Environmental and Ecological Statistics

, Volume 21, Issue 2, pp 313–328 | Cite as

Inference for finite-sample trajectories in dynamic multi-state site-occupancy models using hidden Markov model smoothing

Article

Abstract

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.

Keywords

Amphibians Finite-sample trajectory Hidden Markov model Occupancy Trend estimation Wildlife 

Supplementary material

10651_2013_256_MOESM1_ESM.pdf (335 kb)
Supplementary material 1 (PDF 335 KB)

References

  1. Agresti A (2002) Categorical data analysis. Wiley series in probability and statistics. Wiley Interscience, Hoboken, NJGoogle Scholar
  2. Altman RM (2007) Mixed hidden Markov models. J Am Stat Assoc 102(477):201–210CrossRefGoogle Scholar
  3. Bartolucci F, Farcomeni A, Pennoni F (2012) Latent Markov models for longitudinal data. CRC Press, Boca Raton FLGoogle Scholar
  4. Baum L, Egon J (1967) An inequality with applications to statistical estimation for probabilistic functions of a markov process and to a model for ecology. Bull Am Meteorol Soc 73:360–363CrossRefGoogle Scholar
  5. Baum L, Petrie T, Soules G, Weiss N (1970) A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains. Ann Math Stat 41:164–171CrossRefGoogle Scholar
  6. Cappé O, Moulines E, Rydén T (2005) Inference in hidden Markov models. Springer, BerlinGoogle Scholar
  7. Conn PB, Cooch EG (2009) Multistate capture-recapture analysis under imperfect state observation: an application to disease models. J Appl Ecol 46:486–492CrossRefGoogle Scholar
  8. Dorazio R (2007) On the choice of statistical models for estimating occurrence and extinction from animal surveys. Ecology 88(11):2773–2782PubMedCrossRefGoogle Scholar
  9. Ephraim Y, Merhav N (2002) Hidden Markov processes. IEEE Trans Inf Theory 48(6):1518–1569CrossRefGoogle Scholar
  10. Fiske IJ (2012) Characterizing spatiotemporal trends in amphibian abundance using latent variable models. PhD thesis, North Carolina State University.Google Scholar
  11. Fujiwara M, Caswell H (2002) Estimating population projection matrices from multi-stage mark-recapture data. Ecology 83(12):3257–3265Google Scholar
  12. Giménez O, Viallefont A, Catchpole EA, Choquet R, Morgan BJT (2004) Methods for investigating parameter redundancy. Anim Biodivers Conserv 27(1):561–572Google Scholar
  13. Kendall W, White G, Hines J, Langtimm C, Yoshizaki J (2012) Estimating parameters of hidden markov models based on marked individuals: use of robust design data. Ecology 93:913–920PubMedCrossRefGoogle Scholar
  14. Link W, Sauer J (1997) New approaches to the analysis of population trends in land birds: comment. Ecology 78(8):2632–2634CrossRefGoogle Scholar
  15. MacKenzie D, Nichols J, Seamans M, Gutiérrez R (2009) Modeling species occurrence dynamics with multiple states and imperfect detection. Ecology 90(3):823–835PubMedCrossRefGoogle Scholar
  16. MacKenzie DI, Nichols JD, Lachman GB, Droege S, Royle JA, Langtimm CA (2002) Estimating site occupancy rates when detection probabilities are less than one. Ecology 83(8):2248–2255CrossRefGoogle Scholar
  17. MacKenzie DI, Nichols JD, Hines JE, Knutson MG, Franklin AB (2003) Estimating site occupancy, colonization, and local extinction when a species is detected imperfectly. Ecology 84(8):2200–2207CrossRefGoogle Scholar
  18. 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
  19. McClintock B, Bailey L, Pollock K, Simons T (2010) Experimental investigation of observation error in anuran call surveys. J Wildl Manag 74:1882–1893CrossRefGoogle Scholar
  20. Miller D, Weir L, McClintock B, Grant E, Bailey L, Simons T (2012) Experimental investigation of false positive errors in auditory species occurrence surveys. Ecol Appl 22:1665–1674PubMedCrossRefGoogle Scholar
  21. Nichols JD, Hines JE, MacKenzie DI, Seamans ME, Gutiérrez R (2007) Occupancy estimation and modeling with multiple states and state uncertainty. Ecology 88(6):1395–1400PubMedCrossRefGoogle Scholar
  22. Pradel R (2005) Multievent: an extension of multistate capture-recapture models to uncertain states. Biometrics 61:442–447PubMedCrossRefGoogle Scholar
  23. Rabiner LR (1989) A tutorial on hidden Markov models and selected applications in speech recognition. Proc IEEE 77(2):257–286CrossRefGoogle Scholar
  24. Royle J (2004) Modeling abundance index data from anuran calling surveys. Conserv Biol 18(5):1378–1385CrossRefGoogle Scholar
  25. Royle JA, Kéry M (2007) A bayesian state-space formulation of dynamic occupancy models. Ecology 88(7):1813–1823PubMedCrossRefGoogle Scholar
  26. Royle JA, Link WA (2005) A general class of multinomial mixture models for anuran calling survey data. Ecology 86(9):2505–2512CrossRefGoogle Scholar
  27. Runge JP, Hines JE, Nichols JD (2007) Estimating species-specific survival and movement when species identification is uncertain. Ecology 88(2):282–288PubMedCrossRefGoogle Scholar
  28. Scott SL, James GM, Sugar CA (2005) Hidden Markov models for longitudinal comparisons. J Am Stat Assoc 100(470):359–370CrossRefGoogle Scholar
  29. 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
  30. 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
  31. Welch L (2003) Hidden Markov models and the baum-welch algorithm. IEEE Inf Theory Soc Newslett 53:1–13Google Scholar
  32. Williams D (1991) Probability with martingales. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  33. Zucchini W, MacDonald IL (2009) Hidden Markov models for time series: an introduction using R. CRC Press, Boca Raton, FLGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of StatisticsNorth Carolina State UniversityRaleighUSA
  2. 2.USGS Patuxent Wildlife Research CenterLaurelUSA

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