  We introduce a modified spatial $\Lambda$-Fleming-Viot process to model the
ancestry of individuals in a population occupying a continuous spatial habitat
divided into two areas by a sharp discontinuity of the dispersal rate and
effective population density. We derive an analytical formula for the expected
number of shared haplotype segments between two individuals depending on their
sampling locations. This formula involves the transition density of a skew
diffusion which appears as a scaling limit of the ancestral lineages of
individuals in this model. We then show that this formula can be used to infer
the dispersal parameters and the effective population density of both regions,
using a composite likelihood approach, and we demonstrate the efficiency of
this method on a range of simulated data sets.
