Improved state‐space models for inference about spatial and temporal variation in abundance from count data

Models of population dynamics are frequently used for purposes such as testing hypotheses about density dependence and predicting species' responses to future environmental change or conservation actions. Fitting models of population dynamics to field data is challenging because most data sets are characterized by observation error, which can inflate estimates of process variation if ignored. Recently, state‐space models have been developed to deal with this problem by directly modeling both the observation error and the ecological process of interest. Conventional state‐space models, however, have several important limitations: (1) they assume that random effects are Gaussian distributed, which implies that abundance can be negative and that false positive observation errors are equally likely as false negative errors; (2) they do not admit spatial variation in population dynamics; and (3) some of the parameters of the model are not estimable. We demonstrate how each of these problems can be resolved using a class of hierarchical models proposed by Dail and Madsen (2011) that attributes observation error to imperfect detection. We expand this class of models to accommodate classical growth models (e.g., exponential and Ricker‐logistic), zero‐inflation, and random effects. We also present methods for forecasting population size under future environmental conditions. Implementation of these ideas is possible using either frequentist or Bayesian methods, as demonstrated by accompanying R and JAGS code. Results of a simulation study suggest that bias is negligible and coverage nominal in most cases for the proposed model extensions. An analysis of data from the North American Breeding Bird Survey highlights how these methods can be readily applied to existing data, but it also suggests that precision will be low when direct information about detection probability (such as is collected using distance sampling or replicated counts) is lacking.