Institut für Angewandte Mathematik, University of Bonn, Endenicher Allee 60, 53115, Bonn, Germany.
Institut für Mathematik, Johannes Gutenberg-Universität Mainz, Staudingerweg 9, 55099, Mainz, Germany.
J Math Biol. 2023 Sep 12;87(4):56. doi: 10.1007/s00285-023-01989-3.
We derive rigorous estimates on the speed of invasion of an advantageous trait in a spatially advancing population in the context of a system of one-dimensional F-KPP equations. The model was introduced and studied heuristically and numerically in a paper by Venegas-Ortiz et al. (Genetics 196:497-507, 2014). In that paper, it was noted that the speed of invasion by the mutant trait is faster when the resident population is expanding in space compared to the speed when the resident population is already present everywhere. We use the Feynman-Kac representation to provide rigorous estimates that confirm these predictions.
我们在一维 F-KPP 方程组的背景下，对具有优势特征的空间扩散种群的入侵速度进行了严格的估计。该模型由 Venegas-Ortiz 等人在一篇论文中进行了引入和启发式及数值研究（Genetics 196:497-507, 2014）。在该论文中，指出与居住种群已经无处不在时相比，当居住种群在空间中扩张时，突变特征的入侵速度更快。我们使用费曼-卡茨表示法提供了严格的估计，证实了这些预测。
