Population genetics

Darwin’s Origin of Species still provides the best single account of evolution, but modern discoveries allow us to fill in some details and make some additions. Learn about some of these here!

We now know that inheritance operates through deoxyribonucleic acid (DNA), which contains all the information needed. It is organised into separate long threads called chromosomes. Bacteria have one circular chromosome each, while humans are diploid, which means they have each of their 23 linear chromosomes in two versions, one from their mother and one from their father. For our purposes, we can think of DNA as a sequence of bases, each of which is either A, T, C or G. Mutations are accidental changes in DNA, including point mutations (where one of the four bases at a particular point in the sequence is replaced by a different base), and deletions and insertions (where a subsequence of bases is added or subtracted).  Mutations happen usually during meiosis or mitosis, and these would in a few generations make all individuals in a population genetically different even if by some fluke those at an earlier stage had all been identical. Genetic differences are important, as some variants will cause their bearer to have more offspring in their lifetime: genetic variants in diploids are inherited by half of the offspring, and so those variants will tend to spread and become fixed in the population, while less successful variants will become extinct. This is the essence of ‘natural selection’, though there are complications: sometimes a variant’s advantage will depend on its own frequency, and so, for example, those that start off with an advantage may lose it before fixation and become stabilised at an intermediate frequency.

Darwin did not discuss genetic drift, which is a force in evolution distinct from natural selection. If a variant has only a tiny or zero effect on the average lifetime number of offspring, then whether it spreads will be down to chance. The theory of such neutral and nearly-neutral mutations is very important. Many mutations are nearly neutral, including ‘synonymous’ mutations, those that don’t change the amino acid being coded for in a coding sequence, and those in the ‘junk DNA’ that is never translated and seems to have no function. When we want to know how long it is since the common ancestor of humans and chimpanzees diverged, those neutral changes provide a ‘molecular clock’ to give us an answer. The theory of neutral change is mathematically very simple and has many beautiful results. The theory does not contradict Darwin, as Darwin was interested in evolutionary changes that do affect the appearance and behaviour of the organism.

Darwin argued by analogy to artificial selection, and selection experiments show that virtually any character in any species can be selected. Today, scientists study exactly which genes are changing and how they change as selection takes place. Mathematicians use difference and differential equations to follow gene frequencies over time under simplifying assumptions. Both provide further details about the workings of Darwin’s natural selection in particular cases.

Alan Grafen

Professor Alan Grafen, Tutorial Fellow in Quantitative Biology
I teach population biology in the first year, and statistics and behavioural ecology in the second and third years of the Biological Sciences course.  I also teach Animal Behaviour to Human Scientists at St John’s. My research involves applying mathematical and logical theorising to evolutionary problems. My current research program is my ‘formal Darwinism project’, which aims to capture Darwin’s central argument about evolution by natural selection in a mathematical framework.