Habitat fragmentation and extinction thresholds on fractal landscapes

Habitat fragmentation is a potentially critical factor in determining population persistence. In this paper, we explore the effect of fragmentation when the fragmentation follows a fractal pattern. The habitat is divided into patches, each of which is suitable or unsuitable. Suitable patches are either occupied or unoccupied, and change state depending on rates of colonization and local extinction. We compare the behaviour of two models: a spatially implicit patch-occupancy (PO) model and a spatially explicit cellular automaton (CA) model. The PO model has two fixed points: extinction, and a stable equilibrium with a fixed proportion of occupied patches. Global extinction results when habitat destruction reduces the proportion of suitable patches below a critical threshold. The PO model successfully recreates the extinction patterns found in other models. We translated the PO model into a stochastic cellular automaton. Fractal arrangements of suitable and unsuitable patches were used to simulate habitat fragmentation. We found that: (i) a population on a fractal landscape can tolerate more habitat destruction than predicted by the patch-occupancy model, and (ii) the extinction threshold decreases as the fractal dimension of the landscape decreases. These effects cannot be seen in spatially implicit models. Landscape structure plays a vital role in mediating the effects of habitat fragmentation on persistence.