Evolutionary genetics in extended populations

测试遗传进化模型是具有挑战性的，因为有许多参数和计算负担的大型和多方面的数据集。创新的统计方法对于充分利用现有和未来的数据集是必要的。我的团队开发并应用了整合生物、历史和人口信息的进化数学模型，以更好地理解基因组多样性。******这项提议的目的之一是开发新的方法来模拟等位基因频率在人群中的进化，这种方法比目前的技术更快、更稳定、更准确。我们建议发展基于矩的方法来计算不同进化模型下等位基因频率的分布。利用我们在偏微分方程方面的专业知识和开源软件的开发，因此，我们建议：***1)开发有效的模拟和推理软件，以改进最先进的方法来求解扩散方程***2)将这些求解器推广到扩散近似失败的情况***3)将这些模型应用于基因组多样性数据集***4)研究这些矩方法在遗传学以外的偏微分方程解中的应用。*********我们的第二个目标是开发遗传多样性模型，考虑到扩展种群的连续性。大多数种群遗传学模型假设种群要么在空间上是同质的，要么被细分为少数同质的亚种群，或称为“群”。这样假设的原因是均匀性和随机配合简化了数值计算，减少了自由参数的数量。不幸的是，这些假设在现实人群中往往是不准确的。我们的目标是提高我们对空间扩展种群中遗传多样性分布的理解。我们建议通过以下三种方式来实现这一目标：******1)通过开发扩展群体中群体结构的经验测量***2)通过开发随机模型来有效地模拟这些系统***3)通过应用这些方法来更好地了解扩展群体的遗传多样性。******本建议的第三个目的是在肿瘤和转移瘤的细胞水平上模拟空间异质性。这个目标与前一个目标相关，在某种意义上，它共同模拟遗传进化和空间结构。然而，癌症进化和癌症数据的特殊性意味着我们将使用的数学模型是完全不同的。我们将通过将生长的偏微分方程模型（已经用于基于成像的肿瘤建模）与微观水平随机波动的流体动力学模型相结合，开发多样性的多尺度模型。这里的目标是在细胞尺度上模拟大规模肿瘤的异质性。***********************

Testing genetic evolutionary models is challenging because of the many parameters and the computational burden of large and multi-faceted datasets. Innovative statistical methods are necessary to take full advantage of existing and future datasets. My group develops and applies mathematical models of evolution that integrate biological, historical, and demographic information to better understand genomic diversity. ******One aim of this proposal is to develop new approaches to simulate the evolution of allele frequencies across populations that are faster, more stable, and more accurate than the state-of-the art. We propose to develop moment-based approaches to compute the distribution of allele frequencies under different evolutionary models. Using our expertise in partial differential equations and the development of open-source software, we therefore propose:***1) To develop efficient simulation and inference software that improves upon the state-of-the-art approaches to solving the diffusion equation***2) To generalize these solvers to cases where the diffusion approximation fails***3) To apply these models to genomic diversity datasets***4) To investigate the application of such moment approaches to the solution of partial differential equations beyond genetics. *********Our second aim is to develop genetic diversity models that take into account the continuous nature of extended populations. Most models of population genetics assume that populations are either spatially homogeneous, or subdivided in a small number of homogeneous sub-populations, or “demes”. The reason for such assumptions is that homogeneity and random mating simplifies numerical computation, and reduces the number of free parameters. Unfortunately, these assumptions are often inaccurate in realistic populations. Our goal is to improve our understanding of the distribution of genetic diversity in spatially extended populations. We propose to do this in three ways:******1) By developing empirical measures of population structure in extended populations***2) By developing stochastic models to efficiently simulate such systems***3) By applying these methods to better understand genetic diversity in extended populations.******The third aim of this proposal is to model spatial heterogeneity at the cellular level in tumors and metastases. This aim is related to the previous one, in the sense that it jointly models genetic evolution and spatial structure. However, the peculiarities of cancer evolution and cancer data means that the mathematical models that we will use are completely different. We will develop multi-scale models of diversity by combining partial differential equation models of growth, which are already used for imaging-based tumor modelling, to fluid dynamics models for stochastic fluctuations at the microscopic level. The goal here is to model heterogeneity at the cellular scale in large-scale tumors. ***********************