Aninhamento em redes bipartidas

We present a nestedness index that measures the nestedness pattern of bipartite networks, a problem that arises in theoretical ecology. Our measure is derived using the sum of distances of the occupied elements in the adjacency matrix of the network. This index quantifies directly the deviation of a given matrix from the nested pattern. In the most simple case the distance of the matrix element ai,j is di,j = i+j, the Manhattan distance. A generic distance is obtained as di,j = (i¬ + j¬)1/¬. The nestedness índex is defined by = 1 − where is the temperature of the matrix. We construct the temperature index using two benchmarks: the distance of the complete nested matrix that corresponds to zero temperature and the distance of the average random matrix that is defined as temperature one. We discuss an important feature of the problem: matrix occupancy. We address this question using a metric index ¬ that adjusts for matrix occupancy

Influência da filogenia em redes de interações ecológicas

In this thesis we deal with a class of composed networks that are formed by two tree networks, TP and TA, whose end points touches each other through a bipartite network BPA. We explore this network using a functional approach. We are interested in what extend the topology, or the structure, of TX (X = A or P) determines the links of BPA. This composed structure is an useful model in evolutionary biology, where TP and TA are the phylogenetic trees of plants and animals that interact in an ecological community. We use in this thesis two cases of mutualist interactions: frugivory and pollinator networks. We analyse how the phylogeny of TX determines or is correlated with BPA using a Monte Carlo approach. We use the phylogenetic distance among elements that interact with a given species to construct an index κ that quantifies the influence of TX over BPA. The algorithm is based in the assumption that interaction matrices that follows a phylogeny of TX have a total phylogenetic distance smaller than the average distance of an ensemble of Monte Carlo realizations generated by an adequate shuffling data. We find that the phylogeny of animals species has an effect on the ecological matrix that is more marked than plant phylogeny