Practical Basis of the Geometric Mean Fitness and its Application to Risk-Spreading Behavior

2022 ◽  
Vol 84 (2) ◽  
Author(s):  
Takuya Okabe ◽  
Jin Yoshimura
Keyword(s):  
Geometric Mean ◽  
Spreading Behavior ◽  
Geometric Mean Fitness ◽  
Mean Fitness ◽  
Risk Spreading

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

2015 ◽  
Vol 282 (1798) ◽  
pp. 20141525 ◽  
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.

scholarly journals MUTATION-SELECTION BALANCE WITH STOCHASTIC SELECTION

Genetics ◽  
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.

scholarly journals The evolutionary advantage of heritable phenotypic heterogeneity

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 ◽  
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.

scholarly journals Mathematical equivalence of geometric mean fitness with probabilistic optimization under environmental uncertainty

2009 ◽  
Vol 220 (20) ◽  
pp. 2611-2617 ◽  
Author(s):  
Jin Yoshimura ◽  
Yumi Tanaka ◽  
Tatsuya Togashi ◽  
Shigehide Iwata ◽  
Kei-ichi Tainaka
Keyword(s):  
Geometric Mean ◽  
Environmental Uncertainty ◽  
Probabilistic Optimization ◽  
Geometric Mean Fitness ◽  
Mean Fitness ◽  
Mathematical Equivalence

scholarly journals Evolution of vertical and oblique transmission under fluctuating selection

2018 ◽  
Vol 115 (6) ◽  
pp. E1174-E1183 ◽  
Author(s):  
Yoav Ram ◽  
Uri Liberman ◽  
Marcus W. Feldman
Keyword(s):  
Vertical Transmission ◽  
Cultural Evolution ◽  
Cultural Transmission ◽  
Geometric Mean ◽  
Genetic Modifier ◽  
Fluctuating Selection ◽  
Selection Regime ◽  
Geometric Mean Fitness ◽  
Mean Fitness ◽  
Evolutionarily Stable

The evolution and maintenance of social learning, in competition with individual learning, under fluctuating selection have been well-studied in the theory of cultural evolution. Here, we study competition between vertical and oblique cultural transmission of a dichotomous phenotype under constant, periodically cycling, and randomly fluctuating selection. Conditions are derived for the existence of a stable polymorphism in a periodically cycling selection regime. Under such a selection regime, the fate of a genetic modifier of the rate of vertical transmission depends on the length of the cycle and the strength of selection. In general, the evolutionarily stable rate of vertical transmission differs markedly from the rate that maximizes the geometric mean fitness of the population. The evolution of rules of transmission has dramatically different dynamics from the more frequently studied modifiers of recombination, mutation, or migration.

scholarly journals Sexual reproduction as bet-hedging

2017 ◽  
Keyword(s):  
Reproductive Success ◽  
Sexual Reproduction ◽  
Evolutionary Biology ◽  
De Novo ◽  
Geometric Mean ◽  
Arithmetic Mean ◽  
Bet Hedging ◽  
Sexual And Asexual Reproduction ◽  
Geometric Mean Fitness ◽  
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.

scholarly journals Natural selection with varying selection coefficients – a haploid model

1973 ◽  
Vol 21 (2) ◽  
pp. 115-120 ◽  
Author(s):  
J. H. Gillespie
Keyword(s):  
Exact Solution ◽  
Natural Selection ◽  
Diffusion Equation ◽  
Waiting Time ◽  
Geometric Mean ◽  
Qualitative Result ◽  
Infinite Population ◽  
Geometric Mean Fitness ◽  
Mean Fitness ◽  
Drift Coefficient

SUMMARYIn this paper an exact treatment is given for the stochastic behaviour of the frequency of haploid genotypes in an infinite population when the absolute fitnesses of the two genotypes vary at random over generations. The main qualitative result from this treatment is that natural selection will favour that allele with the largest geometric mean fitness. A diffusion equation is derived whose solution is identical to the exact solution. The drift coefficient for this equation is of the form − μp(1 − p) + σ2(½ − p)p(l − p). This differs from the drift coefficient used in previous treatments of this problem and reduces the rate of quasi-fixation. Various waiting time problems are solved using this diffusion equation.

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

2014 ◽  
Vol 281 (1787) ◽  
pp. 20140706 ◽  
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.

scholarly journals Evolution of vertical and oblique transmission under fluctuating selection

2017 ◽  
Author(s):  
Yoav Ram ◽  
Uri Liberman ◽  
Marcus W. Feldman
Keyword(s):  
Vertical Transmission ◽  
Cultural Transmission ◽  
Geometric Mean ◽  
Genetic Modifier ◽  
Fluctuating Selection ◽  
Selection Regime ◽  
Geometric Mean Fitness ◽  
Mean Fitness ◽  
Evolutionarily Stable

Vertical and oblique cultural transmission of a dichotomous phenotype is studied under constant, periodic cycling, and randomly fluctuating selection. Conditions are derived for the existence of a stable polymorphism in a periodically cycling selection regime. Under such a selection regime, the fate of a genetic modifier of the rate of vertical transmission depends on the length of the cycle and the strength of selection. In general, the evolutionarily stable rate of vertical transmission differs markedly from the rate that maximizes the geometric mean fitness of the population. The evolution of rules of transmission has dramatically different dynamics from the more frequently studied modifiers of recombination, mutation, or migration.

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

2019 ◽  
Author(s):  
Thomas Ray Haaland ◽  
Jonathan Wright ◽  
Irja Ida Ratikainen
Keyword(s):  
Environmental Conditions ◽  
Geometric Mean ◽  
Arithmetic Mean ◽  
Bet Hedging ◽  
Trait Variation ◽  
Fitness Effects ◽  
Fluctuating Environments ◽  
Geometric Mean Fitness ◽  
Mean Fitness

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.

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