The present paper continues the work of two previous papers on the variational behavior, over a large number of generations, of a Wright-Fisher process modelling an even larger reproducing population. It was shown that a Wright-Fisher process subject to random drift and one-way mutation which undergoes a large deviation follows with near certainty a path which can be a trigonometric, exponential, hyperbolic or parabolic function. Here it is shown that a process subject to random drift and gamete selection follows in similar circumstances a path which is, apart from critical cases, a Jacobian elliptic function.
"Elliptic and other functions in the large deviations behavior of the Wright-Fisher process." Ann. Appl. Probab. 8 (1) 182 - 192, February 1998. https://doi.org/10.1214/aoap/1027961039