Equivalence of the Fleming-Viot and Look-down models of Muller's ratchet

We consider Muller's ratchet Fleming-Viot model with compensatory mutations, which is an infinite system of SDE used to study the accumulation of deleterious mutations in asexual population including mutations and selection. We construct a specific look-down model, and we prove that it is equivalent to the previous Muller's ratchet model.