Spatially distributed populations with two sexes may face the problem that males and females concentrate in different parts of the habitat and mating and reproduction does not happen sufficiently often for the population to persist. For simplicity, to explore the impact of sex-dependent dispersal on population survival, we consider a discrete-time model for a semelparous population where individuals reproduce only once in their life-time, during a very short reproduction season. The dispersal of females and males is modeled by Feller kernels and the mating by a homogeneous pair formation function. The spectral radius of a homogeneous operator is established as basic reproduction number of the population, \({{\mathcal {R}}}_0\). If \({{\mathcal {R}}}_0 <1\), the extinction state is locally stable, and if \({{\mathcal {R}}}_0 >1\) the population shows various degrees of persistence that depend on the irreducibility properties of the dispersal kernels. Special cases exhibit how sex-biased dispersal affects the persistence of the population.

具有两种性别的空间分布的种群可能面临雄性和雌性集中在栖息地的不同部分并且交配和繁殖的频率不足以使种群持续存在的问题。为简单起见，为了探索性别依赖性扩散对种群生存的影响，我们考虑了一个半生代种群的离散时间模型，其中个体在其一生中仅在极短的繁殖季节繁殖一次。雌性和雄性的分散由 Feller 核建模，交配由同质对形成函数建模。齐次算子的谱半径被建立为种群的基本再生数\({{\mathcal {R}}}_0\)。如果\({{\mathcal {R}}}_0 <1\)，灭绝状态是局部稳定的，如果\({{\mathcal {R}}}_0 >1\)种群显示出不同程度的持久性，这取决于分散核的不可约性特性。特殊案例展示了性别偏见的传播如何影响人口的持久性。