Spatial organization, grouping strategies and cyclic dominance in asymmetric predator-prey games

Abstract

Predators may attack isolated or grouped preys in a cooperative, collective way. Whether a gregarious behavior is advantageous to each species depends on several conditions and game theory is a useful tool to deal with such a problem. We here extend the Lett-Auger-Gaillard model [Theor. Pop. Biol. 65, 263 (2004)] to spatially distributed groups and compare the resulting behavior with their mean field predictions for the coevolving densities of predator and prey strategies. We show that the coexistence phase in which both strategies for each group are present is stable because of an effective, cyclic dominance behavior similar to a well studied generalizations of the RockPaper-Scissors game with four species (without neutral pairs), a further example of how ubiquitous this mechanism is. In addition, inside the coexistence phase (but interestingly, only for finite size systems) there is a realization of the survival of the weakest effect that is triggered by a percolation crossover.

Cyclic Competition and Percolation in Grouping Predator-Prey Populations

“…The more general version of the model proposed by Lett et al is fully described in Refs. [4,33]. We here present, as also done in Refs.…”

“…Thus, the four possible combinations for each site are (x i y i ): 00, 01, 10 and 11. Interestingly, these strategies obey cyclic dominance relations leading to persistent coexistence for a broad set of parameters [4]. This behavior is reminiscent of the generalizations of the RPS game with more than three species [1,2].…”

“…We here present, as also done in Refs. [4,33], a simplified version in which we reduce the number of free parameters to only two. We consider no reduction in resource intake by the preys when they are grouped (γ = 1 in the notation of Ref.…”

“…One example is three-strategies games with optional participation: Although not explicit in the payoff matrix, dominance emerges in the presence of these agents that do not follow the rules of the game and prefer, instead, to earn a smaller payoff [3]. Another scenario in which cyclic dominance appears is among preys and predators choosing, respectively, their hunt and defense strategy while trying to outcompete each other [4]. Predators may attack in a cooperative, coordinated way, with their actions being correlated in space and time [5].…”

“…The main hypothesis is that grouping, for preys, lowers their risk of being preyed but increases the competition for resources, while predators have a greater probability of success at the expense of having to share the prey with others, sometimes referred to as the "many-eyes, many mouths" trade off [28,29]. Recently, Cazaubiel et al [4] revisited the model and proposed a spatial version with local interactions and binary strategies, unveiling the mechanism underlying the stability of the coexistence phase. In this version, all predators in site i may form a single group (x i = 1) or hunt independently (x i = 0), while the preys have a similar behavior (y i = 0, 1).…”