Before revision:  The extension of the reduction principle is shown topologically to require a manifold of mutation rate alterations that are neutral for a new modifier allele , below which will cause a new modifierallele to increase when rare, and above which cause it to go extinct. This manifold is the same structure as found in a multivariate multilocus model of recombination modification by Zhivotovsky, Feldman, and Christiansen ( 1994 ).
After revision:  The extension of the reduction principle is shown topologically to require a manifold of mutation rate alterations that are neutral for a new modifier allele . New mutation rates survive if and only if they fall below this surface - a generalization of the hyperplane found by Zhivotovsky et al. ( 1994 ).