Field · Emerged 1908 – 1947

Population Genetics

How do gene frequencies change in populations, and is that enough to explain evolution?

5 chapters4 min read5 turning points 1 open problem

Branched from: Evolutionary Biology + Genetics
Branched into: Conservation Biology + Genomics
Figures: G. H. Hardy, Wilhelm Weinberg, Ronald Fisher, J. B. S. Haldane, Sewall Wright, Theodosius Dobzhansky, Motoo Kimura

In brief

Population genetics describes evolution as change in how common different gene versions are in a population, and works out mathematically what makes those frequencies change: natural selection, random chance, mutation, and migration. It was built between 1918 and the 1940s to reconcile Darwin's natural selection with Mendel's genetics, which for twenty years had seemed to contradict each other.

The result, called the Modern Synthesis, made natural selection working on Mendelian genes the central theory of biology. It is also where much of modern statistics was invented.

Key ideas

Allele frequency: The fraction of copies of a gene in a population that are a particular version. In this view, evolution is change in allele frequencies over generations.
Hardy–Weinberg equilibriumEnters 1908: With no selection, drift, mutation or migration, allele frequencies stay constant and genotypes settle at $p^2 : 2pq : q^2$ . It is the null model against which evolution is measured.
Fitness and selectionEnters 1930 – 1932: Fitness is an allele's average contribution to future generations. Even a 1% advantage spreads an allele through a large population in a few thousand generations.
Genetic driftEnters 1930 – 1932: Random fluctuation in allele frequencies because only some individuals happen to reproduce. It matters most in small populations and can fix or lose alleles regardless of their effect.
Neutral theoryEnters 1968: Kimura's proposal that most changes at the level of DNA are neither helpful nor harmful and spread by drift, which makes the molecular "clock" tick at a steady rate.

Draws on other domains

↙ Mathematics
Probability Theory
Genetic drift is a random walk
↙ Mathematics
Statistical Inference
Splitting variation into its causes

Chapter I

Two Camps That Could Not Agree

The rediscovery of Mendel in 1900 should have rescued Darwin. It did the opposite. The early Mendelians, led by William Bateson, saw evolution in the sudden jumps of discrete mutations and thought gradual natural selection was unnecessary. The biometricians, led by Karl Pearson and W. F. R. Weldon, measured continuous traits like height, which vary smoothly and do not look Mendelian at all, and defended gradual selection. For nearly twenty years the two camps fought, often bitterly, and evolutionary biology and genetics pulled apart.

The first bridge came from mathematics. In 1908 G. H. Hardy, a pure mathematician who took pride in the uselessness of his own work, answered a biologist's question in a short letter. Mendelian inheritance alone does not change allele frequencies. Wilhelm Weinberg found the same result independently. Evolution needs a force that changes the frequencies, and natural selection was the obvious candidate.

Chapter II

The Mathematics of Evolution

Ronald Fisher ended the feud in 1918. Many Mendelian genes, each with a small effect, add up to exactly the smooth variation and family resemblances the biometricians measured. Discrete inheritance and continuous traits were compatible after all. To prove it he invented new statistics, including the analysis of variance.

Over the next fourteen years Fisher, J. B. S. Haldane and Sewall Wright built a full mathematical theory of evolution in terms of allele frequencies. They worked out how fast selection spreads a favourable allele, how mutation supplies new variation, how migration mixes populations, and how chance, genetic drift, can fix or erase alleles in small populations. Fisher and Wright disagreed for the rest of their lives about how much evolution is selection and how much is drift.

Chapter III

The Synthesis

The mathematics convinced mathematicians. Theodosius Dobzhansky convinced naturalists. His Genetics and the Origin of Species (1937) showed the theory at work in wild fruit-fly populations. Ernst Mayr explained how new species arise when populations are isolated, George Gaylord Simpson reconciled the fossil record, and Julian Huxley named the result the Modern Synthesis. By the late 1940s natural selection acting on Mendelian genes was the framework of all of biology. Dobzhansky later summed it up: "Nothing in biology makes sense except in the light of evolution."

