Simulation‐based assessment of dynamic N‐mixture models in the presence of density dependence and environmental stochasticity

Abstract

Summary Estimating survival and recruitment over large spatial scales is extremely challenging because it requires ‘expensive’ demographic data from marked animals. Dynamic N‐mixture models (Dail & Madsen ) yield estimates of abundance, apparent survival, recruitment and detection probability from simple counts replicated in space and time, as frequently collected in monitoring programmes all over the world. However, the vital rates are assumed to be density‐independent and constant over time, arguably unrealistic assumptions in many situations. We evaluated the performance of the traditional dynamic N‐mixture model from simulated data generated with density dependence and environmental stochasticity in the vital rates. We then developed a series of more advanced models that take density‐dependent vital rates and environmental stochasticity into account and assessed whether these models provide accurate estimates of vital rates, strength of density dependence and levels of environmental stochasticity. We found that the traditional Dail–Madsen model produced accurate estimates of abundances and vital rates when the assumptions were met, but not when vital rates were subject to density dependence and environmental stochasticity. Accurate parameter estimates were generally obtained when the data generation matched the data analysis model, but accuracy was substantially reduced otherwise. Interestingly, accurate estimates of abundance and detection were obtained from all models, regardless of the data generation model. Shorter time series from more sites yielded estimates of similar accuracy as longer series from fewer sites. The new dynamic N‐mixture models represent a promising basis for developing integrated population models that combine data from different sources to get insights into population dynamics of species over large areas.