  We extend the spatial $\Lambda$-Fleming-Viot process introduced in [Electron.
J. Probab. 15 (2010) 162-216] to incorporate recombination. The process models
allele frequencies in a population which is distributed over the
two-dimensional torus $\mathbb{T}(L)$ of sidelength L and is subject to two
kinds of reproduction events: small events of radius $\mathcal{O}(1)$ and much
rarer large events of radius $\mathcal{O}(L^{\alpha})$ for some
$\alpha\in(0,1]$. We investigate the correlation between the times to the most
recent common ancestor of alleles at two linked loci for a sample of size two
from the population. These individuals are initially sampled from "far apart"
on the torus. As L tends to infinity, depending on the frequency of the large
events, the recombination rate and the initial distance between the two
individuals sampled, we obtain either a complete decorrelation of the
coalescence times at the two loci, or a sharp transition between a first period
of complete correlation and a subsequent period during which the remaining
times needed to reach the most recent common ancestor at each locus are
independent. We use our computations to derive approximate probabilities of
identity by descent as a function of the separation at which the two
individuals are sampled.
