Modelagem de interações ecológicas em ambientes com estrutura espacial

Abstract

The heterogeneity of an ecosystem has a great and decisive influence on the population dynamics of the species. In this work we aimed to investigate how the spatial correlation among the resources of a lattice model influences the space-time dynamics of a prey-predator system, as well as the dynamics of competing species that compete for limiting resources. The heterogeneity of the ecosystem is incorporated through the correlation among the resources, based on a bivariate Gaussian distribution, for the predation and competition model. A second predation model, with fractal distribution of resources, generated by the fractional Brownian motion, was also investigated. In the prey-predator system, with Gaussian distribution, we found after the computational simulations that the correlation among the resources favors the coexistence of the two species, for intermediate values of the probability of reproduction of the predator, since the areas where the two species coexist is extended to intermediate values of the correlation parameter. For the fractal landscape, when we vary the value of the Hurst exponente, 𝐻, the area of coexistence of the two species is enlarged, since when the resource distribution is very homogeneous, for H = 0.99, we observed the largest region with the two species coexisting over time. In the system with competition, we can observe that the number of species that survive in the ecosystem increases gradually as we increase the value of λ, reaching its maximum diversity very close to the maximum correlation of the network.