A spatially explicit hierarchical model to characterize population viability

Many of the processes that govern the viability of animal populations vary spatially, yet population viability analyses (PVAs) that account explicitly for spatial variation are rare. We develop a PVA model that incorporates autocorrelation into the analysis of local demographic information to produce spatially explicit estimates of demography and viability at relatively fine spatial scales across a large spatial extent. We use a hierarchical, spatial, autoregressive model for capture–recapture data from multiple locations to obtain spatially explicit estimates of adult survival (ϕ_ad), juvenile survival (ϕ_juv), and juvenile-to-adult transition rates (ψ), and a spatial autoregressive model for recruitment data from multiple locations to obtain spatially explicit estimates of recruitment (R). We combine local estimates of demographic rates in stage-structured population models to estimate the rate of population change (λ), then use estimates of λ (and its uncertainty) to forecast changes in local abundance and produce spatially explicit estimates of viability (probability of extirpation, P_ex). We apply the model to demographic data for the Sonoran desert tortoise (Gopherus morafkai) collected across its geographic range in Arizona. There was modest spatial variation in (Formula presented.) (0.94–1.03), which reflected spatial variation in (Formula presented.) (0.85–0.95), (Formula presented.) (0.70–0.89), and (Formula presented.) (0.07–0.13). Recruitment data were too sparse for spatially explicit estimates; therefore, we used a range-wide estimate ((Formula presented.) = 0.32 1-yr-old females per female per year). Spatial patterns in demographic rates were complex, but (Formula presented.), (Formula presented.), and (Formula presented.) tended to be lower and (Formula presented.) higher in the northwestern portion of the range. Spatial patterns in P_ex varied with local abundance. For local abundances >500, P_ex was near zero (<0.05) across most of the range after 100 yr; as abundances decreased, however, P_ex approached one in the northwestern portion of the range and remained low elsewhere. When local abundances were <50, western and southern populations were vulnerable (P_ex > 0.25). This approach to PVA offers the potential to reveal spatial patterns in demography and viability that can inform conservation and management at multiple spatial scales, provide insight into scale-related investigations in population ecology, and improve basic ecological knowledge of landscape-level phenomena.