Variability in diapause duration in the chestnut weevil: mixed ESS,genetic polymorphism or bet‐hedging?

Within-generation variability in diapause duration can be viewed either as a mixed Evolutionary Stable Strategy (ESS), a genetic polymorphism of pure strategies, or as bet-hedging. Diapause variability expressed by a single genotype that maximizes mean geometric fitness at the cost of mean arithmetic fitness is a bet-hedging strategy. Bet-hedging differs from mixed ESS and stable genetic polymorphism of pure strategies because in these latter the expected pay-offs for all phenotypes are equal. In insects, individuals with a prolonged diapause (long cycle) lose at least one reproductive opportunity and suffer lower survival before reproduction than those with a short diapause (short cycle). If long-cycle individuals compensate this cost by better adult performance, the compensation leads to a trade-off which could result in mixed ESS or genetic polymorphism of pure strategies since the overall fitness of the two morphs may be similar. In this paper, we show that in the chestnut weevil Curculio elephas adult performance, measured as sex ratio, longevity, weight, and realized fecundity of females, are similar in individuals emerged after one and two years. Long-cycle morphs emerge slightly before short-cycle ones but this eventual advantage for fertility probably does not compensate higher larval mortality and missed reproductive opportunity in long-cycle phenotypes. Therefore, the cost associated with prolonged diapause cannot be completely compensated for by a better adult performance. From these results, and previous data, we conclude that variability in diapause duration cycle is better explained as bet-hedging than mixed ESS or genetic polymorphism of pure strategies.     

Bet-hedging as an evolutionary game: the trade-off between egg size and number

Bet-hedging theory addresses how individuals should optimize fitness in varying and unpredictable environments by sacrificing mean fitness to decrease variation in fitness. So far, three main bet-hedging strategies have been described: conservative bet-hedging (play it safe), diversified bet-hedging (don’t put all eggs in one basket) and adaptive coin flipping (choose a strategy at random from a fixed distribution). Within this context, we analyse the trade-off between many small eggs (or seeds) and few large, given an unpredictable environment. Our model is an extension of previous models and allows for any combination of the bet-hedging strategies mentioned above. In our individual-based model (accounting for both ecological and evolutionary forces), the optimal bet-hedging strategy is a combination of conservative and diversified bet-hedging and adaptive coin flipping, which means a variation in egg size both within clutches and between years. Hence, we show how phenotypic variation within a population, often assumed to be due to non-adaptive variation, instead can be the result of females having this mixed strategy. Our results provide a new perspective on bet-hedging and stress the importance of extreme events in life history evolution.     

Bet-hedging--a triple trade-off between means, variances and correlations

In unpredictably varying environments, strategies that have a reduced variance in fitness can invade a population consisting of individuals that on average do better. Such strategies 'hedge their evolutionary bets' against the variability of the environment. The idea of bet-hedging arises from the fact that appropriate measure of long-term fitness is sensitive to variance, leading to the potential for strategies with a reduced mean fitness to invade and increase in frequency. Our aim is to review the conceptual foundation of bet-hedging as a mechanism that influences short- and long-term evolutionary processes. We do so by presenting a general model showing how evolutionary changes are affected by variance in fitness and how genotypic variance in fitness can be separated into variance in fitness at the level of the individuals and correlations in fitness among them. By breaking down genotypic fitness variance in this way the traditional divisions between conservative and diversified strategies are more easily intuited, and it is also shown that this division can be considered a false dichotomy, and is better viewed as two extreme points on a continuum. The model also sheds light on the ideas of within- and between-generation bet-hedging, which can also be generalized to be seen as two ends of a different continuum. We use a simple example to illustrate the virtues of our general model, as well as discuss the implications for systems where bet-hedging has been invoked as an explanation.     

Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree

We present a general framework for modelling adaptive trait dynamics in which we integrate various concepts and techniques from modern ESS-theory. The concept of evolutionarily singular strategies is introduced as a generalization of the ESS-concept. We give a full classification of the singular strategies in terms of ESS-stability, convergence stability, the ability of the singular strategy to invade other populations if initially rare itself, and the possibility of protected dimorphisms occurring within the singular strategy's neighbourhood. Of particular interest is a type of singular strategy that is an evolutionary attractor from a great distance, but once in its neighbourhood a population becomes dimorphic and undergoes disruptive selection leading to evolutionary branching. Modelling the adaptive growth and branching of the evolutionary tree can thus be considered as a major application of the framework. A haploid version of Levene's soft selection model is developed as a specific example to demonstrate evolutionary dynamics and branching in monomorphic and polymorphic populations.     

