The estimate of parameters of logistic population dynamic probability model
Date Issued
2006
Date
2006
Author(s)
Chen, Chi-Tian
DOI
zh-TW
Abstract
The deterministic logistic model has long been used for modeling the growth of animal population. However, its stochastic counterpart is less known to most of the ecologists partly due to the difficulty in parameter estimation. The estimation method given by Renshaw (1991) was rough and did not take into consideration of repeated measurement data. In this research, we propose an alternative to the estimation of the four parameters of stochastic logistic model.
Our approach includes two major steps. First part of our estimation method is to construct a relationship between the variance of quasi-equilibrium distribution and four parameters which are denoted by a1, a2, b1 and b2. The a’s are intrinsic parameters for birth and death, respectively; the b’s are so-called crowding coefficients. We fit a second-order response surface function of variances σ2 on various probable values of parameters (a1, b1) and denote the function by σ2 = f (a1, b1). Secondly, we employ the method of nonlinear mixed-effects (NME) model to the real growth data usually collected in laboratory or field by scientists. The carrying capacity K of a stochastic logistic model is viewed as a normal random variable whose mean and variance can be estimated by NME method. The variance estimated by this method is far more precise than that obtained by Renshaw’s way of estimation. By plugging the variance estimate into the previously constructed response surface function, we may ‘calibrate’ the possible values of (a1, b1) in a confined interval. We can proceed further by incorporate the mean estimate = (a1－a2)/ (b1＋b2) and other source of information such as probable skewness to determine a reasonable range of parameter estimates.
Six examples are used to illustrate and justified the newly proposed approach; they are from renowned authors such as Gause (1938), Pielou (1977), Renshaw (1991) and Matis et al (1996). Interesting results reveal that parameter estimates found by previous authors are all in the confined intervals obtained from our method.
Subjects
邏輯斯生長模式
環境容納量
內生出生及死亡率
擁擠係數
反應曲面法
非線性混合模式
deterministic logistic model
stochastic logistic model
quasi-equilibrium distribution
intrinsic parameters for birth and death
crowding coefficients
nonlinear mixed-effects (NME) model
Type
thesis
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