Mathematics
Te Tari Pāngarau me te Tatauranga
Department of Mathematics & Statistics
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Marnus Stoltz

Studying for Doctor of Philosophy

Area of study:

Supervisor: David Bryant


Email: mstoltz@maths.otago.ac.nz  


Thesis

Title: Developing mathematical tools for genetic analysis using

SNP data

Supervisor: David Bryant

Cosupervisors: Boris Baeumer, Colin Fox

Previous Degrees:

  • BSc in Actuarial & Financial Mathematics (University of Pretoria, South Africa),
  • BSc(Hons) in Applied Mathematics (University of Pretoria, South Africa),
  • Msc in Applied Mathematics (University of Pretoria, South Africa).

My research consists of developing mathematical methods to efficiently compute the likelihood of a species tree from unlinked binary markers or allele frequency data. The model assumptions are similar to those implemented in SNAPP however, unlike SNAPP, the method can handle hundreds or even thousands of individuals. Our approach is based on a diffusion approximation of gene dynamics. However we work directly with backwards processes to compute the probability of every marker individually, bypassing the need to compute the entire joint allele frequency across all species. Some key elements of developing these methods involve boundary conditions for the backwards diffusion to ensure uniqueness and existence, computational bottlenecks and parameter mappings between models.