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

AbstractBet-hedging evolves in fluctuating environments because long-term genotype success is determined by geometric mean fitness across generations. However, specialist versus generalist strategies are usually considered in terms of arithmetic mean fitness benefits to individuals, as in habitat or foraging preferences. We model how environmental variability affects phenotypic variation within and among individuals to maximize either 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, since geometric mean fitness favors greater within-individual phenotypic variation than arithmetic mean fitness does. Interestingly, this conservative bet-hedging effect outcompetes diversifying bet-hedging. These results link behavioral and ecological specialization and earlier models of bet-hedging, and thus apply to a range of natural phenomena from habitat choice to host specificity in parasites.Impact summaryWhich factors determine whether it is better to be a specialist or a generalist? Environmental fluctuations are becoming larger and more unpredictable across the globe as a result of human-induced rapid environmental change. A key challenge of evolutionary biology is therefore to understand how organisms adapt to such variation within and among generations, and currently represents a knowledge gap in evolutionary theory. Here we focus on how traits evolve when the (changing) environment determines the optimal value of a trait, so that the optimal trait value changes unpredictably over time. Our mathematical model investigates how much variation is optimal in a trait. We expect specialists (low within-individual trait variation) to be favored in stable environments, with generalists (high trait variation) favored in more variable environments. We show that the answer depends on whether we look from the point of view of the individual or all individuals of the same genotype. If an individual does well in the short term, but its offspring all experience a different environment and therefore do badly, the genotype as a whole is in trouble, and will not be favored in the long term. One solution to this problem could be to produce offspring with different trait values, to ensure that at least some of the offspring do well no matter the environmental conditions they grow up in. This “don’t put all your eggs in one basket” diversification strategy is well-known in some organisms, but how helpful is it if there is also some within-individual (i.e. generalist) trait variation? By answering these questions under various environmental scenarios, we link together many different concepts in evolutionary ecology and animal behavior, increasing our understanding about how organisms may cope with the current changes in environmental conditions around the world.

Sexual reproduction as bet-hedging

10.1101/103390 ◽

2017 ◽

Keyword(s):

Reproductive Success ◽

Sexual Reproduction ◽

Evolutionary Biology ◽

De Novo ◽

Geometric Mean ◽

Arithmetic Mean ◽

Bet Hedging ◽

Sexual And Asexual Reproduction ◽

Geometric Mean Fitness ◽

AbstractIn evolutionary biology, bet-hedging refers to a strategy that reduces the variance of reproductive success at the cost of reduced mean reproductive success. In unpredictably fluctuating environments, bet-hedgers benefit from higher geometric mean fitness despite having lower arithmetic mean fitness than their specialist competitors. We examine the extent to which sexual reproduction can be considered a type of bet-hedging, by clarifying past arguments, examining parallels and differences to evolutionary games, and by presenting a simple model examining geometric and arithmetic mean payoffs of sexual and asexual reproduction. Sex typically has lower arithmetic mean fitness than asex, while the geometric mean fitness can be higher if sexually produced offspring are not identical. However, asexual individuals that are heterozygotes can gain conservative bet-hedging benefits of similar magnitude while avoiding the costs of sex. This highlights that bet-hedging always has to be specified relative to the payoff structure of relevant competitors. It also makes it unlikely that sex, at least when associated with significant male production, evolves solely based on bet-hedging in the context of frequently and repeatedly occupied environmental states. Future work could usefully consider bet-hedging in open-ended evolutionary scenarios with de novo mutations.

Bet-hedging across generations can affect the evolution of variance-sensitive strategies within generations

Proceedings of The Royal Society B Biological Sciences ◽

10.1098/rspb.2019.2070 ◽

2019 ◽

Vol 286 (1916) ◽

pp. 20192070 ◽

Author(s):

Thomas R. Haaland ◽

Jonathan Wright ◽

Irja I. Ratikainen

Keyword(s):

