Recombination and Genetic Diversity

In this paper we present a spatial stochastic model for genetic recombination, that answers if diversity is preserved in an infinite population of recombinating individuals distributed spatially. We show that, for finite times, recombination may maintain all the various potential different types, but when time grows infinitely, the diversity of individuals extinguishes off. So under the model premisses, recombination and spatial localization alone are not enough to explain diversity in a population. Further we discuss an application of the model to a controversy regarding the diversity of "Major Histocompatibility Complex" (MHC).

CAPACITY DISTRIBUTIONS IN SPATIAL STOCHASTIC MODELS FOR TELECOMMUNICATION NETWORKS

We consider the stochastic subscriber line model as a spatial stochastic model for telecommunication networks and we are interested in the evaluation of the required capacities at different locations of the network in order to provide, in fine, an estimation of the cable system which has to be installed. In particular, we consider hierarchical telecommunication networks with higher–level components (HLC) and lower–level components (LLC) located on the road system underlying the network. The cable paths are modeled by shortest paths along the edge set of a stationary random tessellation, whereas both HLC and LLC are modeled by Cox processes concentrated on the edges of this tessellation. We then introduce the notion of capacity which depends on the length of some subtree on the edge set of the underlying tessellation. Moreover, we investigate estimators for the density and distribution function of the typical length of this subtree which can be computed based on Monte Carlo simulations of the typical serving zone. In a numerical study, the density of the typical subtree length is determined for different specific models.