| Abstract: |
| A primary driver of species extinctions and declining biodiversity is loss and fragmentation of habitats owing to human activities. Many studies spanning a wide diversity of taxa have described the relationship between population density and habitat patch area, i.e., the density-area relationship (DAR), as positive, neutral, negative or some combination of the three. However, the mechanisms responsible for these relationships remain elusive. In this talk, we will discuss implementation of a reaction-diffusion framework with absorbing boundary conditions to model a habitat specialist dwelling in islands of habitat surrounded by a hostile matrix. We consider patches with both a convex and non-convex geometry. Our results show overall DAR structure can be either 1) positive, 2) positive for small areas and neutral for large, or 3) hump-shaped, i.e., positive for area below a threshold and negative for area above. We will also discuss comparison of our theoretical results with two empirical studies. Close qualitative agreement between theoretical and observed DAR indicates that our model gives a reasonable explanation of the mechanisms underpinning DAR found in those studies. |
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