Evolution and intraspecific competition: winners gain mates, dominance rights, desirable territory, or other advantages that will tend toward transmitting its genes to future generations at higher frequencies than the loser's genes; Total vs. Limited War Scenarios: Group selection as an agent producing adaptations benefiting the species rather than the individual or Individual selection for limited war strategies? Use simulation approaches from Game Theory: all individuals are of equal strength, size and fighting prowess, only differ in fighting strategy - i.e. symmetrical contests; each conflict consists of a series of agonistic moves with provocation, escalation, retaliation, etc.
Hawks & Doves Games: symmetric, discrete, alternative option, two-player, no-information conflict. Consider two individuals which are equal in every respect, except to their particular behavioral strategy. Hawks and doves thus do not refer to two species of birds, but rather to behavioral characteristics during encounters with conspecifics.
Hawks are individuals which always fight when encountering another individual at the resource, the loser is the one who first sustains injury; Doves in contrast run from a hawk and toss a coin when determining the winner of the encounter with another dove; Fitness (expressed in arbitrary fitness units that represent some number of offspring) is gained by winning access to a contested resource (Value: value of reward) and reduced by sustaining an injury (Cost - Cost of injury is paid by loser, no cost for winner); Values of rewards are always positive, costs are always negative. Success is assigned according to a winner and pay-off matrix:
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Can a dove invade a population of hawks? E(D,H) > E(H,H) or 0 > (V-C)/2 or C>V -> HAWK can only be an <Evolutionary Stable Strategy> (ESS) when C<V.
Can a hawk invade a population of doves? E(H,D) > E(D,D) or V > V/2 -> As the value of obtaining the contested resource is positive this condition must always be true, so Dove cannot be a pure ESS.
generally, no pure ESS but a mixed ESS resulting in stable proportions of different strategies: p = proportion of individuals playing hawk, 1-p = proportion of individuals playing dove. An ESS:
Solve for the proportion of Hawks (p) and Doves (1-p) at which the average payoff(Hawk) equals that for the average payoff(Dove).
(p)(E(H,H)) + (1-p)(E(H,D)) = (p)(E(D,H)) + (1-p)(E(D,D))
When you solve for p you obtain
p = V/C
As a thought exercise you can repeat the considerations above for the scenario in which the cost is carried by both combatants, irrespective of whether an animal wins or loses. This cost to both could represent the investment of energy by both, the danger of predation while fighting, or a loss of opportunities for other beneficial activities according to the following winner and pay-off matrix:
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