Patch definition in metapopulation analysis: a graph theory approach to solve the mega-patch problem.

The manner in which patches are delineated in spatially realistic metapopulation models will influence the size, connectivity, and extinction and recolonization dynamics of those patches. Most commonly used patch-definition methods focus on identifying discrete, contiguous patches of habitat from a single temporal observation of species occurrence or from a model of habitat suitability. However, these approaches are not suitable for many metapopulation systems where entire patches may not be fully colonized at a given time. For these metapopulation systems, a single large patch of habitat may actually support multiple, interacting subpopulations. The interactions among these subpopulations will be ignored if the patch is treated as a single unit, a situation we term the "mega-patch problem." Mega-patches are characterized by variable intra-patch synchrony, artificially low inter-patch connectivity, and low extinction rates. One way to detect this problem is by using time series data to calculate demographic synchrony within mega-patches. We present a framework for identifying subpopulations in mega-patches using a combination of spatial autocorrelation and graph theory analyses. We apply our approach to southern California giant kelp (Macrocystis pyrifera) forests using a new, long-term (27 years), satellite-based data set of giant kelp canopy biomass. We define metapopulation patches using our method as well as several other commonly used patch delineation methodologies and examine the colonization and extinction dynamics of the metapopulation under each approach. We find that the relationships between patch characteristics such as area and connectivity and the demographic processes of colonizations and extinctions vary among the different patch-definition methods. Our spatial-analysis/graph-theoretic framework produces results that match theoretical expectations better than the other methods. This approach can be used to identify subpopulations in metapopulations where the distributions of organisms do not always reflect the distribution of suitable habitat.