Efeitos de topologia em sistemas biológicos

Abstract

In this work we analyse two problems coming from theoretical biology. In the first part we propose a spatially structured population model which is defined on a continuous lattice. In the model individuals disperse at a constant rate v and competition is local and delimitated by the competition radius R. Due to dispersal, the neighborhooh size fluctuates over time. We analyse how these variables affect the adaptive process. While the fixation probabilities of beneficial mutations are roughly the same as in a panmitic population for small and intermediate fitness effects s, a dependence on v and R appears for large s. These quantities also strongly influence fixation times. The model exhibits a dual behavior displaying a power-law growth for the fixation rate and speed of adaptation with the beneficial mutation rate as observed in spatially structured population models, but simultaneously showing a non-saturating behavior for the speed of adaptation with the population size. In the second part we numerically study the dynamics of model imune networks with random and scale-free topologies. We observe that a memory state is reached when the antigen is attached to the most connected sites of the network, where as a percolation state may occur when the antigen attaches to the less connected sites. For increasing values of the connectivity, its population converges exponentially to the asymptotic value of the memory state. On the other hand, the next-nearest populations evolve slowly as power-laws towards the virgin-like state.