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Population size models based on cumulative size, with application to aphids

Author

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  • Matis, James H.
  • Kiffe, Thomas R.
  • Matis, Timothy I.
  • Jackman, John A.
  • Singh, Harvir

Abstract

This paper investigates the use of a mechanistic model for describing the size of local aphid populations, specifically of the pecan aphid (Monellia caryella) and of the mustard aphid (Lipaphis erysimi). The mechanistic equation, like the logistic growth model, has parameters for a birth rate and a death rate, however the present mechanistic model generalizes the logistic growth model by incorporating the cumulative size of past generations into growth rate assumptions. A new non-linear regression model is derived, which solves the mechanistic model analytically and which may be fitted to data. The parameters of the regression model are the predicted peak size, Nmax⁡, the predicted time of peak, tmax⁡, and an approximate per capita birth rate, b, all of which are of interest in practical applications. The regression model is shown to fit diverse abundance curves adequately. The model also explains the population growth curves through the underlying rates. Simple approximations, based on these parameters, for the peak count and for the final cumulative aphid density are derived, and shown to be accurate. In general, this paper demonstrates the utility of analyzing local aphid population data using mechanistic models and their underlying rate parameters.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ecomod:v:205:y:2007:i:1:p:81-92
    DOI: 10.1016/j.ecolmodel.2007.02.009
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    Citations

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    Cited by:

    1. Gavin Ross & C. Sarada, 2010. "Reparameterization of nonlinear statistical models: a case study," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(12), pages 2015-2026.
    2. Matis, James H. & Kiffe, Thomas R. & Matis, Timothy I. & Jackman, John A. & Grant, William E. & Singh, Harvir, 2008. "On the use of growth rate parameters for projecting population sizes: Application to aphids," Ecological Modelling, Elsevier, vol. 213(1), pages 133-142.
    3. Grechi, Isabelle & Hilgert, Nadine & Sauphanor, Benoît & Senoussi, Rachid & Lescourret, Françoise, 2010. "Modelling coupled peach tree–aphid population dynamics and their control by winter pruning and nitrogen fertilization," Ecological Modelling, Elsevier, vol. 221(19), pages 2363-2373.
    4. Matis, James H. & Kiffe, Thomas R. & van der Werf, Wopke & Costamagna, Alejandro C. & Matis, Timothy I. & Grant, William E., 2009. "Population dynamics models based on cumulative density dependent feedback: A link to the logistic growth curve and a test for symmetry using aphid data," Ecological Modelling, Elsevier, vol. 220(15), pages 1745-1751.
    5. 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.

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