Chapter IV

A Closer Look: Carriers and the Speed of Selection

Hidden alleles. Cystic fibrosis affects about 1 in 2,500 babies of northern European descent. It is recessive: a child is affected only with two copies of the faulty allele. If the allele has frequency $q$ and mating is random, Hardy and Weinberg's rule says a fraction $q^2$ of people carry two copies. So

q^2 = \frac{1}{2500}, \qquad q = \frac{1}{50} = 0.02 .

The fraction who carry exactly one copy is $2pq$ , with $p = 1 - q = 0.98$ :

2pq = 2 \times 0.98 \times 0.02 \approx 0.039 ,

about 1 person in 25. For every affected child there are about a hundred healthy carriers. This is why selection against rare recessive diseases is so slow: almost all copies of the allele are hidden in carriers, where selection cannot see them.

Selection at work. Now take an allele that gives its carriers a 1% advantage in survival or reproduction, a difference far too small to notice in any one family. Fisher and Haldane showed how its frequency changes. When the allele's effect adds up in each copy, the time to rise from a frequency of 1% to 99% is roughly

t \approx \frac{1}{s} \ln\!\left(\frac{0.99/0.01}{0.01/0.99}\right) = \frac{\ln 9801}{0.01} \approx 920 \text{ generations} .

For humans, with generations of about 25 years, that is some 23,000 years. For bacteria dividing every half hour, it is under three weeks. On the timescale of evolution this is almost instantaneous. Haldane's calculations of this kind convinced biologists that small, invisible advantages were enough to drive evolution, and they are why antibiotic resistance spreads through bacterial populations within years of a new drug's introduction.

Chapter V

Molecules and Neutrality

When protein and DNA sequences arrived in the 1960s, they held a surprise. Species carried far more molecular variation, and changed at a steadier rate, than selection-driven theory expected. Motoo Kimura proposed in 1968 that most molecular changes are neutral and drift at random, and the neutralist–selectionist debate is still running. That debate is now fought with whole genomes, which is where population genetics meets genomics.

Turning points5

1908DISCOVERYContested
The Hardy–Weinberg principle
Asked why dominant traits don't take over populations, the pure mathematician G. H. Hardy shows in a short letter that Mendelian inheritance by itself keeps allele frequencies constant. The German physician Wilhelm Weinberg derived the same result the same year. Heredity alone does not change a population, and something else must.
What is disputed
Credit is shared and was long lopsided. Weinberg's paper, in German in a regional journal, was overlooked for decades, and the principle was known as "Hardy's law" until the 1940s. William Castle had described a special case in 1903, and Karl Pearson and Udny Yule had discussed related results.
G. H. Hardy, Wilhelm Weinberg
› Sources (2)
- Hardy, G. H. (1908). Mendelian proportions in a mixed population. Science 28(706): 49–50.
- Weinberg, W. (1908). Über den Nachweis der Vererbung beim Menschen. Jahreshefte des Vereins für vaterländische Naturkunde in Württemberg 64: 368–382.
1918SYNTHESIS
Fisher shows Mendelism explains continuous variation
Biometricians, who measured continuous traits like height, and Mendelians, who studied discrete ones, had been feuding since 1900. Ronald Fisher shows that many Mendelian genes of small effect produce exactly the smooth, bell-shaped variation and family resemblances the biometricians measured. The feud ends. The paper also introduces the idea of analysing variance.
Ronald Fisher
› Sources (1)
- Fisher, R. A. (1918). The correlation between relatives on the supposition of Mendelian inheritance. Transactions of the Royal Society of Edinburgh 52(2): 399–433.
1930 – 1932SYNTHESISContested
Fisher, Haldane and Wright found population genetics
In three landmark works, Ronald Fisher, J. B. S. Haldane and Sewall Wright build the mathematical theory of how selection, drift, mutation and migration change allele frequencies. Natural selection acting on Mendelian genes turns out to be powerful enough to drive evolution.
What is disputed
The founders disagreed sharply about causation. Fisher saw evolution as mostly selection in large populations. Wright gave a central role to genetic drift in small, partly isolated populations (his "shifting balance" theory). Their dispute ran for decades, and the relative importance of the two processes is still debated.
Ronald Fisher, J. B. S. Haldane, Sewall Wright
› Sources (3)
- Fisher, R. A. (1930). The Genetical Theory of Natural Selection. Clarendon Press, Oxford.
- Wright, S. (1931). Evolution in Mendelian populations. Genetics 16(2): 97–159.
- Haldane, J. B. S. (1932). The Causes of Evolution. Longmans, Green.
1937 – 1947SYNTHESIS
The Modern Synthesis
Theodosius Dobzhansky's Genetics and the Origin of Species (1937) carries the mathematics to wild populations of fruit flies. Ernst Mayr on species, George Gaylord Simpson on fossils and Julian Huxley, who named the "Modern Synthesis" in 1942, bring the rest of biology in. By 1947 natural selection on Mendelian genes is the consensus framework of evolutionary biology.
Theodosius Dobzhansky
› Sources (2)
- Dobzhansky, T. (1937). Genetics and the Origin of Species. Columbia University Press.
- Huxley, J. (1942). Evolution: The Modern Synthesis. Allen & Unwin.
1968CONSENSUS-OVERTURNEDContested
Kimura's neutral theory
Protein sequences from different species reveal far more variation, and far more steady change, than selection alone seemed able to explain. Motoo Kimura proposes that most molecular change is selectively neutral and spreads by drift. The assumption that selection governs everything at the molecular level is overturned, and the steady ticking of neutral change becomes the "molecular clock" for dating evolutionary splits.
What is disputed
The neutralist–selectionist debate has never fully ended. That much molecular variation is neutral is now widely accepted, but how much, and how strongly selection on nearby sites shapes the rest, is still argued with genome-scale data.
Motoo Kimura
› Sources (1)
- Kimura, M. (1968). Evolutionary rate at the molecular level. Nature 217(5129): 624–626.

