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Results for “evolutionarily stable strategy”

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PubMed2002

The contribution of haploids, diploids and clones to fine-scale population structure in the seaweed Cladophoropsis membranacea (Chlorophyta).

Local populations of Cladophoropsis membranacea exist as mats of coalesced thalli composed of free-living haploid and diploid plants including clonally reproduced plants of either phase. None of the phases are morphologically distinguishable. We used eight microsatellite loci to explore clonality and fine-scale patch structure in C. membranacea at six sites on the Canary Islands. Mats were always composites of many individuals; not single, large clones. Haploids outnumbered diploids at all sites (from 2:1 to 10:1). In both haploid and diploid plants, genetic diversity was high and there was no significant difference in allele frequencies. Significant heterozygote deficiencies were found in the diploid plants at five out of six sites and linkage disequilibrium was associated with the haploid phase at all sites. Short dispersal distances of gametes/spores and small effective population sizes associated with clonality probably contribute to inbreeding. Spatial autocorrelation analysis revealed that most clones were found within a radius of approximately 60 cm and rarely further than 5 m. Dominance of the haploid phase may reflect seasonal shifts in the relative frequencies of haploids and diploids, but may alternatively reflect superiority of locally adapted and competitively dominant, haploid clones; a strategy that is theoretically favoured in disturbed environments. Although sexual reproduction may be infrequent in C. membranacea, it is sufficient to maintain both life history phases and supports theoretical modelling studies that show that haploid-diploid life histories are an evolutionarily stable strategy.

Chlorophyta↗

PubMed1985

Genetical ESS-models. I. Concepts and basic model.

Evolutionarily Stable Strategies (ESS) in phenotypic models are used to explain the evolution of animal interactive behaviour. As the behavioural features under consideration are assumed to be genetically determined, the question arises how underlying a genetical system might affect the results of phenotypic ESS-models. This question can be fully treated in terms of ESS-theory. A method of designing Genetical ESS-Models is proposed, which transfers the question of evolutionary stability to a "lower" level, the genetical basis. Genetical ESS-models - although nonlinear even in the simplest cases - can be analysed in a way that is familiar to ESS-theorists and yield immediate results on gene pool ESSs, which then may or may not maintain ESSs on the phenotypic level. Moreover, general results can be obtained to characterize evolutionarily stable gene pool states and their interrelation with commonsense, phenotypic ESSs. This part of the article presents the basic concepts and an outline of the method of genetical ESS-models. It gives, as a demonstration, a complete analysis for phenotypic two-strategy models (linear or nonlinear) based on a diploid, diallelic single-locus system under random mating. The results in this case suggest that a phenotypic ESS should indeed be expected to evolve but, maybe, only after passing through a succession of temporarily stable states.

Animals↗

PubMed2004

The evolutionary economics of immunity.

How much of its resources should an individual invest in a costly immune system? In this article, we apply an evolutionarily stable strategy analysis to an epidemic model to answer this question. On the one hand, an investment in immune function confers protection to infectious agents by reducing host susceptibility, pathogen virulence, or the length of the infectious period. On the other hand, an immune system is costly since it absorbs resources that otherwise might be invested in increasing the host's fertility or longevity. In addition, an active immune system may be able to clear pathogens efficiently but at the same time may result in immunopathology. By means of a reproductive value approach, we show how to compare the costs and benefits of an immune system systematically and how to derive the evolutionarily stable level of immune function. We then apply these methods to various plausible scenarios. The analysis reveals that the relationship between the life span of an organism and the optimal level of investment in immune function is less straightforward than one might expect. First, the prevalence of infection is reduced to the lowest possible level only under special circumstances. Second, members of a long-lived species do not necessarily have to invest more in immune function than those of a short-lived species. In fact, the opposite may be true. Third, the outcome of evolution can be contingent on the initial conditions. Depending on its initial investment strategy, a population may evolve to a state where very much or almost nothing is invested in a costly immune system.

Animals↗

PubMed1999

Retaliatory cuckoos and the evolution of host resistance to brood parasites.

