Mathematics
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Department of Mathematics & Statistics
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Thomas McCone

Studying for Master of Science

Area of study:
Agglomerative Construction of Phylogenetic Networks in Three Dimensions

Supervisor: David Bryant


Email: mccth203@student.otago.ac.nz  


Thesis

Title: Agglomerative Construction of Phylogenetic Networks in Three Dimensions

Supervisor: David Bryant

Previous Degrees:

• BSc in Mathematics (University of Otago); and

• BSc(Hons) in Mathematics (University of Otago), supervised by Iain Raeburn.

Phylogenetic structures have proven to be valuable bioinformatic tools for the visualisation, and subsequent interpretation, of complex genetic data. In a world of increasing data volumes, these tools provide an efficient and intuitive means to guide further study into the structure of such datasets.

We focus specifically on split networks in this study, which are favourable to the representation of complex reticulate biological phenomena, such as horizontal gene transfer. Expanding on the development of NeighbourNet, the main effort of our research is to lift the context of the planar split network to three dimensions, in which a higher volume of data may be more amenable to visual inference.

We study these three-dimensional split networks through the investigation of systems of two-dimensional planar bipartitions of the data (named spherical splits), which, in the maximal case, correspond exactly to the set of topes of a rank 4 uniform oriented matroid on the dataset. We seek to underpin an agglomerative construction of such systems, in the manner of the traditional NeighbourNet, which preserves the qualities of the data in question and provides an informative output.

Ensuring that the method is developed robustly is not trivial, and involves investigating realizable classes of oriented matroids, the connection of planar graphs and polytopes to inscribability of a set of points on the sphere, and a consistent agglomerative procedure.