The importance of intraspecific frequency-dependent selection in modelling competitive coevolution

Summary The coevolution of competitors has been analyzed by two different types of fitness-maximization techniques; ESS methods (Lawlor and Maynard Smith, 1976), and CSS methods (Roughgarden, 1979). This paper argues that CSS methods generally do not predict the outcome of competitive coevolution. Even when there is relatively little variability within species, fitness maximization leads to an ESS rather than a CSS. A simple model is analyzed to show that ESS and CSS predictions about character displacement can differ qualitatively. Previous results of CSS analyses are discussed.     

THE EVOLUTIONARILY STABLE PHENOTYPE DISTRIBUTION IN A RANDOM ENVIRONMENT

In an unpredictably changing environment, phenotypic variability may evolve as a “bet-hedging” strategy. We examine here two models for evolutionarily stable phenotype distributions resulting from stabilizing selection with a randomly fluctuating optimum. Both models include overlapping generations, either survival of adults or a dormant propagule pool. In the first model (mixed-strategies model) we assume that individuals can produce offspring with a distribution of phenotypes, in which case, the evolutionarily stable population always consists of a single genotype. We show that there is a unique evolutionarily stable strategy (ESS) distribution that does not depend on the amount of generational overlap, and that the ESS distribution generically is discrete rather than continuous; that is, there are distinct classes of offspring rather than a continuous distribution of offspring phenotypes. If the probability of extreme fluctuations in the optimum is sufficiently small, then the ESS distribution is monomorphic: a single type fitted to the mean environment. At higher levels of variability, the ESS distribution is polymorphic, and we find stability conditions for dimorphic distributions. For an exponential or similarly broad-tailed distribution of the optimum phenotype, the ESS consists of an infinite number of distinct phenotypes. In the second model we assume that an individual produces offspring with a single, genetically determined phenotype (pure-strategies model). The ESS population then contains multiple genotypes when the environmental variance is sufficiently high. However the phenotype distributions are similar to those in the mixed-strategies model: discrete, with an increasing number of distinct phenotypes as the environmental variance increases.     

Single species evolutionary dynamics

Not long after the introduction of evolutionary stable strategy (ESS) concept, it was noticed that dynamic selection did not always lead to the establishment of the ESS. The concept of continuously stable strategy (CSS) was thereafter developed. It was generally accepted that dynamic selection leads to the establishment of an ESS if it is a CSS. Examination of an evolutionary stability concept which is called neighborhood invader strategy (NIS) shows that it may be impossible for an ESS to be established through dynamic selection even if it is a CSS and no polymorphisms occur. We will examine the NIS concept and its implications for two evolutionary game models: root-shoot allocation in plant competition and Lotka–Volterra competition. In the root-shoot model we show that an ESS will be attained through dynamic selection if it is a NIS. Similarly for the Lotka–Volterra model, we show that an ESS will be attained through dynamic selection even if protected dimorphisms occur during the evolutionary process if it is an NIS.     

Alternative Predictions for Optimal Dispersal in Response to Local Catastrophic Mortality

What dispersal strategy should be employed by an organism in response to local catastrophic mortality? Here we contrast predictions from an analytical solution derived from an ESS model which optimizes competitive ability (Comins et al., 1980) with those from a stochastic, branching process model (Karlson and Taylor, 1992) which maximizes survivorship of a clonal lineage. The optimal dispersal fraction varies directly with the probability of local extinction in the ESS model, yet varies inversely with this probability over much of the parameter space in the latter model. In order to conform more closely with the assumptions of the ESS model, we have modified the branching process model to have a random, Poisson-distributed number of offspring and compared the predictions of these models. Both models invoke dispersal as an escape from local extinction and predict mixed dispersal strategies over a wide range of conditions. However, increasing local catastrophic mortality favors more dispersal in the ESS model, but it can be so severe in the branching process model that no dispersal strategy is adaptive. In this model, the predicted optimal proportion of dispersed offspring is highest at low to intermediate levels of catastrophic mortality depending on the total number of offspring produced. We suggest that this observed discrepancy is sufficiently large to warrant empirical tests of these qualitatively different predictions.     

