Inference for finite-sample trajectories in dynamic multi-state site-occupancy models using hidden Markov model smoothing
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Ecologists and wildlife biologists increasingly use latent variable models to study patterns of species occurrence when detection is imperfect. These models have recently been generalized to accommodate both a more expansive description of state than simple presence or absence, and Markovian dynamics in the latent state over successive sampling seasons. In this paper, we write these multi-season, multi-state models as hidden Markov models to find both maximum likelihood estimates of model parameters and finite-sample estimators of the trajectory of the latent state over time. These estimators are especially useful for characterizing population trends in species of conservation concern. We also develop parametric bootstrap procedures that allow formal inference about latent trend. We examine model behavior through simulation, and we apply the model to data from the North American Amphibian Monitoring Program.
KeywordsAmphibians Finite-sample trajectory Hidden Markov model Occupancy Trend estimation Wildlife
We thank Linda Weir of PWRC for providing NAAMP data, and we thank John Monahan, Brian Reich and Len Stefanski for constructive comments and discussion. IJF and KG were supported by Grant DEB 08-42101 from the National Science Foundation.
- Agresti A (2002) Categorical data analysis. Wiley series in probability and statistics. Wiley Interscience, Hoboken, NJGoogle Scholar
- Bartolucci F, Farcomeni A, Pennoni F (2012) Latent Markov models for longitudinal data. CRC Press, Boca Raton FLGoogle Scholar
- Cappé O, Moulines E, Rydén T (2005) Inference in hidden Markov models. Springer, BerlinGoogle Scholar
- Fiske IJ (2012) Characterizing spatiotemporal trends in amphibian abundance using latent variable models. PhD thesis, North Carolina State University.Google Scholar
- Fujiwara M, Caswell H (2002) Estimating population projection matrices from multi-stage mark-recapture data. Ecology 83(12):3257–3265Google Scholar
- Giménez O, Viallefont A, Catchpole EA, Choquet R, Morgan BJT (2004) Methods for investigating parameter redundancy. Anim Biodivers Conserv 27(1):561–572Google Scholar
- MacKenzie DI, Nichols JD, Royle JA, Pollock KH, Bailey LL, Hines JE (2006) Occupancy estimation and modeling: inferring patterns and dynamics of species occurrence. Academic Press, USAGoogle Scholar
- Weir L, Fiske IJ, Royle JA (2009) Trends in anuran occupancy from northeastern states of the north American Amphibian monitoring program. Herpetol Conserv Biol 4(3):389–402Google Scholar
- Weir LA, Royle JA, Nanjappa P, Jung RE (2005) Modeling anuran detection and site occupancy on north American Amphibian monitoring program (NAAMP) routes in Maryland. J Herpetol 39(4):627–639Google Scholar
- Welch L (2003) Hidden Markov models and the baum-welch algorithm. IEEE Inf Theory Soc Newslett 53:1–13Google Scholar
- Zucchini W, MacDonald IL (2009) Hidden Markov models for time series: an introduction using R. CRC Press, Boca Raton, FLGoogle Scholar