Rodrigo Pereira Rocha — Università di Padova #
Surviving in hostile and heterogeneous environments #
In this work we study the survival probability of single-species in the context of hostile and heterogeneous environments. Here we use spatially random growth rates with negative mean to model hostile and heterogeneous environments i.e. population dynamics in this environment, as modeled by the Fisher equation, is characterized by negative average growth rate (\( \bar{\mu} \)), except in some random spatially distributed patches that may support life (\(\mu_i>0\)). In particular, we are interested in the phase diagram of the survival probability and the critical size problem, i.e., the minimum patch size required for surviving in the long time limit. We propose a measure for the critical size as being proportional to the participation ratio (PR) of the eigenvector corresponding to the largest eigenvalue of the linearized Fisher dynamics. We numerically obtain the (extinction-survival) phase diagram and the critical patch size distribution for two network topologies, namely, the linear chain and the Peano basin fractal. We show that both topologies share the same qualitative features, but the fractal topology requires higher spatial fluctuations to guarantee species survival, which leads to a slightly larger patch size than the linear chain. In addition, we perform a finite-size scaling and we obtain the associated critical exponents.