The past,present and future of reproductive skew theory and experiments

A major evolutionary question is how reproductive sharing arises in cooperatively breeding species despite the inherent reproductive conflicts in social groups. Reproductive skew theory offers one potential solution: each group member gains or is allotted inclusive fitness equal to or exceeding their expectation from reproducing on their own. Unfortunately, a multitude of skew models with conflicting predictions has led to confusion in both testing and evaluating skew theory. The confusion arises partly because one set of models (the ‘transactional’ type) answer the ultimate evolutionary question of what ranges of reproductive skew can yield fitness‐enhancing solutions for all group members. The second set of models (‘compromise’) give an evolutionarily proximate, game‐theoretic evolutionarily stable state (ESS) solution that determines reproductive shares based on relative competitive abilities. However, several predictions arising from compromise models require a linear payoff to increased competition and do not hold with non‐linear payoffs. Given that for most species it may be very difficult or impossible to determine the true relationship between effort devoted to competition and reproductive share gained, compromise models are much less predictive than previously appreciated. Almost all skew models make one quantitative prediction (e.g. realized skew must fall within ranges predicted by transactional models), and two qualitative predictions (e.g. variation in relatedness or competitive ability across groups affects skew). A thorough review of the data finds that these three predictions are relatively rarely supported. As a general rule, therefore, the evolution of cooperative breeding appears not to be dependent on the ability of group members to monitor relatedness or competitive ability in order to adjust their behaviour dynamically to gain reproductive share. Although reproductive skew theory fails to predict within‐group dynamics consistently, it does better at predicting quantitative differences in skew across populations or species. This suggests that kin selection can play a significant role in the evolution of sociality. To advance our understanding of reproductive skew will require focusing on a broader array of factors, such as the frequency of mistaken identity, delayed fitness payoffs, and selection pressures arising from across‐group competition. We furthermore suggest a novel approach to investigate the sharing of reproduction that focuses on the underlying genetics of skew. A quantitative genetics approach allows the partitioning of variance in reproductive share itself or that of traits closely associated with skew into genetic and non‐genetic sources. Thus, we can determine the heritability of reproductive share and infer whether it actually is the focus of natural selection. We view the ‘animal model’ as the most promising empirical method where the genetics of reproductive share can be directly analyzed in wild populations. In the quest to assess whether skew theory can provide a framework for understanding the evolution of sociality, quantitative genetics will be a central tool in future research.     

Evolution of virulence when transmission occurs before disease

Most models of virulence evolution assume that transmission and virulence are constant during an infection. In many viral (HIV and influenza), bacterial (TB) and prion (BSE and CWD) systems, disease-induced mortality occurs long after the host becomes infectious. Therefore, we constructed a model with two infected classes that differ in transmission rate and virulence in order to understand how the evolutionarily stable strategy (ESS) depends on the relative difference in transmission and virulence between classes, on the transition rate between classes and on the recovery rate from the second class. We find that ESS virulence decreases when expressed early in the infection or when transmission occurs late in an infection. When virulence occurred relatively equally in each class and there was disease recovery, ESS virulence increased with increased transition rate. In contrast, ESS virulence first increased and then decreased with transition rate when there was little virulence early in the infection and a rapid recovery rate. This model predicts that ESS virulence is highly dependent on the timing of transmission and pathology after infection; thus, pathogen evolution may either increase or decrease virulence after emergence in a new host.     

Begging scrambles with unequal chicks: interactions between need and competitive ability

When offspring compete for the attentions of provisioning parents, empirical and theoretical work has generally concluded that chicks honestly signal their "need" for resources and that parents control allocation. Here, we develop models to show that when allocation of food resources is determined by competitive begging scrambles between sibs, the offspring's ESS begging levels, shares of food and personal fitness gained will be determined by an interaction between their competitive abilities and their true needs. Many of the predictions of this scramble competition model are qualitatively very similar to models of honest signalling of need, where parents, not offspring, control the allocation of food. Consequently it will be difficult to distinguish between the two mechanisms of food allocation based on empirical observations of the responses of chicks to feeding by parents.     

