微分方程在描述两群体进化过程中的应用

Application of Differential Equation to the Evolution of Two Groups

为了解释生物进化各种过程,在一定的条件下,通过定向选择推导出的微分方程可以研究两个共享同一资源但同时又互不杂交的同类群体的进化过程。虽然人们的直觉是大群体往往能占有生存的良机,但是这种认识是片面的。通过微分方程的各种模拟结果可以得出结论:一方面在简单的适应面上,即当一个群体发生有利突变而产生具有优势的后代,那么无论初始条件如何这个群体将最后侵蚀掉另一群体。大群体因有利突变等概率产生而有更大的几率获得生存的优势。另一方面在略微复杂的适应面上,如果两个群体都发生有利突变只是发生的时间不同。在相同的境遇下,小群体相比大群体反而有更大的可能存活下来而不被灭绝。

In order to explain the process of biological evolution based on some conditions, the differential equation deduced from directional selection describes the evolutionary process of two populations （species） which share the same resource without amalgamation. Although it is generally held that the larger population obtains better chances of survival, such view is not complete. By using differential equations and computer simulations, we found that, when a population gains beneficial mutation, the other population will go extinct regardless of its initial conditions. The larger population is superior since it is more likely to obtain advantageous mutation if the rate of advantageous mutation remains constant between the two populations. On the other hand, if both populations have favorable mutation, the chance of the survival for the smaller population will be apparently better.