Performance of weak species in the simplest generalization of the rock-paper-scissors model to four species

Influence and influenceability: global directionality in directed complex networks

Knowing which nodes are influential in a complex network and whether the network can be influenced by a small subset of nodes is a key part of network analysis. However, many traditional measures of importance focus on node level information without considering the global network architecture. We use the method of trophic analysis to study directed networks and show that both 'influence' and 'influenceability' in directed networks depend on the hierarchical structure and the global directionality, as measured by the trophic levels and trophic coherence, respectively. We show that in directed networks trophic hierarchy can explain: the nodes that can reach the most others; where the eigenvector centrality localizes; which nodes shape the behaviour in opinion or oscillator dynamics; and which strategies will be successful in generalized rock-paper-scissors games. We show, moreover, that these phenomena are mediated by the global directionality. We also highlight other structural properties of real networks related to influenceability, such as the pseudospectra, which depend on trophic coherence. These results apply to any directed network and the principles highlighted-that node hierarchy is essential for understanding network influence, mediated by global directionality-are applicable to many real-world dynamics.

How local antipredator response unbalances the rock-paper-scissors model

Antipredator behavior is a self-preservation strategy present in many biological systems, where individuals join the effort in a collective reaction to avoid being caught by an approaching predator. We study a nonhierarchical tritrophic system, whose predator-prey interactions are described by the rock-paper-scissors game rules. We perform a set of spatial stochastic simulations where organisms of one out of the species can resist predation in a collective strategy. The drop in predation capacity is local, which means that each predator faces a particular opposition depending on the prey group size surrounding it. Considering that the interference in a predator action depends on the prey's physical and cognitive ability, we explore the role of a conditioning factor that indicates the fraction of the species apt to perform the antipredator strategy. Because of the local unbalancing of the cyclic predator-prey interactions, departed spatial domains mainly occupied by a single species emerge. Unlike the rock-paper-scissors model with a weak species because of a nonlocal reason, our findings show that if the predation probability of one species is reduced because individuals face local antipredator response, the species does not predominate. Instead, the local unbalancing of the rock-paper-scissors model results in the prevalence of the weak species' prey. Finally, the outcomes show that local unevenness may jeopardize biodiversity, with the coexistence being more threatened for high mobility.

Lotka-Volterra versus May-Leonard formulations of the spatial stochastic rock-paper-scissors model: The missing link

The rock-paper-scissors (RPS) model successfully reproduces some of the main features of simple cyclic predator-prey systems with interspecific competition observed in nature. Still, lattice-based simulations of the spatial stochastic RPS model are known to give rise to significantly different results, depending on whether the three-state Lotka-Volterra or the four-state May-Leonard formulation is employed. This is true independently of the values of the model parameters and of the use of either a von Neumann or a Moore neighborhood. In this paper, we introduce a simple modification to the standard spatial stochastic RPS model in which the range of the search of the nearest neighbor may be extended up to a maximum Euclidean radius R. We show that, with this adjustment, the Lotka-Volterra and May-Leonard formulations can be designed to produce similar results, both in terms of dynamical properties and spatial features, by means of an appropriate parameter choice. In particular, we show that this modified spatial stochastic RPS model naturally leads to the emergence of spiral patterns in both its three- and four-state formulations.