EVOLUTION OF CHARACTER DISPLACEMENT IN SPADEFOOT TOADS: DIFFERENT PROXIMATE MECHANISMS IN DIFFERENT SPECIES

Character displacement occurs when two species compete, and those individuals most dissimilar from the average resource‐use phenotypes of the other species are selectively favored. Few studies have explored the sequence of events by which such divergence comes about. We addressed this issue by studying two species of spadefoot toads that have undergone ecological character displacement with each other. Previous research revealed that phenotypic shifts between sympatric and allopatric populations of one species, Spea multiplicata, reflect a condition‐dependent maternal effect. Here, we show that analogous shifts in the other species, S. bombifrons, cannot similarly be explained by such a maternal effect, and that these shifts instead appear to be underlain by allelic differences. We hypothesize that these two species have evolved different mechanisms of character displacement because they differ in duration in sympatry. Specifically, because they occur at the edge of a range expansion, populations of S. bombifrons have been exposed to S. multiplicata for a longer period. Consequently, S. bombifrons have likely had more time to accumulate genetic changes that promote character displacement. Generally, character displacement may often progress through an initial phase in which trait differences are environmentally induced to one in which they are constitutively expressed.     

THE EVOLUTION OF STRATEGY VARIATION: WILL AN ESS EVOLVE?

Evolutionarily stable strategy (ESS) models are widely viewed as predicting the strategy of an individual that when monomorphic or nearly so prevents a mutant with any other strategy from entering the population. In fact, the prediction of some of these models is ambiguous when the predicted strategy is "mixed", as in the case of a sex ratio, which may be regarded as a mixture of the subtraits "produce a daughter" and "produce a son." Some models predict only that such a mixture be manifested by the population as a whole, that is, as an "evolutionarily stable state"; consequently, strategy monomorphism or polymorphism is consistent with the prediction. The hawk-dove game and the sex-ratio game in a panmictic population are models that make such a "degenerate" prediction. We show here that the incorporation of population finiteness into degenerate models has effects for and against the evolution of a monomorphism (an ESS) that are of equal order in the population size, so that no one effect can be said to predominate. Therefore, we used Monte Carlo simulations to determine the probability that a finite population evolves to an ESS as opposed to a polymorphism. We show that the probability that an ESS will evolve is generally much less than has been reported and that this probability depends on the population size, the type of competition among individuals, and the number of and distribution of strategies in the initial population. We also demonstrate how the strength of natural selection on strategies can increase as population size decreases. This inverse dependency underscores the incorrectness of Fisher's and Wright's assumption that there is just one qualitative relationship between population size and the intensity of natural selection.     

Fighting for food: a dynamic version of the Hawk-Dove game

Summary The Hawk-Dove game (Maynard Smith, 1982) has been used to analyse conflicts over resources such as food. At the evolutionarily stable strategy (ESS), either a proportionp* of animals always play Hawk, or each animal has a probabilityp* of playing Hawk. We modify the standard Hawk-Dove game to include a state variable,x, that represents the animal's level of energy reserves. A strategy is now a rule for choosing an action as a function ofx and time of day. We consider a non-reproductive period and adopt the criterion of minimizing mortality over this period. We find the ESS, which has the form play Hawk if reserves are belowc* (t) at timet, otherwise play Dove. This ESS is very different from the ESS in the standard Hawk-Dove game. It is a pure ESS that depends on the animal's state and on time. Furthermore, it is characterized by the strong condition that any single mutant that does not adopt the ESS suffers a reduction in fitness. The standard Hawk-Dove game assumes pay-offs that are related to fitness; our approach starts from a definition of fitness and derives the pay-offs in the process of finding the ESS. When the environment becomes worse (e.g. food becomes less reliable or energy expenditure increases) the ESS changes in such a way as to increase the proportion of animals that will play Hawk.     

