Short‐term insurance versus long‐term bet‐hedging strategies as adaptations to variable environments

Understanding how organisms adapt to environmental variation is a key challenge of biology. Central to this are bet‐hedging strategies that maximize geometric mean fitness across generations, either by being conservative or diversifying phenotypes. Theoretical models have identified environmental variation across generations with multiplicative fitness effects as driving the evolution of bet‐hedging. However, behavioral ecology has revealed adaptive responses to additive fitness effects of environmental variation within lifetimes, either through insurance or risk‐sensitive strategies. Here, we explore whether the effects of adaptive insurance interact with the evolution of bet‐hedging by varying the position and skew of both arithmetic and geometric mean fitness functions. We find that insurance causes the optimal phenotype to shift from the peak to down the less steeply decreasing side of the fitness function, and that conservative bet‐hedging produces an additional shift on top of this, which decreases as adaptive phenotypic variation from diversifying bet‐hedging increases. When diversifying bet‐hedging is not an option, environmental canalization to reduce phenotypic variation is almost always favored, except where the tails of the fitness function are steeply convex and produce a novel risk‐sensitive increase in phenotypic variance akin to diversifying bet‐hedging. Importantly, using skewed fitness functions, we provide the first model that explicitly addresses how conservative and diversifying bet‐hedging strategies might coexist.     

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.     

Fluctuating natural selection accounts for the evolution of diversification bet hedging

Natural environments are characterized by unpredictability over all time scales. This stochasticity is expected on theoretical grounds to result in the evolution of ‘bet-hedging’ traits that maximize the long term, or geometric mean fitness even though such traits do not maximize fitness over shorter time scales. The geometric mean principle is thus central to our interpretation of optimality and adaptation; however, quantitative empirical support for bet hedging is lacking. Here, I report a quantitative test using the timing of seed germination—a model diversification bet-hedging trait—in Lobelia inflata under field conditions. In a phenotypic manipulation study, I find the magnitude of fluctuating selection acting on seed germination timing—across 70 intervals throughout five seasons—to be extreme: fitness functions for survival are complex and multimodal within seasons and significantly dissimilar among seasons. I confirm that the observed magnitude of fluctuating selection is sufficient to account for the degree of diversification behaviour characteristic of individuals of this species. The geometric mean principle has been known to economic theory for over two centuries; this study now provides a quantitative test of optimality of a bet-hedging trait in nature.     

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.     

An empirical test of bet-hedging polyandry hypothesis in the field cricket Gryllus bimaculatus

Journal of Ethology - Theory shows that polyandry (mating with multiple males within a reproductive season) works as bet-hedging to increase the geometric mean fitness (GMF) of polyandrous genotype...     

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.     

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 evolution of bet-hedging adaptations to rare scenarios

When faced with a variable environment, organisms may switch between different strategies according to some probabilistic rule. In an infinite population, evolution is expected to favor the rule that maximizes geometric mean fitness. If some environments are encountered only rarely, selection may not be strong enough for optimal switching probabilities to evolve. Here we calculate the evolution of switching probabilities in a finite population by analyzing fixation probabilities of alleles specifying switching rules. We calculate the conditions required for the evolution of phenotypic switching as a form of bet-hedging as a function of the population size N, the rate theta at which a rare environment is encountered, and the selective advantage s associated with switching in the rare environment. We consider a simplified model in which environmental switching and phenotypic switching are one-way processes, and mutation is symmetric and rare with respect to the timescale of fixation events. In this case, the approximate requirements for bet-hedging to be favored by a ratio of at least R are that sN>log(R) and thetaN>square root R .     

Why does a grasshopper have fewer,larger offspring at its range limits?

Analysis of size of offspring reared through three laboratory generations from populations of the field grasshopper Chorthippus brunneus from 27 sites around the British Isles showed that offspring were larger towards the cooler-wetter conditions in the western and northern limits of the range. This variation had a significant genetic component. There was a trade-off between clutch size and offspring size between and within populations. Under favourable thermal and feeding conditions maternal fitness was optimal when individuals produced the largest clutches of the smallest eggs, but under poor conditions maternal fitness was optimal when individuals produced small clutches of very large offspring. Calculation of geometric mean fitness over time indicated that having larger offspring near to the edge of the range could be advantageous as a conservative risk-spreading strategy. As well as geographic variation in egg size, significant environment-genotype interactions in egg size in relation to temperature were observed.     

