Decay of linkage disequilibrium in a finite island model

Time-dependent behaviour of linkage disequilibrium when there was initial linkage disequilibrium is studied in a finite island model assuming neutrality. Explicit expressions for linkage disequilibrium parameters are obtained. From these expressions, the initial and the ultimate decay rates of linkage disequilibrium parameters are found to be increased and decreased, respectively, by finiteness of the population when recombination rate, migration rate and inverse of subpopulation size are of comparable order. Thus, linkage disequilibrium created in the past may persist longer in smaller subdivided populations. Also, differentiation of the gametic parameter of linkage disequilibrium among subpopulations is found to diminish quickly compared to the linkage disequilibrium in the whole population. Implications of these results for the interpretation of linkage disequilibria in natural populations are discussed.