Algebraically informed models of biological sequence evolution

为了理解他们在自然界中看到的模式，从遗传学、流行病学到生物地理学等不同领域的生物学家需要一幅准确的进化史图景。DNA序列提供了一种令人兴奋的方法来建立这幅过去的图景，但要成功破译它，需要DNA如何进化的数学模型。目前的方法已经发现了数学上的不一致。特别是，要理解自然选择在生命树不同部分的效果，就需要模型在面对不断变化的进化过程时表现得很好。这个项目的目的是利用代数方法的洞察力来构建数学上一致的广泛生物效用的模型。

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.