We prove bifurcation theorems for evolutionary game theoretic (Darwinian dynamic) versions of nonlinear matrix equations for structured population dynamics. These theorems generalize existing theorems concerning the bifurcation and stability of equilibrium solutions when an extinction equilibrium destabilizes by allowing for the general appearance of the bifurcation parameter. We apply the theorems to a Darwinian model designed to investigate the evolutionary selection of reproductive strategies that involve either low or high post-reproductive survival (semelparity or iteroparity). The model incorporates the phenotypic trait dependence of two features: population density effects on fertility and a trade-off between inherent fertility and post-reproductive survival. Our analysis of the model determines conditions under which evolution selects for low or for high reproductive survival. In some cases (notably an Allee component effect on newborn survival), the model predicts multiple attractor scenarios in which low or high reproductive survival is initial condition dependent.

我们证明了结构人口动力学的非线性矩阵方程的演化博弈论（达尔文动力学）版本的分叉定理。这些定理通过考虑分叉参数的一般外观，在消光平衡不稳定时，推广了有关平衡解的分叉和稳定性的现有定理。我们将这些定理应用于达尔文模型，该模型旨在研究涉及低或高生殖后存活率（分裂或同胎）的生殖策略的进化选择。该模型结合了两个特征的表型性状依赖性：人口密度对生育力的影响以及固有生育力和生殖后生存之间的权衡。我们对模型的分析确定了选择低或高生殖生存的进化条件。在某些情况下（特别是Allee成分对新生儿生存的影响），该模型预测了多种吸引子场景，在这些场景中，低或高的生殖存活率取决于初始状况。