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The aim of this paper is to study the large population limit of a binarybranching particle system with Moran type interactions: we introduce a newmodel where particles evolve, reproduce and die independently and, with aprobability that may depend on the configuration of the whole system, the deathof a particle may trigger the reproduction of another particle, while abranching event may trigger the death of an other one. We study the occupationmeasure of the new model, explicitly relating it to the Feynman-Kac semigroupof the underlying Markov evolution and quantifying the L2 distance betweentheir normalisations. This model extends the fixed size Moran type interactingparticle system discussed in [18, 19, 6, 7, 57] and we will indeed show thatour model outperforms the latter when used to approximate a birth and deathprocess. We discuss several other applications of our model including theneutron transport equation [36, 15] and population size dynamics.

Binary branching processes with Moran type interactions