Resumen de Buchberger's Algorithm and the Two-Locus, Two-Allele Model

Arthur H. Copeland

• The present paper uses results from algebraic geometry to study the classical model describing the equilibrium frequencies of the four gametic types in the two-locus, two-allele genetic model under the assumption that the fitnesses are constant and that the cis- and trans- fitnesses are equal. It shows that there is a finite process for determining an upper bound on the maximum number of equilibrium frequencies for almost all choices of recombination and fitness parameters, and that this number is finite. It also shows that the solutions are locally continuous for almost all choices of parameters. The paper studies the equilibrium frequencies as functions of the recombination parameter, with attention to the cases when the recombination becomes infinite and when one of the equilibrium frequencies becomes infinite.