Advantage of storage in a fluctuating environment

We will elaborate the evolutionary course of an ecosystem consisting of a population in a chemostat environment with periodically fluctuating nutrient supply. The organisms that make up the population consist of structural biomass and energy storage compartments. In a constant chemostat environment a species without energy storage always out-competes a species with energy reserves. This hinders evolution of species with storage from those without storage. Using the adaptive dynamics approach for non-equilibrium ecological systems we will show that in a fluctuating environment there are multiple stable evolutionary singular strategies (ss's): one for a species without, and one for a species with energy storage. The evolutionary end-point depends on the initial evolutionary state. We will formulate the invasion fitness in terms of Floquet multipliers for the oscillating non-autonomous system. Bifurcation theory is used to study points where due to evolutionary development by mutational steps, the long-term dynamics of the ecological system changes qualitatively. To that end, at the ecological time scale, the trait value at which invasion of a mutant into a resident population becomes possible can be calculated using numerical bifurcation analysis where the trait is used as the free parameter, because it is just a bifurcation point. In a constant environment there is a unique stable equilibrium for one species following the "competitive exclusion" principle. In contrast, due to the oscillatory dynamics on the ecological time scale two species may coexist. That is, non-equilibrium dynamics enhances biodiversity. However, we will show that this coexistence is not stable on the evolutionary time scale and always one single species survives.     

Testing the role of coadapted genes versus bet-hedging for mating strategies in colour polymorphic pygmy grasshoppers

Recent investigations of mate choice indicate that the genetic effect of sires on offspring fitness may depend on the interaction between maternal and paternal genotypes and the environmental conditions experienced by the offspring. Alternative colour morphs of the pygmy grasshopper, Tetrix subulata , represent ecological strategies that differ in body size, life history, thermoregulatory behaviour, and habitat selection. The hypothesis that selection promotes behaviours maintaining coadapted gene complexes predicts individuals to mate assortatively with respect to colour morph. On the other hand, the bet-hedging hypothesis predicts that the temporal variability of the environment inhabited by these animals may select for disassortative mating behaviour resulting in heterogeneous offspring. To distinguish between these competing hypotheses, we investigated mating behaviours using dual-choice experiments. Our results were not in agreement with the prediction of assortative mating but suggest instead that matings were random with regard to colour morph. Polyandry was common, and females mated with the second male regardless of whether the first mating was assortative or disassortative. Polyandry also was equally frequent among females in triads in which the two males belonged to different colour morphs as in triads where both males belonged to the same colour morph. A field experiment confirmed that polyandry occurred also among free-ranging individuals, and uncovered variation in mating success among male colour morphs, probably due to indirect effects of coloration on activity or habitat use. The consequences of this random and polyandrous mating strategy for the evolutionary dynamics of the colour polymorphism remain to be explored.  © 2007 The Linnean Society of London, Biological Journal of the Linnean Society , 2007, 90 , 491–499.     

Advantage of storage in a fluctuating environment

We will elaborate the evolutionary course of an ecosystem consisting of a population in a chemostat environment with periodically fluctuating nutrient supply. The organisms that make up the population consist of structural biomass and energy storage compartments. In a constant chemostat environment a species without energy storage always out-competes a species with energy reserves. This hinders evolution of species with storage from those without storage. Using the adaptive dynamics approach for non-equilibrium ecological systems we will show that in a fluctuating environment there are multiple stable evolutionary singular strategies (ss's): one for a species without, and one for a species with energy storage. The evolutionary end-point depends on the initial evolutionary state. We will formulate the invasion fitness in terms of Floquet multipliers for the oscillating non-autonomous system. Bifurcation theory is used to study points where due to evolutionary development by mutational steps, the long-term dynamics of the ecological system changes qualitatively. To that end, at the ecological time scale, the trait value at which invasion of a mutant into a resident population becomes possible can be calculated using numerical bifurcation analysis where the trait is used as the free parameter, because it is just a bifurcation point. In a constant environment there is a unique stable equilibrium for one species following the “competitive exclusion” principle. In contrast, due to the oscillatory dynamics on the ecological time scale two species may coexist. That is, non-equilibrium dynamics enhances biodiversity. However, we will show that this coexistence is not stable on the evolutionary time scale and always one single species survives.     

