Time-for-space substitution in N-mixture models for estimating population trends: a simulation-based evaluation

N-mixture models usually rely on a meta-population design, in which repeated counts of individuals in multiple sampling locations are obtained over time. The time-for-space substitution (TSS) in N-mixture models allows to estimate population abundance and trend of a single population, without spatial replication. This application could be of great interest in ecological studies and conservation programs; however, its reliability has only been evaluated on a single case study. Here we perform a simulation-based evaluation of this particular application of N-mixture modelling. We generated count data, under 144 simulated scenarios, from a single population surveyed several times per year and subject to different dynamics. We compared simulated abundance and trend values with TSS estimates. TSS estimates are overall in good agreement with real abundance. Trend and abundance estimation is mainly affected by detection probability and population size. After evaluating the reliability of TSS, both against real world data, and simulations, we suggest that this particular application of N-mixture model could be reliable for monitoring abundance in single populations of rare or difficult to study species, in particular in cases of species with very narrow geographic ranges, or known only for few localities.