Darwin’s Regret: What Maths Tells Us about the Evolution of Life

October 22, 2014

DarwinAllan Wilson Centre’s Professor Mike Steel explained the sophisticated ways that biologists have developed to uncover and study the hidden shared ancestry of all life from genetic data since Darwin first developed his Origin of Species ideas 155 years ago.

Mathematics has become an essential tool that allows biologists to tease apart evolutionary signal from noise and bias in data, and to build reliable trees and networks of species.

Prof Steel told his 80 strong audience – half of whom were senior maths and science students at Wakatipu High School – that biologists use these trees widely, for example, to classify new species, trace human migrations, and to help predict next year’s influenza strain.

A main goal for biologists is to reconstruct and study what are called ‘phylogenetic trees’ (or more generally networks) which reveal how species today are related to each other and how they trace back to a common ancestor.

The picture of the `tree of life’ today looks very different from the first sketches by Darwin and his contemporaries in the 19th century, and this is mainly due to the huge amount of genetic data from which large trees can now be built. Biologists are starting to build trees on thousands of species – such as the tree of the (approximately) 10,000 known species of birds, published earlier this year.

The maths that is most useful for these tasks includes topics students will be familiar with like calculus and probability theory as well as areas of `discrete mathematics’, such as graph theory, combinatorics, and algorithms.

Mike concentrated mostly on probability theory, which is essential for building reliable trees, as well as for studying what the `shape’ of these trees tell us about biological processes like speciation and extinction. Using a simple random model that involves drawing coloured balls from a bowl, he showed how it’s easy to predict how balanced large trees should be under uniform speciation rates, and without having to use a calculator.

Click here for a PDF of Mike’s talk