Spatial variation in egg size and egg number reflects trade-offs and bet-hedging in a freshwater fish

1.?Maternal reproductive investment is thought to reflect a trade-off between offspring size and fecundity, and models generally predict that mothers inhabiting adverse environments will produce fewer, larger offspring. More recently, the importance of environmental unpredictability in influencing maternal investment has been considered, with some models predicting that mothers should adopt a diversified bet-hedging strategy whilst others a conservative bet-hedging strategy. 2.?We explore spatial egg size and fecundity patterns in the freshwater fish southern pygmy perch (Nannoperca australis) that inhabits a diversity of streams along gradients of environmental quality, variability and predictability. 3.?Contrary to some predictions, N.?australis populations inhabiting increasingly harsh streams produced more numerous and smaller eggs. Furthermore, within-female egg size variability increased as environments became more unpredictable. 4.?We argue that in harsh environments or those prone to physical disturbance, sources of mortality are size independent with offspring size having only a minor influence on offspring fitness. Instead, maternal fitness is maximized by producing many small eggs, increasing the likelihood that some offspring will disperse to permanent water. We also provide empirical support for diversified bet-hedging as an adaptive strategy when future environmental quality is uncertain and suggest egg size may be a more appropriate fitness measure in stable environments characterized by size-dependent fitness. These results likely reflect spatial patterns of adaptive plasticity and bet-hedging in response to both predictable and unpredictable environmental variance and highlight the importance of considering both trait averages and variance. 5.?Reproductive life-history traits can vary predictably along environmental gradients. Human activity, such as the hydrological modification of natural flow regimes, alters the form and magnitude of these gradients, and this can have both ecological and evolutionary implications for biota adapted to now non-existent natural environmental heterogeneity.     

EVOLUTION OF GENERALISTS AND SPECIALISTS IN SPATIALLY HETEROGENEOUS ENVIRONMENTS

Quantitative genetic models are used to investigate the evolution of generalists and specialists in a coarse-grained environment with two habitat types when there are costs attached to being a generalist. The outcomes for soft and hard selection models are qualitatively different. Under soft selection (e.g., for juvenile or male-reproductive traits) the population evolves towards the single peak in the adaptive landscape. At equilibrium, the population mean phenotype is a compromise between the reaction that would be optimal in both habitats and the reaction with the lowest cost. Furthermore, the equilibrium is closer to the optimal phenotype in the most frequent habitat, or the habitat in which selection on the focal trait is stronger. A specialist genotype always has a lower fitness than a generalist, even when the costs are high. In contrast, under hard selection (e.g., for adult or female-reproductive traits) the adaptive landscape can have one, two, or three peaks; a peak represents a population specialized to one habitat, equally adapted to both habitats, or an intermediate. One peak is always found when the reaction with the lowest cost is not much different from the optimal reaction, and this situation is similar to the soft selection case. However, multiple peaks are present when the costs become higher, and the course of evolution is then determined by initial conditions, and the region of attraction of each peak. This implies that the evolution of specialization and phenotypic plasticity may not only depend on selection regimes within habitats, but also on contingent, historical events (migration, mutation). Furthermore, the evolutionary dynamics in changing environments can be widely different for populations under hard and soft selection. Approaches to measure costs in natural and experimental populations are discussed.     

