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

The spatial \Lambda-Fleming-Viot process on a large torus: Genealogies in the presence of recombination