Estimating survival and transition probabilities from aggregate sightings of animals

Abstract

We compare and contrast two methods for fitting probability models to data which arise when animals are marked in batches, without individual identification, and live in several different sites or states. The methods are suitable for populations in which animals are marked at birth and then resighted over several sites/states, for small animals going through several growth stages (insects, amphibiae, etc.), as well as for the follow-up of animals released after laboratory colour-marking, for example. The methods we consider include a multi-state model for resightings of batch-marked animals, allowing us to estimate survival, transitions, and sighting probabilities. One method is based on the EM algorithm, and the second uses the Kalman filter for computing likelihoods. The methods are illustrated on real data from a cohort of Great Cormorants Phalacrocorax carbo, and their performance is evaluated using simulation. We recommend identifying the batches, for instance in the case of sites, by using a different colour on each site at the time of marking, and in general the use of the Kalman filter rather than the EM-based approach.

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References

  1. Arnason AN, Schwarz CJ, Gerrard JM (1991) Estimating closed population size and number of marked animals from sighting data. J Wildl Manage 55:716–730

    Article  Google Scholar 

  2. Balzter H (2000) Markov chain models for vegetation dynamics. Ecol Model 126:139–154

    Article  Google Scholar 

  3. Besbeas P, Morgan BJT (2010) Kalman filter initialization for modelling population dynamics. (Submitted)

  4. Brown PJ, Payne CD (1986) Aggregate data, ecological regression, and voting transitions. J Am Stat Assoc 81:452–460

    Article  Google Scholar 

  5. Buonaccorsi JP, Harrington LC, Edman JD (2003) Estimation and comparison of mosquito survival rates with release-recapture-removal data. J Med Entomol 40:6–17

    Article  Google Scholar 

  6. Burnham KP, Anderson DR, White GC, Brownie C, Pollock KH (1987) Design and analysis methods for fish survival experiments based on release-recapture, vol 5. American Fisheries Society Monograph

  7. Cameron PJ, Wigley PJ, Elliott S, Madhusudhan VV, Wallace AR, Anderson JAD, Walker GP (2009) Dispersal of potato tuber moth estimated using field application of Bt for mark-capture techniques. Entomol Exper Appl 132:99–109

    Article  Google Scholar 

  8. Chen YX, Yang S (2007) Estimating disaggregate models using aggregate data through augmentation of individual choice. J Mark Res 44:613–621

    Article  Google Scholar 

  9. Choquet R, Reboulet A-M, Pradel R, Gimenez O, Lebreton J-D (2005) M-SURGE: new software specifically designed for multistate capture-recapture models. Anim Biodivers Conserv 27:207–215

    Google Scholar 

  10. Cooch EG, Link WA (1999) Estimating transition probabilities in unmarked populations—entropy revisited. Bird Study 46:S55–S61

    Article  Google Scholar 

  11. Dempster A, Laird N, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J Roy Stat Soc (B) 39:1–38

    Google Scholar 

  12. Durbin J, Koopman SJ (2001) Time series analysis by state space methods. Oxford University Press, Oxford

    Google Scholar 

  13. Gillies MT (1961) Studies on the dispersion and survival of Anopheles gambiae in East Africa, by means of marking and release experiments. Bull Entomol Res 52:99–127

    Article  Google Scholar 

  14. Hagler JR, Jackson CG (2001) Methods for marking insects: current techniques and future prospects. Annu Rev Entomol 46:511–543

    CAS  Article  Google Scholar 

  15. Harvey AC (1989) Structural time series models and the Kalman filter. Cambridge University Press, Cambridge

    Google Scholar 

  16. Hawkins DL, Han CP, Eisenfeld J (1996) Estimating transition probabilities from aggregate samples augmented by haphazard recaptures. Biometrics 52:625–638

    Article  Google Scholar 

  17. Hénaux V, Bregnballe T, Lebreton J-D (2007) Dispersal and recruitment during population growth in a colonial bird, the great cormorant Phalacrocorax carbo sinensis. J Avian Biol 38:44–57

    Article  Google Scholar 

  18. Hill MF, Witman JD, Caswell H (2004) Markov chain analysis of succession in a rocky subtidal community. Am Nat 164:E46

