Using multiscale graph theoretic methods to understand spatial patterns of decline: a case study with lesser prairie-chickens

The lesser prairie-chicken (Tympanuchus pallidicinctus) lek network represents a prime testing ground for examining how analyses of connectivity may help inform why and where population declines occur. We compared how patterns of decline and inactivity were associated with lek structural connectivity. We used lek locations and years of recorded activity from the southern population of lesser prairie-chickens to construct networks at a range of distances representing biological processes. We calculated Kleinberg’s hub score and betweenness score to quantify each lek’s contribution to facilitating connectivity at each distance. We used these scores to predict lek activity based on centrality at multiple scales. The number of years in which a lek was active was positively associated with betweenness score and, to a lesser extent, hub score. Associations varied across spatial scales, with high-persistence leks being more central in smaller-scale clusters (maximum nesting distance), and leks known to have failed being less central at broader scales (average and maximum dispersal distances). Connectivity scores predicted whether a lek was active or not with 80% accuracy. Graph theory can and should be used in predictive conservation modeling for species reliant on spatially explicit features such as leks. Because lesser prairie-chickens are a social species that rely on leks for reproduction, changes to lek connectivity will have a cascading effect on population persistence. Therefore, management actions preventing degradation of highly central leks and restoring habitat between leks will help with the species’ continued persistence.