Ectoparasitic Argulus coregoni (Crustacea: Branchiura) hedge their bets – studies on egg hatching dynamics

Unpredictability in the temporal availability of susceptible hosts is likely to act as a selection pressure affecting the life history strategies of parasites. In highly variable environments the future of the lineage can be secured by spreading the risk, for example, by producing descendants that differ in their timing of emergence. Counter to this, in predictable environments a single "best-adapted" phenotype is expected. We asked whether ectoparasitic Argulus coregoni egg hatching pattern can be explained as a genetically canalized individual trait; an instance of phenotypic plasticity or bet-hedging. We collected egg clutches laid by individual A. coregoni females in early and late reproductive period of the lice population and randomized the clutches within 3 treatments. Intra- and inter-clutch variability in the hatching dynamics of A. coregoni eggs was monitored and the reproductive potential assessed. On average A. coregoni females laid 317 (SD±176.6) eggs. We found that the plasticity in the hatching dynamics among A. coregoni eggs was remarkable. Noticeable peaks in hatching were followed each of the repeated artificial "winter treatments" in 1°C. Repeated 2 weeks cold treatments induced relatively bigger hatching peaks than 2 days cold treatments compared to controls at room temperature. However, in all treatments, egg clutches hatched through an extended period of 7 months on average and the total hatching percentages were similar. We found that intra-clutch variability in hatching among eggs laid by single A. coregoni females was greater than inter-clutch variability. Our data support the predictions of the adaptive bet-hedging strategy in relation to egg-hatching dynamics. Response to cooling and bet-hedging may be adaptive for such species like A. coregoni since by synchronizing the life-cycle with the seasonal environment will assist transmission and parasite fitness.     

Evolutionary bet-hedging in the real world: empirical evidence and challenges revealed by plants

Understanding the adaptations that allow species to live in temporally variable environments is essential for predicting how they may respond to future environmental change. Variation at the intergenerational scale can allow the evolution of bet-hedging strategies: a novel genotype may be favoured over an alternative with higher arithmetic mean fitness if the new genotype experiences a sufficiently large reduction in temporal fitness variation; the successful genotype is said to have traded off its mean and variance in fitness in order to ‘hedge its evolutionary bets’. We review the evidence for bet-hedging in a range of simple plant systems that have proved particularly tractable for studying bet-hedging under natural conditions. We begin by outlining the essential theory, reiterating the important distinction between conservative and diversified bet-hedging strategies. We then examine the theory and empirical evidence for the canonical example of bet-hedging: diversification via dormant seeds in annual plants. We discuss the complications that arise when moving beyond this simple case to consider more complex life-history traits, such as flowering size in semelparous perennial plants. Finally, we outline a framework for accommodating these complications, emphasizing the central role that model-based approaches can play.     

Female multiple mating as a genetic bet-hedging strategy when mate choice criteria are unreliable

Female multiple mating (or polyandry) is considered to act as a genetic bet-hedging mechanism, by which females can reduce the assessment error in regard to mates genetic quality when only uncertain information is available. In spite of frequent verbal arguments, no theoretical examination has been carried out to determine the effectiveness of bet-hedging by multiple mating. In the present paper, I show that three factors, female population size, remating costs and environmental fluctuation, all affect the effectiveness of bet-hedging. A mathematical model predicts that bet-hedging effectively works only in small populations, and computer simulations were used to confirm this prediction. The results of simulations differed according to the degree of environmental fluctuation. In relatively stable environments, if there is no remating cost, the fixation probability of a multiple mating strategy is slightly higher than that of a single mating strategy, independent of female population size. However, with very slight fitness costs, multiple mating drastically loses its advantage as population size increases, and almost always becomes extinct within large populations. This means that the evolution of polyandry solely by the mechanism of bet-hedging is unlikely in stable environments. However, in unpredictable environments, or when negative frequency-dependent selection on fitness-related loci is introduced, a multiple mating strategy is sometimes successful against a single mating strategy, even if it entails a small fitness cost. Therefore, female multiple mating may possibly evolve only in these limited conditions. In most cases, some deterministic mechanisms such as postcopulatory sperm selection by multiply mated females (or direct material benefits) are more reasonable as the evolutionary causes of polyandry.     

