Haplotype mapping has emerged in the past few years as a powerful tool for the fine mapping of disease genes. It is typically carried out on a sample of affected individuals from a population isolate. If the chromosome neighborhood of a disease gene is saturated with markers, then each new mutation in the population or existing mutation introduced by a population founder exhibits a unique haplotype signature at the time of its introduction. Partial disruption of these signatures by recombination can be visualized in affects and provide important clues to the location of the disease gene. The current paper models haplotype evolution with the intention of clarifying the most favorable circumstances for haplotype mapping. Comparisons with linkage mapping are stressed. For dominant diseases, both deterministic and stochastic models are suggested. Numerical examples based on Finnish population parameters illustrate the general theory in the presence of the complications of selection, mutation, and slow, exponential growth of the isolate.