Abstract
Many biological systems include a portion of the target population that is unobservable during certain life history stages. Transition to and from an unobservable state may be of primary interest in many ecological studies and such movements are easily incorporated into multi-state models. Several authors have investigated properties of open-population multi-state mark-recapture models with unobservable states, and determined the scope and constraints under which parameters are identifiable (or, conversely, are redundant), but only in the context of a single observable and a single unobservable state (Schmidt et al. 2002; Kendall and Nichols 2002; Schaub et al. 2004; Kendall 2004). Some of these constraints can be relaxed if data are collected under a version of the robust design (Kendall and Bjorkland 2001; Kendall and Nichols 2002; Kendall 2004; Bailey et al. 2004), which entails >1 capture period per primary period of interest (e.g., 2 sampling periods within a breeding season). The critical assumption shared by all versions of the robust design is that the state of the individual (e.g. observable or unobservable) remains static for the duration of the primary period (Kendall 2004). In this paper, we extend previous work by relaxing this assumption to allow movement among observable states within primary periods while maintaining static observable or unobservable states. Stated otherwise, both demographic and geographic closure assumptions are relaxed, but all individuals are either observable or unobservable within primary periods. Within these primary periods transitions are possible among multiple observable states, but transitions are not allowed among the corresponding unobservable states.
Our motivation for this work is exploring potential differences in population parameters for pond-breeding amphibians, where the quality of habitat surrounding the pond is not spatially uniform. The scenario is an example of a more general case where individuals move between habitats both during the breeding season (within primary periods; transitions among observable states only) and during the non-breeding season (between primary periods; transitions between observable and unobservable states). Presumably, habitat quality affects demographic parameters (e.g. survival and breeding probabilities). Using this model we are able to test this prediction for amphibians and determine if individuals move to more favorable habitats to increase survival and breeding probabilities.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Arnason AN (1972) Parameter estimates from mark-recapture experiments on two populations subject to migration and death. Researches on Population Ecology 13:97–113
Arnason AN (1973) The estimation of population size, migration rates, and survival in a stratified population. Researches on Population Ecology 15:1–8
Bailey LL, Kendall WL, Church DR, Wilbur HM (2004) Estimating survival and breeding probabilities for pond-breeding amphibians: a modified robust design. Ecology 85:2456–2466
Barker RJ, White GC, McDougall, M (2005) Movement of Paradise Shelduck between molt sites: a joint multistate-dead recovery mark-recapture model. Journal of Wildlife Management 69:1194–1201
Burnham KP (1993) A theory for combined analysis of ring recovery and recapture data. In: Marked Individuals in the Study of Bird Populations, Lebreton JD, North PM (eds) Birkhauser-Verlag, Basel, pp. 199–214
Burnham KP, Anderson DR (2002) Model Selection and Multimodel Inference. Springer-Verlag, New York
Burnham KP, Anderson DR, White GC, Brownie C, Pollock KH (1987) Design and analysis of methods for fish survival experiments based on release-recapture. American Fisheries Society Monograph 5:1–437
Catchpole EA, Morgan BJT (1997) Detecting parameter-redundant models. Biometrika 88: 187–196
Catchpole EA, Morgan BJT, Viallefont A (2002) Solving problems in parameter redundancy using computer algebra. Journal of Applied Statistics 29:625–636
Choquet R, Reboulet M, Pradel R, Gimenez O, Lebreton JD (2005) M-SURGE 1-8 User’s Manual. CEFE, Montpellier, France (http://ftp.cefe.cnrs.fr/biom/soft-cr/)
Church DR (2004) Population Ecology of Ambystoma tigrinum and Occupancy Dynamics in an Appalachian Pond-Breeding Amphibian Assemblage. Dissertation. University of Virginia, Charlottesville, VA, USA
Church DR, Bailey LL, Wilbur HM, Kendall WL, Hines JE (2007) Iteroparity in the variable environment of the salamander Ambystoma tigrinum. Ecology 88:891–903.
Converse SJ, Kendall WL, Doherty PF, Naughton, N (2008) A traditional and less-invasive robust design: choices in optimizing effort allocation for seabird studies. In: Thomson DL, Cooch EG, Conroy MJ (eds.) Modeling Demographic Processes in Marked Populations. Environmental and Ecological Statistics, Springer, New York.
