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.     

Generalists versus specialists in fluctuating environments: a bet-hedging perspective

Bet-hedging evolves in fluctuating environments because long-term genotype success is determined by geometric (rather than arithmetic) mean fitness across generations. Diversifying bet-hedging produces different specialist offspring, whereas conservative bet-hedging produces similar generalist offspring. However, many fields, such as behavioral ecology and thermal physiology, typically consider specialist versus generalist strategies only in terms of maximizing arithmetic mean fitness benefits to individuals. Here we model how environmental variability affects optimal amounts of phenotypic variation within and among individuals to maximise genotype fitness, and we disentangle the effects of individual-level optimization and genotype-level bet-hedging by comparing long-term arithmetic versus geometric mean fitness. For traits with additive fitness effects within lifetimes (e.g. foraging-related traits), genotypes of similar generalists or diversified specialists perform equally well. However, if fitness effects are multiplicative within lifetimes (e.g. sequential survival probabilities), generalist individuals are always favored. In this case, geometric mean fitness optimization requires even more within-individual phenotypic variation than does arithmetic mean fitness, causing individuals to be more generalist than required to simply maximize their own expected fitness. In contrast to previous results in the bet-hedging literature, this generalist conservative bet-hedging effect is always favored over diversifying bet-hedging. These results link the evolution of behavioral and ecological specialization with earlier models of bet-hedging, and we apply our framework to a range of natural phenomena from habitat choice to host specificity in parasites.     

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.     

ADAPTIVE DYNAMICS OF DORMANCY DURATION VARIABILITY: EVOLUTIONARY TRADE-OFF AND PRIORITY EFFECT LEAD TO SUBOPTIMAL ADAPTATION

Many plants, insects, and crustaceans show within-population variability in dormancy length. The question of whether such variability corresponds to a genetic polymorphism of pure strategies or a mixed bet-hedging strategy, and how the level of phenotypic variability can evolve remain unknown for most species. Using an eco-genetic model rooted in a 25-year ecological field study of a Chestnut weevil, Curculio elephas , we show that its diapause-duration variability is more likely to have evolved by the spread of a bet-hedging strategy than by the establishment of a genetic polymorphism. Investigating further the adaptive dynamics of diapause-duration variability, we find two unanticipated patterns of general interest. First, there is a trade-off between the ability of bet-hedging strategies to persist on an ecological time scale and their ability to invade. The optimal strategy (in terms of persistence) cannot invade, whereas suboptimal bet-hedgers are good invaders. Second, we describe an original evolutionary dynamics where each bet-hedging strategy (defined by its rate of prolonged diapause) resists invasion by all others, so that the first type of bet-hedger to appear persists on an evolutionary time scale. Such "evolutionary priority effect" could drive the evolution of maladapted levels of diapause-duration variability.     

Intragenomic bet-hedging

The notion of intragenomic bet-hedging is introduced by modeling a system where one locus is seen as setting the “environment” for selection in a two-locus genetic system. Using a spatially structured simulation model I show that bet-hedging alleles with a lower mean fitness and lower variance of fitness across genotypes at a different locus can go to fixation, potentially providing a mechanism for the reduction of severe heterozygote advantage.     

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.     

Genetic variation in tolerance of competition and neighbour suppression in Arabidopsis thaliana

Intraspecific competitive interactions can profoundly influence phenotypic evolution. However, prior studies have rarely evaluated the evolutionary potential of the two components of competitive ability, tolerance of competition and suppression of neighbours. Here, we grow a set of 20 Arabidopsis thaliana recombinant inbred lines in three competitive treatments (noncompetitive, intra‐genotypic competition and inter‐genotypic competition) to examine if there is genetic variation for the components of competitive ability and whether neighbour relatedness has an effect on fitness. We find evidence for genetic variation in tolerance of competition and neighbour suppression and that these two competitive strategies are correlated, such that genotypes that tolerate competition will also strongly suppress neighbours. We further observe that the effect of neighbour relatedness on fitness of target individuals depends on neighbour identity, i.e. whether target individuals perform better when competing against self vs. nonself individuals depends on the genotypic identity of the nonself neighbour. The results are particularly relevant to evolutionary responses under multi‐level selection.     

