When shape matters: using a simple mathematical model to estimate critical area sizes in conservation.

Abstract

In the analysis of anthropogenic impact on the environment arises the question of whether the shapes of preserved habitat fragments play an important role in the conservation of wild species. In this work we use a very simple mathematical model based on a reaction-diffusion equation to analyze the effects of geometric shape and area on the permanence of populations in habitat fragments. Our results indicate that a dimensionless quantity calculated from a combination of biological variables is the main component that determines if the species survives in the preserved fragment and whether its geometric shape is important. We provide a methodology to calculate critical area sizes for which population size is most affected by fragment shape. The methodology is illustrated in a preliminary study, in which the model is used to estimate threshold area sizes for habitat fragments of a threatened species Sapajus xanthosternos.