Cooch, EG,, White GC (2006) Program MARK: A Gentle Introduction. http://www.phidot.org/software/mark/docs/book/
deMaynaider PG, Hunter ML (1995) The relationship between forest management and amphibian ecology: a review of the North American literature. Environmental Reviews 3:230–261
deMaynaider PG, Hunter ML (1998) Effects of silvercultural edges on the distribution and abundance of amphibians in Maine. Conservation Biology 12:340–352
Dutton DL, Dutton PH, Chaloupka M, Boulon RH (2005) Increase of a Caribbean leatherback turte Dermochelys coriacea nesting population linked to long-term nest protection. Biological Conservation 126:186–194
Fox DA, Hightower JE, Paruka FM (2000) Gulf sturgeon spawning migration and habitat in the Choctawhatchee River system, Alabama–Florida. Transactions of the American Fisheries Society 129:811–826
Fujiwara M, Caswell H (2002) A general approach to temporary emigration in mark-recapture analysis. Ecology 83:3266–3275
Gimenez O, Choquet R, Lebreton JD (2003) Parameter redundancy in multi-state capture–recapture models. Biometrical Journal 45:704–722
Gimenez O, Viallefont A, Catchpole EA, Choquet R, Morgan BJT (2004) Methods for investigating parameter redundancy. Animal Biodiversity and Conservation 27:561–572
Hunter CM, Caswell H (2008) Rank and redundancy of multistate mark-recapture models for seabird populations with unobservable states. In: Thomson DL, Cooch EG, Conroy MJ (eds.) Modeling Demographic Processes in Marked Populations. Environmental and Ecological Statistics, Springer, New York.
Kendall WL (1999) Robustness of closed capture–recapture methods to violations of the closure assumption. Ecology 80:2517–2525
Kendall WL (2004) Coping with unobservable and mis-classified states in capture–recapture studies. Animal Biodiversity and Conservation 27:97–107
Kendall WL, Bjorkland R (2001) Using open robust design models to estimate temporary emigration from capture–recapture data. Biometrics 57:1113–1122
Kendall WL, Nichols JD (2002) Estimating state-transition probabilities for unobservable states using capture–recapture/resighting data. Ecology 83:3276–3284
Kendall WL, Nichols JD, Sauer JS, Hines JE (1997) Estimating temporary emigration using capture–recapture data with Pollock’s robust design. Ecology 78:563–578
Kéry M, Gregg KB (2004) Demographic estimation methods for plants with dormancy. Animal Biodiversity and Conservation 27.1: 129–131
Lebreton JD, Pradel R (2002) Multi-state recapture models: modeling incomplete individual histories. Journal of Applied Statistics 29:353–369
Lebreton JD, Burnham KP, Clobert J, Anderson DR (1992) Modeling survival and testing biological hypotheses using marked animals: a unified approach with case studies. Ecological Monographs 62:67–118
Lebreton JD, Hines JE, Pradel R, Nichols JD, Spendelow JA (2003) Estimation by capture–recapture of recruitment and dispersal over several sites. OIKOS 101:253–264
Nichols JD, Noon BR, Stokes SL, Hines JE (1981) Remarks on the use of mark-recapture methodology in estimating avian population size. In: Estimating the Numbers of Terrestrial Birds Ralph CJ, Scott MJ (eds), Study of Avian Biology, Cooper Ornithological Society, Allen Press, Inc. Lawrence, Kansas, USA, vol 6, 121–136
Pollock KH (1982) A capture–recapture design robust to unequal probability of capture. Journal of Wildlife Management 46:757–760
Rivalan P, Prevot-Julliard AC, Choquet R, Pradel R, Jacquemin B, Girondot M (2005) Trade-off between current reproductive effort and delay to next reproduction in the leatherback sea turtle. Oecologia 145:564–574
Schaub M, Gimenez O, Schmidt BR, Pradel R (2004) Estimating survival and temporary emigration in the multistate capture-recapture framework. Ecology 85: 2107–2113
Schlaepfer MA, Runge MC, Sherman, PW (2002) Ecological and evolutionary traps. Trends in Ecology and Evolution 17: 474–480
Schmidt BR, Schaub M, Anholt BR (2002) Why you should use capture–recapture methods when estimating survival and breeding probabilities: on bias, temporary emigration, overdispersion, and common toads. Amphibia-Reptilia 23:375–388
Schwarz CJ, Stobo WT (1997) Estimation temporary migration using the robust design. Biometrics 53:178–194
Shefferson RP, Sandercock BK, Proper J, Beissinger SR (2001) Estimating dormancy and survival of a rare herbaceous perennial using mark-recapture models. Ecology 82:145–156
Sulak KJ, Clugston JP (1999) Recent advances in life history of Gulf of Mexico sturgeon, Acipenser oxyrinchus desotoi, in the Suwannee River, Florida, USA: a synopsis. Journal of Applied Ichthyology-Zeitschrift für Angewandte Ichthyologie 15:116–128
Viallefont A, Lebreton JD, Reboulet AM, Gory G (1998) Parameter identifiability and model selection in capture–recapture models: a numerical approach. Biometrical Journal 40:1–13
White GC, Burnham KP (1999) Program MARK: survival estimation from populations of marked animals. Bird Study 46:120–139
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Bailey, L.L., Kendall, W.L., Church, D.R. (2009). Exploring Extensions to Multi-State Models with Multiple Unobservable States. In: Thomson, D.L., Cooch, E.G., Conroy, M.J. (eds) Modeling Demographic Processes In Marked Populations. Environmental and Ecological Statistics, vol 3. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-78151-8_31
Download citation
DOI: https://doi.org/10.1007/978-0-387-78151-8_31
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-78150-1
Online ISBN: 978-0-387-78151-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)