Relative effects of sample size, detection probability, and study duration on estimation in integrated population models

Understanding mechanistic causes of population change is critical for managing and conserving species. Integrated population models (IPMs) allow for quantifying population changes while directly relating environmental drivers to vital rates, but power of IPMs to detect trends and environmental effects on vital rates remains understudied. We simulated data for an IPM under 41 scenarios to determine power to detect trends and environmental effects on vital rates based on study duration, sample size, detection probability, and effect size. Our results indicated that temporal duration of a study and effect size, rather than sample size of each individual data set or detection probability, had the greatest influence on the power to identify trends in adult survival and fecundity. When using only 10 years of data, we were unable to identify a 50% increase in adult survival but were able to identify this increase with 22 years of data. When using only capture-recapture data in a traditional Cormack-Jolly-Seber analysis, we lacked sufficient power to identify trends in survival, and power of the Cormack-Jolly-Seber model was always less than the IPM. The IPM had greater power to identify trends and environmental effects on fecundity (e.g., we detected a 58% change in fecundity using 12 years of data). Models with effects of environmental variables on vital rates had less power than trends, likely due to increased annual variation in the vital rate when modeling responses to environmental effects that varied by year. Lack of power in the Cormack-Jolly-Seber analysis could be due to the relatively small variability in adult survival compared to fecundity given the life history of our simulated species. As interannual variation in environmental conditions will likely increase with climate change, this type of analysis can help inform the study duration needed, which may be a shifting target given future climate uncertainty and the complex nature of environmental correlations with demography.