Until recently, attempts to map disease genes on the basis of population associations with linked markers have been based on expected values of linkage disequilibrium. These methods suffer from the large variances imposed on disequilibrium measures by the evolutionary process, but a more serious problem for many diseases is that they assume an equilibrium population. For diseases that arose only a few hundred generations ago, it is more appropriate to concentrate on the initial growth phase of the disease. We invoke a Poisson branching process for this early growth, and estimate the likelihood for the recombination fraction between marker and disease loci, on the basis of simulated disease populations. The limits of the resulting support intervals for the recombination fraction vary inversely with the age of the disease in generations. We illustrate the procedure with data on cystic fibrosis and diastrophic dysplasia, for which the method appears appropriate, and for Friedreich ataxia and Huntington disease, for which it does not. A valuable aspect of the method is the ability in some cases to compare likelihoods of the three orders for a disease locus and two linked marker loci.