We present a dynamic model of the evolution of host resistance to avian brood parasites, when the latter can retaliate against hosts that reject parasitic eggs. In a verbal model, Zahavi (1979, American Naturalist, 113, 157-159) suggested that retaliatory cuckoos might prevent the evolution of host resistance by reducing the reproductive success of rejecter hosts (i.e. by destroying their eggs or nestlings). Here we develop a model based on the association between the great spotted cuckoo, Clamator glandarius, and its main host, the European magpie, Pica pica, because this is the only system that has provided supportive evidence, to date, for the existence of retaliatory behaviour. Our aims were (1) to derive the conditions for invasion of the retaliation strategy in a nonretaliatory parasite population and (2) to investigate the consequences of retaliation for the evolution of host defence. If we assume a cost of discrimination for rejecter hosts in the absence of parasitism, and a cost paid by a retaliator for monitoring nests, our model shows cyclical dynamics. There is no evolutionarily stable strategy, and populations of both hosts and parasites will cycle indefinitely, the period of the cycles depending on mutation and/or migration rate. A stable polymorphism of acceptors and rejecters occurs only when parasites are nonretaliators. The spread of retaliator parasites drives rejecter hosts to extinction. Copyright 1999 The Association for the Study of Animal Behaviour.

Journal Article↗

PubMed1997

Sex, the Prisoner's Dilemma Game, and the evolutionary inevitability of cooperation.

It will be a universal feature of sexual populations that individuals prefer mates with typical rather than rare characteristics--essentially because most mutations reduce fitness. This is termed koinophilia. Koinophilia will also apply to behaviour. In particular, individuals will prefer mates that behave in social interactions that follow whatever rules are common in that population. Suppose that individuals interact in situations which can be represented by the Iterated Prisoner's Dilemma Game (IPD). If koinophilia is ignored, previous authors have shown that it is hard to find an evolutionarily stable strategy, and that strategies cycle indefinitely. However, if koinophilia is included, it has the effect of increasing the fitness of whatever happens to be the common strategy. This, in turn, has the effect of stabilizing almost any strategy (that has, for whatever reason, become the local norm) in the IPD. Different, partially isolated groups will thus become evolutionarily trapped in different behaviours, which are defended against alternative strategies originating through mutation or immigration. Groups that happen, by chance, to reach a cooperative strategy will be fitter, as groups, than those that reach defection (even though, in one-to-one encounters, it is the selfish individual who always wins). The ultimate result will be the replacement of selfish groups by cooperative groups.

Animals↗

PubMed2004

Evolution of size-dependent flowering in a variable environment: partitioning the effects of fluctuating selection.

In a stochastic environment, two distinct processes, namely nonlinear averaging and non-equilibrium dynamics, influence fitness. We develop methods for decomposing the effects of temporal variation in demography into contributions from nonlinear averaging and non-equilibrium dynamics. We illustrate the approach using Carlina vulgaris, a monocarpic species in which recruitment, growth and survival all vary from year to year. In Carlina the absolute effect of temporal variation on the evolutionarily stable flowering strategy is substantial (ca. 50% of the evolutionarily stable flowering size) but the net effect is much smaller (ca. 10%) because the effects of temporal variation do not influence the evolutionarily stable strategy in the same direction.

Analysis of Variance↗

PubMed1998

Alternative reproductive strategies in the ruff, Philomachus pugnax: a mixed ESS?

In the ruff, there are two alternative male reproductive strategies. The majority of males of this lekking bird attempt to establish and defend territories on leks, and are referred to as Independents. Other males, referred to as Satellites, forego this behaviour and instead attempt to get access to the territories defended by Independents by acting submissively. The system is thought to be an example of a mixed evolutionarily stable strategy (ESS), where the two strategies have equal fitness payoffs and are maintained by negative frequency-dependent selection. Satellites visited leks at the same time as females, and were associated with territory-holding Independents which were successful in attracting females. This appeared to be an effect both of Satellites following females, and of females being attracted to Independents that dominated submissive Satellites. Males pursuing the two strategies benefited from the presence of each other, at least to some extent. In this study, Satellites got fewer copulations than expected by their proportion in the population. Satellites on leks might have increased longevity or reproductive life span, and gained copulations off leks and while migrating, to compensate for their low observed mating success on leks. The Satellite strategy may be a low-cost, low-benefit strategy, which may have equal average lifetime reproductive success as the territorial strategy Copyright 1998 The Association for the Study of Animal Behaviour

Journal Article↗

PubMed2005

Diversity in times of adversity: probabilistic strategies in microbial survival games.

