Seminar - Visualization and directional measures of population differentiation based on the saddlepoint approximation method

School of Mathematics and Statistics Research Seminar

Speaker: Dr Louise McMillan
Time: Thursday 20th February 2020 at 04:00 PM - 05:00 PM
Location: Cotton Club, Cotton 350
Groups: "Mathematics" "Statistics and Operations Research"

Add to Calendar Add to your calendar

Abstract

Biologists have a multitude of software packages available to them for analysing population genetics: the study of variation between groups of animals in different sampling locations. Many of these tools perform genetic assignment, indicating which is the most likely source population for a given animal. However, the visualizations for these methods are difficult to interpret, when they are available at all.

We have developed a method for visualizing genetic assignment data by characterizing the distribution of genetic profiles for each candidate source population (McMillan & Fewster, 2017). This method enhances the assignment method of Rannala & Mountain (1997) by calculating appropriate graph positions for individuals for which some genetic data are missing. It uses the saddlepoint method (Daniels, 1954, and Lugannani & Rice, 1980), a highly accurate method for approximating distributions. The visualization method makes it straightforward to detect features of population structure and to judge the discriminative power of the genetic data for assigning individuals to source populations.

I will also describe new methods for quantifying population genetic structure. The measures we propose are closely related to the visualization approach, and enable visual features obvious from the plots to be expressed more formally. One measure is incumbent detection probability: for two random genotypes arising from populations A and B, the probability that the one from A has the better fit to A and thus would be correctly identified as the “incumbent” in A. Another measure is home assignment probability: the probability that a random genotype arising from A would be correctly assigned to A rather than B.

These measures are sensitive to subtle population structure, and are particularly useful for eliciting asymmetric features of the populations being studied, e.g. where one population has undergone extensive genetic drift but the other population has remained large enough to retain greater genetic diversity.

I will illustrate these methods using microsatellite genotype data from ship rats and southern right whales, and will discuss future plans for multi-population measures and goodness-of-fit tests.

Go backGo back to the seminar list