Department of Mathematics, Uppsala University, Box 480, Uppsala, 751 06, Sweden.
CNRS, Université Rennes 1, ECOBIO (écosystèmes, biodiversité, évolution) - UMR 6553, Avenue du général Leclerc, 35042, Rennes, France.
J Math Biol. 2021 Feb 25;82(4):22. doi: 10.1007/s00285-021-01559-5.
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，我们考虑了一个具有特征依赖性物种形成、灭绝和转变率的两型种模型，这些率在进化时间尺度下起作用。标度方法和扩散逼近技术在数理种群遗传学中被广泛应用，为物种动态的研究提供了建模工具和概念背景，并有助于探索特征依赖性物种多样化与种群遗传设置中等位基因频率进化之间的类比。然后，将指定的分析框架应用于包含多样性依赖性的模型，以便从净物种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，使用时变变换技术，可以在部分对称的场景下分析稀有特征的长期命运。
