Boundary constraints on population dynamics in a percolating habitat

Abstract

The spatial distribution of suitable environmental conditions defines a species habitat, and colonization-extinction dynamics within this habitat determine the distribution of species populations. In addition, the success of colonization and the risk of extinction are expected to be influenced by the proximity to habitat boundary. We address here the influence of boundary vicinity for a contact-process model of population dynamics in a percolating habitat lattice. To separate the influence of boundary vicinity from that of fragment area, we investigate population dynamics in the very large spanning cluster of the percolating habitat. The geometry of the spanning cluster varies when habitat density in the lattice is tuned away from the percolation threshold. We expect that the colonization success decreases closer to the boundary, leading to depleted site occupancy in the cluster, and that this effect is even more pronounced near the extinction threshold of the contact process. For the set of suitable sites of the cluster and unsuitable sites next to its boundary, we quantify the boundary density, σ, as the probability to draw a pair of suitable and unsuitable sites. The cluster boundary is most rugged and σ is maximal close to the percolation threshold of the habitat. We expect that the global influence of boundary on population dynamics in the cluster is greater when the boundary is more rugged. We thus investigate population dynamics in the spanning cluster for varying values of σ. We determine the stationary properties of population dynamics in the spanning cluster according to σ and to the species-specific ratio of extinction and colonization rates, denoted r. Using both numerical simulations and a pair-approximation model, we assess global species persistence and site occupancy patterns in the spanning cluster. We show that the extinction threshold rc depends crucially on σ, i.e., increasing σ limits global species persistence. Furthermore, increasing σ decreases the probability of site occupancy in the spanning cluster. A key result is that this influence extends to sites far from the boundary when r gets close to rc. Therefore, species that are at risk of extinction are more sensitive to the influence of habitat boundary. These results are of both theoretical and practical interest for understanding and forecasting species viability in heterogeneous and fragmented habitats.