一类群体迁移的数学模型分析

研究两个同物种大孟德尔二倍体生物群体在迁移作用下的变化规律。结果表明:两群体的个体数量与它们的初始个体数量和迁移比例有关,迁移比例是影响个体数量变化的因素;两群体的基因频率与它们的初始个体数量、初始基因频率以及迁移比例有关,迁移比例是影响基因频率变化的因素;经过无限多时间的迁移之后,两群体的个体数量、基因频率会趋向于一种动态平衡状态,两群体个体数量不同,基因频率相同。模拟分析结果验证了理论推导的结论。

Analysis of Mathematics Model of a Population Migration

Affected by migration, regularity changes and development trend of two big Mendel biological populations whose members were diploid and identical species were studied in this paper. Results showed that every individual quantity of the two populations was closely relative to their original quantity and migration proportion and migration proportion was the factor which could influence the change of individual quantity. Every gene frequency of the two populations was relative with original individual quantity, the original gene frequency and the migration proportion, migration proportion was the factor which could influence the change of gene frequency. After migration of enough much time, the individual quantity and gene frequency of two populations would tend to reach a dynamical equilibrium, that is, the individual quantities of the two populations are different, but gene frequencies become identical. All results were proved by simulating with MATLAB.