Specialist and generalist herbivores exert opposing selection on a chemical defense

* Plant defense traits often show high levels of genetic variation, despite clear impacts on plant fitness. This variation may be partly maintained by trade-offs in the defense against multiple herbivore species, for example between generalists and coevolved specialists. Despite a long-standing discussion in the literature on the subject, no study to date has specifically manipulated specialist and generalist herbivores independently of one another to determine whether the two guilds exert opposing selection pressures on specific defensive traits. * In two separate experiments, the dominant specialist and generalist herbivores of Brassica nigra were independently manipulated to test whether the composition of the herbivore community altered the direction of selection on a major defensive trait of the plant, sinigrin concentration. * It was found that generalist damage was negatively correlated but specialist loads were positively correlated with increasing sinigrin concentrations; and sinigrin concentration was favored when specialists were removed, disfavored (past an intermediate point) when generalists were removed and selectively neutral when plants faced both generalists and specialists.     

Among‐individual heterogeneity in maternal behaviour and physiology affects reproductive allocation and offspring life‐history traits in the garter snake Thamnophis elegans

Accumulating evidence suggests that within‐individual plasticity of behavioural and physiological traits is limited, resulting in stable among‐individual differences in these aspects of the phenotype. Furthermore, these traits often covary within individuals, resulting in a continuum of correlated phenotypic variation among individuals within populations and species. This heterogeneity, in turn, affects individual fitness and can have cross‐generational effects. Patterns of trait covariation, among‐individual differences, and subsequent fitness consequences have long been recognized in reptiles. Here, we provide a test of patterns of among‐individual heterogeneity in behaviour and physiology and subsequent effects on reproduction and offspring fitness in the garter snake Thamnophis elegans. We find that measures of activity levels vary among individuals and are consistent within individuals in reproductive female snakes, indicating stable behavioural phenotypes. Blood hormone and glucose concentrations are not as stable within individuals, indicating that these traits do not describe consistent physiological phenotypes. Nonetheless, the major axes of variation in maternal traits describe behavioural and physiological phenotypes that interact to predict offspring body condition and mass at birth. This differential allocation of energy to offspring, in turn, strongly influences subsequent offspring growth and survival. This pattern suggests the potential for strong selection on phenotypes defined by behaviour–physiology interactions.     

Evolution and population dynamics in stochastic environments

Inter-generational temporal variability of the environment is important in the evolution and adaptation of phenotypic traits. We discuss a population-dynamic approach which plays a central role in the analysis of evolutionary processes. The basic principle is that the phenotypes with the greatest long-term average growth rate will dominate the entire population. The calculation of longterm average growth rates for populations under temporal stochasticity can be highly cumbersome. However, for a discrete non-overlapping population, it is identical to the geometric mean of the growth rates (geometric mean fitness), which is usually different from the simple arithmetic mean of growth rates. Evolutionary outcomes based on geometric mean fitness are often very different from the predictions based on the usual arithmetic mean fitness. In this paper we illustrate the concept of geometric mean fitness in a few simple models. We discuss its implications for the adaptive evolution of phenotypes, e.g. foraging under predation risks and clutch size. Next, we present an application: the risk-spreading egg-laying behaviour of the cabbage white butterfly, and develop a two-patch population dynamic model to show how the optimal solution diverges from the ssual arithmetic mean approach. The dynamics of these stochastic models cannot be predicted from the dynamics of simple deterministic models. Thus the inclusion of stochastic factors in the analyses of populations is essential to the understanding of not only population dynamics, but also their evolutionary dynamics.     

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.     

Trophic niche width,offspring condition and immunity in a raptor species

Strategies developed by organisms to maximize foraging efficiency have a strong influence on fitness. The way in which the range of food resources is exploited has served to classify species, populations and individuals from more specialist (narrow trophic niche) to more generalist (broad trophic niche). Recent studies have provided evidence that many of the considered generalist species/populations are actually composed of different specialist individuals (individual specialization). Even the existence of generalism as an adaptive strategy has been questioned. In this study, we investigated the relationship between trophic niche width, individual quality and offspring viability in a population of common kestrel Falco tinnunculus during 4 years. We showed that the diet of kestrels varied significantly among years and that individuals of better quality fed their offspring with a higher diversity of prey species and a higher amount of food. Moreover, body condition and immune response of nestlings were positively correlated with diversity of prey delivered by parents. Our study suggests that generalism has the potential to increase fitness and that broadening the trophic niche may be an adaptive strategy in unpredictable environments.     

