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.
KeywordsRobust Design Capture Probability Survival Estimate Akaike Weight Annual Survival
- Buergelt CD, Bonde RK, Beck CA, O’Shea TJ (1984) Pathologic findings in manatees in Florida. Journal of the American Veterinary Medical Association 185:1331–1334.Google Scholar
- Burnham KP, Anderson DR (1998) Model selection and inference: a practical information-theoretic approach, 2nd edn. Springer-Verlag, New York, USA.Google Scholar
- Burnham KP, Anderson DR, White GC, Brownell C, Pollock KH (1987) Design and analysis methods for fish survival experiments based on release-recapture. Monograph 5. American Fisheries Society, Bethesda, MD, USA.Google Scholar
- Cooch E, White G (2006) Program MARK- a gentle introduction, 5th edn. (http://www.phidot.org/software/mark/docs/book/)
- Cochran WG (1963) Sampling techniques, 2nd edn. John Wiley & Sons, New York.Google Scholar
- Choquet R, Reboulet AM, Lebreton JD, Gimenez O, Pradel R (2005) U-Care 2.2 User’s Manual. CEFE, Montpellier, France. (http://ftp.cefe.cnrs.fr/biom/Soft-CR/).
- Deutsch CJ, Reid JP, Bonde RK, Easton DE, Kochman HI, O'Shea TJ (2003) Seasonal movements, migratory behavior, and site fidelity of West Indian manatees along the Atlantic Coast of the United States. Wildlife Monographs 151:1–77.Google Scholar
- Hartman DS (1979) Ecology and behavior of the manatee (Trichechus manatus) in Florida. American Society of Mammalogists Special Publication 5:1–153.Google Scholar
- Kendall WL (2001) The robust design for capture–recapture studies: analysis using Program MARK. In: Field R, Warren RJ, Okarma H, Seivert PR (eds) Wildlife, land, and people: priorities for the 21st century. Proceedings of the Second International Wildlife Management Congress. The Wildlife Society, Bethesda, MD, pp 357–360.Google Scholar
- Kendall WL (2006) The “robust design”. In: Cooch E, White G (eds) Program MARK- a gentle introduction, 5th edn., pp 16.1–16.35.Google Scholar
- Kendall WL, Nichols JD (2002) Estimating state-transition probabilities for unobservable states using capture–recapture/resighting data. Ecology 83:3276–3284.Google Scholar
- Kendall WL, Nichols JD, Hines JE (1997) Estimating temporary emigration using capture–recapture data with Pollock’s robust design. Ecology 78:563–578.Google Scholar
- Langtimm CA, O’Shea TJ, Pradel R, Beck CA (1998) Estimates of annual survival probabilities for adult Florida manatees (Trichechus manatus latirostris). Ecology 79:981–997.Google Scholar
- O’Shea TJ, Langtimm CA (1995) Estimation of survival of adult Florida manatees in the Crystal River, at Blue Spring, and on the Atlantic coast. In: O’Shea TJ, Ackerman BB, Percival HF (eds) Population biology of the Florida manatee. US Department of the Interior, National Biological Service, Information and Technology Report 1. pp 194–222.Google Scholar