Estimating statewide carrying capacity of bobcats ( Lynx rufus ) using improved maximum clique algorithms

Context Maximum clique analysis (MCA) can approximate landscape carrying capacity ( N k ) for populations of territorial wildlife. However, MCA has not been widely adopted for wildlife applications, mainly due to computational constraints and software wildlife biologists may find difficult to use. Moreover, MCA does not incorporate uncertainty into estimates of N k . Objectives We extended MCA by applying a vertex cover algorithm to compute N k over a large (92,789 km 2 ), continuous spatial scale for female bobcats ( Lynx rufus ) in Indiana, USA. We incorporated uncertainty by calculating confidence intervals for N k across five thresholds of habitat suitability using 10 replicate suitability maps from bootstrapped datasets. For portions of the landscape too large to be solved with the vertex cover algorithm, we compared predictions from a linear model and a “greedy” algorithm. Results Mean estimates of N k for female bobcats in Indiana across habitat suitability thresholds ranged from 539 (0.75 threshold) to 1200 territories (0.25 threshold). On average, each 12.5 percentile reduction in the suitability threshold increased estimates for N k by 1.2-fold. Both the predictive and greedy algorithm produced reasonable estimates of maximum cliques for areas that were too large to compute with the vertex cover algorithm. The greedy algorithm produced smaller confidence intervals compared to the predictive approach but underestimated maximum cliques by 1.2%. Conclusions Our research demonstrates effective application of MCA to species occupying large landscapes while accounting for uncertainty. We believe our methods, coupled with availability of annotated scripts developed in R, will make MCA more broadly accessible to wildlife biologists.