The ideal free distribution as an evolutionarily stable state in density‐dependent population games

In classical games that have been applied to ecology, individual fitness is either density independent or population density is fixed. This article focuses on the habitat selection game where fitness depends on the population density that evolves over time. This model assumes that changes in animal distribution operate on a fast time scale when compared to demographic processes. Of particular interest is whether it is true, as one might expect, that resident phenotypes who use density‐dependent optimal foraging strategies are evolutionarily stable with respect to invasions by mutant strategies. In fact, we show that evolutionary stability does not require that residents use the evolutionarily stable strategy (ESS) at every population density; rather it is the combined resident–mutant system that must be at an evolutionary stable state. That is, the separation of time scales assumption between behavioral and ecological processes does not imply that these processes are independent. When only consumer population dynamics in several habitats are considered (i. e. when resources do not undergo population dynamics), we show that the existence of optimal foragers forces the resident‐mutant system to approach carrying capacity in each habitat even though the mutants do not die out. Thus, the ideal free distribution (IFD) for the single‐species habitat selection game becomes an evolutionarily stable state that describes a mixture of resident and mutant phenotypes rather than a strategy adopted by all individuals in the system. Also discussed is how these results are affected when animal distribution and demographic processes act on the same time scale.     

Mating portfolios: bet-hedging,sexual selection and female multiple mating

Polyandry (female multiple mating) has profound evolutionary and ecological implications. Despite considerable work devoted to understanding why females mate multiply, we currently lack convincing empirical evidence to explain the adaptive value of polyandry. Here, we provide a direct test of the controversial idea that bet-hedging functions as a risk-spreading strategy that yields multi-generational fitness benefits to polyandrous females. Unfortunately, testing this hypothesis is far from trivial, and the empirical comparison of the across-generations fitness payoffs of a polyandrous (bet hedger) versus a monandrous (non-bet hedger) strategy has never been accomplished because of numerous experimental constraints presented by most ‘model’ species. In this study, we take advantage of the extraordinary tractability and versatility of a marine broadcast spawning invertebrate to overcome these challenges. We are able to simulate multi-generational (geometric mean) fitness among individual females assigned simultaneously to a polyandrous and monandrous mating strategy. Our approaches, which separate and account for the effects of sexual selection and pure bet-hedging scenarios, reveal that bet-hedging, in addition to sexual selection, can enhance evolutionary fitness in multiply mated females. In addition to offering a tractable experimental approach for addressing bet-hedging theory, our study provides key insights into the evolutionary ecology of sexual interactions.     

Trait positions for elevated invasiveness in adaptive ecological networks

Our ability to predict the outcome of invasion declines rapidly as non-native species progress through intertwined ecological barriers to establish and spread in recipient ecosystems. This is largely due to the lack of systemic knowledge on key processes at play as species establish self-sustaining populations within the invaded range. To address this knowledge gap, we present a mathematical model that captures the eco-evolutionary dynamics of native and non-native species interacting within an ecological network. The model is derived from continuous-trait evolutionary game theory (i.e., Adaptive Dynamics) and its associated concept of invasion fitness which depicts dynamic demographic performance that is both trait mediated and density dependent. Our approach allows us to explore how multiple resident and non-native species coevolve to reshape invasion performance, or more precisely invasiveness, over trait space. The model clarifies the role of specific traits in enabling non-native species to occupy realised opportunistic niches. It also elucidates the direction and speed of both ecological and evolutionary dynamics of residing species (natives or non-natives) in the recipient network under different levels of propagule pressure. The versatility of the model is demonstrated using four examples that correspond to the invasion of (i) a horizontal competitive community; (ii) a bipartite mutualistic network; (iii) a bipartite antagonistic network; and (iv) a multi-trophic food web. We identified a cohesive trait strategy that enables the success and establishment of non-native species to possess high invasiveness. Specifically, we find that a non-native species can achieve high levels of invasiveness by possessing traits that overlap with those of its facilitators (and mutualists), which enhances the benefits accrued from positive interactions, and by possessing traits outside the range of those of antagonists, which mitigates the costs accrued from negative interactions. This ‘central-to-reap, edge-to-elude’ trait strategy therefore describes the strategic trait positions of non-native species to invade an ecological network. This model provides a theoretical platform for exploring invasion strategies in complex adaptive ecological networks.

