1: Introduction

Our population is made up of a set of interbreeding individuals, the genetic composition of which is made up of the genomes that each individual carries. The genetic composition of the population alters due to the death of individuals or the migration of individuals in or out of the population. If our individuals vary in the number of children they have, this also alters the genetic composition of the population in the next generation. Every new individual born into the population subtly changes the genetic composition of the population. Their genome is a unique combination of their parents’ genomes, having been shuffled by segregation and recombination during meioses, and possibly changed by mutation. These individual events seem minor at the level of the population, but it is the accumulation of small changes in aggregate across individuals and generations that is the stuff of evolution. It is the compounding of these small changes over tens, hundreds, and millions of generations that drives the amazing diversity of life that has emerged on this earth.

Population genetics is the study of the genetic composition of natural populations and its evolutionary causes and consequences. Quantitative genetics is the study of the genetic basis of phenotypic variation and how phenotypic changes evolve over time. Both fields are closely conceptually aligned as we’ll see throughout these notes. They seek to describe how the genetic and phenotypic composition of populations can be changed over time by the forces of mutation, recombination, selection, migration, and genetic drift. To understand how these forces interact, it is helpful to develop simple theoretical models to help our intuition. In these notes we will work through these models and summarize the major areas of population- and quantitative-genetic theory.

While the models we will develop will seem naı̈ve, and indeed they are, they are nonetheless incredibly useful and powerful. Throughout the course we will see that these simple models often yield accurate predictions, such that much of our understanding of the process of evolution is built on these models. We will also see how these models are incredibly useful for understanding real patterns we see in the evolution of phenotypes and genomes, such that much of our analysis of evolution, in a range of areas from human medical genetics to conservation, is based on these models. Therefore, population and quantitative genetics are key to understanding various applied questions, from how medical genetics identifies the genes involved in disease to how we preserve species from extinction.

All models are wrong but some are useful.” - George Box

Population genetics emerged from early efforts to reconcile Mendelian genetics with Darwinian thought. Part of the power of population genetics comes from the fact that the basic rules of transmission genetics are simple and nearly universal. One of the truly remarkable things about population genetics is that many of the important ideas and mathematical models emerged before the 1940s, long before the mechanistic-basis of inheritance (DNA) was discovered, and yet the usefulness of these models has not diminished. This is a testament to the fact that the models are established on a very solid foundation, building from the basic rules of genetic transmission combined with simple mathematical and statistical models.

Much of this early work traces to the ideas of R.A. Fisher, Sewall Wright, and J.B.S. Haldane, who, along with many others, described the early principals and mathematical models underlying our understanding of the evolution of populations. Building on this conceptual fusion of genetics and evolution, there followed a flourishing of evolutionary thought, the modern evolutionary synthesis, combining these ideas with those from the study of speciation, biodiversity, and paleontology. In total, this work showed that both short-term evolutionary change and the long-term evolution of biodiversity could be well understood through the gradual accumulation of evolutionary change within and among populations. This evolutionary synthesis continues to this day, combining new insights from genomics, phylogenetics, ecology, and developmental biology.

Population and quantitative genetics are a necessary but not sufficient description of evolution; it is only by combining the insights of many fields that a rich and comprehensive picture of evolution emerges. We certainly do not need to know the genes underlying the displays of the birds of paradise to study how the divergence of these displays, due to sexual selection, may drive speciation. Indeed, as we’ll see in our discussion of quantitative genetics, we can predict how populations respond to selection, including sexual selection and assortative mating, without any knowledge of the loci involved. Nor do we need to know the precise selection pressures and the ordering of genetic changes to study the emergence of the tetrapod body plan. We do not necessarily need to know all the genetic details to appreciate the beauty of these, and many other, evolutionary case studies. However, every student of biology gains from understanding the basics of population and quantitative genetics, allowing them to base their studies on a solid bedrock of understanding of the processes that underpin all evolutionary change.