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Results for “evolutionarily stable strategy”

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At least 217 records · Page 12Linked to original sources

PubMed1998

Natal dispersal and senescence.

The potential existence of natal dispersal strategies depending on parental age has been suggested by Hamilton and May [Hamilton, W. D. & May, R. M. (1977) Nature 269, 578-581] for organisms whose survival rates decline with age. When competition between parent and offspring is strong, any individual should disperse a smaller fraction of its offspring when it ages. Here, we verify their verbal prediction. First, we determine the evolutionarily stable dispersal strategy conditional on parental age, associated with a particular senescence curve. We show that such a conditional dispersal strategy should evolve independently from the genotype controlling the offspring dispersal behavior. Second, studying a population of common lizards, we provide empirical evidence of a relation between dispersal of female offspring and maternal senescence, in agreement with our theoretical predictions.

Aging↗

PubMed2000

Coevolution of Contrary Choices in Host-Parasitoid Systems.

We investigate patch selection strategies of hosts and parasitoids in heterogeneous environments. Previous theoretical work showed that when host traits vary among patches, coevolved populations of hosts and parasitoids make congruent choices (i.e., hosts and parasitoids preferentially select the same patches) and exhibit direct density dependence in the distribution of percent parasitism. However, host-parasitoid systems in the field show a range of patterns in percent parasitism, while behavioral studies indicate that hosts and parasitoids can exhibit contrary choices (i.e., hosts avoid patches favored by the parasitoid). We extend previous theory by permitting life-history traits of the parasitoid as well as the host to vary among patches. Our analysis implies that in coevolutionarily stable populations, hosts preferentially select patches that intrinsically support higher host equilibrium numbers (i.e., the equilibrium number achieved by hosts when both populations are confined to a single patch) and that parasitoids preferentially select patches that intrinsically support higher parasitoid equilibrium numbers (i.e., the equilibrium number achieved by the parasitoids when both populations are confined to a patch). Using this result, we show how variation in life-history traits among patches leads to contrary or congruent choices or leads to direct density dependence, inverse density dependence, or density independence in the distribution of percent parasitism. In addition, we determine when populations playing the coevolutionarily stable strategies are ecologically stable. Our analysis shows that heterogeneous environments containing patches where the intrinsic rate of growth of the host and the survivorship rate of the parasitoid are low result in the coevolved populations exhibiting contrary choices and, as a result, promote ecological stability.

coevolution↗

PubMed1989

Mistakes allow evolutionary stability in the repeated prisoner's dilemma game.

The repeated prisoner's dilemma game has been widely used in analyses of the evolution of reciprocal altruism. Recently it was shown that no pure strategy could be evolutionarily stable in the repeated prisoner's dilemma. Here I show that if there is always some probability that individuals will make a mistake, then a pure strategy can be evolutionarily stable provided that it is "strong perfect equilibria" against itself. To be a strong perfect equilibrium against itself, a strategy must be the best response to itself after every possible sequence of behavior. I show that both unconditional defection and a modified version of tit-for-tat have this property.

Altruism↗

PubMed2005

Function-valued adaptive dynamics and the calculus of variations.

Adaptive dynamics has been widely used to study the evolution of scalar-valued, and occasionally vector-valued, strategies in ecologically realistic models. In many ecological situations, however, evolving strategies are best described as function-valued, and thus infinite-dimensional, traits. So far, such evolution has only been studied sporadically, mostly based on quantitative genetics models with limited ecological realism. In this article we show how to apply the calculus of variations to find evolutionarily singular strategies of function-valued adaptive dynamics: such a strategy has to satisfy Euler's equation with environmental feedback. We also demonstrate how second-order derivatives can be used to investigate whether or not a function-valued singular strategy is evolutionarily stable. We illustrate our approach by presenting several worked examples.

Biological Evolution↗

PubMed2001

On fitness in structured metapopulations.

In this paper we derive a general expression measuring fitness in general structured metapopulation models. We apply the theory to a model structured by local population size and in which local dynamics is explicitly modelled. In particular, we calculate the evolutionarily stable dispersal strategy for individuals that can assess the local population density in the case where only dispersal is subject to evolutionary control but all other model in gredients are assumed fixed. We show that there exists a threshold size such that at ESS everyone should stay as long as the population size is below the threshold and everyone should disperse immediately as the population size reaches the threshold.