The risks of parenthood II. Parent-offspring conflict

Summary Previous work has demonstrated the value of dynamic programming models for the analysis of parental decision making. In the present paper we extend this approach to analyse conflicts between parents and their offspring, and develop a dynamic ESS model of feeding and fledging of nestling birds. In order to simplify the formulation and solution of the dynamic ESS model, we adopt an assumption of alternating decisions: in each time period the parent first decides whether to continue provisioning the nestling, after which the nestling decides whether to leave the nest. The model takes into account numerous tradeoffs involved in parent-offspring decisions, including differential growth and mortality rates for offspring in and out of the nest, risk of fledging, relation between long-term survival and post-breeding mass of offspring, and parental mortality risk associated with provisioning of offspring. Depending on assumed parameter values, the model is capable of predicting a wide range of feeding-fledging behaviour. The model is applied specifically to the juvenile life history of dovekies (Alle alle), and provides a behavioural explanation for the phenomenon of pre-fledging mass recession in this species.     

Multi-species evolutionary dynamics

Dynamical attainability of an evolutionarily stable strategy (ESS) through the process of mutations and natural selection has mostly been addressed through the use of the continuously stable strategy (CSS) concept for species evolutionary games in which strategies are drawn from a continuum, and by the adaptive trait dynamics method. We address the issue of dynamical attainability of an ESS in coevolving species through the use of the concept of an ESNIS. It is shown that the definition of an ESNIS coalition for coevolving species is not in general equivalent to other definitions for CSS given in the literature. We show under some additional conditions that, in a dynamic system which involves the strategies of a dimorphic ESNIS coalition and at most two strategies that are not members of ESNIS coalition, the ESNIS coalition will emerge as the winner. In addition an ESNIS will be approached because of the invasion structure of strategies in its neighborhood. This proves that under the above conditions an ESNIS has a better chance of being attained than a strategy coalition which is a CSS. The theory developed is applied to a class of coevolutionary game models with Lotka–Volterra type interactions and we show that for such models, an ESS coalition will be dynamically attainable through mutations and natural selection if the ESS coalition is also an ESNIS coalition.Co-ordinating editor: Metz     

Three‐dimensional cell culture model utilization in cancer stem cell research

Three‐dimensional (3D) cell culture models are becoming increasingly popular in contemporary cancer research and drug resistance studies. Recently, scientists have begun incorporating cancer stem cells (CSCs) into 3D models and modifying culture components in order to mimic in vivo conditions better. Currently, the global cell culture market is primarily focused on either 3D cancer cell cultures or stem cell cultures, with less focus on CSCs. This is evident in the low product availability officially indicated for 3D CSC model research. This review discusses the currently available commercial products for CSC 3D culture model research. Additionally, we discuss different culture media and components that result in higher levels of stem cell subpopulations while better recreating the tumor microenvironment. In summary, although progress has been made applying 3D technology to CSC research, this technology could be further utilized and a greater number of 3D kits dedicated specifically to CSCs should be implemented.     

Character analysis in morphological phylogenetics: problems and solutions

Many aspects of morphological phylogenetics are controversial in the theoretical systematics literature and yet are often poorly explained and justified in empirical studies. In this paper, I argue that most morphological characters describe variation that is fundamentally quantitative, regardless of whether they are coded qualitatively or quantitatively by systematists. Given this view, three fundamental problems in morphological character analysis (definition, delimitation, and ordering of character states) may have a common solution: coding morphological characters as continuous quantitative traits. A new parsimony method (step-matrix gap-weighting, a modification of Thiele's approach) is proposed that allows quantitative traits to be analyzed as continuous variables. The problem of scaling or weighting quantitative characters relative to qualitative characters (and to each other) is reviewed, and three possible solutions are described. The new coding method is applied to data from hoplocercid lizards, and the results show the sensitivity of phylogenetic conclusions to different scaling methods. Although some authors reject the use of continuous, overlapping, quantitative characters in phylogenetic analysis, quantitative data from hoplocercid lizards that are coded using the new approach contain significant phylogenetic structure and exhibit levels of homoplasy similar to those seen in data that are coded qualitatively.     

