Persistence and management of spatially distributed populations

Hastings, A., 2014. Persistence and management of spatially distributed populations. Population Ecology, 56(1), pp.21-26.

This review paper describes a framework for organizing management approaches for species persistence (i.e., for endangered species) and elimination (i.e., for invasive species) based on the local population growth (e.g., Allee effects) and spatial connectivity. Using this framework for thinking about management, Hastings provides an overview of models for determining persistence conditions in a spatial context, and couples each with corresponding management recommendations. Throughout the paper, he emphasizes deterministic approaches.
Metapopulations are simple spatially implicit models to considering persistence. In these models, persistence occurs when the rate of colonization exceeds the rate of extinction. There are many extensions to the simple Levin’s Metapopulation model that lead to more complex spatially implicit models. For example, Hastings describes how the rate of colonization or extinction could depend on the time since a patch was occupied as a way to describe the effects of spatial location. Empirical studies have validated this assumption: if a species has spent a long amount of time in a location, the rate of local extinction would decrease. Another way to include space is by representing habitats on a lattice and so each cell’s rate of extinction and colonization depend on the neighboring cells. These models help us understand how management for changes in the extinction or colonization rate impact population persistence. They have also given key insights into how changes in the availability of suitable habitat change population persistence.
While metapopulation models describe space as discrete, and describe individuals moving long distances between habitats, diffusion models describe space and time as continuous and can show the effects of short distance dispersal. Diffusion models typically describe the simplest form of no heterogeneity within the region of interest. Here, the boundary condition (where the habitat ends) plays a large role in species persistence. The final model that Hastings presents is the integro-difference equation which is typically used for species that reproduce once per year. As Hastings acknowledges, an advantage to using this model formulation over the reaction diffusion equation is that it can account for dispersal through poor habitat. This type of model, with areas of unhabitatable space, can make key recommendations about necessary size of reserve and amount of dispersal throughout. Finally, network models of persistence can describe how the geometry of habitat connects change a population’s persistence. The main goals of this paper were to (1) introduce a general framework for understanding persistence as the interaction between local dynamics and connectivity and (2) to describe the general principles that emerge from this characterization.