Non-random Temporary Emigration and the Robust Design: Conditions for Bias at the End of a Time Series

Deviations from model assumptions in the application of capture–recapture models to real life situations can introduce unknown bias. Understanding the type and magnitude of bias under these conditions is important to interpreting model results. In a robust design analysis of long-term photo-documented sighting histories of the endangered Florida manatee, I found high survival rates, high rates of non-random temporary emigration, significant time-dependence, and a diversity of factors affecting temporary emigration that made it difficult to model emigration in any meaningful fashion. Examination of the time-dependent survival estimates indicated a suspicious drop in survival rates near the end of the time series that persisted when the original capture histories were truncated and reanalyzed under a shorter time frame. Given the wide swings in manatee emigration estimates from year to year, a likely source of bias in survival was the convention to resolve confounding of the last survival probability in a time-dependent model with the last emigration probabilities by setting the last unmeasurable emigration probability equal to the previous year’s probability when the equality was actually false. Results of a series of simulations demonstrated that if the unmeasurable temporary emigration probabilities in the last time period were not accurately modeled, an estimation model with significant annual variation in survival probabilities and emigration probabilities produced bias in survival estimates at the end of the study or time series being explored. Furthermore, the bias propagated back in time beyond the last two time periods and the number of years affected varied positively with survival and emigration probabilities. Truncating the data to a shorter time frame and reanalyzing demonstrated that with additional years of data surviving temporary emigrants eventually return and are detected, thus in subsequent analysis unbiased estimates are eventually realized.

Knowing the extent and magnitude of the potential bias can help in making decisions as to what time frame provides the best estimates or the most reliable opportunity to model and test hypotheses about factors affecting survival probability. To assess bias, truncating the capture histories to shorter time frames and reanalyzing the data to compare time-specific estimates may help identify spurious effects. Running simulations that mimic the parameter values and movement conditions in the real situation can provide estimates of standardized bias that can be used to identify those annual estimates that are biased to the point where the 95% confidence intervals are inadequate in describing the uncertainty of the estimates.