How frugal is mother nature with haplotypes?

Motivation: Inference of haplotypes from genotype data is crucial and challenging for many vitally important studies. The first, and most critical step, is the ascertainment of a biologically sound model to be optimized. Many models that have been proposed rely partially or entirely on reducing the number of unique haplotypes in the solution. Results: This article examines the parsimony of haplotypes using known haplotypes as well as genotypes from the HapMap project. Our study reveals that there are relatively few unique haplotypes, but not always the least possible, for the datasets with known solutions. Furthermore, we show that there are frequently very large numbers of parsimonious solutions, and the number increases exponentially with increasing cardinality. Moreover, these solutions are quite varied, most of which are not consistent with the true solutions. These results quantify the limitations of the Pure Parsimony model and demonstrate the imperative need to consider additional properties for haplotype inference models. At a higher level, and with broad applicability, this article illustrates the power of combinatorial methods to tease out imperfections in a given biological model.