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Results for “evolutionarily stable strategy”

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PubMed2003

Quantifying male attractiveness.

Genetic models of sexual selection are concerned with a dynamic process in which female preference and male trait values coevolve. We present a rigorous method for characterizing evolutionary endpoints of this process in phenotypic terms. In our phenotypic characterization the mate-choice strategy of female population members determines how attractive females should find each male, and a population is evolutionarily stable if population members are actually behaving in this way. This provides a justification of phenotypic explanations of sexual selection and the insights into sexual selection that they provide. Furthermore, the phenotypic approach also has enormous advantages over a genetic approach when computing evolutionarily stable mate-choice strategies, especially when strategies are allowed to be complex time-dependent preference rules. For simplicity and clarity our analysis deals with haploid mate-choice genetics and a male trait that is inherited phenotypically, for example by vertical cultural transmission. The method is, however, easily extendible to other cases. An example illustrates that the sexy son phenomenon can occur when there is phenotypic inheritance of the male trait.

Animals↗

PubMed1992

Evolutionarily stable age at first reproduction in a density-dependent model.

We develop a new model of life history evolution to investigate the evolution of age at first reproduction. Density dependence is taken into account. For a given "species", age of maturity, offspring survival, immature survival, adult survival, fecundity, immature age-classes entering in competition with adults and immature competitive ability are traits adjustable by natural selection, and constitute a particular strategy. On the contrary, the type of intraspecific competition (scramble or contest), strength of competition and inherent net reproductive rate Ro(inh) are fixed (specific) characteristics. As a consequence of fixing Ro(inh), the evolution of any trait will affect trade-offs between others. Evolutionarily stable strategies are determined numerically by using the mathematical concept of Lyapunov exponents. Altogether, we consider 960 different hypothetical "species" (i.e. different combinations of fixed traits). Corresponding ESSs are analyzed with respect to their age at first reproduction, adult survival and immature competitive ability components. They appear to be gathered in three groups. One is intuitive and characterized by a reduction of immature competitive ability and a correlation of age of maturity with adult survival; populations reach mainly equilibria. The two other groups respectively include "species" with low age of maturity but high adult survival, and "species" close to semelparity with delayed maturity; immature competitive ability may not be minimized, and populations possibly exhibit complex dynamics. In conclusion, the hypothesis that the evolution of a demographic parameter modifies trade-offs between others turns out to have important consequences. We argue that life history theory cannot ignore the source and mode-of-operation of density dependence and must regard potential short-term instability as essential.

Animals↗

PubMed1997

Allelopathy in Spatially Distributed Populations

In a homogeneously mixing population of E. coli, colicin-producing and colicin-sensitive strategies both may be evolutionarily stable for certain parameter ranges, with the outcome of competition determined by initial conditions. In contrast, in a spatially-structured population, there is a unique ESS for any given set of parameters; the outcome is determined by how effective allelopathy is in relation to its costs. Furthermore, in a spatially-structured environment, a dynamic equilibrium may be sustained among a colicin-sensitive type, a high colicin-producing type, and a "cheater" that expends less on colicin production but is resistant. Copyright 1997 Academic Press Limited

Journal Article↗

PubMed2004

Male "mixed" reproductive strategies in biparental species: Trivers was probably right, but why?

Trivers proposed that, if parental care by both sexes is advantageous, males should practice a "mixed" strategy of seeking extrapair copulations, while restricting their parental investment to offspring of social mates. We explore circumstances under which males should limit their parental care in the predicted manner. We find that Trivers's "mixed" strategy will generally be evolutionarily stable so long as either socially monogamous or polygynous males usually sire more offspring per brood from a social mate than they typically sire in broods of extrapair mates. Polygynous males should spread investment across their home nests unless the expected number of chicks sired in them differs widely. Whether polygynous males should restrict paternal care to social mates' offspring hinges additionally on resident male investment in broods containing extrapair young: if resident males contribute minimally, some investment by a polygynous extrapair male becomes more advantageous. Recently reviewed data on extrapair fertilization distributions within monogamous and polygynous passerines suggest that extrapair offspring often predominate numerically within their broods, consistent with sperm expenditure theory. Nevertheless, most species conform to the model's criterion regarding relative parentage levels in broods of social versus extrapair mates. Patterns of extrapair parentage thus appear sufficient to stabilize biparental care systems.

Animals↗

PubMed2004

Adaptation and constraint in the evolution of environmental sex determination.

