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 calculation is based on four quantitative variables: maximum per capita reproduction rate, per capita mortality rate outside the fragment, carrying capacity in the conserved environment and mobility in the disturbed environment. The methodology is illustrated by a preliminary study, in which the model is used to estimate threshold area sizes for habitat fragments for the threatened species Sapajus xanthosternos .