Publications - Published papers

Please find below publications of our group. Currently, we list 500 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 (access) is restricted to our local network and chosen collaborators. If you have problems accessing electronic information, please let us know:

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Combinatorial Vector Fields and the Valley Structure of Fitness Landscapes

Bärbel M. R. Stadler, Peter F. Stadler


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J Math Biol. 61: 877–898 (2010)


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.


Fitness landscape, Adaptive Walk, Barrier tree, Combinatorial Vector Field