Estimating Latent Time of Maturation and Survival Costs of Reproduction in Continuous Time from Capture–Recapture Data

  • Torbjørn Ergon
  • Nigel G. Yoccoz
  • James D. Nichols

Abstract

In many species, age or time of maturation and survival costs of reproduction may vary substantially within and among populations. We present a capture-mark-recapture model to estimate the latent individual trait distribution of time of maturation (or other irreversible transitions) as well as survival differences associated with the two states (representing costs of reproduction). Maturation can take place at any point in continuous time, and mortality hazard rates for each reproductive state may vary according to continuous functions over time. Although we explicitly model individual heterogeneity in age/time of maturation, we make the simplifying assumption that death hazard rates do not vary among individuals within groups of animals. However, the estimates of the maturation distribution are fairly robust against individual heterogeneity in survival as long as there is no individual level correlation between mortality hazards and latent time of maturation. We apply the model to biweekly capture–recapture data of overwintering field voles (Microtus agrestis) in cyclically fluctuating populations to estimate time of maturation and survival costs of reproduction. Results show that onset of seasonal reproduction is particularly late and survival costs of reproduction are particularly large in declining populations.

Keywords

Capture-mark-recapture Latent traits Life-history theory Maximum likelihood Multi-state/multi-strata Continuous time Hazard rates Heterogeneity Maturation Cost of reproduction Disease infection dynamics 

