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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