Population diversification strategies are ubiquitous among microbes, encompassing random phase-variation (RPV) of pathogenic bacteria, viral latency as observed in some bacteriophage and HIV, and the non-genetic diversity of bacterial stress responses. Precise conditions under which these diversification strategies confer an advantage have not been well defined. We develop a model of population growth conditioned on dynamical environmental and cellular states. Transitions among cellular states, in turn, may be biased by possibly noisy readings of the environment from cellular sensors. For various types of environmental dynamics and cellular sensor capability, we apply game-theoretic analysis to derive the evolutionarily stable strategy (ESS) for an organism and determine when that strategy is diversification. We find that: (1) RPV, effecting a sort of Parrondo paradox wherein random alternations between losing strategies produce a winning strategy, is selected when transitions between different selective environments cannot be sensed, (2) optimal RPV cell switching rates are a function of environmental lifecycle asymmetries and environmental autocorrelation, (3) probabilistic diversification upon entering a new environment is selected when sensors can detect environmental transitions but have poor precision in identifying new environments, and (4) in the presence of excess additive noise, low-pass filtering is required for evolutionary stability. We show that even when RPV is not the ESS, it may minimize growth rate variance and the risk of extinction due to 'unlucky' environmental dynamics.

Bacteria↗

PubMed1996

Frequency-Dependent Stability for Two-Species Interactions

Evolutionary game theory is extended to models of two-species interactions where fitnesses are based on individual characteristics (strategies) rather than on a population dynamic that assumes homogeneous species. It is shown that the coevolutionary theories in the literature that combine ecology with genetic viability selection are part of this extended theory and that the dynamic stability resulting from a separation of ecological and evolutionary processes actually follows from game-theoretic solution concepts. The main focus of the paper is to investigate the application of the ESS (evolutionarily stable strategy) solution concept to dynamic stability when fitnesses are given by random interactions between individuals as opposed to viability selection. For two-species frequency-dependent interactions, the ESS criterion that implies stability asserts that, in any system near the ESS, at least one of the species is better off (i.e., more fit) if it evolves towards the ESS. The global stability of a polymorphic two-species ESS that is shown for two-species matrix games gives a powerful tool to predict the course of evolution through static fitness comparisons.

Journal Article↗

PubMed2003

Evolution of complex flowering strategies: an age- and size-structured integral projection model.

We explore the evolution of delayed age- and size-dependent flowering in the monocarpic perennial Carlina vulgaris, by extending the recently developed integral projection approach to include demographic rates that depend on size and age. The parameterized model has excellent descriptive properties both in terms of the population size and in terms of the distributions of sizes within each age class. In Carlina the probability of flowering depends on both plant size and age. We use the parameterized model to predict this relationship, using the evolutionarily stable strategy (ESS) approach. Despite accurately predicting the mean size of flowering individuals, the model predicts a step-function relationship between the probability of flowering and plant size, which has no age component. When the variance of the flowering-threshold distribution is constrained to the observed value, the ESS flowering function contains an age component, but underpredicts the mean flowering size. An analytical approximation is used to explore the effect of variation in the flowering strategy on the ESS predictions. Elasticity analysis is used to partition the agespecific contributions to the finite rate of increase (lambda) of the survival-growth and fecundity components of the model. We calculate the adaptive landscape that defines the ESS and generate a fitness landscape for invading phenotypes in the presence of the observed flowering strategy. The implications of these results for the patterns of genetic diversity in the flowering strategy and for testing evolutionary models are discussed. Results proving the existence of a dominant eigenvalue and its associated eigenvectors in general size- and age-dependent integral projection models are presented.

Adaptation, Biological↗

PubMed2000

Resource Allocation and the Evolution of Self-Fertilization in Plants.

