Publications - Published papers
Please find below publications of our group. Currently, we list 565 papers. Some of the publications are in collaboration with the group of Sonja Prohaska and are also listed in the publication list for her individual group. Access to published papers (
) is restricted to our local network and chosen collaborators.
If you have problems accessing electronic information, please let us know:
) is restricted to our local network and chosen collaborators.
If you have problems accessing electronic information, please let us know:©NOTICE: All papers are copyrighted by the authors; If you would like to use all or a portion of any paper, please contact the author.
Combinatorial Vector Fields and the Valley Structure of Fitness Landscapes
Bärbel M. R. Stadler, Peter F. Stadler
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Status: Published
J Math Biol. 61: 877–898 (2010)
Abstract
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 landscapes. As an application, we propose a
refined approximation for transition rates between macrostates that are
associated with the valleys of the landscape.
Keywords
Fitness landscape, Adaptive Walk, Barrier tree, Combinatorial Vector Field