Life Histories ◽

Environmental Variability ◽

Geometric Mean ◽

Simulation Models ◽

Arithmetic Mean ◽

Bet Hedging ◽

Individual Fitness ◽

Mean Fitness ◽

Selection For ◽

Independent Decision

In order to understand how organisms cope with ongoing changes in environmental variability, it is necessary to consider multiple adaptations to environmental uncertainty on different time scales. Conservative bet-hedging (CBH) represents a long-term genotype-level strategy maximizing lineage geometric mean fitness in stochastic environments by decreasing individual fitness variance, despite also lowering arithmetic mean fitness. Meanwhile, variance-prone (aka risk-prone) strategies produce greater variance in short-term payoffs, because this increases expected arithmetic mean fitness if the relationship between payoffs and fitness is accelerating. Using evolutionary simulation models, we investigate whether selection for such variance-prone strategies is counteracted by selection for bet-hedging that works to adaptively reduce fitness variance. In our model, variance proneness evolves in fine-grained environments (lower correlations among individuals in energetic state and/or payoffs), and with larger numbers of independent decision events over which resources accumulate prior to selection. Conversely, multiplicative fitness accumulation, caused by coarser environmental grain and fewer decision events selection, favours CBH via greater variance aversion. We discuss examples of variance-sensitive strategies in optimal foraging, migration, life histories and cooperative breeding using this bet-hedging perspective. By linking disparate fields of research studying adaptations to variable environments, we should be better able to understand effects of human-induced rapid environmental change.

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

Proceedings of The Royal Society B Biological Sciences ◽

10.1098/rspb.2014.1525 ◽

2015 ◽

Vol 282 (1798) ◽

pp. 20141525 ◽

Cited By ~ 28

Author(s):

Francisco Garcia-Gonzalez ◽

Yukio Yasui ◽

Jonathan P. Evans

Keyword(s):

Sexual Selection ◽

Evolutionary Ecology ◽

Multiple Mating ◽

Geometric Mean ◽

Bet Hedging ◽

Broadcast Spawning ◽

Geometric Mean Fitness ◽

Mean Fitness ◽

Risk Spreading ◽

Considerable Work

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 across generations can affect the evolution of variance-sensitive strategies within generations

10.1101/600452 ◽

2019 ◽

Author(s):

Thomas R. Haaland ◽

Jonathan Wright ◽

Irja I. Ratikainen

Keyword(s):

Life Histories ◽

Environmental Variability ◽

Geometric Mean ◽

Simulation Models ◽

Arithmetic Mean ◽

Bet Hedging ◽

Individual Fitness ◽

Mean Fitness ◽

Selection For ◽

Independent Decision

AbstractIn order to understand how organisms cope with ongoing changes in environmental variability it is important to consider all types of adaptations to environmental uncertainty on different time-scales. Conservative bet-hedging represents a long-term genotype-level strategy that maximizes lineage geometric mean fitness in stochastic environments by decreasing individual fitness variance, despite also lowering arithmetic mean fitness. Meanwhile, variance-prone (aka risk-prone) strategies produce greater variance in short-term payoffs because this increases expected arithmetic mean fitness if the relationship between payoffs and fitness is accelerating. Using two evolutionary simulation models, we investigate whether selection for such variance-prone strategies are counteracted by selection for bet-hedging that works to adaptively reduce fitness variance. We predict that variance-prone strategies will be favored in scenarios with more decision events per lifetime and when fitness accumulates additively rather than multiplicatively. In our model variance-proneness evolved in fine-grained environments (with lower correlations among individuals in energetic state and/or in payoffs when choosing the variable decision), and with larger numbers of independent decision events over which resources accumulate prior to selection. In contrast, geometric fitness accumulation caused by coarser environmental grain and fewer decision events prior to selection favors conservative bet-hedging via greater variance-aversion. We discuss examples of variance-sensitive strategies in optimal foraging, migration, life histories and cooperative breeding in light of these results concerning bet-hedging. By linking disparate fields of research studying adaptations to variable environments we should be more able to understand the effects in nature of human-induced rapid environmental change.Data depositionR code is available upon request.

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

Proceedings of The Royal Society B Biological Sciences ◽

10.1098/rspb.2014.0706 ◽

2014 ◽

Vol 281 (1787) ◽

pp. 20140706 ◽

Cited By ~ 39

Author(s):

Jeffrey K. Graham ◽

Myron L. Smith ◽

Andrew M. Simons

Keyword(s):

Neurospora Crassa ◽

Experimental Evolution ◽

Geometric Mean ◽

Environmental Uncertainty ◽

Evolutionary Analysis ◽

Bet Hedging ◽

Genetic Lineages ◽

Geometric Mean Fitness ◽

Mean Fitness ◽

Fitness Measures

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.