This article develops a simple evolutionarily stable strategy (ESS) model of resource allocation in partially selfing plants, which incorporates reproductive and sex allocation into a single framework. The analysis shows that, if female fitness gain increases linearly with resource investment, total reproductive allocation is not affected by sex allocation, defined as the fraction of reproductive resources allocated to male function. All else being equal, the ESS total reproductive allocation increases with increasing selfing rate if the fitness of selfed progeny is more than half that of outcrossed progeny, while the ESS sex allocation is always a decreasing function of the selfing rate. Self-fertilization is much more common in annual than in perennial plants, and this association has been commonly interpreted in terms of an effect of life history on mating system. The model in this article shows that self-fertilization can itself cause the evolution of the annual habit. Incorporating the effects of pollen discounting may not have any influence on total reproductive allocation if female fitness gain is a linear function of resource investment, although the evolutionarily stable sex allocation is altered. Evolution of the selfing rate is found to be independent of reproductive and sex allocation under the mass-action assumption that self- and outcross pollen are deposited simultaneously on receptive stigmas and compete for access to ovules.

inbreeding depression↗

PubMed1999

Sperm competition. II-post-copulatory guarding

A two round sperm competition model is analysed to determine which male strategy is advantageous for fertilization of a given set of eggs; guarding a particular female or searching for another copulation. A guarding male is one who would guard if he mates in the first round (which may not occur) whilst a non-guarding male decides on how much sperm to allocate if given the opportunity to inseminate a female in round one. Guarding behaviour is defined in terms of a probability of preventing a further insemination if challenged by a rival male. Sperm success with a single female obeys the "raffle principle". An evolutionarily stable strategy (ESS) approach is used to ascertain the best non-guarding ejaculation strategy. We show that for each fixed proportion of guarders in the population the strategies are ordered and that only a single guarding strategy need be considered. The model predicts that there will be evolution to either the guarding strategy or a single non-guarding strategy or a polymorphic combination of guarding and some (or all) of the non-guarding strategies. The conditions for coexistence to occur were shown to be rare in comparison to those necessary for a monomorphism. Copyright 1999 Academic Press.

Journal Article↗

PubMed2006

The evolutionary psychology of left and right: costs and benefits of lateralization.

Why do the left and right sides of the vertebrate brain play different functions? Having a lateralized brain, in which each hemisphere carries out different functions, is ubiquitous among vertebrates. The different specialization of the left and right side of the brain may increase brain efficiency--and some evidence for that is reported here. However, lateral biases due to brain lateralization (such as preferences in the use of a limb or, in animals with laterally placed eyes, of a visual hemifield) usually occur at the population level, with most individuals showing similar direction of bias. Individual brain efficiency does not require the alignment of lateralization in the population. Why then are not left--and right-type individuals equally common? Not only humans, but most vertebrates show a similar pattern. For instance, in the paper I report evidence that most toads, chickens, and fish react faster when a predator approaches from the left. I argue that invoking individual brain efficiency (lateralization may increase fitness), evolutionary chance or direct genetic mechanisms cannot explain this widespread pattern. Instead, using concepts from mathematical theory of games, I show that alignment of lateralization at the population level may arise as an "evolutionarily stable strategy" when individually asymmetrical organisms must coordinate their behavior with that of other asymmetrical organisms. Thus, the population structure of lateralization may result from genes specifying the direction of asymmetries which have been selected under "social" pressures.

Animals↗

PubMed1998

Discrete conventional signalling of a continuous variable.

In aggressive interactions, animals often use a discrete set of signals, while the properties being signalled are likely to be continuous, for example fighting ability or value of victory. Here we investigate a particular model of fighting that allows for conventional signalling of subjective resource value to occur. Perfect signalling and no signalling are not evolutionarily stable strategies (ESSs) in the model. Instead, we find ESSs in which partial information is communicated, with discrete displays signalling a range of values rather than a precise one. The result also indicates that communication should be more precise in conflicts over small resources. Signalling strategies can exist in fighting because of the common interest in avoiding injuries, but communication is likely to be limited because of the fundamental conflict over the resource. Our results reflect a compromise between these two factors. Data allowing for a thorough test of the model are lacking; however, existing data seem consistent with the obtained theoretical results. Copyright 1998 The Association for the Study of Animal Behaviour.

