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Dynamic Models for Longitudinal Butterfly Data

Author

Listed:
  • Emily B. Dennis

    (University of Kent
    Butterfly Conservation)

  • Byron J. T. Morgan

    (University of Kent)

  • Stephen N. Freeman

    (Benson Lane, Crowmarsh Gifford)

  • David B. Roy

    (Benson Lane, Crowmarsh Gifford)

  • Tom Brereton

    (Butterfly Conservation)

Abstract

We present models which provide succinct descriptions of longitudinal seasonal insect count data. This approach produces, for the first time, estimates of the key parameters of brood productivities. It may be applied to univoltine and bivoltine species. For the latter, the productivities of each brood are estimated separately, which results in new indices indicating the contributions from different generations. The models are based on discrete distributions, with expectations that reflect the underlying nature of seasonal data. Productivities are included in a deterministic, auto-regressive manner, making the data from each brood a function of those in the previous brood. A concentrated likelihood results in appreciable efficiency gains. Both phenomenological and mechanistic models are used, including weather and site-specific covariates. Illustrations are provided using data from the UK Butterfly Monitoring Scheme, however the approach is perfectly general. Consistent associations are found when estimates of productivity are regressed on northing and temperature. For instance, for univoltine species productivity is usually lower following milder winters, and mean emergence times of adults for all species have become earlier over time, due to climate change. The predictions of fitted dynamic models have the potential to improve the understanding of fundamental demographic processes. This is important for insects such as UK butterflies, many species of which are in decline. Supplementary materials for this article are available online.

Suggested Citation

  • Emily B. Dennis & Byron J. T. Morgan & Stephen N. Freeman & David B. Roy & Tom Brereton, 2016. "Dynamic Models for Longitudinal Butterfly Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(1), pages 1-21, March.
  • Handle: RePEc:spr:jagbes:v:21:y:2016:i:1:d:10.1007_s13253-015-0216-3
    DOI: 10.1007/s13253-015-0216-3
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    References listed on IDEAS

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    1. John F. Y. Brookfield, 2001. "Predicting the future," Nature, Nature, vol. 411(6841), pages 999-999, June.
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    Cited by:

    1. Dennis, Emily B. & Kéry, Marc & Morgan, Byron J.T. & Coray, Armin & Schaub, Michael & Baur, Bruno, 2021. "Integrated modelling of insect population dynamics at two temporal scales," Ecological Modelling, Elsevier, vol. 441(C).
    2. Eleni Matechou & Stephen N. Freeman & Richard Comont, 2018. "Caste-Specific Demography and Phenology in Bumblebees: Modelling BeeWalk Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(4), pages 427-445, December.
    3. Stephen N. Freeman & Nicholas J. B. Isaac & Panagiotis Besbeas & Emily B. Dennis & Byron J. T. Morgan, 2021. "A Generic Method for Estimating and Smoothing Multispecies Biodiversity Indicators Using Intermittent Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(1), pages 71-89, March.

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