title: Modelling the dynamics of traits involved in fighting-predators-prey system.
abstract: We study the dynamics of a predator-prey system where predators fight for captured prey besides searching for and handling (and digestion) of the prey. Fighting for prey is modelled by a continuous time hawk-dove game dynamics where the gain depends on the amount of disputed prey while the costs for fighting is constant per fighting event. The strategy of the predator-population is quantified by a trait being the proportion of the number of predator-individuals playing hawk tactics. The dynamics of the trait is described by two models of adaptation: the replicator dynamics (RD) and the adaptive dynamics (AD). In the RD-approach a variant individual with an adapted trait value changes the population's strategy, and consequently its trait value, only when its payoff is larger than the population average. In the AD-approach successful replacement of the resident population after invasion of a rare variant population with an adapted trait value is a step in a sequence changing the population's strategy, and hence its trait value. The main aim is to compare the consequences of the two adaptation models. In an equilibrium predator-prey system this will lead to convergence to a neutral singular strategy, while in the oscillatory system to a continuous singular strategy where in this endpoint the resident population is not invasible by any variant population. In equilibrium (low prey carrying capacity) RD and AD-approach give the same results, however not always in a periodically oscillating system (high prey carrying-capacity) where the trait is density-dependent. For low costs the predator population is monomorphic (only hawks) while for high costs dimorphic (hawks and doves). These results illustrate that intra-specific trait dynamics matters in predator-prey dynamics.
authors.affiliation: Department of Theoretical Biology, VU University, de Boelelaan 1085, 1081 HV, Amsterdam, The Netherlands. bob.kooi@vu.nl.
authors.forename: B W
authors.initials: BW
authors.lastname: Kooi
mesh_terms: D000222:Adaptation, Physiological; D000818:Animals; D005075:Biological Evolution; D017753:Ecosystem; D020387:Food Chain; D005716:Game Theory; D055641:Mathematical Concepts; D008954:Models, Biological; D011157:Population Dynamics; D011235:Predatory Behavior / Q000502:physiology*
keywords: Aggregation technique; Bifurcation analysis; Evolutionary game theory; Hawk–dove game theory; Learning models; Paradox of enrichment