When environments differentially influence male and female performance, environmental sex determination (ESD) might evolve. The conclusion from several previous theoretical models was that reaction norms for sex determination should have a single, sharp threshold, with only females being produced in some environments and only males in others. These reaction norms can be disadvantageous in fluctuating environments, however, because they lead to sex-ratio fluctuations. We analysed the evolution of ESD, looking for equilibrium strategies in unconstrained as well as constrained strategy spaces. We identified situations where a single-threshold reaction norm is not evolutionarily stable. In these cases, we found stable strategies in the form of complex reaction norms, showing an oscillatory pattern of sex determination with respect to variation in an environmental variable. Considering that constraints could prevent such phenotypes from being realized, we found that certain randomized reaction norms, with probabilistic sex determination for a range of environments, would achieve nearly the same fitness. We also investigated reaction norms constrained to have a single threshold and found that genetic polymorphism in the environmental threshold value could evolve, producing a similar effect as a randomized reaction norm. We argue that the appearance of genetic variation can be regarded as an alternative outcome when constraints prevent the evolution of a more complex or a randomized strategy.

Adaptation, Physiological↗

PubMed2003

Nectarless flowers: ecological correlates and evolutionary stability.

In animal-pollinated flowers, the pollinators cannot detect the presence of nectar before entering flowers, and therefore flowers may cheat by not producing nectar. An earlier model suggested that a mixed strategy of producing nectarful and nectarless flowers would be evolutionarily stable. Here we compare nectarless flowers as a cheating strategy with three competing hypotheses namely "visit-more-flowers", "cross-pollination enhancement" and "better contact". We collected field data on 28 species of plants to test some of the differential predictions of the hypotheses. Nectarless flowers were detected in 24 out of 28 plant species. Correlations of percent nectarless flowers with floral and ecological variables support the cheater flower hypothesis. We further model the cost-benefits of cheating and show that an evolutionary stable ratio of nectarless to nectarful flowers can be reached. The equilibrium ratio is mainly decided by factors associated with pollinator density and pollinator learning.

Animals↗

PubMed2003

Genetic analysis of two distinct reproductive strategies in sexual and asexual field populations of an endoparasitic wasp, Venturia canescens.

Asexual (thelytokous) females of the parasitoid Venturia canescens, which develop inside another insect, exhibit evolutionarily stable mixtures of life-history strategies, allowing two genetically distinct wasp lines to coexist sympatrically on the same host resources. Since the two asexual lines differ in a virus-like particle protein-coding gene (VLP1), the question is whether the VLP1 gene is genetically associated with the phenotype. The recent isolation of facultative sexual (arrhenotokous) and asexual V. canescens strains from the same location in Southern France has enabled an investigation of the genetic basis for the observed phenotypic differences, by comparing the two asexual lines with the corresponding homozygous VLP1 genotypes in arrhenotokous strains. This analysis showed similar patterns of morphological and functional differences exist in the ovaries of the two asexual VLP1 lines and in the two homozygous VLP1 genotypes from the field, suggesting that the VLP1 gene alteration either causes the ovarian phenotype or is genetically closely linked to the putative gene. However, the VLP1-gene may not be the only gene contributing to the phenotypic effects observed in the asexual lines. Although the two VLP1-alleles segregate with the relative differences in the ovary distribution of eggs, the absolute egg numbers differ in the corresponding asexual and sexual genotypes. This suggests that an additional unlinked gene may be involved in the transfer of eggs from the ovarioles into the oviduct.

Animals↗

PubMed2000

Polygyny, mate-guarding, and posthumous fertilization as alternative male mating strategies.

Alternative male mating strategies within populations are thought to be evolutionarily stable because different behaviors allow each male type to successfully gain access to females. Although alternative male strategies are widespread among animals, quantitative evidence for the success of discrete male strategies is available for only a few systems. We use nuclear microsatellites to estimate the paternity rates of three male lizard strategies previously modeled as a rock-paper-scissors game. Each strategy has strengths that allow it to outcompete one morph, and weaknesses that leave it vulnerable to the strategy of another. Blue-throated males mate-guard their females and avoid cuckoldry by yellow-throated "sneaker" males, but mate-guarding is ineffective against aggressive orange-throated neighbors. The ultradominant orange-throated males are highly polygynous and maintain large territories; they overpower blue-throated neighbors and cosire offspring with their females, but are often cuckolded by yellow-throated males. Finally, yellow-throated sneaker males sire offspring via secretive copulations and often share paternity of offspring within a female's clutch. Sneaker males sire more offspring posthumously, indicating that sperm competition may be an important component of their strategy.

Animals↗

PubMed2006

Evolution of handling time can destroy the coexistence of cycling predators.