Journal Article↗

PubMed1999

Seasonal patterns of singing in the willow warbler: evidence against the fertility announcement hypothesis.

Males of many bird species use a variety of behaviour patterns that reduce their chances of being cuckolded. The 'fertility announcement' hypothesis (Møller 1991, American Naturalist, 138, 994-1014) proposes that song might be one such paternity guard. According to this hypothesis, paired males would announce their female's fertile status by singing. This has been interpreted as an honest signalling, evolutionarily stable strategy. Contrary to the predictions of this hypothesis, male willow warblers, Phylloscopus trochilus, sang very little when females were fertile. Intrusions by other males in the fertile period were not less common when males sang at higher rates. Mate guarding and singing are best interpreted as two conflicting behaviours during this period, the former being directed to the fertile female and the latter to attracting a second female, or an extrapair female. A survey of recent studies suggests that, in most passerine species studied, males do not sing during the fertile period of their females. The different conclusions of Møller (1991) are probably due to his use of population-wide estimates of the timing of singing behaviour and egg laying. Breeding asynchronies within populations would be responsible for the apparent matching between the peaks of singing activity and fertility. Copyright 1999 The Association for the Study of Animal Behaviour.

Journal Article↗

PubMed1993

Evolutionary stability in the asymmetric war of attrition.

It is shown that there are at least two evolutionarily stable strategies, or ESSs, in the war of attrition with a role asymmetry when players make an error with a small but positive probability in implementing their strategy choices. This result proves Maynard Smith's original conjecture that players should choose asymmetric pure strategies in the asymmetric war of attrition. It is also in contrast to the standard non-existence result of an ESS in this game under complete information. To derive this result we discretize the original game and apply the limit ESS condition introduced by Selten. The result is also compared with other evolutionary analyses of this game.

Animals↗

PubMed1994

The evolution of virulence in parasites and pathogens: reconciliation between two competing hypotheses.

According to conventional wisdom, parasites and pathogens should evolve reduced virulence to their hosts, because more virulent parasites and pathogens are more likely to drive their hosts, and themselves, to extinction. But this view has been criticized for its reliance on group selection. According to an alternative perspective, selection will favor whatever level of virulence maximizes the rate of increase of the parasite or pathogen. This optimum virulence depends on the functional relationship between a parasite or pathogen's transmissibility and its effect on host mortality, with selection often favoring an intermediate degree of virulence. The thesis of this paper is that models in which intermediate levels of virulence are favored lead quite naturally to the further conclusion that parasites and pathogens should-up to a point-become less virulent over time, once the feedbacks between ecological and evolutionary processes are incorporated into the analysis. As a consequence of successive adaptations by the parasite or pathogen, the density of susceptible hosts is reduced, thereby altering the balance between selective forces so as to favor reduced virulence. However, the evolutionarily stable strategy that is achieved is bounded away from complete avirulence. We conclude that models in which intermediate virulence is favored do not necessarily contradict the conventional wisdom in the long run; in fact, these models provide a simple mechanistic explanation for the evolution of reduced virulence.

Animals↗

PubMed1995

George Price's contributions to evolutionary genetics.

George Price studied evolutionary genetics for approximately seven years between 1967 and 1974. During that brief period Price made three lasting contributions to evolutionary theory; these were: (i) the Price Equation, a profound insight into the nature of selection and the basis for the modern theories of kin and group selection; (ii) the theory of games and animal behavior, based on the concept of the evolutionarily stable strategy; and (iii) the modern interpretation of Fisher's fundamental theorem of natural selection, Fisher's theorem being perhaps the most cited and least understood idea in the history of evolutionary genetics. This paper summarizes Price's contributions and briefly outlines why, toward the end of his painful intellectual journey, he chose to focus his deep humanistic feelings and sharp, analytical mind on abstract problems in evolutionary theory.

Animals↗