     

Female polymorphism, frequency dependence, and rapid evolutionary dynamics in natural populations

Rapid evolutionary change over a few generations has been documented in natural populations. Such changes are observed as organisms invade new environments, and they are often triggered by changed interspecific interactions, such as differences in predation regimes. However, in spite of increased recognition of antagonistic male-female mating interactions, there is very limited evidence that such intraspecific interactions could cause rapid evolutionary dynamics in nature. This is because ecological and longitudinal data from natural populations have been lacking. Here we show that in a color-polymorphic damselfly species, male-female mating interactions lead to rapid evolutionary change in morph frequencies between generations. Field data and computer simulations indicate that these changes are driven by sexual conflict, in which morph fecundities are negatively affected by frequency- and density-dependent male mating harassment. These frequency-dependent processes prevent population divergence by maintaining a female polymorphism in most populations. Although these results contrast with the traditional view of how sexual conflict enhances the rate of population divergence, they are consistent with a recent theoretical model of how females may form discrete genetic clusters in response to male mating harassment.     

High Altitude Frogs (Rana kukonoris) Adopt a Diversified Bethedging Strategy in the Face of Environmental Unpredictability

Environmental unpredictability can influence strategies of maternal investment among eggs within a clutch. Models predict that breeding females should adopt a diversified bet-hedging strategy in unpredictable environments, but empirical field evidence from Asia is scarce. Here we tested this hypothesis by exploring spatial patterns in egg size along an altitudinal gradient in a frog species(Rana kukunoris) inhabiting the Tibetan Plateau. Within-clutch variability in egg size increased as the environment became variable(e.g., lower mean monthly temperature and mean monthly rainfall at higher altitudes), and populations in environments with more unpredictable rainfall produced eggs that were smaller and more variable in size. We provide support for a diversified bet-hedging strategy in high-altitude environments, which experience dynamic weather patterns and therefore are of unpredictable environmental quality. This strategy may be an adaptive response to lower environmental quality and higher unpredictable environmental variance. Such a strategy should increase the likelihood of breeding success and maximize maternal lifetime fitness by producing offspring that are adapted to current environmental conditions. We speculate that in high-altitude environments prone to physical disturbance, breeding females are unable to consistently produce the optimal egg size due to physiological constraints imposed by environmental conditions(e.g., duration of the active season, food availability). Species and populations whose breeding strategies are adapted to cope with uncertain environmental conditions by adjusting offspring size and therefore quality show a remarkable degree of ability to cope with future climatic changes.     

Microbial seed banks: the ecological and evolutionary implications of dormancy

Dormancy is a bet-hedging strategy used by a wide range of taxa, including microorganisms. It refers to an organism's ability to enter a reversible state of low metabolic activity when faced with unfavourable environmental conditions. Dormant microorganisms generate a seed bank, which comprises individuals that are capable of being resuscitated following environmental change. In this Review, we highlight mechanisms that have evolved in microorganisms to allow them to successfully enter and exit a dormant state, and discuss the implications of microbial seed banks for evolutionary dynamics, population persistence, maintenance of biodiversity, and the stability of ecosystem processes.     

Optimality under noise: higher memory strategies for the alternating prisoner's dilemma.

