碩士 / 國立臺灣大學 / 農藝學研究所 / 94 / 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.
| Identifer | oai:union.ndltd.org:TW/094NTU05417005 |
| Date | January 2006 |
| Creators | Chi-Tian Chen, 陳啟天 |
| Contributors | 彭雲明 |
| Source Sets | National Digital Library of Theses and Dissertations in Taiwan |
| Language | zh-TW |
| Detected Language | English |
| Type | 學位論文 ; thesis |
| Format | 57 |
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