Evolutionary genetics in extended populations

由于大数据集和多方面数据集的许多参数和计算负担，测试遗传进化模型是具有挑战性的。要充分利用现有和未来的数据集，必须采用创新的统计方法。我的团队开发并应用了进化的数学模型，这些模型整合了生物、历史和人口信息，以更好地了解基因组多样性。*这项提议的一个目标是开发新的方法来模拟人群中等位基因频率的进化，比最先进的方法更快、更稳定、更准确。我们建议开发基于矩的方法来计算不同进化模型下的等位基因频率分布。因此，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，我们建议：*1)开发高效的模拟和推理软件，改进最先进的求解扩散方程的方法*2)将这些解算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)研究这种矩方法在解决遗传以外的偏微分方程方面的应用。*我们的第二个目标是开发考虑到扩展种群的连续性的遗传多样性模型。大多数种群遗传学模型假定种群要么在空间上是同质的，要么细分为少数同质的亚种群，或称为“Demes”。这些假设的原因是，齐性和随机交配简化了数值计算，并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。我们建议通过三种方式来做到这一点：*1)通过开发扩展种群中种群结构的经验度量*2)通过开发随机模型来有效地模拟这样的系统*3)通过应用这些方法来更好地理解扩展种群中的遗传多样性。*本建议的第三个目标是在细胞水平上模拟肿瘤和转移的空间异质性。这个目标与前一个目标有关，因为它联合对遗传进化和空间结构进行建模。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完全不同。我们将开发多尺度的多样性模型，将已经用于基于成像的肿瘤建模的生长偏微分方程模型与微观水平上随机波动的流体动力学模型相结合。这里的目标是在细胞尺度上对大规模肿瘤的异质性进行建模。***********************

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. ***********************