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.
After revision:  The extension of the reduction principle is found: reduction results at individual loci combine topologically to produce a surface 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.