This project brings techniques in algebra and algebraic geometry to address questions arising in phylogenetics, the study of evolutionary relationships between species (or other biological taxa such as genera, or populations). While probabilistic and combinatorial methods have been applied successfully in this field of biology, the tools of algebraic geometry yield new insight and help researchers to gain a better understanding of many of the underlying mathematical issues. The goals of this project are to develop new algorithms for the search of tree space, develop a new statistical measure of support for local features in a phylogenetic tree, and to develop, formalize, and study new mathematical models of sequence evolution. Improving phylogenetic methods by speeding up heuristic searches of tree space will have significant value in practical phylogenetics, allowing the investigation of phylogenetic relationships for larger data sets and for increased thoroughness in the search of tree space. The work will be carried out at the University of Alaska Fairbanks and involves researchers with connections to the Institute of Arctic Biology.
Phylogenetic inference from sequence data is used widely throughout the biological sciences, and improvements in methods and theoretical understanding will have a far-reaching impact. As phylogenetic data sets become larger and biological explanations of the evolutionary process at the sequence level improve, understanding the more complicated models describing the processes at work is necessary for developing valid and effective methods of statistical inference. This work develops emerging connections between the areas of algebraic geometry and mathematical biology and brings about significant broader impacts ranging from the interdisciplinary training of students and software dissemination to collaborations with researchers outside of Alaska.