently mechanistic, treats the phenotype as an agent with generative potential, and prompts a distinction between continuous and discontinuous variation in evolutionary theory.     

Modeling social and evolutionary games

When game theory was introduced to biology, the components of classic game theory models were replaced with elements more befitting evolutionary phenomena. The actions of intelligent agents are replaced by phenotypic traits; utility is replaced by fitness; rational deliberation is replaced by natural selection. In this paper, I argue that this classic conception of comprehensive reapplication is misleading, for it overemphasizes the discontinuity between human behavior and evolved traits. Explicitly considering the representational roles of evolutionary game theory brings to attention areas of overlap that are often neglected, and so a range of evolutionary possibilities that are often overlooked. The clarifications this analysis provides are well illustrated by-and particularly valuable for-game theoretic treatments of the evolution of social behavior.     

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

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

Strategic analysis in evolutionary genetics and the theory of games

This paper is written in memory of John Maynard Smith. In a brief survey it discusses essential aspects of how game theory in biology relates to its counterpart in economics, the major transition in game theory initiated by Maynard Smith, the discrepancies between genetic and phenotypic models in evolutionary biology, and a balanced way of reconciling these models. In addition, the paper discusses modern problems in understanding games at the genetic level using the examples of conflict between endosymbionts and their hosts, and the molecular interactions between parasites and the mammalian immune system.     

Effect of Spatial Dispersion on Evolutionary Stability: A Two-Phenotype and Two-Patch Model

In this paper, we investigate a simple two-phenotype and two-patch model that incorporates both spatial dispersion and density effects in the evolutionary game dynamics. The migration rates from one patch to another are considered to be patch-dependent but independent of individual’s phenotype. Our main goal is to reveal the dynamical properties of the evolutionary game in a heterogeneous patchy environment. By analyzing the equilibria and their stabilities, we find that the dynamical behavior of the evolutionary game dynamics could be very complicated. Numerical analysis shows that the simple model can have twelve equilibria where four of them are stable. This implies that spatial dispersion can significantly complicate the evolutionary game, and the evolutionary outcome in a patchy environment should depend sensitively on the initial state of the patches.     

Optimality and evolutionary genetics: complementary procedures for evolutionary analysis in behavioural ecology

The concepts and tools of optimality and game theory are a major component of research in behavioural ecology. In contrast, the theory and practice of evolutionary, ecological, population and quantitative genetics have made less of an impact on those studying the evolution of animal behaviour. A more complete understanding of the evolution of behaviour can be achieved by pursuing research that combines optimality and genetics, thereby overcoming some of the limitations inherent in a single approach.     

Genetic variance for behavioural ‘predictability’ of stress response

Genetic factors underpinning phenotypic variation are required if natural selection is to result in adaptive evolution. However, evolutionary and behavioural ecologists typically focus on variation among individuals in their average trait values and seek to characterize genetic contributions to this. As a result, less attention has been paid to if and how genes could contribute towards within‐individual variance or trait ‘predictability’. In fact, phenotypic ‘predictability’ can vary among individuals, and emerging evidence from livestock genetics suggests this can be due to genetic factors. Here, we test this empirically using repeated measures of a behavioural stress response trait in a pedigreed population of wild‐type guppies. We ask (a) whether individuals differ in behavioural predictability and (b) whether this variation is heritable and so evolvable under selection. Using statistical methodology from the field of quantitative genetics, we find support for both hypotheses and also show evidence of a genetic correlation structure between the behavioural trait mean and individual predictability. We show that investigating sources of variability in trait predictability is statistically tractable and can yield useful biological interpretation. We conclude that, if widespread, genetic variance for ‘predictability’ will have major implications for the evolutionary causes and consequences of phenotypic variation.     

