, Volume 5, Issue 2, pp 127-148

On adaptation: A reduction of the Kauffman-Levin model to a problem in graph theory and its consequences

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Abstract

It is shown that complex adaptations are best modelled as discrete processes represented on directed weighted graphs. Such a representation captures the idea that problems of adaptation in evolutionary biology are problems in a discrete space, something that the conventional representations using continuous adaptive landscapes does not. Further, this representation allows the utilization of well-known algorithms for the computation of several biologically interesting results such as the accessibility of one allele from another by a specified number of point mutations, the accessibility of alleles at a local maximum of fitness, the accessibility of the allele with the globally maximum fitness, etc. A reduction of a model due to Kauffman and Levin to such a representation is explicitly carried out and it is shown how this reduction clarifies the biological questions that are of interest.