Genetics so far has followed genes through families. Population genetics follows them through whole groups across generations, asking why some alleles become common and others vanish. It is the link between Mendel and Darwin, and it explains a good deal about human history and health.

A baseline of no change

In 1908 the English mathematician G. H. Hardy and the German physician Wilhelm Weinberg independently answered a question that puzzled early geneticists: would dominant alleles naturally spread until they took over? No. The Hardy-Weinberg principle shows that allele frequencies stay constant from generation to generation unless something acts to change them. If one allele has frequency p and the other q, the proportions of genotypes settle at p squared, 2pq and q squared. Real populations are never perfectly balanced, but the principle works like a level drawn on a graph: departures from it tell you a force is at work.

Four forces

Four main forces change allele frequencies. Mutation creates new alleles. Natural selection raises the frequency of alleles that help their carriers survive and reproduce. Gene flow, the movement of people or other organisms between populations, mixes their alleles. And genetic drift is change in allele frequencies by pure chance. Drift is strongest in small populations, where chance matters more, just as a coin tossed ten times is far likelier than one tossed a thousand times to come up 70 percent heads.

Founders and bottlenecks

When a small group starts a new population, its alleles are a chance sample of the larger group's, so rare alleles can become common in a population started by a few people. This is the founder effect. The Old Order Amish of Lancaster County, Pennsylvania, descend from a few hundred eighteenth-century immigrants and rarely marry outside the community. Ellis-van Creveld syndrome, a rare form of dwarfism with extra fingers, is far more common among them than elsewhere and has been traced to one founding couple. Finland, settled by small groups and long isolated, has about three dozen rare conditions, called the Finnish disease heritage, that are more common there than anywhere else. A bottleneck is related: a sharp drop in numbers leaves only a fraction of the old diversity, even if the population later recovers. Cheetahs are so genetically alike, probably after bottlenecks thousands of years ago, that skin grafts between unrelated animals can take.

Selection in human history

Most adult mammals lose the ability to digest lactose, the sugar in milk, after weaning. Yet many adults in northern Europe, East Africa, parts of the Middle East and South Asia keep it, a trait called lactase persistence. It spread as people herded cattle, goats and camels and drank their milk. Strikingly, different mutations producing the same trait arose separately in Europe and East Africa, a clear case of natural selection solving the same problem twice. Another case comes from the Tibetan plateau, where a variant of the gene EPAS1 helps people live at high altitude without dangerously thick blood. In 2014 researchers showed that the variant came from interbreeding with Denisovans, an extinct group of archaic humans, tens of thousands of years ago.

Out of Africa, in our genes

Modern humans arose in Africa, and small groups later spread across the world. Each migration carried only part of the diversity of the population it left, a chain of founder effects. As a result, African populations hold more genetic diversity than any other part of the world, and two people from different African groups can differ more genetically than a European and an East Asian do. Humanity as a whole is also unusually uniform: any two people share about 99.9 percent of their DNA sequence, and there is less genetic variation among all humans than within some single groups of chimpanzees.

Family trees tell a similar story. Because the number of ancestors doubles each generation, family lines quickly cross and merge. Computer models published in 2004 by Douglas Rohde, Steve Olson and Joseph Chang estimated that everyone alive shares at least one common ancestor who lived within the last few thousand years, perhaps as recently as about 3,000 years ago. The exact date is uncertain, but the conclusion that all living people are closely related is robust. Equal human worth does not depend on any fact of biology, but it is worth knowing that genetics gives no support to the idea of separate human stocks. It describes one large, recently connected family.

Worked example: counting carriers

About one baby in 2,500 born to parents of northern European ancestry has cystic fibrosis. How many people carry the allele? Using Hardy-Weinberg, the share with two copies is q squared, so q squared equals 1/2,500 and q, the allele's frequency, is 1/50. The working allele's frequency, p, is 49/50. Carriers make up 2pq, which is 2 times 49/50 times 1/50, or about 1 in 25. That matches what carrier testing finds. The calculation also shows why recessive conditions cannot be removed by policies aimed at affected people: for every person with cystic fibrosis there are about a hundred healthy carriers, invisibly holding the allele in the population. Early eugenicists who hoped to breed out such traits by sterilizing affected people had misunderstood their own arithmetic.