Szucs J M
Department of General Academics, Texas A&M University, Galveston 77553.
J Math Biol. 1991;29(7):587-627. doi: 10.1007/BF00163915.
Equilibria and convergence of gene frequencies are studied in the case of a diallelic X-linked locus under the influence of selection and mutation. The model used is that of an infinite diploid population with nonoverlapping discrete generations and random mating. It is proved that if the mutation rates and fitnesses are constant and the mutation rates are less than one-third, then global convergence of gene frequencies to equilibria occurs. The phase portraits of the dynamical system describing the change of allelic frequencies from one generation to the next are determined. Convergence of gene frequencies is monotone from a certain generation on if every other generation is skipped. In the case without mutation, our proof of this monotone convergence simplifies G. Palm's original proof.
在选择和突变的影响下，研究了双等位基因X连锁位点的基因频率平衡和收敛性。所使用的模型是具有不重叠离散世代和随机交配的无限二倍体种群模型。证明了如果突变率和适应度是恒定的，且突变率小于三分之一，那么基因频率会全局收敛到平衡状态。确定了描述等位基因频率从一代到下一代变化的动态系统的相图。如果每隔一代跳过一代，从某一代开始基因频率的收敛是单调的。在没有突变的情况下，我们对这种单调收敛的证明简化了G. 帕尔姆的原始证明。
