I'm a math undergrad looking for some papers on modelling the process of natural selection. The only paper I've been able to find is by the pre-eminent mathematician Herbert Wilf from 2010,
Unfortunately, Wilf's model is extremely simplistic - he calculates the number of 'generations' required to spell out a 'word', if we allow each letter to 'mutate' with certain probability every generation, and we stop mutating a letter once it is correct (this is the 'selective' feature of the model). So to spell the word 'Evolution' by randomly placing scrabble tiles would require 5.4 trillion generations, but if we keep the correctly placed letters each generation and only allow incorrect letters to 'mutate', Wilf calculates we'd only need about 57 generations on average.
Wilf's model is a good first step towards modelling natural selection, but it's clearly only a first step. In particular, the fact that nature seems to know in advance exactly what letters it needs to keep in particular places and what it needs to throw out to construct a complex genetic 'word' is dubious at best.
As a young maths student the idea of the incredible complexity and diversity of life developing by a directed stochastic process gets me shamelessly excited :) I have been very surprised at just how little mathematical literature there seems to be on this topic, as I say, Wilf's one super-simplistic model is all I've been able to find. Can someone direct me to any other theoretical analyses of the power of natural selection?