Hidden Markov Model for Dependent Mark Loss and Survival Estimation

• Published in: Journal of agricultural, biological, and environmental statistics biological, and environmental statistics, 2014-12, Vol.19 (4), p.522-538
• Main Authors: Laake, Jeffrey L, Johnson, Devin S, Diefenbach, Duane R, Ternent, Mark A
• Format: Article
• Language: English
• Subjects: Agriculture; Analysis; animals; Biostatistics; Black bear; Business losses; data collection; ear tags; Health Sciences; Markov processes; Mathematics and Statistics; Medicine; Monitoring/Environmental Analysis; Statistics; Statistics for Life Sciences; Ursus americanus
• ISSN: 1085-7117; 1537-2693
• DOI: 10.1007/s13253-014-0190-1

Mark-recapture estimators assume no loss of marks to provide unbiased estimates of population parameters. We describe a hidden Markov model (HMM) framework that integrates a mark loss model with a Cormack–Jolly–Seber model for survival estimation. Mark loss can be estimated with single-marked animals as long as a sub-sample of animals has a permanent mark. Double-marking provides an estimate of mark loss assuming independence but dependence can be modeled with a permanently marked sub-sample. We use a log-linear approach to include covariates for mark loss and dependence which is more flexible than existing published methods for integrated models. The HMM approach is demonstrated with a dataset of black bears (Ursus americanus) with two ear tags and a subset of which were permanently marked with tattoos. The data were analyzed with and without the tattoo. Dropping the tattoos resulted in estimates of survival that were reduced by 0.005–0.035 due to tag loss dependence that could not be modeled. We also analyzed the data with and without the tattoo using a single tag. By not using.Supplementary materials accompanying this paper appear on-line.