Masaru Iizuka

Compensatory evolution in diploid populations

Compensatory mutations are individually deleterious but harmless in appropriate combinations either at more than two sites within a gene or on separate genes. Considering that dominance effects of selection and heterodimer formation of gene products may affect the rate of compensatory evolution, we investigate compensatory neutral mutation models for diploid populations. Our theoretical analysis on the average time until fixation of compensatory mutations shows that these factors play an important role in reducing the fixation time of compensatory mutations if mutation rates are not low. Compensatory evolution of heterodimers is shown to occur more easily if the deleterious effects of single mutants are recessive.

Effective population size of a population with stochastically varying size.

For a Wright–Fisher model with mutation whose population size fluctuates stochastically from generation to generation, a heterozygosity effective population size is defined by means of the equilibrium average heterozygosity of the population. It is shown that this effective population size is equal to the harmonic mean of population size if and only if the stochastic changes of population size are uncorrelated. The effective population size is larger (resp. smaller) than the harmonic mean when the stochastic changes of population size are positively (resp. negatively) autocorrelated. These results and those obtained so far for other stochastic models with fluctuating population size suggest that the property that effective population sizes are always larger than the harmonic mean under the fluctuation of population size holds only for continuous time models such as diffusion and coalescent models, whereas effective population sizes can be equal to or smaller than the harmonic mean for discrete time models.

Models of compensatory molecular evolution: Effects of back mutation

Compensatory mutations are individually deleterious but appropriate combinations of mutants are harmless. For several models of compensatory molecular evolution, we consider the effects of back mutation. It is shown that the effects of back mutation on the rate of compensatory molecular evolution are weak. Further we estimate the values of selection parameter of deleterious single mutants for the models of compensatory molecular evolution both with and without back mutation using sequence data of folded RNA molecules and compare them with the previous results.

Conditional Processes Induced by Birth and Death Processes

For birth and death processes with finite state space consisting of N + 1 points (N ≥ 2), we consider stochastic processes induced by conditioning on hitting the right boundary point before hitting the left boundary point. We call the induced stochastic processes the conditional processes. We show that the conditional processes are again birth and death processes when the right boundary point is absorbing. On the other hand, it is shown that for N ≥ 3 the conditional processes do not have Markov property and they are not birth and death processes when the right boundary point is reflecting. The conditional processes have been introduced in population genetics. Our results are applied to stochastic models in population genetics and their conditional processes.