Maintenance affects the stability of a two-tiered microbial 'food chain'?

Recent studies have shown that constraints on available resources may play an important role in the evolution of cooperation, especially when individuals do not posses the capacity to recognize other individuals, memory or other developed abilities, as it is the case of most unicellular organisms, algae or even plants. We analyze the evolution of cooperation in the case of a limiting resource, which is necessary for reproduction and survival. We show that, if the strategies determine a prisoner's dilemma, the outcome of the interactions may be modified by the limitation of resources allowing cooperators to invade the entire population. Analytic expressions for the region of cooperation are provided. Furthermore we derive expressions for the connection between fitness, as understood in evolutionary game theory, and resource exchanges, which may be of help to link evolutionary game theoretical results with resource based models.     

Are dormant plants hedging their bets? Demographic consequences of prolonged dormancy in variable environments

During the growing season, some individuals in perennial plant populations may remain alive belowground while others emerge. This phenomenon, known as prolonged dormancy, seems maladaptive, because prolonged dormancy delays growth and reproduction. However, prolonged dormancy may offer the benefit of safety while belowground, leading to the hypothesis that prolonged dormancy is a bet-hedging strategy. We evaluated this hypothesis using a 25-year demographic study of Astragalus scaphoides, an iteroparous perennial plant. First, we determined the relationship between prolonged dormancy and fitness using data from individuals in our population. This analysis showed that prolonged dormancy decreased arithmetic mean fitness and reduced variance in fitness. Geometric mean fitness was maximized at intermediate levels of prolonged dormancy. Empirical patterns of lifetime reproductive success confirm this relationship. We also compared fitness of plants in our population to hypothetical plants without prolonged dormancy, which generally revealed benefits of prolonged dormancy, even if plants could forgo prolonged dormancy without costs to other vital rates. Therefore, prolonged dormancy may indeed function as a bet-hedging strategy, but the benefits of remaining belowground outweigh the costs only for a subset of individuals. Bet hedging has been demonstrated in plants with simple life histories, such as annuals and monocarpic perennials; we present evidence that bet hedging may be important for plants with more complex life histories.     

Bet-Hedging Diapause Strategies in Stochastic Environments

In many insect species, adult emergence spreads over several years because of the existence of prolonged diapause in certain individuals. From stochastic models, we show that diversified bet-hedging strategies (mixed strategies with emergence after 1 or 2 yr) are more fit than simple diapause strategy (emergence after 1 yr) or fixed prolonged diapause strategy (emergence after 2 yr) in isolated chestnut weevil populations. This conclusion applies to a large range of survival rates in prolonged diapause and is insensitive to initial conditions, magnitude of temporal autocorrelation, distribution of demographic parameters, and quoted values of population size limitation. However, the shape of the fitness distribution as a function of prolonged diapause frequency changes greatly in the absence of population size limitation. Whatever the survival rate during prolonged diapause, we find that there is no genotypic advantage to extending diapause for all chestnut weevil larvae to more than 1 yr. Our models predict selection of bet-hedging strategies over a large range of prolonged diapause frequencies. This result is consistent with the existence of several mixed strategies in a population. Emergences after 3 yr are not crucial for selection or for the dynamics of mixed strategies in the chestnut weevil.     

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.     

Transgenerational Effects of Early Life Starvation on Growth,Reproduction, and Stress Resistance in Caenorhabditis elegans

