By studying the rate of recombination between genetic markers and disease genes with linkage analysis, scientists have successfully mapped the locations of disease-influencing genes to within one centiMorgan. However, one centiMorgan corresponds to a sequence of about one million base pairs of DNA, which is prohibitively large for a physical search for a specific gene. Therefore, other genetic mapping techniques are needed to define search regions that are small enough for physical mapping techniques to be feasible. One such method is called linkage disequilibrium mapping. Linkage disequilibrium can serve as a complement, or even an alternative, to linkage analysis. It is capable of estimating genetic distances that are as small as tens of kilobases of DNA, a great improvement over the resolution of linkage analysis. However, one must describe the joint transmission of disease genes and linked marker loci through many generations in order to use linkage disequilibrium for genetic mapping purposes. This thesis examines two classes of population models, Galton-Watson branching processes and Moran/Coalescent models, within the framework of linkage disequilibrium. That is, it uses moments of allele frequencies derived from these models to form approximate likelihood functions for the recombination rate. These likelihoods make it possible to estimate the location of a disease-influencing mutation, particularly when the likelihoods from several markers within a small region of DNA are combined to form a composite likelihood. Application of this composite likelihood methodology to both simulated and published data demonstrates that linkage disequilibrium mapping can be successfully used for fine-scale mapping purposes.