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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Evolutionary “Bet-Hedgers” under Cultivation: Investigating the Domestication of Erect Knotweed (<Emphasis Type="Italic">Polygonum erectum</Emphasis> L.) using Growth Experiments

Evolutionary “bet-hedging” refers to situations in which organisms sacrifice mean fitness for a reduction in fitness variance over time. Germination heteromorphism is the quintessential and most well understood bet-hedging strategy. It has evolved in many different plants, including the wild progenitors of some crops. Erect knotweed (Polygonum erectum L.), an annual seed crop, was cultivated in Eastern North America between c. 3000–600 BP. By c. 900 BP, cultivation had produced a domesticated subspecies with greatly reduced germination heteromorphism. Field observations and greenhouse experiments suggest that cultivation eliminated the selective pressures that maintain the bet-hedging strategy in erect knotweed, while humans also directly selected for seeds that germinated reliably and for seedlings with rapid early growth. The protection provided to erect knotweed under cultivation explains the domestication syndrome that has been observed in some archaeological assemblages. Dormancy provides seeds a means of escaping adverse conditions in time, while dispersal provides an escape in space. Farmers relaxed selective pressures that maintained dormancy in erect knotweed by acting as seed dispersers, spreading disturbance-adapted plants to predictable and protected environments, and by saving and exchanging seed stock. Experimental data also indicate that adaptive transgenerational plasticity may have been working against the expression of domestication syndrome in this case.     

The effects of serotiny and rainfall-cued dispersal on fitness: bet-hedging in the threatened cactus <Emphasis Type="Italic">Mammillaria pectinifera</Emphasis>

Serotiny—the retention of seeds in the mother plant for over a year—in unpredictable environments may increase the probability that at least some seeds are dispersed during favorable periods. Propagules may be expelled when environmental cues announcing favorable conditions occur, or be gradually released into the environment. This could be a bet-hedging strategy increasing the long-term fitness by reducing interannual variability in reproduction. However, the impact of seed retention on the population dynamics of serotinous species and its contribution to fitness has been barely explored under field conditions. We assessed these issues in the threatened Mammillaria pectinifera, a small globose cactus that gets established only in exceptionally rainy years. This species expels some seeds actively during unusually rainy periods, while dispersing others passively over several years. Dynamics of the seeds in the mother plant over two very contrasting years in terms of precipitation was incorporated into a stochastic matrix model. Seed retention was found to increase significantly the probability that some of the seeds retained in any given year are dispersed within a subsequent rainy period. Active seed-expulsion raises this probability even further. As expected in bet hedgers, seed retention increased fitness in the presence of temporal variability. Active fruit expulsion did not affect fitness, but reduced demographic stochasticity. The incomplete serotiny and fruit expulsion observed is the evolutionary outcome expected for the environment and life-history attributes of the species.     

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.     

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 via dispersal aids the evolution of plastic responses to unreliable cues

Adaptive plasticity is expected to evolve when informative cues predict environmental variation. However, plastic responses can be maladaptive even when those cues are informative, if prediction mistakes are shared across members of a generation. These fitness costs can constrain the evolution of plasticity when initial plastic mutants use of cues of only moderate reliability. Here, we model the barriers to the evolution of plasticity produced by these constraints and show that dispersal across a metapopulation can overcome them. Constraints are also lessened, though not eliminated, when plastic responses are free to evolve gradually and in concert with increased reliability. Each of these factors be viewed as a form of bet-hedging: by lessening correlations in the fates of relatives, dispersal acts as diversifying bet-hedging, while producing submaximal responses to a cue can be understood as a conservative bet-hedging strategy. While poor information may constrain the evolution of plasticity, the opportunity for bet-hedging may predict when that constraint can be overcome.     

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.     

Experimental evolution of bet hedging under manipulated environmental uncertainty in Neurospora crassa

All organisms are faced with environmental uncertainty. Bet-hedging theory expects unpredictable selection to result in the evolution of traits that maximize the geometric-mean fitness even though such traits appear to be detrimental over the shorter term. Despite the centrality of fitness measures to evolutionary analysis, no direct test of the geometric-mean fitness principle exists. Here, we directly distinguish between predictions of competing fitness maximization principles by testing Cohen''s 1966 classic bet-hedging model using the fungus Neurospora crassa. The simple prediction is that propagule dormancy will evolve in proportion to the frequency of ‘bad’ years, whereas the prediction of the alternative arithmetic-mean principle is the evolution of zero dormancy as long as the expectation of a bad year is less than 0.5. Ascospore dormancy fraction in N. crassa was allowed to evolve under five experimental selection regimes that differed in the frequency of unpredictable ‘bad years’. Results were consistent with bet-hedging theory: final dormancy fraction in 12 genetic lineages across 88 independently evolving samples was proportional to the frequency of bad years, and evolved both upwards and downwards as predicted from a range of starting dormancy fractions. These findings suggest that selection results in adaptation to variable rather than to expected environments.     

