Emergence of unusual coexistence states in cyclic game systems

Abstract

Evolutionary games of cyclic competitions have been extensively studied to gain insights into one of the most fundamental phenomena in nature: biodiversity that seems to be excluded by the principle of natural selection. The Rock-Paper-Scissors (RPS) game of three species and its extensions [e.g., the Rock-Paper-Scissors-Lizard-Spock (RPSLS) game] are paradigmatic models in this field. In all previous studies, the intrinsic symmetry associated with cyclic competitions imposes a limitation on the resulting coexistence states, leading to only selective types of such states. We investigate the effect of nonuniform intraspecific competitions on coexistence and find that a wider spectrum of coexistence states can emerge and persist. This surprising finding is substantiated using three classes of cyclic game models through stability analysis, Monte Carlo simulations and continuous spatiotemporal dynamical evolution from partial differential equations. Our finding indicates that intraspecific competitions or alternative symmetry-breaking mechanisms can promote biodiversity to a broader extent than previously thought.Fundamental to species coexistence and biodiversity are competitions. In ecosystems there are two types of competitions: interspecific (competitions among individuals from different species) and intraspecific (competitions among individuals in the same species), where both types can either promote or hinder species coexistence 1, 2 . The purpose of this paper is to demonstrate, through a systematic study of several models of cyclic evolutionary game, that intraspecific competitions can induce unusual states of coexistence that have not been reported previously. Intraspecific competitions may thus be more fundamental to biodiversity than previously thought.A natural and typical mechanism for interspecific competitions is predator-prey interaction, while intraspecific competitions occur because individuals in the same species compete for essential life-sustaining resources such as food, water, light, and opposite sex. A well known type of intraspecific competitions is cannibalism or intraspecific predation 3-10 , which can occur with high likelihood especially when there is lack of sufficient resources. Such competitions can also occur when individuals fight each other for mating opportunities, which were observed for side-blotched lizards in California 11 . In the past decade there were studies of the effect of intraspecific competitions on biodiversity [12][13][14][15][16] , with results such as the experimental finding that the competitions tend to drive disruptive selection 12 , enhanced host survival through intraspecific competition between co-infecting parasite strains 13 , and directional selection of certain fish species 15,16 .To understand coexistence and biodiversity, the approach of mathematical modeling has proven to be useful, providing fundamental insights into the various mechanisms underlying species coexistence at both the macroscopic, population [17][18][19] and the microscopic, individual...

The effect of territorial awareness in a three-species cyclic predator–prey model

“…Even if different k are considered, the panels in Fig. 2 show features similar to previous works 11 , 14 – 16 , 18 , 20 : coexistence and extinction for tops and bottoms, respectively. At the low mobility as shown in Fig.…”

“…To investigate the evolution of cyclically competing species with intraspecific interaction which sensitively plays to the territory awareness, we employ the spatial RPS model 11 , 19 , 20 , 23 . At the microscopic level, the model can be demonstrated on a lattice system, and for convenience, we consider a square lattice of size N with periodic boundary conditions where all sites have von Neumann neighbors.…”

“…In contrast to the classic spatial RPS game 11 , recent studies on the RPS system with intraspecific interaction exhibit persistent coexistence when the strength of intraspecific interaction exceeds a certain value 15 , 18 , 19 , 21 . In addition, considering symmetry-breaking on intraspecific interaction can yield diverse survival states which can realize the survival of subgroup population 20 , 22 . For such features, we found that the effect of mobility has been disappeared, i.e., coexistence and diverse survival states are independent to mobility.…”

“…Thus considering the territorial imbalance of (local) species is necessary to understand intraspecific interaction. Nevertheless, most results in previous works above have been established with constant rates: either uniform rate of intraspecific interaction for all groups 15 , 18 , 19 , 21 , or nonuniform rates depending on characteristic of groups 20 , 22 . In other words, given that intraspecific interaction is related to the territorial consciousness of individuals, it has not been rigorously studied.…”

Three-species competition with non-deterministic outcomes

“…Variation of the winning probabilities can take the competition network from the non-transitive deterministic setting which has been the subject of previous studies [13][14][15][17][18][19][20]23,26,28,[31][32][33][34] [ Fig. 1(a)], when P AB = P BC = P CA = 1 or P AB = P BC = P CA = 0, to the transitive deterministic setting [e.g., Fig.…”