The Alternating Prisoner's Dilemma is a variant of the iterated Prisoner's Dilemma in which the players alternate in the roles of actor and recipient. We searched for strategies which are "optimal" in the Alternating Prisoner's Dilemma with noise (a non-zero probability that a player's decision will be transmitted incorrectly). In order to achieve success against a variety of other strategies, a strategy must be "self-cooperating" (able to achieve mutual cooperation with its clone), "C-exploiting" (able to exploit unconditional cooperators), and "D-unexploitable" (able to resist exploitation by defectors). It must also have high evolutionary "dominance", a general measure of evolutionary performance which considers both resistance to invasion and the ability to invade other strategies. A strategy which meets these optimality criteria can evolve cooperation by invading a population of defectors and establishing a stable cooperative society. Most of the strategies commonly discussed in the Alternating Prisoner's Dilemma literature are low-memory strategies such as Tit For Tat, Pavlov, and Firm But Fair, but none of these strategies can simultaneously meet all of the optimality criteria. However, we discovered a class of higher memory "Firm Pavlov" strategies, which not only meet our stringent optimality criteria, but also achieve remarkable success in round-robin tournaments and evolutionary interactions. These higher memory strategies are friendly enough to cooperate with their clone, pragmatic enough to exploit unconditional cooperators, and wary enough to resist exploitation by defectors: they are truly "optimal under noise" in the Alternating Prisoner's Dilemma.     

The evolution of phenotypic polymorphism: randomized strategies versus evolutionary branching

A population is polymorphic when its members fall into two or more categories, referred to as alternative phenotypes. There are many kinds of phenotypic polymorphisms, with specialization in reproduction, feeding, dispersal, or protection from predators. An individual's phenotype might be randomly assigned during development, genetically determined, or set by environmental cues. These three possibilities correspond to a mixed strategy of development, a genetic polymorphism, and a conditional strategy. Using the perspective of adaptive dynamics, I develop a unifying evolutionary theory of systems of determination of alternative phenotypes, focusing on the relative possibilities for random versus genetic determination. The approach is an extension of the analysis of evolutionary branching in adaptive dynamics. It compares the possibility that there will be evolutionary branching, leading to genetic polymorphism, with the possibility that a mixed strategy evolves. The comparison is based on the strength of selection for the different outcomes. An interpretation of the resulting criterion is that genetic polymorphism is favored over random determination of the phenotype if an individual's heritable genotype is an adaptively advantageous cue for development. I argue that it can be helpful to regard genetic polymorphism as a special case of phenotypic plasticity.     

Comparing environmental and genetic variance as adaptive response to fluctuating selection

Phenotypic variation within populations has two sources: genetic variation and environmental variation. Here, we investigate the coevolution of these two components under fluctuating selection. Our analysis is based on the lottery model in which genetic polymorphism can be maintained by negative frequency-dependent selection, whereas environmental variation can be favored due to bet-hedging. In our model, phenotypes are characterized by a quantitative trait under stabilizing selection with the optimal phenotype fluctuating in time. Genotypes are characterized by their phenotypic offspring distribution, which is assumed to be Gaussian with heritable variation for its mean and variance. Polymorphism in the mean corresponds to genetic variance while the width of the offspring distribution corresponds to environmental variance. We show that increased environmental variance is favored whenever fluctuations in the selective optima are sufficiently strong. Given the environmental variance has evolved to its optimum, genetic polymorphism can still emerge if the distribution of selective optima is sufficiently asymmetric or leptokurtic. Polymorphism evolves in a diagonal direction in trait space: one type becomes a canalized specialist for the more common ecological conditions and the other type a de-canalized bet-hedger thriving on the less-common conditions. All results are based on analytical approximations, complemented by individual-based simulations.     

The danger within: the role of genetic,behavioural and ecological factors in population persistence of colour polymorphic species

Polymorphic species have been the focus of important work in evolutionary biology. It has been suggested that colour polymorphic species have specific evolutionary and population dynamics that enable them to persist through environmental changes better than less variable species. We suggest that recent empirical and theoretical work indicates that polymorphic species may be more vulnerable to extinction than previously thought. This vulnerability arises because these species often have a number of correlated sexual, behavioural, life history and ecological traits, which can have a simple genetic underpinning. When exacerbated by environmental change, these alternate strategies can lead to conflict between morphs at the genomic and population levels, which can directly or indirectly affect population and evolutionary dynamics. In this perspective, we identify a number of ways in which the nature of the correlated traits, their underpinning genetic architecture, and the inevitable interactions between colour morphs can result in a reduction in population fitness. The principles illustrated here apply to all kinds of discrete polymorphism (e.g. behavioural syndromes), but we focus primarily on colour polymorphism because they are well studied. We urge further empirical investigation of the genetic architecture and interactions in polymorphic species to elucidate the impact on population fitness.