The effects of linkage and density-dependent regulation on gene flow.

The rate of gene flow across a hybrid zone may be reduced by the presence of a physical barrier, by a reduction of population density caused by reduced fitness of hybrids (the "hybrid sink" effect), and by linkage. If the reduction in hybrid fitness is not extreme, the strength of the barrier to gene flow caused by these effects is B = w(rho *+/rho *0)2(W*+/W*0)(2/R + 1/r). Here, w is the width of the cline; rho * is the carrying capacity; W* is the mean fitness of the population, excluding effects of density; R is the strength of density-dependent regulation; and r is the harmonic mean recombination rate between the locus whose flow is being calculated, and loci under selection. +, 0 denote populations outside the hybrid zone, and at its centre, respectively. This relation is illustrated using data from hybrid zones in Bombina and Podisma, and its implications for interpretation of data from nature are discussed.