arXiv subjects

T. A. Pereira

Publications and source records attributed to T. A. Pereira.

3 recordsLinked to original sources

arXiv2019

Expanding spatial domains and transient scaling regimes in populations with local cyclic competition

We investigate a six-species class of May-Leonard models leading to formation two types of competing spatial domains, each one inhabited by three-species with their own internal cyclic rock-paper-scissors dynamics. We study the resulting population dynamics using stochastic numerical simulations in two-dimensional space. We find that as three-species domains shrink, there is an increasing probability of extinction of two of the species inhabiting the domain, with the consequent creation of one-species domains. We determine the critical initial radius beyond which these one-species spatial domains are expected to expand. We further show that a transient scaling regime, with a slower average growth rate of the characteristic length scale $L$ of the spatial domains with time $t$, takes place before the transition to a standard $L \propto t^{1/2}$ scaling law, resulting in an extended period of coexistence.

nlin.AO↗

arXiv2019

Uneven rock-paper-scissors models: patterns and coexistence

We study a class of the stochastic May-Leonard models, with three species dominating each other in a cyclic nonhierarchical way, according to the rock-paper-scissors game. We introduce an unevenness in the system, by considering that one of the species is weaker because of a lower selection probability. The simulation results show that the pattern formation is drastically affected by the presence of the weaker species, with no spiral waves arising immediately from random initial conditions. Instead, single-species spatial domains cyclically dominate the entire territory until a region occupied by the weaker species is sufficiently narrow to be crossed by individuals without being selected. This leads to the appearance of spatial patterns responsible for the species coexistence. We verify that the asymmetry in the selection probabilities leads to different spatial autocorrelation function and average relative species abundances. Finally, we investigate the coexistence probability and show that the surviving species depends on the level of unevenness of the model and the mobility of individuals.

q-bio.PE↗

arXiv2018

Interface networks in models of competing alliances

We study a subclass of the May-Leonard stochastic model with an arbitrary, even number of species, leading to the arising of two competing partnerships where individuals are indistinguishable. By carrying out a series of accurate numerical stochastic simulations, we show that alliances compete each other forming spatial domains bounded by inter- faces of empty sites. We solve numerically the mean field equations associated to the stochastic model in one and two spatial dimensions. We demonstrate that the stationary interface profile presents topological properties which are related to the asymptotic spa- tial distribution of species of enemy alliances far away from the interface core. Finally, we introduce a theoretical approach to model the formation of stable interfaces using spontaneous breaking of a discrete symmetry. We show that all the results provided by the soliton topological model, presented here for the very first time, are in agreement with the stochastic simulations and may be used as a tool for understanding the complex biodiversity in Nature.

nlin.PS↗