Thomas graduated from the University of St Andrews in 2018 with an MMath in Mathematics. During his studies, he became interested in population genetics and the application of novel statistical methods to genetic data. In his Master’s project, he studied a class of classification algorithms and analysed the effectiveness of their application to gene-expression data. Currently he is also interested in statistical inference for models used in evolutionary biology. Outside of maths, he enjoys watching films, exercise and playing the piano.

Research project title:
Accessibility percolation in dynamic fitness landscapes

Supervisor(s):
Marcel Ortgiese, Tiffany Taylor

Project description:
The fitness landscape concept originates in evolutionary biology as a metaphor to describe adaptive pathways taken by populations, where fitness is thought of as a height above a multidimensional genotypic space. Such landscapes can be modelled by representing the genotype space as a finite graph and the fitness function as a random vector associated to the vertices of the graph. Researchers have recently made progress in understanding the statistical properties of the number of so-called ‘accessible paths’ – sequences of adjacent vertices of increasing fitness. Thomas is studying how the accessibility properties of a graph are affected by a time-varying fitness function. The first case is where the fitness values are re-sampled according to a Markov chain; to analyse this he is adapting methods from first-passage percolation and dynamic percolation theory. Other situations to be considered include continuously changing landscapes and pairs of interacting landscapes. The aim is also to use the theoretical results obtained to explain the observed patterns of evolution of flagella in a recent experimental study of particular bacterial strains under varying selective pressures.