Genetics: Inheritance, Chance and What Genes Can't Tell You

Your eyes are not exactly your mother's or your father's. Your sister, with the same two parents, looks different from you again. Some families carry a rare illness across generations that skips whole branches. And yet a pea plant, a fruit fly and a person all obey the same few rules of inheritance, written down first by a monk with a garden.

Genetics is the science of that regularity and of what breaks it. It began as arithmetic on counted plants, grew into a map of chromosomes, and is now the statistics of millions of people's genomes. It is also the subject whose misuse has done real harm, so this piece tells that history too.

Mendel, and why he was lucky

Gregor Mendel, an Augustinian friar in Brno (then Brünn, now in the Czech Republic), crossed pea plants for years and counted the offspring. He presented the results in 1865 and published them in 1866. His key choice was to look at single, clear-cut traits: round or wrinkled seed, yellow or green. Cross a pure round line with a pure wrinkled one and every child is round. Cross those children with each other and about a quarter of the grandchildren are wrinkled again. His counts for seed shape were 5,474 round and 1,850 wrinkled, a ratio of 2.96 to 1.

From such counts came two ideas. Segregation: each plant carries two copies of each factor (we say alleles of a gene), and each pollen or egg cell gets just one. Independent assortment: factors for different traits are shuffled separately. A dominant allele shows when present; a recessive one shows only with two copies. Dominant does not mean common or healthy. It is a statement about how the two copies combine.

He was lucky in ways that are worth knowing. Each trait he chose depends mostly on one gene, with one allele fully dominant, which is rare for traits in general. He started from pure-breeding lines. And the trait pairs he crossed were not tightly linked on a chromosome, which would have blurred his ratios. Nobody read the work: it was rediscovered in 1900 by Hugo de Vries, Carl Correns and Erich von Tschermak. In 1936 the statistician R. A. Fisher noted that Mendel's counts sit closer to the ideal ratios than chance usually allows. Historians still argue about why (stopping a count at a convenient point, rounding, an overeager helper). Nobody has shown the laws are wrong; thousands of later crosses confirm them. Sampling noise is the lesson: try it.

At 8 offspring a "3 to 1" cross often looks like 5 to 3 or 7 to 1. At several thousand it settles close to 3 to 1. A p-value near 1 means suspiciously perfect, a very low one means something other than chance is going on, and most real crosses sit in the middle. That is also the first lesson of Statistics (34/05): a ratio from a small sample is a rumour.

Chromosomes and linkage

Genes live on chromosomes. In 1902 and 1903 Walter Sutton and Theodor Boveri noticed that chromosomes pair and split in the same pattern as Mendel's factors. In 1910 Thomas Hunt Morgan, at Columbia, found a white-eyed male fruit fly among red-eyed ones, and traced the trait to the X chromosome. Humans have 23 pairs: 22 pairs of autosomes and the sex chromosomes (XX or XY). Shuffling whole chromosomes alone can give one person about 2²³, over 8 million, different gametes.

Genes on the same chromosome travel together, except when crossing over swaps stretches between the two copies. The further apart two genes are, the likelier a swap between them. In 1913 Alfred Sturtevant, then a student in Morgan's lab, turned that into the first genetic map: 1% recombinant offspring means 1 map unit, now called a centimorgan. Genes 50 or more centimorgans apart look unlinked, as if on different chromosomes. That is the situation Mendel stumbled into.

Mutation: where new variants come from

Every allele began as a copy that went slightly wrong (see Molecular Biology, 35/45). A mutation can swap one letter, delete or insert some, or repeat a stretch many times. It matters in the germline (eggs and sperm, so it can be inherited) or in a somatic cell (which affects only that body, as in a cancer). In humans the rate is about 1.1 to 1.2 × 10⁻⁸ per letter per generation, so a child has roughly 60 to 70 new mutations that neither parent carried. Most come from the father, and the count rises with his age, by about two for every extra year. Since only some 1 to 2% of the genome codes for protein, a typical child has on the order of one new mutation in the coding part, and most of those are harmless.

Examples show the range. Sickle cell disease is one letter changed (Glu6Val). The commonest cause of cystic fibrosis is a three-letter deletion that removes one amino acid, F508del. Huntington's disease is a stretch of CAG repeats that has grown too long. The ability to digest milk as an adult, lactase persistence, comes from changes next to the lactase gene that stop it switching off, and it arose independently several times, in Europe and in East Africa.

