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

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.Thanks are due to William Wimsatt, James F. Crow, and the referees for Biology and Philosophy for comments on an earlier version of this paper. Remarks by members of the audience, especially Abner Shimony, of a seminar at Boston University, February 19, 1988, were also very helpful. The diagrams were prepared with the assistance of Tracy Lubas.