We derive and study a Darwinian dynamic model based on a low-dimensional discrete- time population model focused on two features: density-dependent fertility and a trade-off between inherent (density free) fertility and post-reproduction survival. Both features are assumed to be dependent on a phenotypic trait subject to natural selection. The model tracks the dynamics of the population coupled with that of the population mean trait. We study the stability properties of equilibria by means of bifurcation theory. Whether post-reproduction survival at equilibrium is low or high is shown, in this model, to depend significantly on the nature of the trait dependence of the density effects. An Allee effect can also play a significant role.

中文翻译：

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繁殖后生存进化的达尔文动态模型

我们推导并研究了基于低维离散时间人口模型的达尔文动态模型，该模型侧重于两个特征：密度依赖性生育率以及固有（无密度）生育率与繁殖后存活率之间的权衡。假设这两个特征都依赖于受自然选择影响的表型性状。该模型跟踪人口的动态以及人口平均特征的动态。我们利用分岔理论研究平衡的稳定性性质。在这个模型中，平衡时的繁殖后存活率是低还是高，显着取决于密度效应的性状依赖性的性质。Allee 效应也可以发挥重要作用。