References

  1. Arnason AN (1972) Parameter estimates from mark-recapture experiments on two populations subject to migration and death. Researches on Population Ecology 13:97–113.CrossRefGoogle Scholar
  2. Arnason AN (1973) The estimation of population size, migration rates and survival in a stratified population. Researches on Population Ecology 15:1–8.CrossRefGoogle Scholar
  3. Begon M, Bennett M, Bowers RG, French NP, Hazel SM, Turner, J (2002) A clarification of transmission terms in host-microparasite models: numbers, densities and areas. Epidemiology and Infection 129(1):147–153.CrossRefGoogle Scholar
  4. Both C, Bouwhuis S, Lessells CM, Visser ME (2006) Climate change and population declines in a long-distance migratory bird. Nature 441:81–83.CrossRefGoogle Scholar
  5. Brownie C, Hines JE, Nichols JD, Pollock KH, Hestbeck, JB (1993) Capture–recapture studies for multiple strata including non-Markovian transitions. Biometrics 49:1173–1187.CrossRefMATHGoogle Scholar
  6. Burnham KP, Anderson DR (2002) Model selection and inference: a practical information-theoretic approach. New York, Springer-Verlag.Google Scholar
  7. Burthe S, Telfer S, Lambin X, Bennett M, Carslake D, Smith A, Begon M (2006) Cowpox virus infection in natural field vole Microtus agrestis populations: delayed density dependence and individual risk. Journal of Animal Ecology 75(6):1416–1425.CrossRefGoogle Scholar
  8. Cam E (2008) Contribution of capture-mark-recapture modeling to studies of evolution by natural selection. In: Thomson DL, Cooch EG, Conroy MJ (eds.) Modeling Demographic Processes in Marked Populations. Environmental and Ecological Statistics, Springer, New York, Vol. 3, pp. 83–130.Google Scholar
  9. Cam E, Link WA, Cooch EG, Monnat JY, Danchin E (2002) Individual covariation in life-history traits: Seeing the trees despite the forest. The American Naturalist 159:96–105.CrossRefGoogle Scholar
  10. Cam E, Cooch EG, and Monnat JY (2005) Earlier recruitment or earlier death? On the assumption of equal survival in recruitment studies. Ecological Monographs 75:419–434.CrossRefGoogle Scholar
  11. Charnov EL (1989) Natural selection on age at maturity in shrimp. Evolutionary Ecology 3: 236–239.CrossRefGoogle Scholar
  12. Charnov EL (1993) Life history invariants. Oxford, Oxford University Press, UK.Google Scholar
  13. Clobert J, Lebreton JD, Allainé D, and Gaillard, JM (1994) The estimation of age-specific breeding probabilities from recaptures or resightings in vertebrate populations. II. Longitudinal models. Biometrics 50:375–387.CrossRefGoogle Scholar
  14. Cole LC (1954) The population consequences of life history phenomena. Quarterly Review of Biology 29:103–137.CrossRefGoogle Scholar
  15. Conroy MJ (2008) Application of capture–recapture to addressing questions in evolutionary ecology. In: Thomson DL, Cooch EG, Conroy MJ (eds.) Modeling Demographic Processes in Marked Populations. Environmental and Ecological Statistics, Springer, New York, Vol. 3, pp. 131–156.Google Scholar
  16. Conroy MJ, Anderson JE, Rathbun SL, and Krementz, DG (1996) Statistical inference on patch-specific survival and movement rates from marked animals. Environmental and Ecological Statistics 3:99–116.CrossRefGoogle Scholar
  17. Cox DR (1972) Regression models and life tables. Journal of the Royal Statistical Society B 74:187–220.Google Scholar
  18. Crespin L, Harris MP, Lebreton JD, Frederiksen M, Wanless S (2006) Recruitment to a seabird population depends on environmental factors and on population size. Journal of Animal Ecology 75:228–238.CrossRefGoogle Scholar
  19. Ergon T (2003) Fluctuating life-history traits in overwintering field voles (Microtus agrestis). PhD thesis. Faculty of Mathematics and Natural Sciences. Norway: University of Oslo.Google Scholar
  20. Ergon T, (2007) Optimal onset of seasonal reproduction in stochastic environments: when should overwintering small rodents start breeding? Ecoscience 14(3):330–346.CrossRefGoogle Scholar
  21. Ergon T, Lambin X, and Stenseth NC (2001) Life-history traits of voles in a fluctuating population respond to the immediate environment. Nature 411:1043–1045.CrossRefGoogle Scholar
  22. Ergon T Speakman JR, Scantlebury M, Cavanagh R, Lambin X (2004) Optimal body size and energy expenditure during winter: why are voles smaller in declining populations? American Naturalist 163(3):442–457.CrossRefGoogle Scholar
  23. Fairbairn DJ (1977) Why breed early? A study of reproductive tactics in Peromyscus. Canadian Journal of Zoology 55:862–871.CrossRefGoogle Scholar
  24. Fujiwara M, Caswell H (2002) Estimating population projection matrices from multi-stage mark-recapture data. Ecology 83:3257–3265.Google Scholar
  25. Gaillard JM, Loison A, Viallefont A, Festa-Bianchet M (2004) Assessing senescence patterns in populations of large mammals. Animal Biodiversity and Conservation 27:47–58.Google Scholar
  26. Gaillard JM, Yoccoz NG, Lebreton JD, Bonenfant C, Devillard S, Loison A, Pontier D, Allainé D (2005) Generation time: a reliable metric to measure life-history variation among mammalian populations. American Naturalist 166:119–123.CrossRefGoogle Scholar
  27. Hadley GL, Rotella JJ, Garrott RA, Nichols J (2006) Variation in probability of first reproduction of Weddell seals. Journal of Animal Ecology 75:1058–1070.CrossRefGoogle Scholar
  28. Hestbeck JB (1995) Bias in transition-specific survival and movement probabilities estimated using capture-recapture data. Journal of Applied Statistics 22:737–750.CrossRefGoogle Scholar
