Phylogeographic estimation and simulation of global diffusive dispersal

The analysis of time-resolved phylogenies (timetrees) and geographic location data allows estimation of dispersal rates, for example for invasive species and infectious diseases. Many estimation methods are based on the Brownian Motion model for diffusive dispersal on a 2-dimensional plane, however the accuracy of these methods deteriorates substantially when dispersal occurs at global scales because Spherical Brownian Motion (SBM) differs from planar Brownian Motion. No statistical method exists for estimating SBM diffusion coefficients from a given timetree and tip coordinates, and no method exists for simulating SBM along a given timetree. Here I present new methods for simulating SBM along a given timetree, and for estimating SBM diffusivity from a given timetree and tip coordinates using a modification of Felsenstein's independent contrasts and maximum-likelihood. My simulation and fitting methods can accommodate arbitrary time-dependent diffusivities and scale efficiently to trees...对时间分辨系统发育树（timetrees）与地理位置数据开展分析，可用于估算扩散速率，例如入侵物种与传染性疾病的扩散速率。现有诸多估算方法基于二维平面上扩散传播的布朗运动模型，但当扩散发生在全球尺度时，这些方法的精度会大幅下降——这是因为球面布朗运动（SBM）与平面布朗运动存在显著差异。目前尚无既能基于给定时间树与末端坐标估算SBM扩散系数，又能沿给定时间树模拟SBM过程的统计方法。本文提出了两种全新方法：一是沿给定时间树模拟SBM过程，二是通过修正费尔森斯坦独立对比法（Felsenstein's independent contrasts）与最大似然法，基于给定时间树与末端坐标估算SBM扩散率。本研究提出的模拟与拟合方法可支持任意随时间变化的扩散率设置，且能高效适配大规模系统发育树的分析需求……