Animals↗

PubMed2005

Comparative statics of games between relatives.

According to Hamilton's theory of kin selection, species tend to evolve behavior such that each organism appears to be attempting to maximize its inclusive fitness. In particular, two neighbors are likely to help each other if the cost of doing so is less than the benefit multiplied by r, their coefficient of relatedness. Since the latter is less than unity, mutual altruism benefits both neighbors. However, is it theoretically possible that acting so as to maximize the inclusive, rather than personal, fitness may harm both parties. This may occur in strategic symmetric pairwise interactions (more specifically, nxn games), in which the outcome depends on both sides' actions. In this case, the equilibrium outcome may be less favorable to the interactants' personal fitness than if each of them acted so as to maximize the latter. This paper shows, however, that such negative effect of relatedness on fitness is incompatible with evolutionary stability. If the symmetric equilibrium strategies are evolutionarily stable, a higher coefficient of relatedness can only entail higher personal fitness for the two neighbors. This suggests that negative comparative statics as above are not likely to occur in nature.

Altruism↗

PubMed1999

Dispersal and Inbreeding Avoidance.

Using a game-theoretical approach, we investigate the dispersal patterns expected if inbreeding avoidance were the only reason for dispersal. The evolutionary outcome is always complete philopatry by one sex. The rate of dispersal by the other sex depends on patch size and mating system, as well as inbreeding and dispersal costs. If such costs are sex independent, then two stable equilibria coexist (male or female philopatry), with symmetric domains of attraction. Which sex disperses is determined entirely by history, genetic drift, and gene flow. An asymmetry in costs makes one domain of attraction extend at the expense of the other. In such a case, the dispersing sex might also be, paradoxically, the one that incurs the higher dispersal costs. As asymmetry increases, one equilibrium eventually disappears, which may result in a sudden evolutionary shift in the identity of the dispersing sex. Our results underline the necessity to control for phylogenetic relationships (e.g., through the use of independent-comparisons methods) when investigating empirical trends in dispersal. Our model also makes quantitative predictions on the rate of dispersal by the dispersing sex and suggests that inbreeding avoidance may only rarely be the sole reason for dispersal.

evolutionarily stable strategy↗

PubMed2000

Evolutionarily Stable Dispersal Rates Do Not Always Increase with Local Extinction Rates.

Earlier models on the evolution of dispersal have suggested that evolutionarily stable dispersal rates should increase with the frequency of local extinctions. Most metapopulation models assume site saturation (i.e., no local population dynamics), yet the majority of species distributed as metapopulations rarely attain carrying capacity in all occupied patches. In this article, we relax this assumption and examine the evolutionarily stable dispersal rate under nonsaturated but still competitive demographic conditions. Contrary to previous predictions, we show that increasing local extinction rates may allow decreasing dispersal rates to evolve.

dispersal↗

PubMed1994

Combining behaviour and population dynamics with applications for predicting consequences of habitat loss.

A population model for migratory vertebrates is developed by combining game theory models of foraging behaviour with population biology. Models of foraging behaviour which incorporate interference and resource depletion are developed to determine the density-dependent mortality occurring within sites. Population size can then be related to the strength of interference, the variance in competitive ability and the rate at which resources are depleted. The model is extended to predict evolutionarily stable migration strategies. This novel framework is then used to predict the population decline resulting from habitat loss.

Animals↗

PubMed2003

A tale of two defectors: the importance of standing for evolution of indirect reciprocity.

Indirect reciprocity occurs when the cooperative behavior between two individuals is contingent on their previous behavior toward others. Previous theoretical analysis indicates that indirect reciprocity can evolve if individuals use an image-scoring strategy. In this paper, we show that, when errors are added, indirect reciprocity cannot be based on an image-scoring strategy. However, if individuals use a standing strategy, then cooperation through indirect reciprocity is evolutionarily stable. These two strategies differ with respect to the information to which they attend. While image-scoring strategies only need attend to the actions of others, standing strategies also require information about intent. We speculate that this difference may shed light on the evolvability of indirect reciprocity. Additionally, we show that systems of indirect reciprocity are highly sensitive to the availability of information. Finally, we present a model which shows that if indirect reciprocity were to evolve, selection should also favor trusting behavior in relations between strangers.

