Modelagem computacional de ecossistemas com competição por recursos e evolução em ambientes heterogêneos

Abstract

In this thesis we study an ecosystem model with a spatial structure in which species compete for resources and evolve in a heterogeneous environment. Environmental heterogeneity is introduced through the allocation of resources, which are distributed on the network through a fractal landscape generated through the simulation of the fractional Brownian movement. Thus, the roughness of the landscape is controlled by Hurst’s exponent, H. Each species is characterized by a set of half-saturation constants, which define the e ciency of the species in the use of each resource. Only one species is initially introduced into the system, and new species are generated from mutations that occur with probability ѵ. The set of half-saturation constants that characterize the mutant species is obtained from the set of the ancestral species, in which one of the constants is modified and obtained through a normal distribution in which the mean is equal to that of the ancestral species and three di erent values for the variance are studied. In the first part of the work, we studied the behavior of diversity patterns presented by the system. We observed that the mean diversity presented a lower value for H = 0:01 (very rough landscape) for the case in which the probability of mutation of the species is lower. We also verify that the species-area relationship has two power law regimes in which S ~ Az, where the exponents obtained for large areas are greater than those obtained for small areas. We also investigated the relationship between the mean number of species and the Hurst exponent, H. For the highest mutation probability value, we note that a higher value of variance in the distribution of the half-saturation constants leads to less diversity. For the case in which the probability of mutation is lower, we observed an increase in the average number of species with H, and less diversity for the case in which the variance of the distribution of the half-saturation constants is smaller. In the second part of the work we did a more statistical study, where we analyzed the behavior of the distribution of the fluctuations in the temporal evolution of diversity. We also studied the relationship between diversity and di erent mutation probability values. We saw that the stretched exponential distribution provided a good fit of the behavior of heavy tail distributions, as were the distributions of the histograms of increments of diversity. We find an adjustment exponent β ≈ 1 indicating that the system has memory for low mutation probabilities, and an exponent β = 2 for higher mutation probabilities, from which we infer that the system behaves like a Markov process. We also noticed a behavior change in the relationship between the exponent and the β mutation probability. For low mutation probability values this relationship follows a power law. For high mutation probabilities, β becomes independent of ѵ. We realized that changing the fluctuation in diversity only depends on the probability of mutation.