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Bayesian inference for generalized stochastic population growth models with application to aphids

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  • Colin S. Gillespie
  • Andrew Golightly

Abstract

Summary. We analyse the effects of various treatments on cotton aphids (Aphis gossypii). The standard analysis of count data on cotton aphids determines parameter values by assuming a deterministic growth model and combines these with the corresponding stochastic model to make predictions on population sizes, depending on treatment. Here, we use an integrated stochastic model to capture the intrinsic stochasticity, of both observed aphid counts and unobserved cumulative population size for all treatment combinations simultaneously. Unlike previous approaches, this allows us to explore explicitly and more accurately to assess treatment interactions. Markov chain Monte Carlo methods are used within a Bayesian framework to integrate over uncertainty that is associated with the unobserved cumulative population size and estimate parameters. We restrict attention to data on aphid counts in the Texas High Plains obtained for three different levels of irrigation water, nitrogen fertilizer and block, but we note that the methods that we develop can be applied to a wide range of problems in population ecology.

Suggested Citation

  • Colin S. Gillespie & Andrew Golightly, 2010. "Bayesian inference for generalized stochastic population growth models with application to aphids," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(2), pages 341-357, March.
    • Handle: RePEc:bla:jorssc:v:59:y:2010:i:2:p:341-357
    DOI: 10.1111/j.1467-9876.2009.00696.x
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    References listed on IDEAS

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    1. Matis, James H. & Kiffe, Thomas R. & Matis, Timothy I. & Jackman, John A. & Singh, Harvir, 2007. "Population size models based on cumulative size, with application to aphids," Ecological Modelling, Elsevier, vol. 205(1), pages 81-92.
    2. Golightly, A. & Wilkinson, D.J., 2008. "Bayesian inference for nonlinear multivariate diffusion models observed with error," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1674-1693, January.
    3. Giarola, L.T.P. & Martins, S.G.F. & Toledo Costa, M.C.P., 2006. "Computer simulation of Aphis gossypii insects using Penna aging model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 147-154.
    4. A. Golightly & D. J. Wilkinson, 2005. "Bayesian Inference for Stochastic Kinetic Models Using a Diffusion Approximation," Biometrics, The International Biometric Society, vol. 61(3), pages 781-788, September.
    5. Eraker, Bjorn, 2001. "MCMC Analysis of Diffusion Models with Application to Finance," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 177-191, April.
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    Cited by:

    1. Christoph Zimmer, 2016. "Experimental Design for Stochastic Models of Nonlinear Signaling Pathways Using an Interval-Wise Linear Noise Approximation and State Estimation," PLOS ONE, Public Library of Science, vol. 11(9), pages 1-37, September.
    2. Golightly, Andrew & Bradley, Emma & Lowe, Tom & Gillespie, Colin S., 2019. "Correlated pseudo-marginal schemes for time-discretised stochastic kinetic models," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 92-107.

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