Starvation during early development can have lasting effects that influence organismal fitness and disease risk. We characterized the long-term phenotypic consequences of starvation during early larval development in Caenorhabditis elegans to determine potential fitness effects and develop it as a model for mechanistic studies. We varied the amount of time that larvae were developmentally arrested by starvation after hatching (“L1 arrest”). Worms recovering from extended starvation grew slowly, taking longer to become reproductive, and were smaller as adults. Fecundity was also reduced, with the smallest individuals most severely affected. Feeding behavior was impaired, possibly contributing to deficits in growth and reproduction. Previously starved larvae were more sensitive to subsequent starvation, suggesting decreased fitness even in poor conditions. We discovered that smaller larvae are more resistant to heat, but this correlation does not require passage through L1 arrest. The progeny of starved animals were also adversely affected: Embryo quality was diminished, incidence of males was increased, progeny were smaller, and their brood size was reduced. However, the progeny and grandprogeny of starved larvae were more resistant to starvation. In addition, the progeny, grandprogeny, and great-grandprogeny were more resistant to heat, suggesting epigenetic inheritance of acquired resistance to starvation and heat. Notably, such resistance was inherited exclusively from individuals most severely affected by starvation in the first generation, suggesting an evolutionary bet-hedging strategy. In summary, our results demonstrate that starvation affects a variety of life-history traits in the exposed animals and their descendants, some presumably reflecting fitness costs but others potentially adaptive.     

Evolutionary Stability for Interactions among Kin under Quantitative Inheritance

The theory of evolutionarily stable strategies (ESS) predicts the long-term evolutionary outcome of frequency-dependent selection by making a number of simplifying assumptions about the genetic basis of inheritance. I use a symmetrized multilocus model of quantitative inheritance without mutation to analyze the results of interactions between pairs of related individuals and compare the equilibria to those found by ESS analysis. It is assumed that the fitness changes due to interactions can be approximated by the exponential of a quadratic surface. The major results are the following. (1) The evolutionarily stable phenotypes found by ESS analysis are always equilibria of the model studied here. (2) When relatives interact, one of the two conditions for stability of equilibria differs between the two models; this can be accounted for by positing that the inclusive fitness function for quantitative characters is slightly different from the inclusive fitness function for characters determined by a single locus. (3) The inclusion of environmental variance will in general change the equilibrium phenotype, but the equilibria of ESS analysis are changed to the same extent by environmental variance. (4) A class of genetically polymorphic equilibria occur, which in the present model are always unstable. These results expand the range of conditions under which one can validly predict the evolution of pairwise interactions using ESS analysis.     

Stochastic Fluctuations Through Intrinsic Noise in Evolutionary Game Dynamics

A one-step (birth–death) process is used to investigate stochastic noise in an elementary two-phenotype evolutionary game model based on a payoff matrix. In this model, we assume that the population size is finite but not fixed and that all individuals have, in addition to the frequency-dependent fitness given by the evolutionary game, the same background fitness that decreases linearly in the total population size. Although this assumption guarantees population extinction is a globally attracting absorbing barrier of the Markov process, sample trajectories do not illustrate this result even for relatively small carrying capacities. Instead, the observed persistent transient behavior can be analyzed using the steady-state statistics (i.e., mean and variance) of a stochastic model for intrinsic noise that assumes the population does not go extinct. It is shown that there is good agreement between the theory of these statistics and the simulation results. Furthermore, the ESS of the evolutionary game can be used to predict the mean steady state.     

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.     

Natural selection on fecundity variance in subdivided populations: kin selection meets bet hedging

In a series of seminal articles in 1974, 1975, and 1977, J. H. Gillespie challenged the notion that the "fittest" individuals are those that produce on average the highest number of offspring. He showed that in small populations, the variance in fecundity can determine fitness as much as mean fecundity. One likely reason why Gillespie's concept of within-generation bet hedging has been largely ignored is the general consensus that natural populations are of large size. As a consequence, essentially no work has investigated the role of the fecundity variance on the evolutionary stable state of life-history strategies. While typically large, natural populations also tend to be subdivided in local demes connected by migration. Here, we integrate Gillespie's measure of selection for within-generation bet hedging into the inclusive fitness and game theoretic measure of selection for structured populations. The resulting framework demonstrates that selection against high variance in offspring number is a potent force in large, but structured populations. More generally, the results highlight that variance in offspring number will directly affect various life-history strategies, especially those involving kin interaction. The selective pressures on three key traits are directly investigated here, namely within-generation bet hedging, helping behaviors, and the evolutionary stable dispersal rate. The evolutionary dynamics of all three traits are markedly affected by variance in offspring number, although to a different extent and under different demographic conditions.     