Molecular tracking of jaguar melanism using faecal DNA

Major evolutionary questions remain elusive due to persistent difficulties in directly studying the genetics of variable phenotypes in natural populations. Many phenotypic variants may be of adaptive relevance, and thus important to consider in the context of conservation genetics. However, since the dynamics of these traits is usually poorly understood in the wild, their incorporation in conservation strategies is difficult to accomplish. For animals which exhibit intriguing phenotypic variation but are difficult to track in the wild, innovative approaches are required to investigate such issues. Here we demonstrate that non-invasive DNA sampling can be used to study the genetics and ecology of melanism in the jaguar, by directly genotyping the molecular polymorphism underlying this coloration trait. These results open new prospects for the in-depth investigation of this polymorphism, and highlight the broader potential of non-invasive DNA-based phenotype tracking for wildlife in general.     

Evolutionary developmental biology and the problem of variation

Abstract. One of the oldest problems in evolutionary biology remains largely unsolved. Which mutations generate evolutionarily relevant phenotypic variation? What kinds of molecular changes do they entail? What are the phenotypic magnitudes, frequencies of origin, and pleiotropic effects of such mutations? How is the genome constructed to allow the observed abundance of phenotypic diversity? Historically, the neo‐Darwinian synthesizers stressed the predominance of micromutations in evolution, whereas others noted the similarities between some dramatic mutations and evolutionary transitions to argue for macromutationism. Arguments on both sides have been biased by misconceptions of the developmental effects of mutations. For example, the traditional view that mutations of important developmental genes always have large pleiotropic effects can now be seen to be a conclusion drawn from observations of a small class of mutations with dramatic effects. It is possible that some mutations, for example, those in cis‐regulatory DNA, have few or no pleiotropic effects and may be the predominant source of morphological evolution. In contrast, mutations causing dramatic phenotypic effects, although superficially similar to hypothesized evolutionary transitions, are unlikely to fairly represent the true path of evolution. Recent developmental studies of gene function provide a new way of conceptualizing and studying variation that contrasts with the traditional genetic view that was incorporated into neo‐Darwinian theory and population genetics. This new approach in developmental biology is as important for micro‐evolutionary studies as the actual results from recent evolutionary developmental studies. In particular, this approach will assist in the task of identifying the specific mutations generating phenotypic variation and elucidating how they alter gene function. These data will provide the current missing link between molecular and phenotypic variation in natural populations.     

Assessing the impacts of phenotypic plasticity on evolution

In the past decade, there has been a resurgent interest in whether and how phenotypic plasticity might impact evolutionary processes. Of fundamental importance is how the environment influences individual phenotypic development while simultaneously selecting among phenotypic variants in a population. Conceptual and theoretical treatments of the evolutionary implications of plasticity are numerous, as are criticisms of the conclusions. As such, the time is ripe for empirical evidence to catch up with theoretical predictions. To this end, I provide a summary of eight hypotheses at the core of this issue, highlighting various approaches by which they can be tested. My goal is to provide practical guidance to those seeking to understand the complex ways by which phenotypic plasticity can influence evolutionary innovation and diversification.     

Testing the phenotypic gambit: phenotypic, genetic and environmental correlations of colour

Evolutionary theory is primarily concerned with genetic processes, yet empirical testing of this theory often involves data collected on phenotypes. To make this tenable, the implicit assumption is often made that phenotypic patterns are good predictors of genetic patterns; an assumption that coined the phenotypic gambit. Although this assumption has been validated for traits with high heritability, such as morphology, its generality for traits with low heritabilities, such as life-history and behavioural traits, remains controversial. Using a large-scale cross-fostering experiment, we were able to measure genetic, common environmental and phenotypic correlations between four colour traits and two skeletal traits in a wild population of passerine birds, the blue tit (Parus caeruleus). Colour traits had little heritable variation but common environment effects were found to be important; skeletal traits showed the opposite pattern. Positive correlations because of a shared natal environment were found between all traits, obscuring negative genetic correlations between some colour and skeletal traits. Consequently, phenotypic patterns were poor surrogates for genetic patterns and we suggest that this may be common if trade-offs or substantial parental effects exist. For this group of traits, the phenotypic gambit cannot be made and we suggest caution when inferring genetic patterns from phenotypic data, especially for behavioural and life-history traits.