Evolution of variance in offspring number: The effects of population size and migration

It was shown by Gillespie [1974. Am. Nat. 108, 145–151], that if two genotypes produce the same average number of offspring on but have a different variance associated within each generation, the genotype with a lower variance will have a higher effective fitness. Specifically, the effective fitness is {ei65-1}, where w is the mean fitness, {ei65-2} is the variance in offspring number, and N is the total population size. The model also predicts that if a strategy has a higher arithmetic mean fitness and a higher variance than the competitor, the outcome of selection will depend on the population size (with larger population sizes favoring the highvariance, high-mean genotype). This suggests that for metapopulation sizes favoring the high-variance, high-mean genotype). This suggests that for metapopulations with large numbers of (relatively) small demes, a strategy with lower variance and lower mean may be favored if the migration rate is low while higher migration rates (consistent with a larger effective population size) favor the opposite strategy. Individual-based simulation confirms that this is indeed the case for an island model of migration, though the effect of migration differs greatly depending on whether migration precedes or follows selection. It is noted in the appendix that while Gillespie [1974. Am. Nat. 108, 145–151] does seem to be heuristically accurate, it is not clear that the definition of effective fitness follows from his derivation.     

Dealing with stochastic environmental variation in space and time: bet hedging by generalist,specialist, and diversified strategies

Building on previous work, we derive an optimization model for a two-state stochastic environment and evaluate the fitnesses of five reproductive strategies across generations. To do this, we characterize spatiotemporal variation and define grain (=patch) size as the scale of fitness autocorrelation. Fitness functions of environmental condition are Gaussian. The strategies include two specialists on each of the environmental conditions; two generalists that each fare equally well under both conditions, but one (a conservative bet hedger) optimizes the shape of the fitness function; and a diversified bet hedger producing an optimal mix of the two specialists within individual broods. When the environment is primarily in one of the two states, the specialist on that state achieves the highest fitness. In the more interesting situation where the two environments are equally prevalent in the long term, with low-moderate environmental variation, a generalist strategy (that copes with both states well) does best. Higher variation favors diversified bet hedgers, or surprisingly, specialists, depending mainly on whether spatial or temporal variation predominates. These strategies reduce variance in fitness and optimize the distribution of offspring among patches differently: specialists by spreading offspring among many independently varying patches, while diversified bet hedgers put all offspring into a few patches or a single patch. We distinguish features consistent with strategies like diversified bet hedgers that spread risk in time from features linked to strategies like specialists that spread risk in space. Finally, we present testable hypotheses arising from this study and suggest directions for future work.     

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.     

Antagonistic multilevel selection on size and architecture in variable density settings

In some ecological settings, an individual's fitness depends on both its own phenotype (individual-level selection) as well as the phenotype of the individuals with which it interacts (group-level selection). Using contextual analysis to measure multilevel selection in experimental stands of Arabidopsis thaliana, we detected significant linear selection that reversed across individual versus group levels for two composite phenotypic traits, "size" and "elongation." In both cases, selection at the individual level acted to increase values of these traits, presumably due to their positive effect on resource acquisition. Group selection favored decreased values of the same traits. Nonlinear selection was weak but significant in several cases, including stabilizing selection on developmental rate; individuals with very rapid development likely had lower than average fitness due to their reduced resource level at reproduction, while very delayed reproduction may have resulted in lower fitness if prolonged competition for resources reduced overall environmental quality and fitness of all individuals in a group. Under this scenario, stabilizing selection on individual traits is evidence of selection at the group level. Significant density-dependent selection suggests that a threshold density must be reached before group selection acts. Below this threshold, selection at the individual level affects phenotypic evolution more strongly than group selection. A second experiment measured multilevel selection in progeny stands of the original experimental plants. Multilevel selection again acted antagonistically on a composite trait that included size and elongation as well as on an architectural trait, branch production. The magnitude of individual versus group selection was relatively similar in the progeny generation, and the observed balance of individual versus group selection across densities is generally consistent with the hypotheses that multilevel selection can contribute to phenotypic evolution and to important demographic phenomena, including soft selection and the "law of constant yield."