COEVOLUTION AS AN EVOLUTIONARY GAME

Coevolution is modeled as a continuous game where the fitness-maximizing strategy of an individual is assumed to be a function of the strategy of other individuals who are also under selection to maximize fitness. An evolutionary stable strategy (ESS) is sought such that no rare alternative strategies can invade the community. The approach can be used to model coevolution because the ESS may be composed of a coalition of more than one strategy. This work, by modeling frequency-dependent selection, extends the approach of Roughgarden (1976) which only considered density-dependent selection. In particular, we show that the coevolutionary model of Rummel and Roughgarden (1985) does contain frequency-dependent selection, and thus, their application of Roughgarden's criterion for evolutionary stability to a model for which it is not applicable leads to the erroneous conclusion that the ecological and evolutionary processes are in conflict. The utility of the game theoretic approach is illustrated by two examples. The first considers an ESS composed of a single strategy, the second an ESS composed of a coalition of two strategies. Evolution occurs on a frequency-dependent adaptive landscape. For this reason, the approach is appropriate for modeling competitive speciation (Rosenzweig, 1978). Also, the game theoretic approach is designed to combine the interplay between the background environment (including the biotic components) and the evolutionary potential of the populations or organisms. The actual application of this theory will require knowledge of both.     

Hedging one's evolutionary bets, revisited

Evolutionary bet-hedging involves a trade-off between the mean and variance of fitness, such that phenotypes with reduced mean fitness may be at a selective advantage under certain conditions. The theory of bet-hedging was first formulated in the 1970s, and recent empirical studies suggest that the process may operate in a wide range of plant and animal species.     

On the evolution of dispersal via heterogeneity in spatial connectivity

Dispersal has long been recognized as a mechanism that shapes many observed ecological and evolutionary processes. Thus, understanding the factors that promote its evolution remains a major goal in evolutionary ecology. Landscape connectivity may mediate the trade-off between the forces in favour of dispersal propensity (e.g. kin-competition, local extinction probability) and those against it (e.g. energetic or survival costs of dispersal). It remains, however, an open question how differing degrees of landscape connectivity may select for different dispersal strategies. We implemented an individual-based model to study the evolution of dispersal on landscapes that differed in the variance of connectivity across patches ranging from networks with all patches equally connected to highly heterogeneous networks. The parthenogenetic individuals dispersed based on a flexible logistic function of local abundance. Our results suggest, all else being equal, that landscapes differing in their connectivity patterns will select for different dispersal strategies and that these strategies confer a long-term fitness advantage to individuals at the regional scale. The strength of the selection will, however, vary across network types, being stronger on heterogeneous landscapes compared with the ones where all patches have equal connectivity. Our findings highlight how landscape connectivity can determine the evolution of dispersal strategies, which in turn affects how we think about important ecological dynamics such as metapopulation persistence and range expansion.     

On a genetic model of intraspecific competition and stabilizing selection

A genetic model is investigated in which two recombining loci determine the genotypic value of a quantitative trait additively. Two opposing evolutionary forces are assumed to act: stabilizing selection on the trait, which favors genotypes with an intermediate phenotype, and intraspecific competition mediated by that trait, which favors genotypes whose effect on the trait deviates most from that of the prevailing genotypes. Accordingly, fitnesses of genotypes have a frequency-independent component describing stabilizing selection and a frequency- and density-dependent component modeling competition. We study how the underlying genetics, in particular recombination rate and relative magnitude of allelic effects, interact with the conflicting selective forces and derive the resulting, surprisingly complex equilibrium patterns. We also investigate the conditions under which disruptive selection on the phenotypes can be observed and examine how much genetic variation can be maintained in such a model. We discovered a number of unexpected phenomena. For instance, we found that with little recombination the degree of stably maintained polymorphism and the equilibrium genetic variance can decrease as the strength of competition increases relative to the strength of stabilizing selection. In addition, we found that mean fitness at the stable equilibria is usually much lower than the maximum possible mean fitness and often even lower than the fitness at other, unstable equilibria. Thus, the evolutionary dynamics in this system are almost always nonadaptive.