A synthetic theory of molecular evolution

According to the neo-Darwinian view of evolution evolution rate v depends solely on the environment variation rate gamma, whereas in the non-Darwinian view evolution rate is determined mainly by the mutation rate mu. We have studied two kinds of population genetics models which exhibit both types of evolution in different parametric regions: one is a dynamical model representing infinite population, and the other is a Markov process model representing a nearly monomorphic finite population. In the infinite population model, after proving general time-derivative and p-derivative formulas for the population average of quantitative traits, we show that if the mutation rate is adaptively determined, mu must be larger than v in the stationary state. Loads of evolution are obtained in both regions. A high evolution rate such as v = 1 per genome per generation is consistent with Haldane's value of tolerable load if and only if the functional constraint is not large and selection is weak, independent of whether the evolution is neo-Darwinian or non-Darwinian. As the selection intensity increases, v is shown to change discontinuously from nearly mu to gamma at the transition point. In the finite population model, the transition of v is not discontinuous, but is very steep. On the other hand, no steep change of polymorphism takes place at the transition point. The steepness of the transition in our model suggests that real molecular evolution can be divided into either neo-Darwinian or non-Darwinian, and that the intermediate type of evolution is rather rare.