Tracing evolutionary links between species

The idea that all life on earth traces back to a common beginning dates back at least to Charles Darwin’s Origin of Species. Ever since, biologists have tried to piece together parts of this ‘tree of life ’ based on what we can observe today: fossils, and the evolutionary signal that is present in the genomes and phenotypes of different organisms. Mathematics has played a key role in helping transform genetic data into phylogenetic (evolutionary) trees and networks. Here, I will explain some of the central concepts and basic results in phylogenetics, which benefit from several branches of mathematics, including combinatorics, probability and algebra. 1 What is phylogenetics? All living organisms on earth harbor within their DNA a signature of their evolutionary heritage. By studying patterns and differences between the genetic makeup of different species, molecular biologists are able to piece together parts of the story of how life today traces back a common origin. In this way, many basic questions can be answered. When did animals and plants diverge? Are fungi more closely related to plants or animals? How and when did photosynthesis arise? What is the closest living animal to the whales? Does speciation occur in bursts or at a steady rate? Other topics are proving more difficult to resolve – fo