Nonlinear stochastic modeling of aphid population growth

被引:26
作者
Matis, JH [1 ]
Kiffe, TR
Matis, TI
Stevenson, DE
机构
[1] Texas A&M Univ, Dept Stat, College Stn, TX 77843 USA
[2] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA
[3] New Mexico State Univ, Dept Ind Engn, Las Cruces, NM 88003 USA
[4] Texas Cooperat Extens, College Stn, TX 77843 USA
关键词
cumulant truncation; normal approximation; birth death processes;
D O I
10.1016/j.mbs.2005.07.009
中图分类号
Q [生物科学];
学科分类号
07 [理学]; 0710 [生物学]; 09 [农学];
摘要
his 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 it) 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. (c) 2005 Elsevier Inc. All rights reserved.
引用
收藏
页码:148 / 168
页数:21
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