Scaling limits of bisexual Galton–Watson processes

Bisexual Galton–Watson processes are discrete Markov chains where reproduction events due to mating of males and females. Owing this interaction, the standard branching property is lost. We prove tightness for conveniently rescaled bisexual processes, based on recent techniques developed in [V. Bansaye, M.E. Caballero, S. Méléard, Scaling limits population evolution random environment, Electron. J. Probab. 24(19) (2019), pp. 1–38]. also identify possible these as solutions a stochastic system, coupling two equations through singular coefficients Poisson terms added square roots Brownian motions. Under some additional integrability assumptions, pathwise uniqueness limiting system differential convergence obtained. Two examples corresponding mutual fidelity considered.