Dinâmica estocástica de sistemas biológicos: caos e o efeito do predador de topo

Abstract

To understand how different species interact and the mechanisms responsible for maintaining biodiversity observed in nature is a still open issue in ecology. Several simplified models have been proposed and extensively studied in the last few decades. As an example we can mention the acyclic predator-prey model of Lotka-Volterra, used to study the transitive competing relationship (hierarchical) between two or more species, and the rock-paper-scissors models involving three or more species in a intransitive relationship. It is well known that intransitivity may lead to biodiversity. On the other hand, in transitive relationship, the ecological importance of the apex predator has has been the focus of several investigations. The presence of an apex predator in a given ecosystem may favor coexistence of species, since it can diminish the process of competitive exclusion, imposing its own order to the set of species. This is known as predator-mediated coexistence and has been identified in several distinct settings, such as coral reef communities, communities of birds, and vegetationally diverse environments. This thesis deals with the effects of an apex predator on the cyclic competition among three distinct species that follow the rules of rock-paper-scissors game. We add the apex predator as the fourth species in the system that contains three species that evolve following the standard rules of migration, reproduction and predation, and study how the system evolves in this new environment, in comparison with the case in the absence of the apex predator. We use the principle of maximum entropy to derive a mathematical expression to connect the density of maxima of an observable to its autocorrelation function. We use the Hamming distance concept to differentiate the random behavior from the chaotic behavior of the systems studied. The results show that species in a cyclic competition engenders the tendency to cluster as a survival mechanism and the apex predator tends to spread uniformly in the lattice, diminishing the average size of the clusters of the species that compete cyclically.