Applications

Where it is used

Statistics↗ Mathematics · Probability Theory
The invention of modern statistical method
Much of modern statistics was invented to do population genetics and agricultural science. Fisher introduced the analysis of variance, randomised experiments and maximum likelihood, now used in every field that runs experiments, from medicine to economics.
› Sources (1)
- Fisher, R. A. (1935). The Design of Experiments. Oliver & Boyd.
Conservation
Genetic rescue of endangered populations
Small, isolated populations lose diversity to drift and suffer from inbreeding. When only a few dozen Florida panthers remained, eight female pumas from Texas were released among them in 1995. Heart defects and other inbreeding problems fell, and the population grew, as population-genetic theory predicted.
› Sources (1)
- Johnson, W. E. et al. (2010). Genetic restoration of the Florida panther. Science 329(5999): 1641–1645.
Human history
Reading migrations from gene frequencies
Differences in allele frequencies between populations record their history: when they split, how large they were, and when they mixed. These methods underlie the reconstruction of humanity's spread out of Africa and of later migrations.

Open problems

Where the map runs out

Open

Lewontin's paradox

Open as of 2026; candidate explanations exist, but none accounts for the full pattern.

Simple theory says a species' genetic diversity should scale with its population size. Yet diversity varies less than a thousandfold across animal species whose populations differ by many orders of magnitude, from whales to insects. Richard Lewontin highlighted the puzzle in 1974.

Why it is hard: Candidate explanations include selection at linked sites sweeping away diversity, fluctuating population sizes that keep diversity low, and differences in mutation rate. Each accounts for part of the pattern, and measuring long-term population sizes and selection across many species is difficult.
What resolving it unlocks: It would reveal how strongly natural selection shapes whole genomes, and improve the tools used to reconstruct species' histories from their DNA.

› Sources (2)

Lewontin, R. C. (1974). The Genetic Basis of Evolutionary Change. Columbia University Press.
Leffler, E. M. et al. (2012). Revisiting an old riddle: what determines genetic diversity levels within species? PLoS Biology 10(9): e1001388.