In this work, we consider a two-type species model with trait-dependent speciation, extinction and transition rates under an evolutionary time scale. The scaling approach and the diffusion approximation techniques which are widely used in mathematical population genetics provide modeling tools and conceptual background to assist in the study of species dynamics, and help exploring the analogy between trait-dependent species diversification and the evolution of allele frequencies in the population genetics setting. The analytical framework specified is then applied to models incorporating diversity-dependence, in order to infer effective results from processes in which the net diversification of species depends on the total number of species. In particular, the long term fate of a rare trait may be analyzed under a partly symmetric scenario, using a time-change transform technique.

在这项工作中，我们考虑在进化时间尺度下具有特征依赖的物种形成，灭绝和过渡速率的两类物种模型。数学种群遗传学中​​广泛使用的缩放方法和扩散近似技术提供了建模工具和概念背景，以协助进行物种动力学研究，并帮助探索特质相关物种多样化与等位基因频率进化之间的类比。人口遗传学设置。然后将指定的分析框架应用于包含多样性依赖性的模型，以便从物种的净多样化取决于物种总数的过程中推断出有效的结果。特别是，可以在部分对称的情况下分析稀有性状的长期命运，