Osei B M, Ellingwood C D, Hoffmann J P, Bentil D E
Department of Mathematics and Computer Science, Eastern Connecticut State University, 83 Wndham St, Willimantic, CT 06226, USA.
Theory Biosci. 2011 Jun;130(2):145-52. doi: 10.1007/s12064-011-0122-3. Epub 2011 Feb 4.
We use a reaction diffusion equation, together with a genetic algorithm approach for model selection to develop a general modeling framework for biological invasions. The diffusion component of the reaction diffusion model is generalized to include dispersal and advection. The reaction component is generalized to include both linear and non-linear density dependence, and Allee effect. A combination of the reaction diffusion and genetic algorithm is able to evolve the most parsimonious model for invasive species spread. Zebra mussel data obtained from Lake Champlain, which demarcates the states of New York and Vermont, is used to test the appropriateness of the model. We estimate the minimum wave spread rate of Zebra mussels to be 22.5 km/year. In particular, the evolved models predict an average northward advection rate of 60.6 km/year (SD ± 1.9), which compares very well with the rate calculated from the known hydrologic residence time of 60 km/year. A combination of a reaction diffusion model and a genetic algorithm is, therefore, able to adequately describe some of the hydrodynamic features of Lake Champlain and the spread of a typical invasive species--Zebra mussels within the lake.
我们使用反应扩散方程，并结合遗传算法进行模型选择，以开发一种用于生物入侵的通用建模框架。反应扩散模型的扩散部分被推广到包括扩散和平流。反应部分被推广到包括线性和非线性密度依赖以及阿利效应。反应扩散和遗传算法的结合能够演化出用于入侵物种扩散的最简约模型。从尚普兰湖获取的斑马贻贝数据（尚普兰湖划分了纽约州和佛蒙特州的边界）用于测试该模型的适用性。我们估计斑马贻贝的最小波传播速率为22.5千米/年。特别是，演化出的模型预测平均向北平流速率为60.6千米/年（标准差±1.9），这与根据已知水文停留时间计算出的60千米/年的速率非常吻合。因此，反应扩散模型和遗传算法的结合能够充分描述尚普兰湖的一些水动力特征以及典型入侵物种——斑马贻贝在湖中的扩散情况。