Altruism↗

PubMed2004

Conditional dispersal under kin competition: extension of the Hamilton-May model to brood size-dependent dispersal.

I consider a site-based model with contest competition among siblings, and assume that dispersal is conditional on the number of offspring in the natal site. Evolutionarily stable populations contain threshold dispersal strategies, which retain a certain number of offspring in the natal site and disperse the rest (if the actual number of offspring is less than the threshold, then all offspring are retained). Due to the discrete nature of the strategy set (the threshold must be integer), the ESS may not be unique or may not exist. In the latter case, two neighboring threshold strategies coexist in the evolutionarily stable population. Dispersal first decreases and then increases as a function of dispersal mortality, such that all but one offspring should be dispersed both when dispersal mortality is very small or very high. Population-level dispersal fractions are often similar to the unconditional ESS, but differ strongly when fecundity is small and dispersal mortality is high.

Adaptation, Physiological↗

PubMed2006

Evolution of pathogens towards low R0 in heterogeneous populations.

Maximization of the basic reproduction ratio or R(0) is widely believed to drive the emergence of novel pathogens. The presence of exploitable heterogeneities in a population, such as high variance in the number of potentially infectious contacts, increases R(0) and thus pathogens that can exploit heterogeneities in the contact structure have an advantage over those that do not. However, exploitation of heterogeneities results in a more rapid depletion of the potentially susceptible neighbourhood for an infected host. Here a simple model of pathogen evolution in a heterogeneous environment is developed and placed in the context of HIV transmission. In this model, it is shown that pathogens may evolve towards lower R(0), even if this results in pathogen extinction. For sufficiently high transmissibility, two locally stable strategies exist for an evolving pathogen, one that exploits heterogeneities and results in higher R(0), and one that does not, and results in lower R(0). While the low R(0) strategy is never evolutionarily stable, invading strains with higher R(0) will also converge to the low R(0) strategy if not sufficiently different from the resident strain. Heterogenous transmission is increasingly recognized as fundamental to epidemiological dynamics and the evolution of pathogens; here, it is shown that the ability to exploit heterogeneity is a strategy that can itself evolve.

Disease Outbreaks↗

PubMed2003

Play and the evolution of fairness: a game theory model.

Bekoff [J. Consci. Stud. 8 (2001) 81] argued that mammalian social play is a useful behavioral phenotype on which to concentrate in order to learn more about the evolution of fairness. Here, we build a game theoretical model designed to formalize some of the ideas laid out by Bekoff, and to examine whether 'fair' strategies can in fact be evolutionarily stable. The models we present examine fairness at two different developmental stages during an individual's ontogeny, and hence we create four strategies-fair at time 1/fair at time 2, not fair at time 1/not fair at time 2, fair at time 1/not fair at time 2, not fair at time 1/fair at time 2. Our results suggest that when considering species where fairness can be expressed during two different developmental stages, acting fairly should be more common than never acting fairly. In addition, when no one strategy was evolutionarily stable, we found that all four strategies we model can coexist at evolutionary equilibrium. Even in the absence of an overwhelming database from which to test our model, the general predictions we make have significant implications for the evolution of fairness.

Journal Article↗

PubMed2003

The evolution of resource use.

The evolution of a consumer exploiting two resources is investigated. The strategy x under selection represents the fraction of time or energy an individual invests into extracting the first resource. In the model, a dimensionless parameter alpha quantifies how simultaneous consumption of both resources influences consumer growth; alpha<0 corresponds to hemi-essential resources, 0 1 corresponds to antagonistic resources. An analysis of the ecological and evolutionary dynamics leads to five conclusions. First, when alpha< or =1, there is a unique singular strategy x* for the adaptive dynamics and it is evolutionarily stable and globally convergent stable. Second, when alpha=1, the singular strategy x* corresponds to the populations exhibiting an ideal free distribution and a population playing this strategy can invade and displace populations playing any other strategy. Third, when alpha>1, the strategies x=0 and x=1 are evolutionarily stable and convergent stable. Hence, if the populations initially specialize on one resource, evolution amplifies this specialization. Fourth, when alpha is slightly larger than one (i.e. the resources are slightly antagonistic), there is a convergent stable singular strategy whose basin of attraction is almost the entire strategy space (0,1). This singular strategy is evolutionarily unstable and serves as an evolutionary branching point. Following evolutionary branching, our analysis and numerical simulations suggest that evolutionary dynamics are driven toward an end state consisting of two populations specializing on different resources. Fifth, when alpha>>1, there is only one singular strategy and it is convergent unstable and evolutionarily unstable. Hence, if resources are overly antagonistic, evolutionary branching does not occur and ultimately only one resource is exploited.

