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Journal of Mathematical Biology

, Volume 61, Issue 6, pp 877–898

First Online: 22 January 2010Received: 25 September 2009Revised: 29 December 2009


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. Here we develop a framework that interprets adaptive walks as deterministic trajectories in combinatorial vector fields and in return associate these combinatorial vector fields with weights that measure their steepness across the landscape. We show 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 landscape. As an application, we propose a refined approximation for transition rates between macrostates that are associated with the valleys of the landscape.

KeywordsFitness landscape Adaptive walk Barrier tree Combinatorial vector field Mathematics Subject Classification 200005C20 90C27 68R10  Download to read the full article text

Autor: Bärbel M. R. Stadler - Peter F. Stadler


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