Nonstationary Demographic State-Space Models Using Unreplicated Counts for Species Undergoing Environmental Stressors

Abstract A fundamental task in ecological statistics is to estimate abundance and growth rate distributions from wildlife monitoring data to inform conservation management. Modeling time series of wildlife populations presents a number of challenges from both statistical and ecological perspectives, including discreteness; lack of replication; nonstationarity; and observation, demographic, and other phenomenological processes. Nonstationary dynamics are often exhibited by populations undergoing environmental stressors. Models must account for these characteristics to produce reliable estimates of abundance and trends, yet estimation can be challenging with unreplicated data. We propose nonstationary demographic state-space models using unreplicated counts for populations undergoing environmental stressors. A reduced growth rate model matches the complexity of the unreplicated count data, and a fecundity bound on growth rate distributions allows the separation of processes affecting growth rates like environmental stressors from those affecting abundance external to growth rates like migration. NDSSMs allow for the embedding of nonstationary model components, and we explore the use of changepoints, volatility clustering, and migration processes. We apply the proposed nonstationary models in case studies of herons affected by predator/competitor reestablishment and three bat species affected by a fungal pathogen causing white-nose syndrome. Nonstationary models outperform stationary models and generalized linear mixed effects models according to model scoring and visual inspection of predictions, and provide estimates more consistent with published values. Incorporating migration improves model fit universally, even with approximate one-way immigration, most likely because populations are extirpated, recolonized, and increase multiple-fold over the upper bound set by species fecundity. In addition, estimates of the timing and severity of the environmental stressor differed for models with migration. Including nonstationary and demographic components in a fecundity-bounded growth rate model improves inference and benefits interpretability of hyperparameters. In turn, this adjusts uncertainties in predictions of abundance and growth rates over time, providing the ingredients needed for informed conservation analysis and for directing future monitoring of at-risk species. Supplementary materials accompanying this paper appear online.