TY - JOUR

T1 - Nonlinear stochastic modeling of aphid population growth

AU - Matis, James H.

AU - Kiffe, Thomas R.

AU - Matis, Timothy I.

AU - Stevenson, Douglass E.

PY - 2005/12

Y1 - 2005/12

N2 - This paper develops a stochastic population size model for the black-margined pecan aphid. Prajneshu [Prajneshu, A nonlinear statistical model for aphid population growth. J. Indian Soc. Agric. Statist. 51 (1998), p. 73] proposes a novel nonlinear deterministic model for aphid abundance. The per capita death rate in his model is proportional to the cumulative population size, and the solution is a symmetric analytical function. This paper fits Prajneshu's deterministic model to data. An analogous stochastic model, in which both the current and the cumulative aphid counts are state variables, is then proposed. The bivariate solution of the model, with parameter values suggested by the data, is obtained by solving a large system of Kolmogorov equations. Differential equations are derived for the first and second order cumulants, and moment closure approximations are obtained for the means and variances by solving the set of only five equations. These approximations, which are simple for ecologists to calculate, are shown to give accurate predictions of the two endpoints of applied interest, namely (1) the peak aphid count and (2) the final cumulative aphid count.

AB - This paper develops a stochastic population size model for the black-margined pecan aphid. Prajneshu [Prajneshu, A nonlinear statistical model for aphid population growth. J. Indian Soc. Agric. Statist. 51 (1998), p. 73] proposes a novel nonlinear deterministic model for aphid abundance. The per capita death rate in his model is proportional to the cumulative population size, and the solution is a symmetric analytical function. This paper fits Prajneshu's deterministic model to data. An analogous stochastic model, in which both the current and the cumulative aphid counts are state variables, is then proposed. The bivariate solution of the model, with parameter values suggested by the data, is obtained by solving a large system of Kolmogorov equations. Differential equations are derived for the first and second order cumulants, and moment closure approximations are obtained for the means and variances by solving the set of only five equations. These approximations, which are simple for ecologists to calculate, are shown to give accurate predictions of the two endpoints of applied interest, namely (1) the peak aphid count and (2) the final cumulative aphid count.

KW - Birth-death processes

KW - Cumulant truncation

KW - Normal approximation

UR - http://www.scopus.com/inward/record.url?scp=28244493359&partnerID=8YFLogxK

U2 - 10.1016/j.mbs.2005.07.009

DO - 10.1016/j.mbs.2005.07.009

M3 - Article

C2 - 16183082

AN - SCOPUS:28244493359

SN - 0025-5564

VL - 198

SP - 148

EP - 168

JO - Mathematical Biosciences

JF - Mathematical Biosciences

IS - 2

ER -