Landscape construction and non-fixation in infinite potential

Details Landscape construction and non-fixation in infinite potential Landscape construction and non-fixation in infinite potential

2011-08-06

arxiv.org/abs/1108.1484v4

Biology

Quantitative Biology

Populations and Evolution

Scientific paper

We analytically construct the evolutionary landscape as a potential function in the Wright-Fisher process. We extend this classical concept to integrate other factors besides selection. Compared to previous work, our formulation is valid in the whole parameter space and does not require a normalizable equilibrium distribution. We discuss the uphill and downhill dynamics on the landscape and the associated timescales. When studying the average time to escape from an infinite potential peak, we find a new way to analytically approximate the result. Our results extend the use of Kramers' escape formula to the non-Gaussian cases and bridge previous results in two limits. We conclude that such a divergent equilibrium distribution does not necessarily imply the fixation of an allele type. We show how further biological insights can be gained from our framework by discussing three related issues.

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