Impact of demographic distribution and population growth rate on haplotypic diversity linked to a disease gene and their consequences for the estimation of recombination rate: example of a French Canadian population.

A disease gene introduced into a rapidly growing population by a single individual remains in strong linkage disequilibrium with the surrounding molecular markers. Mapping strategies taking advantage of this phenomenon allow increased mapping resolution as compared to pedigree analysis. Demographic models underlying these strategies usually assume the population exponential growth approximated by Poisson distribution of the number of children per individual. Knowing the real demographic distribution in the studied French-Canadian population, we analyzed the validity of the Poisson approximation. We adapted the existing model of the Poisson branching process to the case of a rapidly growing population and to non-Poisson distributions. In consequence, we were able to apply maximum-likelihood methods to estimate the recombination rate under various demographic scenarios. Our analysis shows that the growth rate has a higher impact on the estimation of recombination rate than the shape of the demographic distribution. The choice of the demographic model (Poisson vs. non-Poisson) has little effect on the estimation of the recombination rate but affects the expected distribution of haplotype frequencies. This distribution, however, depends much more on the population growth rate. Finally, we also demonstrate the usefulness of the Luria-Delbrück method, which gives a correct estimation of the recombination rate in a growing population, provided the sampling error is taken into account in the confidence intervals.