Nonindependent evolution of duplicated genes is called concerted evolution. In this article, we study the evolutionary process of duplicated regions that involves concerted evolution. The model incorporates mutation and gene conversion: the former increases d, the divergence between two duplicated regions, while the latter decreases d. It is demonstrated that the process consists of three phases. Phase I is the time until d reaches its equilibrium value, d6. In phase II d fluctuates around d0, and d increases again in phase III. Our simulation results demonstrate that the length of concerted evolution (i.e., phase II) is highly variable, while the lengths of the other two phases are relatively constant. It is also demonstrated that the length of phase II approximately follows an exponential distribution with mean τ, which is a function of many parameters including gene conversion rate and the length of gene conversion tract. On the basis of these findings, we obtain the probability distribution of the level of divergence between a pair of duplicated regions as a function of time, mutation rate, and T. Finally, we discuss potential problems in genomic data analysis of duplicated genes when it is based on the molecular clock but concerted evolution is common.
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