Abstract In Jacob et al. [A General Class of Population-Dependent Two-Sex Processes with Random Mating. Bernoulli 2017, 23, 1737–1758], a new class of two-sex branching processes in discrete time was introduced. These processes present the novelty that, in each generation, mating between females and males is randomly governed by a set of Bernoulli distributions allowing polygamous behavior with only perfect fidelity on the part of female individuals. Moreover, mating as well as reproduction can be influenced by the number of females and males in the population. In that article, the authors study conditions leading to the almost sure extinction or to the possible survival with positive probability of such processes. In this work, we continue the research about this class of two-sex processes by investigating the rate of growth of the population in case of survival. In particular, we provide conditions for a simultaneous geometric growth of the number of females and males and conditions for the geometric growth of females with a stable population of males.

中文翻译：

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随机交配的种群依赖两性分支过程：增长率

摘要在雅各布等人。[具有随机交配的人口依赖性两性过程的一般类别。Bernoulli 2017, 23, 1737–1758]，引入了一类新的离散时间两性分支过程。这些过程呈现出新奇之处，即在每一代中，雌性和雄性之间的交配是由一组伯努利分布随机控制的，允许一夫多妻行为，而雌性个体只有完美的保真度。此外，交配和繁殖会受到种群中雌性和雄性数量的影响。在那篇文章中，作者研究了导致几乎可以肯定的灭绝或可能存在这种过程的正概率生存的条件。在这项工作中，我们通过调查生存情况下的人口增长率继续研究这类两性过程。特别是，我们为雌性和雄性的数量同时几何增长提供了条件，并为具有稳定的雄性种群的雌性几何增长提供了条件。