Linkage and association analysis based on haplotype transmission disequilibrium can be more informative than single marker analysis. Several works have been proposed in recent years to extend the transmission disequilibrium test (TDT) to haplotypes. Among them, a powerful approach called the evolutionary tree TDT (ET-TDT) incorporates information about the evolutionary relationship among haplotypes using the cladogram of the locus.In this work we extend this approach by taking into consideration the sparsity of causal mutations in the evolutionary history. We first introduce the notion of a Bradley-Terry (BT) graph representation of a haplotype locus. The most important property of the BT graph is that sparsity of the edge set of the graph corresponds to small number of causal mutations in the evolution of the haplotypes. We then propose a method to test the null hypothesis of no linkage and association against sparse alternatives under which a small number of edges on the BT graph have non-nil effects.We compare the performance of our approach to that of the ET-TDT through a power study, and show that incorporating sparsity of causal mutations can significantly improve the power of a haplotype-based TDT.