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  • 1
    Electronic Resource
    Electronic Resource
    On the war of attrition and other games among kin (1996)
    Springer
    Journal of mathematical biology 34 (1996), S. 253-270 
    Details
    ISSN: 1432-1416
    Keywords: ESS ; Game theory ; Contest behavior ; Kin selection
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Evolutionarily stable strategies or ESSs of games among kin have been calculated in the literature by both “personal-fitness” and “inclusive-fitness” methods. These methods were compared by Hines and Maynard Smith (1979) for games with bilinear payoffs. Although Hines and Maynard Smith regarded the first method as correct, they regarded the second method as useful because the inclusive-fitness conditions for an ESS gave necessary conditions for a personal-fitness ESS in the class of games they considered. In general, however, satisfying the inclusive-fitness conditions is neither necessary nor sufficient for satisfying the personal-fitness conditions, although the two methods may often yield identical ESSs. This result is established by reformulating the classic war-of-attrition model to allow variation in energy reserves, assumed to have a Gamma distribution. For this game, the two methods may disagree for intermediate values of relatedness. By the correct method, if the coefficient of variation in energy reserves is sufficiently high, then the game has a unique ESS in pure strategies at which populations with higher coefficients of variation or relatedness display for shorter times. Unrelated contestants are prepared to expend at least half of their reserves. For populations with lower variation coefficients, the ESS exists only if the cost of displaying per unit time is low compared to the rate at which remaining reserves translate into expected future reproductive success for the victor. The critical variation coefficient, below which the ESS exists regardless of cost, decreases from 0.52 to 0 as the coefficient of relatedness increases from 0 to 1. Although there is no assessment, contests are always won by the animal with greater energy reserves in a population at the ESS.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00160496
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  • 2
    Electronic Resource
    Electronic Resource
    Ecotypic variation in the asymmetric Hawk-Dove game: When is Bourgeois an evolutionarily stable strategy? (1992)
    Springer
    Evolutionary ecology 6 (1992), S. 198-222 
    Details
    ISSN: 1573-8477
    Keywords: ESS ; game theory ; fighting ; spiders
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Summary This paper develops a mathematical model of an iterated, asymmetric Hawk-Dove game with the novel feature that not only are successive pairs of interactants — in the roles of owner and intruder contesting a site — drawn randomly from the population, but also the behaviour adopted at one interaction affects the role of a contestant in the next. Under the assumption that a site is essential for reproduction, the evolutionarily stable strategy (ESS) of the population is found to depend on the probability, w, that the game will continue for at least a further period (which is inversely related to predation risk), and five other parameters; two of them are measures of site scarcity, two are measures of fighting costs, and the last is a measure of resource holding potential (RHP). Among the four strategies — Hawk (H), Dove (D), Bourgeois (B) and anti-Bourgeois (X) — only D is incapable of being an ESS; and regions of parameter space are found in which the ESS can be only H, or only X, or only B; or either H or X; or either X or B; or either H or B; or any of the three. The scarcer the sites or the lower the costs of fighting, or the lower the value of w, the more likely it is that H is an ESS; the more abundant the sites or the higher the costs of fighting, or the higher the value of w, the more likely it is that X or B is an ESS. The different ESSs are interpreted as different ecotypes. The analysis suggests how a non-fighting population could evolve from a fighting population under decreasing risk of predation. If there were no RHP, or if RHP were low, then the ESS in the non-fighting population would be X; only if RHP were sufficiently high would the ESS be B, and the scarcer the sites, the higher the RHP would have to be. These conclusions support the thesis that if long-term territories are essential for reproduction and sites are scarce, then ownership is ruled out not only as an uncorrelated asymmetry for settling disputes in favour of owner, but also as a correlated asymmetry.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02214162
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  • 3
    Electronic Resource
    Electronic Resource
    The Hawk—Dove game revisited: Effects of continuous variation in resource-holding potential on the frequency of escalation (1994)
    Springer
    Evolutionary ecology 8 (1994), S. 230-247 
    Details
    ISSN: 1573-8477
    Keywords: ESS ; game theory ; aggression ; resource holding potential ; beetles
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Summary The classic Hawk—Dove game is extended to deal with continuous variation in resource-holding potential or RHP, when RHP is observable (via any sensory modality) but RHP difference is less than perfectly reliable as a predictor of the outcome of an escalated contest. The relationship between sensory and physical magnitudes of RHP is assumed to be governed by Fechner's psychophysical law, whose effect is that contestants interact as if they had perfect information about their relative RHP (as opposed to RHP difference). Thus, an animal is aggressive if its RHP exceeds a certain fraction, called its threshold, of its opponent's RHP and otherwise is non-aggressive; and the classic Hawk and Dove strategies correspond to zero and infinite thresholds, respectively. For RHPs drawn at random from an arbitrary Gamma distribution there is a unique evolutionarily stable strategy or ESS, which depends on a parameter α measuring the reliability of RHP as a predictor of the outcome of a fight, on the ratio of the valueV of winning to the costC of losing (both measured in units of reproductive fitness) and on the mean µ and variance σ2 of the RHP distribution. In a population at this ESS, ifV/C 〈 1 then the threshold is 1 and there is no fighting. AsV/C increases beyond 1 to a second critical value ζ, however, the threshold decreases steadily from 1 to 0 and remains 0 forV/C 〉 ζ; ζ is an increasing function of α, but a decreasing function of σ2. That a lower variance of RHP can imply a lower escalation frequencyp is a novel insight of the analysis. The prediction is at first counterintuitive, because if the aggression threshold were fixed then larger variance would imply lowerp (dispersion effect of variance). When natural selection acts on the threshold, however, increasing the variance not only reduces the probability that an animal with larger RHP will be attacked by an animal with lower RHP at the existing threshold, but also reduces the expected costs of adopting that particular threshold, so that a mutant with a somewhat lower threshold can invade the population (selection effect of variance). Forp, the selection effect dominates toward the upper end of the interval 1 ≤V/C ≤ ζ.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01238275
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    Paper (German National Licenses)
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