Several consumers (predators) with Holling type II functional response may robustly coexist even if they utilize the same resource (prey), provided that the population exhibits nonequilibrium dynamics and the handling time of predators is sufficiently different. We investigate the evolution of handling time and, in particular, its effect on coexistence. Longer handling time is costly in terms of lost foraging time, but allows more nutrients to be extracted from a captured prey individual. Assuming a hyperbolically saturating relationship between handling time and the number of new predators produced per prey consumed, we obtain three results: (i) There is a globally evolutionarily stable handling time; (ii) At most two predator strategies can coexist in this model; (iii) When two predators coexist, a mutant with intermediate handling time can always invade. This implies that there is no evolutionarily stable coexistence, and the evolution of handling time eventually leads to a single evolutionarily stable predator. These results are proven analytically and are valid for arbitrary (not only small) mutations; they however depend on the relationship between handling time and offspring production and on the assumption that predators differ only in their prey handling strategy.

Animals↗

PubMed2002

Evolutionary suicide and evolution of dispersal in structured metapopulations.

We study the evolution of dispersal in a structured metapopulation model. The metapopulation consists of a large (infinite) number of local populations living in patches of habitable environment. Dispersal between patches is modelled by a disperser pool and individuals in transit between patches are exposed to a risk of mortality. Occasionally, local catastrophes eradicate a local population: all individuals in the affected patch die, yet the patch remains habitable. We prove that, in the absence of catastrophes, the strategy not to migrate is evolutionarily stable. Under a given set of environmental conditions, a metapopulation may be viable and yet selection may favor dispersal rates that drive the metapopulation to extinction. This phenomenon is known as evolutionary suicide. We show that in our model evolutionary suicide can occur for catastrophe rates that increase with decreasing local population size. Evolutionary suicide can also happen for constant catastrophe rates, if local growth within patches shows an Allee effect. We study the evolutionary bifurcation towards evolutionary suicide and show that a discontinuous transition to extinction is a necessary condition for evolutionary suicide to occur. In other words, if population size smoothly approaches zero at a boundary of viability in parameter space, this boundary is evolutionarily repelling and no suicide can occur.

Adaptation, Biological↗

PubMed2001

Two distinct reproductive strategies are correlated with an ovarian phenotype in co-existing parthenogenetic strains of a parasitic wasp.

The question whether different organisms are able to compete for the same resource is of fundamental importance to evolutionary biology. Sympatric co-existence of similar species on a single resource has long been claimed to be unstable. However, indirect evidence suggests that parasitic wasps exhibit evolutionarily stable mixtures of life-history strategies. Here we describe genetically distinct strains of a parthenogenetic wasp Venturia canescens, with different ovarian phenotypes that affect egg numbers in oviducts. Wasp females with large egg load search for caterpillars and deposit eggs immediately after host encounter, whereas females with fewer eggs delay parasitism. Since the outcome of interlarval competition within super-parasitized caterpillars depends on the age distribution of competing larvae, the two egg deposition strategies may co-exist under conditions that favor super-parasitism.

Journal Article↗

PubMed1999

The continuous Prisoner's dilemma: II. Linear reactive strategies with noise.

We present a general model for the Continuous Prisoner's Dilemma and study the effect of errors. We find that cooperative strategies that can resist invasion by defectors are optimistic (make high initial offers), generous (always offer more cooperation than the partner did in the previous round) and uncompromising (offer full cooperation only if the partner does). A necessary condition for the emergence of cooperation in the continuous Prisoner's Dilemma with noise is b (1-p)>c, where b and c denote, respectively, the benefit and cost of cooperation, while p is the error rate. This relation can be reformulated as an error threshold: cooperation can only emerge if the probability of making a mistake is below a critical value. We note, however, that cooperation in the continuous Prisoner's Dilemma with noise does not seem to be evolutionarily stable: while it is possible to find cooperative strategies that resist invasion by defectors, such cooperators are generally invaded by more cooperative strategies which eventually yield to defectors. Thus, the long-term evolution of the continuous Prisoner's Dilemma is either characterized by unending cycles or by stable polymorphisms of cooperators and defectors.

Biological Evolution↗

PubMed2000

Daily Patterns of Optimal Producer and Scrounger Use under Predation Hazard: A State-Dependent Dynamic Game Analysis.

Feeding in groups often gives rise to joining: feeding from other's discoveries. The joining decision has been modeled as a producer-scrounger game where the producer strategy consists of searching for one's food and the scrounger strategy consists of searching for food discovered by others. Previous models revealed that the evolutionarily stable proportion of scrounging mostly depends on the fraction of each food patch available only to its producer. These early models are static and state independent and are therefore unable to explore whether the time of day, the animal's state, and the degree of predation hazard influence an individual's decision of whether to use the producer or scrounger strategy. To investigate these issues, we developed a state-dependent dynamic producer-scrounger game model. The model predicts that, early in the day, low reserves promote a preference for the scrounger strategy, while the same condition late in the day favors the use of the producer strategy. Under rich and clumped food, the availability of scrounging can improve the daily survival of any average group member. The model suggests only weak effects of predation hazard on the use of scrounging. Future developments should consider the effects of dominance asymmetries and allowing foragers a choice between foraging alone or in a group harboring an evolutionarily stable frequency of scrounger.

producer‐scrounger game↗

PubMed2001

Variable timing of reproduction in unpredictable environments: adaption of flood plain plants.

