Algebraically informed models of biological sequence evolution

为了理解他们在自然界中看到的模式，遗传学，流行病学和地理学等不同领域的生物学家需要准确的进化史。DNA序列提供了一种令人兴奋的手段来建立这幅过去的图景，但要成功地解码它，需要DNA进化的数学模型。目前的方法在数学上存在不一致之处。特别是，理解自然选择在生命之树不同部分的影响，需要模型在面对不断变化的进化过程时表现得稳健。该项目旨在利用代数方法的见解来构建具有广泛生物实用性的数学一致模型。

To make sense of the patterns they see in the natural world, biologists across fields as diverse as genetics, epidemiology and biogeography need an accurate picture of evolutionary history. DNA sequences provide an exciting means to establish this picture of the past, but to decode it successfully requires mathematical models of how DNA evolves. Mathematical inconsistencies have been identified with current approaches. In particular, understanding the effect of natural selection in different parts of the tree of life requires models that behave robustly in the face of shifting evolutionary processes. This project aims to use insights from algebraic methods to construct mathematically consistent models of wide biological utility.