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Cormack–Jolly–Seber models: time and age perspectives

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Abstract

Survival is a key demographic characteristic in many areas including both human demography and population ecology. However, it is often the case that data collection protocols are different in these areas, resulting in different models and methods of analysis. This paper is motivated for the different emphasis given to the elicitation of the temporal scale (and consequently, on the origin time) in ecological and medical survival studies. Specifically, in medical studies, the origin time is often determined in advance with individuals followed over a period of time at regular (or irregular) intervals, thus focusing on time within study (or age to a given reference point). However, in ecological capture–recapture studies, the capture occasions are typically fixed in advance, with an imperfect detection process observing individuals at these times. Moreover, the temporal scale is often primarily specified at the capture occasion level. In this work we focus on an ecological capture–recapture study related to guillemots and compare and contrast two different temporal scales: (1) calendar (or capture occasion); and (2) age (or time within study), in terms of the way the data may be represented and in relation to the ecological Cormack–Jolly–Seber-type model. The different temporal scales provides insights into the different underlying structures, which can then be combined into a joint (calendar and age) dependence model.

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Acknowledgements

Blanca Sarzo has a research Grant (BES-2014-070766) supported by MTM2013-42323-P from the Spanish Ministry of Economy and Competitiveness. This work has been partially supported by Grants MTM2016-77501-P and TEC2016-81900-REDT from the Spanish Ministerio de Ciencia, Innovación y Universidades. Agencia Estatal de Investigación (jointly financed by the European Regional Development Fund, FEDER). RK was funded by a Leverhulme Research Fellowship. Field work on Stora Karlsö has been made possible through a long-term engagement in the Baltic Seabird project by WWF Sweden. We thank a large number of field workers and volunteers at Stora Karlsö in the period 2006–2016 for support with ringing and observation studies. Karlsö Jagt-och Djurskyddsfrenings AB provided logistical support.

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Authors and Affiliations

  1. Department of Statistics and O.R., University of Valencia, Burjassot, Spain

    Blanca Sarzo & David Conesa

  2. School of Mathematics, University of Edinburgh, Edinburgh, UK

    Ruth King

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  1. Blanca Sarzo
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  2. David Conesa
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  3. Ruth King
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Correspondence to Blanca Sarzo.

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Appendix

Appendix

In order to highlight differences in data presentation when using both temporal scales and for reproducibility issues, here we present the ten cohort m-arrays in age scale (Tables 8, 9, 10, 11, 12, 13, 14, 15, 16, 17) and the four age m-arrays in calendar scale (Tables 18, 19, 20, 21), corresponding to the study database.

Table 8 M-array cohort 1 in age scale
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Table 9 M-array cohort 2 in age scale
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Table 10 M-array cohort 3 in age scale
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Table 11 M-array cohort 4 in age scale
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Table 12 M-array cohort 5 in age scale
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Table 13 M-array cohort 6 in age scale
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Table 14 M-array cohort 7 in age scale
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Table 15 M-array cohort 8 in age scale
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Table 16 M-array cohort 9 in age scale
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Table 17 M-array cohort 10 in age scale
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Table 18 Age 1 m-array in calendar scale
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Table 19 Age 2 m-array in calendar scale
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Table 20 Age 3 m-array in calendar scale
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Table 21 Age 4+ m-array in calendar scale
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Sarzo, B., Conesa, D. & King, R. Cormack–Jolly–Seber models: time and age perspectives. Stoch Environ Res Risk Assess 34, 1683–1698 (2020). https://doi.org/10.1007/s00477-020-01840-x

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