单纯形加速法拟合生态学中的非线性模型

本文以Logistic模型,Taylor幂法则模型,Holling功能反应模型,以及种群内禀增长力Rm等模型的拟合和参数估计为例,探讨单纯形加速法在生态模型优化拟合和参数估计中的应用.结果表明,单纯形加速法拟合生态学中的非线性模型不仅适用广泛,而且拟合过程是直接求原来非线性模型的最优拟合,因而优于生态学中通常使用的将原模型“线性化后再拟合”的方法,而与其它一些最优化方法,如:麦夸方法、枚举选优法等比较,由于单纯形法不需计算目标函数的偏导数,因而计算不受目标函数及其偏导函数复杂程度的限制,而且对于各种模型其求优计算过程十分相似,可以编制统一的计算程序.本研究所编制的计算机程序对于本文未提到的其它一些模型也是完全适用的,在应用时仅需修改定义目标函数的自定义函数语句即可.研究也发现,在求优过程中,只要搜索系数选择适当和实际数据合理,是可以保证寻优成功的.

OPTIMIZATION OF NONLINEAR ECOLOGICAL MODELS WITH THE ACCELERATED SIMPLEX ALGORITHM

The application of accelerated simplex algorithm to optimization of nonlinear ecological models and estimation of ecological parameters are discussed and demonstrated with the Logistic model, Taylor's power law model, Hollings functional response model, and population intrinsic growth rate model as examples, It concludes that: the accelerated simplex algorithm is not only widely applicable in the optimization of nonlinear ecological models,but also suprior to the commonly used"fitting after linear transformtion"i,e,first transform the original model into a linear form and then fit the transformed model), because the original nonlinear model is directly optimized with the simplex method. Compared with other function optimization algorithms, such as Marquardt's algorithm, and optmization method of Enumeration, etc., the simplex has the advantage that it is not necessary to calculate the partial derivatives of goal function. Therefore the suitability of the simplex method is not restricted by the complexity of ecological models and that makes it possible to develop a unified computer program appllicable to general nonlinear ecological models. And this computer program has been developed with BASIC in the study. It is also proved that the searching convergence of the simplex algorithm can be guaranteed at least by selection of model parameters values obta- ined from common used method such as above-mentioned"fitting after transformation" as initial simplex, but in general the selection of initial parameters can be done according to general ecological knowledge.