A comparison of three different stochastic population models with regard to persistence time

被引:91
作者
Allen, LJS [1 ]
Allen, EJ [1 ]
机构
[1] Texas Tech Univ, Dept Math & Stat, Lubbock, TX 79409 USA
基金
美国国家科学基金会;
关键词
persistence time; birth and death process; logistic equation; Markov chain; stochastic differential equation;
D O I
10.1016/S0040-5809(03)00104-7
中图分类号
Q14 [生态学(生物生态学)];
学科分类号
071012 ; 0713 ;
摘要
Results are summarized from the literature on three commonly used stochastic population models with regard to persistence time. In addition, several new results are introduced to clearly illustrate similarities between the models. Specifically, the relations between the mean persistence time and higher-order moments for discrete-time Markov chain models, continuous-time Markov chain models, and stochastic differential equation models are compared for populations experiencing demographic variability. Similarities between the models are demonstrated analytically, and computational results are provided to show that estimated persistence times for the three stochastic models are generally in good agreement when the models are consistently formulated. As an example, the three stochastic models are applied to a population satisfying logistic growth. Logistic growth is interesting as different birth and death rates can yield the same logistic differential equation. However, the persistence behavior of the population is strongly dependent on the explicit forms for the birth and death rates. Computational results demonstrate how dramatically the mean persistence time can vary for different populations that experience the same logistic growth. (C) 2003 Elsevier Inc. All rights reserved.
引用
收藏
页码:439 / 449
页数:11
相关论文
共 45 条
[1]  
Allen EJ, 1999, DYN CONTIN DISCRET I, V5, P271
[2]   Modelling and simulation of a schistosomiasis infection with biological control [J].
Allen, EJ ;
Victory, HD .
ACTA TROPICA, 2003, 87 (02) :251-267
[3]  
Allen L. J, 2010, An Introduction to Stochastic Processes with Applications to Biology
[4]  
[Anonymous], 1974, Stochastic Models in Biology
[5]  
[Anonymous], 1997, Numerical Solution of Stochastic Differential Equations through Computer Experiments
[6]  
Busenberg S., 1993, Vertically Transmitted Disease: Models and Dynamics
[7]  
Caswell Hal, 2001, pi
[8]  
CUSHING JM, 1998, SIAM CBMS NSF REGION, V71
[9]  
DeAngelis D.L., 1992, Individual-based models and approaches in ecology: populations, communities and ecosystems, DOI DOI 10.1201/9781351073462
[10]   ANALYSIS OF STEADY-STATE POPULATIONS WITH THE GAMMA-ABUNDANCE MODEL - APPLICATION TO TRIBOLIUM [J].
DENNIS, B ;
COSTANTINO, RF .
ECOLOGY, 1988, 69 (04) :1200-1213