1. Evolutionary graphs

Evolutionary concepts naturally give rise to representations as graphs (dots connected by lines). The processes of reproduction, modification by mutation, and differential survival (natural selection) immediately suggests a tree-like process of lineages branching over time.

This part of this book describes various ways that we use graphs in population genetics. We focus on the description of the graphical objects themselves and delay any formal discussion of how they arise. In other words, we need to understand how our pictures work before we understand how evolutionary processes give rise to them.

It is important to keep in mind that these graph structures themselves are usually not observable. Rather, we have data, such as the characteristics of different species or the genotypes of many individuals from the same species. These data can be used to make inferences about evolutionary histories. The concept that there is some graph that relates our various pieces of data is the conceptual bridge between data and inference.

We will begin with species trees. For the most part, we don’t need such trees in order to do a lot of interesting population genetics. However, these objects are likely familiar from previous coursework, making them a good place to discuss fundamental concepts.

We then turn to pedigrees, starting with the standard types of medical pedigrees seen in genetics courses. We illustrate “gene dropping” here, which illustrates how quickly direct DNA ties to previous generations can be lost. We expand on these points with some examples of pedigrees in randomly mating populations.

We will then look at DNA changes on gene trees and then at how we use graphs to conceptualize the relationships between populations of a species.