Estimating landscape carrying capacity through maximum clique analysis

Habitat suitability (HS) maps are widely used tools in wildlife science and establish a link between wildlife populations and landscape pattern. Although HS maps spatially depict the distribution of optimal resources for a species, they do not reveal the population size a landscape is capable of supporting--information that is often crucial for decision makers and managers. We used a new approach, "maximum clique analysis," to demonstrate how HS maps for territorial species can be used to estimate the carrying capacity, N(k), of a given landscape. We estimated the N(k) of Ovenbirds (Seiurus aurocapillus) and bobcats (Lynx rufus) in an 1153-km2 study area in Vermont, USA. These two species were selected to highlight different approaches in building an HS map as well as computational challenges that can arise in a maximum clique analysis. We derived 30-m2 HS maps for each species via occupancy modeling (Ovenbird) and by resource utilization modeling (bobcats). For each species, we then identified all pixel locations on the map (points) that had sufficient resources in the surrounding area to maintain a home range (termed a "pseudo-home range"). These locations were converted to a mathematical graph, where any two points were linked if two pseudo-home ranges could exist on the landscape without violating territory boundaries. We used the program Cliquer to find the maximum clique of each graph. The resulting estimates of N(k) = 236 Ovenbirds and N(k) = 42 female bobcats were sensitive to different assumptions and model inputs. Estimates of N(k) via alternative, ad hoc methods were 1.4 to > 30 times greater than the maximum clique estimate, suggesting that the alternative results may be upwardly biased. The maximum clique analysis was computationally intensive but could handle problems with < 1500 total pseudo-home ranges (points). Given present computational constraints, it is best suited for species that occur in clustered distributions (where the problem can be broken into several, smaller problems), or for species with large home ranges relative to grid scale where resampling the points to a coarser resolution can reduce the problem to manageable proportions.