  29. Hestbeck JB, Nichols JD, Malecki RA (1991) Estimates of movement and site fidelity using mark-resight data of wintering Canada geese. Ecology 72:523–533.CrossRefGoogle Scholar
  30. Hochachka W (1990) Seasonal decline in reproductive performance of song sparrows. Ecology 71:1279–1288.CrossRefGoogle Scholar
  31. Joe M, Pollock KH (2002) Separation of survival and movement rates in multi-state tag-return and capture–recapture models. Journal of Applied Statistics 29:373–384.CrossRefMATHMathSciNetGoogle Scholar
  32. Kendall WL, Hines JE, Nichols JD (2003) Adjusting multistate capture–recapture models for misclassification bias: Manatee breeding proportions. Ecology 84:1058–1066.CrossRefGoogle Scholar
  33. Lambin X, Yoccoz NG (2001) Adaptive precocial reproduction in voles: reproductive costs and multivoltine life-history strategies in seasonal environments. Journal of Animal Ecology 70:191–200.CrossRefGoogle Scholar
  34. Lebreton JD, Burnham KP, Clobert J, Anderson DR (1992) Modelling survival and testing biological hypotheses using marked animals: a unified approach with case studies. Ecological Monographs 62:67–118.CrossRefGoogle Scholar
  35. Lebreton JD, Almeras T, Pradel R (1999) Competing events, mixtures of information and multistratum recapture models. Bird Study 46:39–46.CrossRefGoogle Scholar
  36. 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.CrossRefGoogle Scholar
  37. omnicki A (1988) Population ecology of individuals. Princeton, NJ: Princeton University Press.Google Scholar
  38. Oli MK, Venkataraman M, Klein PA, Wendland LD, Brown MB (2006) Population dynamics of infectious diseases: a discrete time model. Ecological Modelling 198(1–2):83–194.Google Scholar
  39. Pintilie MM (2006) Competing risks : a practical perspective. Chichester: John Wiley & Sons, Ltd.Google Scholar
  40. Pradel R, Lebreton JD (1999) Comparison of different approaches to the study of local recruitment of breeders. Bird Study 46:74–81.CrossRefGoogle Scholar
  41. Roff DA (1992) The evolution of life histories. London: Chapman and Hall.Google Scholar
  42. Roff DA (2002) Life history evolution. Sunderandl, MA: Sinauer Associates, Inc.Google Scholar
  43. Rotella J (2008) Estimating reproductive costs with multi-state mark-recapture models, multiple observable states, and temporary emigration. In: Thomson DL, Cooch EG, Conroy MJ (eds.) Modeling Demographic Processes in Marked Populations. Environmental and Ecological Statistics, Springer, New York, Vol. 3, pp. 157–172.Google Scholar
  44. Schwarz CJ, Arnason AN (2000) Estimation of age-specific breeding probabilities from capture-recapture data. Biometrics 56(1):59–64.CrossRefMATHGoogle Scholar
  45. Schwarz CJ, Schweigert JF, Arnason AN (1993) Estimating migration rates using tag-recovery data. Biometrics 49:177–193.CrossRefGoogle Scholar
  46. Skrondal A, Rabe-Hesketh S (2004) Generalized latent variable modeling. London: Chapman & Hall.Google Scholar
  47. Smith MJ, White A, Lambin X, Sherratt JA, Begon M (2006) Delayed density-dependent season length alone can lead to rodent population cycles. American Naturalist 167:695–704.CrossRefGoogle Scholar
  48. Spendelow JA, Nichols JD, Hines JE, Lebreton JD, Pradel R (2002) Modelling postfledging survival and age-specific breeding probabilities in species with delayed maturity: a case study of Roseate Terns at Falkner Island, Connecticut. Journal of Applied Statistics 29:385–405.CrossRefMATHMathSciNetGoogle Scholar
  49. Stearns SC (1992) The evolution of life histories. Oxford: Oxford University Press.Google Scholar
  50. Stenseth NC, Mysterud A, Ottersen G, Hurrell JW, Chan KS, Lima M (2002) Ecological effects of climate fluctuations. Science 297:1292–1296.CrossRefGoogle Scholar
  51. Telfer S, Bennett M, Bown K, Cavanagh R, Crespin L, Hazel S, Jones T, Begon, M (2002) The effects of cowpox virus on survival in natural rodent populations: increases and decreases. Journal of Animal Ecology 71(4):558–568.CrossRefGoogle Scholar
  52. Visser ME, Holleman LJM (2001) Warmer springs disrupt the synchrony of oak and winter moth phenology. Proceedings of the Royal Society, London B 268:289–294.CrossRefGoogle Scholar
  53. Visser ME, van Noordwijk AJ, Tinbergen JM, Lessells CM (1998) Warmer springs lead to mistimed reproduction in great tits (Parus major). Proceedings of the Royal Society, London B 265:1867–1870.CrossRefGoogle Scholar
  54. Weladji RB, Gaillard JM, Yoccoz NG, Holand Ø, Mysterud A, Loison A, Nieminen M, Stenseth NC (2006) Good reindeer mothers live longer and become better in raising offspring. Proceedings of the Royal Society B-Biological Sciences 273:1239–1244.CrossRefGoogle Scholar
  55. Williams B, Nichols JD, Conroy MJ (2002) Analysis and Management of Animal Populations. Academic Press, San Diego.Google Scholar
  56. Winkler DW, Allen PE (1996) The seasonal decline in tree swallow clutch size: physiological constraint or strategic adjustment? Ecology 77:922–932.CrossRefGoogle Scholar
  57. Zens MS, Peart DR (2003) Dealing with death data: individual hazards, mortality and bias. Trends in Ecology and Evolution 18:366–374.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Torbjørn Ergon
    • 1
  • Nigel G. Yoccoz
  • James D. Nichols
  1. 1.Centre for Ecological and Evolutionary Synthesis, Department of Biology (now at Program for Integrative Biology)University of OsloBlindernNorway

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