    Article  Google Scholar 

  19. Kalbfleisch J, Lawless J (1984) Least-square estimation of transition probabilities from aggregate data. Can J Stat 12:169–182

    Article  Google Scholar 

  20. Kalman RE (1963) Mathematical description of linear dynamical systems. SIAM J Control 1:152–192

    Google Scholar 

  21. Krishnan P, Sangadasa A (1975) Stochastic indicators of occupational mobility, Canada: 1951–1961. Soc Indic Res 1:485–493

    Article  Google Scholar 

  22. Lawless JF, McLeish DL (1984) The information in aggregate data from Markov chains. Biometrika 71:419–430

    Article  Google Scholar 

  23. Lebreton J-D, Almeras T, Pradel R (1999) Competing events, mixtures of information and multistratum recapture models. Bird Study 46:S39–S46

    Article  Google Scholar 

  24. Maciel De Freitas R, Eiras AE, Lourenco de Oliveira R (2008) Calculating the survival rate and estimated population density of gravid Aedes aegypti (Diptera, Culicidae) in Rio de Janeiro, Brazil. Cad Saude Publica 24:2747–2754

    Article  Google Scholar 

  25. Macneale KH, Peckarsky BL, Likens GE (2005) Stable isotopes identify dispersal patterns of stonefly populations living along stream corridors. Freshw Biol 50:1117–1130

    Article  Google Scholar 

  26. Midega JT, Mbogo CM, Mwambi H, Wilson MD, Mwangangi JM, Nzovu JG, Githure JI, Yan G, Beier JC (2007) Estimating Dispersal and Survival of Anopheles gambiae and Anopheles funestus along the Kenyan Coast by using mark-release-recapture methods. J Med Entomol 44:923–929

    Article  Google Scholar 

  27. Minta S, Mangel M (1989) A simple population estimate based on simulation for capture-recapture and capture-resight data. Ecology 70:1738–1751

    Article  Google Scholar 

  28. Miyatake T, Kohama T, Shimoji Y, Kawasaki K, Moriya S, Kishita M, Yamamura K (2000) Dispersal of released male sweetpotato weevil, Cylas formicarius (Coleoptera : Brentidae) in different seasons. Appl Entomol Zool 35:441–449

    Article  Google Scholar 

  29. Muir LE, Kay BH (1998) Aedes aegypti survival and dispersal estimated by mark-release-recapture in northern Australia. Am J Trop Med Hyg 58:277–282

    CAS  Article  Google Scholar 

  30. Qureshi JA, Buschman LL, Throne JE, Ramaswamy SB (2006) Dispersal of adult Diatraea grandiosella (Lepidoptera : Crambidae) and its implications for corn borer resistance management in Bacillus thuringiensis maize. Ann Entomol Soc Am 99:279–291

    Article  Google Scholar 

  31. Scarratt SL, Wratten SD, Shishehbor P (2008) Measuring parasitoid movement from floral resources in a vineyard. Biol Control 46:107–113

    Article  Google Scholar 

  32. Schneider JC (1999) Dispersal of a highly vagile insect in a heterogeneous environment. Ecology 80:2740–2749

    Google Scholar 

  33. Seber G (1982) The estimation of animal abundance and related parameters. Griffin, London

  34. Shumway RH, Stoffer DS (2000) Time series analysis and its applications. Springer, New York

    Google Scholar 

  35. Sullivan PJ (1992) A Kalman filter approach to catch-at-length analysis. Biometrics 48:237–258

    Article  Google Scholar 

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Acknowledgments

This work was achieved during a research stay of A.V. at the SMSAS in Canterbury. The work of R.Mc.C. was supported by the EPSRC grant to the National Centre for Statistical Ecology. We are very grateful to Thomas Bregnballe, National Environmental Research Institute, Aarhus University, for giving us access to and permission to use the data on Great Cormorants, and to two anonymous referees for remarks and suggestions that helped enhance this paper.

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Correspondence to Anne Viallefont.

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Communicated by M. Schaub.

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Viallefont, A., Besbeas, P., Morgan, B.J.T. et al. Estimating survival and transition probabilities from aggregate sightings of animals. J Ornithol 152, 381–391 (2012). https://doi.org/10.1007/s10336-010-0588-7

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Keywords

  • Aggregate survival data
  • Batch-marking
  • Grouped data
  • Interval censoring
  • Macrodata