Adaptive significance of amylase polymorphism in <Emphasis Type="Italic">Drosophila</Emphasis>: Effect of substrates with different carbohydrate composition on some life-history traits of <Emphasis Type="Italic">Drosophila subobscura</Emphasis>

The Amy locus polymorphism of Drosophila subobscura is used as a model system for an experimental population genetic study of adaptive significance of α-amylase activity on substrates of different carbohydrate compositions. So far, fitness components have not commonly been included in ecological-genetic studies of α-amylase polymorphism in this species. In the present paper, fitness components are analyzed in relation to different amylase activities in D. subobscura individuals homozygous for the “slow” and the “fast” Amy allele, associated with substrates of different carbohydrate compositions. The results indicate a significant effect of substrate carbohydrate composition on fitness components of the genotypes homozygous for S or F Amy allele in D. subobscura through their enzyme activity. The text was submitted by the authors in English.     

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...     

HYPOTHESES FOR THE PRODUCTION OF EXCESS ZYGOTES: MODELS OF BET-HEDGING AND SELECTIVE ABORTION

Two hypotheses can explain the overproduction of zygotes. Bet-hedging assumes that optimal brood size varies unpredictably among breeding attempts. Excess zygotes are produced so that the number of independent offspring can be flexibly adjusted downward to the optimum number for that attempt. Selective abortion suggests that parents overproduce zygotes, identify those with the highest fitness expectations, then kill or abandon those with lower fitness in order to concentrate investment in those with the best prospects. Both hypotheses for the overproduction of zygotes work in principle, alone or together, and can lead to impressive levels of zygote overproduction. For both hypotheses, high levels of zygote overproduction are only attained when the unit cost of an aborted embryo is low relative to the cost of an independent offspring. Under bet-hedging, it is also important that the variability of environmental conditions important for breeding success be high. The two hypotheses together make clear when a parent could increase its fitness by killing or abandoning its offspring.     

Mate choice for major histocompatibility complex genetic divergence as a bet-hedging strategy in the Atlantic salmon (Salmo salar)

Major histocompatibility complex (MHC)-dependent mating preferences have been observed across vertebrate taxa and these preferences are expected to promote offspring disease resistance and ultimately, viability. However, little empirical evidence linking MHC-dependent mate choice and fitness is available, particularly in wild populations. Here, we explore the adaptive potential of previously observed patterns of MHC-dependent mate choice in a wild population of Atlantic salmon (Salmo salar) in Québec, Canada, by examining the relationship between MHC genetic variation and adult reproductive success and offspring survival over 3 years of study. While Atlantic salmon choose their mates in order to increase MHC diversity in offspring, adult reproductive success was in fact maximized between pairs exhibiting an intermediate level of MHC dissimilarity. Moreover, patterns of offspring survival between years 0+ and 1+, and 1+ and 2+ and population genetic structure at the MHC locus relative to microsatellite loci indicate that strong temporal variation in selection is likely to be operating on the MHC. We interpret MHC-dependent mate choice for diversity as a likely bet-hedging strategy that maximizes parental fitness in the face of temporally variable and unpredictable natural selection pressures.     

Adaptive values of genotypes ofArabidopsis thaliana (L.)Heynh. Carrying one mutant allele on different genetic backgrounds

InArabidopsis thaliana the relative measure of Darwinian fitness — the adaptive values of the two homozygotes related to the reference heterozygous genotype in one locus system were estimated on the original and on three changed genetic backgrounds. It was stated that the change of the genetic background with different gene-modifiers of the pleiotropic effect of a given gene on fitness may be important for the existence of mutations in populations, especially if we take into consideration not only the selection pressure against the homozygotes but also a certain real percentage of outcrossing. Special attention is paid to statistical elaboration of the experimental data.