The Risk Premium on Ordinary Shares

British Actuarial Journal ◽

10.1017/s1357321700001094 ◽

1995 ◽

Vol 1 (2) ◽

pp. 251-330 ◽

Cited By ~ 5

Author(s):

A.D. Wilkie

Keyword(s):

Risk Premium ◽

Geometric Mean ◽

Arithmetic Mean ◽

Short Term ◽

Arithmetic Means ◽

Price Inflation ◽

Geometric Means ◽

True Model ◽

The Difference

ABSTRACTThe risk premium on ordinary shares is investigated, by studying the total returns on ordinary shares, and on both long-term and short-term fixed-interest investments over the period 1919 to 1994, and by analysing the various components of that return. The total returns on ordinary shares exceeded those on fixed-interest investments by over 5% p.a. on a geometric mean basis and by over 7% p.a. on an arithmetic mean basis, but it is argued that these figures are misleading, because most of the difference can be accounted for by the fact that price inflation turned out to be about 4.5% p.a. over the period, whereas investors had been expecting zero inflation.Quotations from contemporary authors are brought forward to demonstrate what contemporary attitudes were. Simulations are used along with the Wilkie stochastic asset model to show what the results would be if investors make various assumptions about the future, but the true model turns out to be different from what they expected. The differences between geometric means of the data and arithmetic means are shown to correspond to differences between using medians or means of the distribution of future returns, and it is suggested that, for discounting purposes, medians are the better measure.

Temporal variability and cooperative breeding: testing the bet-hedging hypothesis in the acorn woodpecker

Proceedings of The Royal Society B Biological Sciences ◽

10.1098/rspb.2015.1742 ◽

2015 ◽

Vol 282 (1816) ◽

pp. 20151742 ◽

Cited By ~ 14

Author(s):

Walter D. Koenig ◽

Eric L. Walters

Keyword(s):

Reproductive Success ◽

Cooperative Breeding ◽

Group Living ◽

Bet Hedging ◽

Hedging Strategy ◽

Ecological Conditions ◽

Variable Environments ◽

Melanerpes Formicivorus ◽

Cooperative breeding is generally considered an adaptation to ecological constraints on dispersal and independent breeding, usually due to limited breeding opportunities. Although benefits of cooperative breeding are typically thought of in terms of increased mean reproductive success, it has recently been proposed that this phenomenon may be a bet-hedging strategy that reduces variance in reproductive success (fecundity variance) in populations living in highly variable environments. We tested this hypothesis using long-term data on the polygynandrous acorn woodpecker ( Melanerpes formicivorus ). In general, fecundity variance decreased with increasing sociality, at least when controlling for annual variation in ecological conditions. Nonetheless, decreased fecundity variance was insufficient to compensate for reduced per capita reproductive success of larger, more social groups, which typically suffered lower estimated mean fitness. We did, however, find evidence that sociality in the form of larger group size resulted in increased fitness in years following a small acorn crop due to reduced fecundity variance. Bet-hedging, although not the factor driving sociality in general, may play a role in driving acorn woodpecker group living when acorns are scarce and ecological conditions are poor.

MUTATION-SELECTION BALANCE WITH STOCHASTIC SELECTION

Genetics ◽

10.1093/genetics/86.3.687 ◽

1977 ◽

Vol 86 (3) ◽

pp. 687-696

Author(s):

Daniel L Hartl

Keyword(s):

Allele Frequency ◽

Numerical Study ◽

Selection Process ◽

Diffusion Theory ◽

Geometric Mean ◽

Natural Populations ◽

Deterministic Models ◽

Geometric Mean Fitness ◽

Mean Fitness ◽

Stochastic Selection

ABSTRACT Diffusion theory has been used to analyze a model of mutation-selection balance in which the selection process is assumed to be stochastic in time. The limiting outcome of the mutation-stochastic selection process is determined qualitatively by the geometric mean fitnesses of the genotypes, and the conditions for fixation or polymorphism are similar to those that determine the outcome of the mutation-selection process when selection is constant. However, in the case of a completely recessive allele, detailed numerical study of the polymorphism associated with stochastic selection has shown that the average allele frequency maintained is greater than the equilibrium frequency expected when selection is constant, even when the geometric mean fitness of the recessive homozygotes is identical in the stochastic and deterministic models. Thus, allele frequencies in natural populations that are too high to be plausibly explained by a balance between mutation and constant selection can be accounted for if selection is stochastic.

