by Walter ReMine
CRS Quarterly, Volume 43 Number 2, September 2006, pp. 111-120.
Abstract:
This paper extends the applicability and accuracy of the cost of substitution beyond its traditional range, and demonstrates a useful calculation method. Using my previous clarification of the fundamental cost concept, this paper derives a method for computing the cost of substitution under wide genetic circumstances, including haploids; and diploids with varying degrees of dominance, inbreeding, and with a sex-linked locus. Unlike the traditional approaches, this method is accurate even under fluctuations in parameter values (such as population size, selection coefficient, dominance, and inbreeding coefficient). To display general- purpose results, the parameters are then held constant, and the total cost of substitution is graphed. This includes cases where the selection coefficient is not small and where the traditional equations become highly inaccurate. It is shown that neither environmental change nor soft selection reduces cost problems, at least in single substitutions.
Note added in publication: This paper offers previously unpublished clarifications, derivations and graphs, and refutes widely accepted solutions to a central problem in evolutionary genetics known as Haldane’s Dilemma. It was submitted to the journal Theoretical Population Biology, where all the peer-reviewers found no errors. Nonetheless, they rejected it from publication on the grounds that it is not a “sufficient advance,” and “there is little interest in this subject today among population biologists; it is one of those subjects which has sunk almost beyond trace.” This has all been very unfortunate, as there continues to be widespread misunderstanding within the scientific community regarding these important matters, even among those who have studied the cost literature for years. It is hoped that the clarifications presented in this paper will eventually reach the greater scientific community.