And mutation is random with respect to need. In 1943 Salvador Luria and Max Delbrück showed that resistance in bacteria appears before the bacteria meet the virus that selects it, not because of it (Nobel Prize, 1969). That is the foundation of Evolution (35/47).

Hardy–Weinberg: why carriers vastly outnumber the affected

In 1908 the English mathematician G. H. Hardy and the German physician Wilhelm Weinberg independently pointed out something simple. If mating is random and nothing pushes allele frequencies around, they stay put, and the three genotypes appear in fixed proportions. For two alleles with frequencies p and q (p + q = 1):

Take a recessive condition seen in 1 birth in 2,500. Then q² = 1/2,500, so q = 0.02. Carriers are 2pq = 2 × 0.98 × 0.02, about 3.9%, roughly 1 person in 25. A rare recessive allele hides almost entirely in healthy carriers, which is why such conditions seem to "come out of nowhere" in families with no history. (Cystic fibrosis in some European-ancestry populations is close to this; figures vary by population.) Sickle cell shows the opposite lesson: where malaria is common, carrying one copy protects against severe malaria (A. C. Allison, 1954), so the allele stays frequent in parts of Africa, the Mediterranean, the Middle East and India.

When relatives have children, rare alleles meet more often. With an inbreeding coefficient F, affected children are q² + Fpq. First cousins' children have F = 1/16, which here raises the risk from 1 in 2,500 to about 1 in 615.

The same arithmetic undid an old idea. In 1917 R. C. Punnett pointed out that preventing carriers of a rare recessive from breeding changes the allele frequency very slowly: removing every affected person's genes each generation takes the frequency from q to q/(1 + q), so the time to halve a frequency of 1% is about a hundred generations. Slow, and costly in human lives. We will meet the consequences in a moment.

Complex traits and polygenic scores

Most traits people care about, such as height, blood pressure and risk of common illnesses, are not Mendelian. In 1918 Fisher showed that many genes each adding a small effect make a smooth bell curve, as dice do when you add up many. This is the polygenic picture, and sequencing has confirmed it. The largest study of height (Yengo and colleagues, 2022, in Nature, with about 5.4 million people) found 12,111 common variants linked to height. Together they predict about 40% of the variation in people of European ancestry. Twin studies put the heritability of height around 80%, so there is still a gap, and it is partly rare variants and effects not yet measured.

A polygenic score adds up a person's copies of the variants, each weighted by its estimated effect. It is a statistic about populations, with four limits. First, it predicts a range, not a destiny: even with a good score, many individuals fall far from the prediction. Second, it works much less well in people whose ancestry differs from the studied group: studies of this transfer problem (Martin and colleagues, 2019) found scores several times less accurate in people of African ancestry than in Europeans, because most data come from Europe. Third, scores for behavioural traits such as years of schooling pick up family environment as well as direct genetic effects, and shrink when siblings are compared. Fourth, genes work through environments: the same score predicts different outcomes in different places and times.

Notice what the numbers say. Set heritability to 100% and one gene gives three lumps; 40 genes give a bell. At 60% heritability and a score holding half the genes, the score explains about 30% of the variation, a correlation near 0.55, and the top tenth by score are only moderately enriched for the top tenth by trait. That is the best case in a model with no ancestry gap.

Human genetic variation, told correctly

Any two people share about 99.9% of their DNA; a typical genome differs from the reference at roughly four to five million sites (1000 Genomes Project, 2015). Where does the difference sit? In 1972 Richard Lewontin analysed protein markers across populations and found that about 85% of the variation lay within local populations, and only a small remainder between groups. Later work with hundreds to hundreds of thousands of markers, from Noah Rosenberg and colleagues in 2002 (377 markers) onwards, found the same broad pattern: most variation, in the region of 85 to 95% depending on the markers and populations, is within populations.

Two further facts keep this honest. First, A. W. F. Edwards pointed out in 2003 that combining many markers lets you place a person's ancestry accurately, which is why ancestry tests work. Both statements are true: groups can be told apart statistically, and individuals within a group differ far more than the group averages do. Second, variation is mostly continuous and geographic, not boxed. Africa holds more genetic diversity than the rest of the world, because modern humans spent longest there; people elsewhere descend from smaller groups that left, and diversity falls with distance from Africa.

Traits that look like clear categories often are not. Light skin evolved more than once, with different genes in Europe and East Asia. Sickle trait follows malaria, not "race". Lactase persistence arose several times. Genes also depend on environment: phenylketonuria is a recessive inherited condition whose harm can be prevented by diet, found by newborn screening. Heritability, as Personality & Individual Differences (35/26) explains, is a population statistic in one environment; it does not measure how fixed anything is, and it cannot be compared between groups living in different conditions.