THE PARADOX OF THE PHYLOGENY: CHARACTER DISPLACEMENT OF ANALYSES OF BODY SIZE IN ISLAND ANOLIS

The evolution of body size in Anolis lizards of the Lesser Antilles Islands has been the subject of intensive, if divisive, study. Early research by Schoener revealed a regularity in the number of Anolis species that coexisted on islands and the difference in body size between coexisting congeners in the Northern Lesser Antilles. This consistent pattern of body size was suggested to be the result of competitive character displacement. Two recent studies critically evaluated this hypothesis by incorporating information about the phylogenetic relationships of insular Anolis. Roughgarden and Pacala suggested that the patterns of body-size differences in the Northern Lesser Antilles could be explained as a cyclical phenomenon that they labeled a taxon cycle. However, Losos supported the character-displacement hypothesis (“size adjustment”). The conflict between these two studies is important because both investigations were based on the same phylogenetic hypothesis. We investigated body-size evolution in Lesser Antilles Anolis to resolve the differences in the conclusions of these studies. Our new analysis supported the taxon-cycle hypothesis but nevertheless failed to reject the character-displacement hypothesis. We argue that this curious scenario is largely a function of the method by which phylogenetic information is incorporated in comparative analyses. Different comparative analyses may lead to dramatic differences in results and ambiguity in the conclusions to be drawn. We suggest that ecologists and evolutionary biologists specifically consider the underlying assumptions and models of character evolution inherent to each of the phylogenetically based analytical methods now available.     

Co-evolution of seed size and seed predation

Using the evolutionarily stable strategy (ESS) approach in a model for the co-evolution of seed size and seed predation, I show that seed size variation within individual plants is favoured if there is a trade-off in the predator's attack rate for different seed sizes. A single seed size is not evolutionarily stable because a predator that is optimally adapted to one particular seed size cannot prevent invasion by plants with a different seed size. The model generates the following predictions. The ESS consists of a continuous range of seed sizes. Small seeds tend to be attacked more frequently than big seeds. Plants with many resources and plants with low (frequency-independent) juvenile mortality have more variable seeds than plants with few resources and a high juvenile mortality. Seed size variation is higher in fluctuating populations regulated by seed predation alone than in stable populations (partially) regulated by seedling competition. Predator searching behaviour does not directly affect the ESS seed size range, but may have an indirect effect by affecting population stability or the significance of seedling competition as a population regulating mechanism. Moreover, seed size distributions are found to be more skewed in favour of small seeds if predation is spatially non-uniform than if predation is more even. Application of the model to systems of several co-evolving plant and predator species is discussed.     

THE MIXED-MODEL ANALYSIS OF VARIANCE APPLIED TO QUANTITATIVE GENETICS: BIOLOGICAL MEANING OF THE PARAMETERS

The mixed-model factorial analysis of variance has been used in many recent studies in evolutionary quantitative genetics. Two competing formulations of the mixed-model ANOVA are commonly used, the “Scheffe” model and the “SAS” model; these models differ in both their assumptions and in the way in which variance components due to the main effect of random factors are defined. The biological meanings of the two variance component definitions have often been unappreciated, however. A full understanding of these meanings leads to the conclusion that the mixed-model ANOVA could have been used to much greater effect by many recent authors. The variance component due to the random main effect under the two-way SAS model is the covariance in true means associated with a level of the random factor (e.g., families) across levels of the fixed factor (e.g., environments). Therefore the SAS model has a natural application for estimating the genetic correlation between a character expressed in different environments and testing whether it differs from zero. The variance component due to the random main effect under the two-way Scheffe model is the variance in marginal means (i.e., means over levels of the fixed factor) among levels of the random factor. Therefore the Scheffe model has a natural application for estimating genetic variances and heritabilities in populations using a defined mixture of environments. Procedures and assumptions necessary for these applications of the models are discussed. While exact significance tests under the SAS model require balanced data and the assumptions that family effects are normally distributed with equal variances in the different environments, the model can be useful even when these conditions are not met (e.g., for providing an unbiased estimate of the across-environment genetic covariance). Contrary to statements in a recent paper, exact significance tests regarding the variance in marginal means as well as unbiased estimates can be readily obtained from unbalanced designs with no restrictive assumptions about the distributions or variance-covariance structure of family effects.     