We study the evolutionarily stable reproductive timing of annual plants that face unpredictable environmental disturbances. Plants living in a riverbed often experience a disturbance before they reproduce, suffering major fitness loss. Plants reproducing prior to the flood season are free from the risk of lost reproduction, but a small flowering plant can produce only a few numbers of seeds. If the date of disturbance is unpredictable, a mixed strategy of reproductive timing may evolve in which individuals of the same genotype have different reproductive dates. We calculate the evolutionarily stable phenotype distribution analytically. Depending on parameters, the ESS distribution is either (1) a timid strategy-the plant reproduces when small, prior to the major disturbance season; (2) a bold strategy-the plant reproduces only when it is fully grown; (3) a mixture of early and late reproduction; or (4) dates of reproduction spread over a wide interval. We also examine the effects of developmental and environmental noises that make realized flowering dates deviate from that programmed by the genotype, which follows the ESS distribution. In the presence of noise, the ESS distribution of programmed timing of reproduction is discrete.

Climate↗

PubMed2003

Site-specific selfish genes as tools for the control and genetic engineering of natural populations.

Site-specific selfish genes exploit host functions to copy themselves into a defined target DNA sequence, and include homing endonuclease genes, group II introns and some LINE-like transposable elements. If such genes can be engineered to target new host sequences, then they can be used to manipulate natural populations, even if the number of individuals released is a small fraction of the entire population. For example, a genetic load sufficient to eradicate a population can be imposed in fewer than 20 generations, if the target is an essential host gene, the knockout is recessive and the selfish gene has an appropriate promoter. There will be selection for resistance, but several strategies are available for reducing the likelihood of it evolving. These genes may also be used to genetically engineer natural populations, by means of population-wide gene knockouts, gene replacements and genetic transformations. By targeting sex-linked loci just prior to meiosis one may skew the population sex ratio, and by changing the promoter one may limit the spread of the gene to neighbouring populations. The proposed constructs are evolutionarily stable in the face of the mutations most likely to arise during their spread, and strategies are also available for reversing the manipulations.

Animals↗

PubMed1999

The Balance of Terror: An Alternative Mechanism for Competitive Trade-Offs and Its Implications for Invading Species.

This article uses models to propose an explanation for three observations in community ecology: the apparent overreaction of prey to attack by specialist predators, the existence of a common trade-off among components of competitive ability in communities of unrelated competitors, and the ability of invading species to break the native trade-off. Strategies that increase resource collection ability are assumed to increase vulnerability to attack by specialist consumers according to a vulnerability function. If competitors compete for a common resource and share the same form of the vulnerability function, then they are favored to converge on the same evolutionarily stable level of competitiveness or trade-off curve even if the parameters describing their specialized consumers differ. The position of the common strategy or trade-off curve depends on the whole guild, with more speciose guilds tending to favor higher levels of competitiveness. Invaders can break the native trade-off if they come from a guild with a higher trade-off curve, an effect possibly enhanced evolutionarily by escape from specialist consumers.

competition↗

PubMed1996

Evolutionary stability in the n-person iterated prisoner's dilemma.

The iterated prisoner's dilemma game has been used extensively in the study of the evolution of cooperative behaviours in social and biological systems. The concept of evolutionary stability provides a useful tool to analyse strategies for playing the game. Most results on evolutionary stability, however, are based on the 2-person iterated prisoner's dilemma game. This paper extends the results in the 2-person game and shows that no finite mixture of pure strategies in the n-person iterated prisoner's dilemma game can be evolutionarily stable, where n > 2. The paper also shows that evolutionary stability can be achieved if mistakes are allowed in the n-person game.

Animals↗

PubMed2006

Involuntary defection and the evolutionary origins of empathy.

An occasional involuntary defection (IVD)--being unable, rather than unwilling, to donate help to others--is an intrinsic attribute of reciprocal cooperation (2003. J. Theor. Biol. 225-285). In fact, it is easy to see that--barring special circumstances--individuals that can donate help whenever requested do not need help of the same kind from others. That is, it is by no means clear why such individuals should participate in symmetric reciprocity interactions. In this paper, I analyse the consequences of introducing IVD into direct reciprocity modeling and show that a simple form of empathy--not retaliating after being punished for IVD--is a prerequisite for evolutionarily stable cooperation. Furthermore: we will see that the stability of this, empathic retaliator, strategy increases with the number of opportunities for cooperative exchanges in the life of an average individual.

Biological Evolution↗