Animals↗

PubMed2005

A microbial modified prisoner's dilemma game: how frequency-dependent selection can lead to random phase variation.

Random phase variation (RPV) is a control strategy in which the expression of a cell state or phenotype randomly alternates between discrete 'on' and 'off' states. Though this mode of control is common for bacterial virulence factors like pili and toxins, precise conditions under which RPV confers an advantage have not been well defined. In Part I of this study, we predicted that fluctuating environments select for RPV if transitions between different selective environments cannot be reliably sensed (J. Theor. Biol. (2005)). However, selective forces both inside and outside of human hosts are also likely to be frequency dependent in the sense that the fitnesses of some bacterial states are greatest when rare. Here we show that RPV at slow rates can provide a survival advantage in such a frequency-dependent environment by generating population heterogeneity, essentially mimicking a polymorphism. More surprisingly, RPV at a faster 'optimal' rate can shift the population composition toward an optimal growth rate that exceeds that possible for polymorphic populations, but this optimal strategy is not evolutionarily stable. The population would be most fit if all cells randomly phase varied at the optimal rate, but individual cells have a growth-rate incentive to defect (mutate) to other switching rates or non-phase variable phenotype expression, leading to an overall loss of fitness of the individual and the population. This scenario describes a modified Prisoner's Dilemma game (Evolution and the Theory of Games, Cambridge University Press, Cambridge, New York, 1982, viii, 224pp.; Nature 398 (6726) (1999) 367), with random phase variation at optimal switching rates serving as the cooperation strategy.

Bacteria↗

PubMed1981

Ess-theory for finite populations.

On the basis of some principles from the philosophy of science, the inadequacy of the ESS-theory as introduced by Maynard Smith and Price as a biological theory is discussed, and an improved ESS-theory for finite populations is presented which can adopt the ideas of the original formalism, although modified. Resulting are explicit conditions on the population sizes that ensure certain strategies to be evolutionarily stable.

Biological Evolution↗

PubMed1996

Evolutionary strategies of stochastic learning automata in the prisoner's dilemma.

Stochastic learning automata (SLA) model stimulus-response species which receive feedback from the environment and adjust their mixed strategies in a Prisoner's Dilemma. A large heterogeneous population consists of SLA applying different strategies (i.e. different learning parameters) and other players applying deterministic strategies, Tit-For-Tat (TFT) or Always-Defect (ALLD). The predicted equilibria determine the payoffs within a generation for applying particular strategies and these equilibria are confirmed by simulation. The resultant population dynamics over many generations show that SLA with insensitive penalty responses strongly favor defection and dominate in subsequent generations over SLA with sensitive penalty responses. The SLA strategies are not evolutionarily stable as they can be invaded by TFT or ALLD. With the introduction of memory in the stimulus-response model, SLA learn to cooperate with TFT players.

Computer Simulation↗

PubMed2006

Do tiny males grow up? Sperm competition and optimal resource allocation schedule of dwarf males of barnacles.

Barnacles, marine crustaceans, have three sexual patterns: simultaneous hermaphroditism, dioecy and androdioecy. In dioecy and androdioecy, large individuals (females and hermaphrodites, respectively) are attached by dwarf males. Depending on species, some dwarf males grow up, others do not in their life time. To investigate which environmental conditions affect growth patterns of dwarf males of barnacles, we investigate the evolutionarily stable life history strategy of dwarf males using Pontryagin's maximum principle. Sperm competition among dwarf males and that among dwarf males and large hermaphrodites is taken into account. Dwarf males grow up in food-rich environments, while they do not grow at all in food-poor environments. ESS of the resource allocation schedule between reproduction and growth follows an "intermediate growth strategy" (simultaneous growth and reproduction) for dioecious species, in which sperm competition is not severe. On the other hand, it approaches "bang-bang control" (switching from allocating all resources toward growth then to reproduction), as sperm competition against surrounding large hermaphrodites becomes severe in androdioecious species.

Animals↗