We consider a random fitness landscape on the space of haploid diallelic
genotypes with n genetic loci, where each genotype is considered either
inviable or viable depending on whether or not there are any incompatibilities
among its allele pairs. We suppose that each allele pair in the set of all
possible allele pairs on the n loci is independently incompatible with
probability p=c/(2n). We examine the connectivity of the viable genotypes under
single locus mutations and show that, for 0<c<1, the number of clusters of
viable genotypes in this landscape converges weakly (in n) to N=2^{Psi} where
Psi is Poisson distributed; while for c>1, there are no viable genotypes with
probability converging to one. The genotype space is equivalent to the
n-dimensional hypercube and the viable genotypes are solutions to a random
2-SAT problem, so the same result holds for the connectivity of solutions in
the hypercube to a random 2-SAT problem.Comment: 13 pages, 1 figur