PREDICTING ADAPTATION UNDER MIGRATION LOAD: THE ROLE OF GENETIC SKEW

Quantitative genetics models have been used to predict the constraints on local adaptation caused by gene flow between populations under migration–selection balance. One key assumption of this approach is that genetic values within a population are normally distributed. Gene flow, however, may generate distributions that are skewed toward the immigrant's mean value. If the response to selection from a skewed distribution is different from that expected under the assumption of normality, models may result in inaccurate predictions. We use individual-based computer simulations to explore this problem, comparing our results to a recent model developed by Hendry et al. (2001) . We show that this model underestimates the equilibrium divergence between populations at migration–selection balance. The extent of this underestimation is correlated with the amount of genetic skew generated by migration and is partly explained by the fact that the analytical model ignores direct selection against hybrid phenotypes. We also show that all else being equal, response to selection in a population with a skewed distribution of genotypes is greater than in a population with normally distributed genotypes. The production of skew under migration–selection balance, however, is itself dependent upon the genetic architecture, with greater deviations from normality produced when alleles contributing to population differentiation have very different effect sizes. We find that both the skew and discrepancies between the models are greatest at intermediate migration rates and moderate to strong selection, which is exactly the region of parameter space that is most empirically relevant.     

THE CONTRIBUTION OF MATERNAL EFFECTS TO SELECTION RESPONSE: AN EMPIRICAL TEST OF COMPETING MODELS

Maternal effects can dramatically influence the evolutionary process, in some cases facilitating and in others hindering adaptive evolution. Maternal effects have been incorporated into quantitative genetic models using two theoretical frameworks: the variance‐components approach, which partitions variance into direct and maternal components, and the trait‐based approach, which assumes that maternal effects are mediated by specific maternal traits. Here, we demonstrate parallels between these models and test their ability to predict evolutionary change. First, we show that the two approaches predict equivalent responses to selection in the absence of maternal effects mediated by traits that are themselves maternally influenced. We also introduce a correction factor that may be applied when such cascading maternal effects are present. Second, we use several maternal effect models, as well as the standard breeder's equation, to predict evolution in response to artificial selection on flowering time in American bellflower, Campanulastrum americanum. Models that included maternal effects made much more accurate predictions of selection response than the breeder's equation. Maternal effect models differed somewhat in their fit, with a version of the trait‐based model providing the best fit. We recommend fitting such trait‐based models when possible and appropriate to make the most accurate evolutionary predictions.     

The genetics of phenotypic plasticity. V. Evolution of reaction norm shape

We present a general quantitative genetic model for the evolution of reaction norms. This model goes beyond previous models by simultaneously permitting any shaped reaction norm and allowing for the imposition of genetic constraints. Earlier models are shown to be special cases of our general model; we discuss in detail models involving just two macroenvironments, linear reaction norms, and quadratic reaction norms. The model predicts that, for the case of a temporally varying environment, a population will converge on (1) the genotype with the maximum mean geometric fitness over all environments, (2) a linear reaction norm whose slope is proportional to the covariance between the environment of development and the environment of selection, and (3) a linear reaction norm even if nonlinear reaction norms are possible. An examination of experimental studies finds some limited support for these predictions. We discuss the limitations of our model and the need for more realistic gametic models and additional data on the genetic and developmental bases of plasticity.