The evolutionary advantage of heritable phenotypic heterogeneity

10.1101/028795 ◽

2015 ◽

Author(s):

Oana Carja ◽

Joshua B. Plotkin

Keyword(s):

Phenotypic Plasticity ◽

Environmental Changes ◽

Geometric Mean ◽

Adaptive Immune System ◽

Fixation Probability ◽

Infinite Population ◽

Evolutionary Changes ◽

Evolutionary Advantage ◽

Geometric Mean Fitness ◽

AbstractPhenotypic plasticity is an evolutionary driving force in diverse biological processes, including the adaptive immune system, the development of neoplasms, and the bacterial acquisition of drug resistance. It is essential, therefore, to understand the evolutionary advantage of an allele that confers cells the ability to express a range of phenotypes. Of particular importance is to understand how this advantage of phenotypic plasticity depends on the degree of heritability of non-genetically encoded phenotypes between generations, which can induce irreversible evolutionary changes in the population. Here, we study the fate of a new mutation that allows the expression of multiple phenotypic states, introduced into a finite population otherwise composed of individuals who can express only a single phenotype. We analyze the fixation probability of such an allele as a function of the strength of inter-generational phenotypic heritability, called memory, the variance of expressible phenotypes, the rate of environmental changes, and the population size. We find that the fate of a phenotypically plastic allele depends fundamentally on the environmental regime. In a constant environment, the fixation probability of a plastic allele always increases with the degree of phenotypic memory. In periodically fluctuating environments, by contrast, there is an optimum phenotypic memory that maximizes the probability of the plastic allele’s fixation. This same optimum value of phenotypic memory also maximizes geometric mean fitness, in steady state. We interpret these results in the context of previous studies in an infinite-population framework. We also discuss the implications of our results for the design of therapies that can overcome resistance, in a variety of diseases.

What kind of maternal effects are selected for in fluctuating environments?

10.1101/034546 ◽

2015 ◽

Author(s):

Stephen R Proulx ◽

Henrique Teotonio

Keyword(s):

Maternal Effects ◽

Developmental Plasticity ◽

Ancestral State ◽

Bet Hedging ◽

Alternative Phenotypes ◽

Fluctuating Environments ◽

Small Set ◽

The One ◽

Maternal Strategy

Adaptation to temporally fluctuating environments can be achieved through direct phenotypic evolution, by phenotypic plasticity (either developmental plasticity or trans-generational plasticity), or by randomizing offspring phenotypes (often called diversifying bet-hedging). Theory has long held that plasticity can evolve when information about the future environment is reliable while bet-hedging can evolve when mixtures of phenotypes have high average fitness (leading to low among generation variance in fitness). To date, no study has studied the evolutionary routes that lead to the evolution of randomized offspring phenotypes on the one hand or deterministic maternal effects on the other. We develop simple, yet general, models of the evolution of maternal effects and are able to directly compare selection for deterministic and randomizing maternal effects and can also incorporate the notion of differential maternal costs of producing offspring with alternative phenotypes. We find that only a small set of parameters allow bet hedging type strategies to outcompete deterministic maternal effects. Not only must there be little or no informative cues available, but also the frequency with which different environments are present must fall within a narrow range. By contrast, when we consider the joint evolution of the maternal strategy and the set of offspring phenotypes we find that deterministic maternal effects can always invade the ancestral state (lacking any form of maternal effect). The long-term ESS may, however, involve some form of offspring randomization, but only if the phenotypes evolve extreme differences in environment-specific fitness. Overall we conclude that deterministic maternal effects are much more likely to evolve than offspring randomization, and offspring randomization will only be maintained if it results in extreme differences in environment-specific fitness.