A Differential Equation for Mutation Rates in Environmental Coevolution.

Abstract

In their paper Natural selection for least action (Kaila and Annila 2008) they depict evolution as a process conforming to the Principle of Least Action (PLA). From this concept, together with the Coevolution model of Lewontin, an equation of motion for environmental coevolution is derived which shows that it is the time rate (frequency) of evolutionary change of the organism (mutations) that responds to changes in the environment. It is not possible to compare the theory with viral or bacterial mutation rates, as these are not measured on a time base. There is positive evidence from population level avian studies where the coefficient of additive evolvability (Cav) and its square (IA) change with environmental favourability in agreement with this model. Further analysis shows that the time rate of change of the coefficient of additive evolvability (Cav) and its square (IA) are linear with environmental favourability, which could help in defining the Lagrangian of the environmental effects.