Combinatorial Vector Fields and the Valley Structure of Fitness Landscapes

Adaptive (downhill) walks are a computationally convenient way of analyzing the geometric structure of fitness landscapes. Their inherently stochastic nature has limited their mathematical analysis, however. In this talk, a framework that interprets adaptive walks as deterministic trajectories in combinatorial vector fields will be presented.

These combinatorial vector fields are associated with weights that measure their steepness across the landscape.

It will be shown that the combinatorial vector fields and their weights have a product structure that is governed by the neutrality of the landscape. This product structure makes practical computations feasible. The framework presented here also provides an alternative, and mathematically more convenient, way of defining notions of valleys, saddle points, and barriers in landscapes.