The history of eugenics

Francis Galton, Darwin's cousin, coined eugenics in 1883 for the idea that society should improve its heredity by encouraging some people to have children and discouraging others. It spread around the world in the early twentieth century, across the United States, Britain, Germany, the Nordic countries, Latin America, Japan and beyond, and respectable scientists and reformers backed it. It rested on three mistakes: it treated complex traits as simple Mendelian ones, it read social disadvantage as inherited defect, and it assumed some people's lives were worth less. It was also racist in practice.

Where and when	What happened
United States, from 1907	Indiana passed the first sterilisation law in 1907; many states followed. Buck v. Bell (1927) upheld Virginia's law, with Justice Holmes writing that "three generations of imbeciles are enough." Estimates of people sterilised under such laws are in the tens of thousands.
Nazi Germany, 1933 to 1945	A 1933 law led to the sterilisation of over 400,000 people. The "euthanasia" programmes killed many thousands of disabled people, and the same personnel and methods fed into the Holocaust.
Sweden, 1934 to 1976	A government inquiry in 2000 estimated about 21,000 people forcibly and about 6,000 coercively sterilised, mostly women.
Alberta, Canada, 1928 to 1972	About 2,800 sterilisations under the province's Sexual Sterilization Act.
Japan, 1948 to 1996	The Eugenic Protection Law led to about 25,000 forced sterilisations; Japan's Supreme Court held it unconstitutional in July 2024.
Peru, 1995 to 2000	A national family-planning programme sterilised about 25,000 men and some 330,000 women according to a 2002 report; coercion of poor and Indigenous women was alleged and investigated.
India, 1975 to 1977	During the Emergency, millions of vasectomies were carried out, many under pressure.

Many early critics were geneticists, as the Punnett argument above shows. The practice fell out of favour after 1945, though states went on sterilising for decades. Today's questions are subtler: prenatal screening, which is a choice, but one made in a society that treats some lives as lesser; and companies offering embryo selection using polygenic scores, which the European Society of Human Genetics has called unproven. Disability-rights writers and geneticists alike warn that the old logic can return in softer forms. The lesson of the history is not that genetics is dangerous. It is that a statistic about populations is not a verdict on a person.

What a graduate just sees

• Ratios from small samples are noisy. A "3 to 1" cross of 8 offspring is not a failed law.
• Dominant describes how alleles combine, not how common or healthy they are.
• Genes close together travel together; genes far apart behave as if on different chromosomes.
• Most new mutations are neutral, and they arise without regard to need.
• Rare recessive alleles hide in carriers, who are far more common than the affected.
• Most traits are polygenic: many small effects, a bell curve, and a score that predicts a range for a population, not an outcome for a person.
• Most human genetic variation is within populations, and it is geographic and continuous, not boxed.
• Heritability is about variation in a population in an environment; it is not fate and not a ranking of groups.
• Eugenics was mainstream science plus prejudice, and it is a reason to be careful with every new use of genetic prediction.

Where it shows up next

• Evolution (35/47): Hardy–Weinberg is the null model; selection, drift, migration and mutation are the forces that break it.
• Developmental Biology (35/51): the same genes act at different times and places; mutations that change regulation change bodies.
• Bioinformatics & Genomics (35/52): genome-wide studies, polygenic scores and ancestry inference are statistics on exactly these ideas.
• Medicine and the clinic: carrier screening, newborn screening, inherited cancer risk, pharmacogenetics and genetic counselling.
• Agriculture: crop and livestock breeding, from Mendel's peas to marker-assisted selection.

If you want to go deeper

• 📘 Textbook. Anthony Griffiths and others, Introduction to Genetic Analysis (Macmillan/W. H. Freeman, 12th edition, 2020). A standard course text, strong on problem-solving.
• 📘 Textbook. Benjamin Pierce, Genetics: A Conceptual Approach (Macmillan, 7th edition, 2020). Clearer on the concepts, with many worked problems.
• 📘 Gentler. Adam Rutherford, A Brief History of Everyone Who Ever Lived (2016) and Control: The Dark History and Troubling Present of Eugenics (2022); Kathryn Paige Harden, The Genetic Lottery (Princeton, 2021); Siddhartha Mukherjee, The Gene (2016).
• 🌐 Free course. MIT OpenCourseWare 7.03 Genetics (Fall 2004), and the genetics chapters of OpenStax Biology 2e.