Survival of Species in Patchy Landscapes: Percolation in Space and Time

One of the major challenges in conservation biology is how to preserve natural populations in landscapes where various human activities (deforestation, urbanization, etc.) are shrinking the habitable area, and thus, natural populations can only exist in isolated or fragmented habitat patches. Theoretical considerations warn that gradual habitat loss can lead to a sudden breakdown in habitat connectivity. This fragmentation process is a critical transition, and can be described by models of isotropic percolation. On the other hand, a dispersal-limited population can get fragmented even in a homogeneously suitable area, and consequently, the regulation of population density becomes deficient. The transition from survival to extinction is also a critical transition, but belongs to a different universality class: directed percolation. We connect the two percolation processes, linking landscape dynamics with population dynamics. Focusing on the critical parameter region near to extinction, we review the scaling laws that describe the decline of population density, and the divergence of spatial and temporal correlations in the population. These laws may help to predict extinction, and define proper management techniques to prolong persistence.