Chen Gu. Geometric Algorithms in Modeling Biological Evolution. PhD Dissertation. Stanford University, December 2013.


Evolutionary biology is a field that studies the change of a species over time. Mathematical models can provide hypotheses to explain the observed phenomena and predict what type of changes will occur in the future. From a computational perspective, there are three main challenges: The first challenge is the data, which in general comes from two different types of sources. With computer simulation, people are able to study conformational changes at very detailed level. In this case, we often have very large data sets and would like to understand dynamics at more macroscopic level. On the other hand, data from real experiment is more expensive and thus very limited. We present methods to extract useful information when the data is too much, and to synthesize data when it is too little. The second challenge is the distances between configurations in the data set. Since we are modeling evolution, it is more important to measure their kinetic similarity rather than structural similarity. We define distance functions that incorporate kinetic information and develop efficient clustering algorithms. The third challenge is the correspondences between identities in different configurations. They may have one-to-one, partial, or even no correspondence in various settings. We show biological examples in each case and present ways to compare configurations with both distinct and indistinct identities.


author = {Chen Gu},
title = {Geometric Algorithms in Modeling Biological Evolution},
school = {Stanford University},
year = {2013},