2.6 — Mendel and the Patterns of Inheritance

Two parents with brown eyes have a blue-eyed child. Two parents with normal hearing have a deaf child. A man with an inherited disease has four children and none of them are affected, while his brother has two children and both are.

None of that is random luck, and all of it was explained by a monk counting peas in a garden in Brno, forty years before anyone knew what a chromosome did.

What Mendel actually did, and why it worked when others failed

Gregor Mendel spent from 1856 to 1863 breeding pea plants — around 28,000 of them. Others had tried plant breeding experiments before and got nowhere. Three choices made the difference.

He chose traits with exactly two clean states. Seed shape round or wrinkled. Flower colour purple or white. Pod colour green or yellow. Plant tall or short. No in-between, so no judgement calls in the data.

He started with true-breeding lines. He spent two years confirming that each line produced only its own type before he began crossing anything.

He counted, and applied arithmetic. This is the real innovation. The prevailing idea was that inheritance was a blending of fluids, like mixing paint. Mendel treated it as discrete units and did statistics, which was not how biology was done at the time. It is closer to physics than to natural history, and it is probably why the paper he published in 1866 was ignored for thirty-four years until three separate researchers rediscovered the same rules in 1900.

The experiment and what it forced him to conclude

Cross a true-breeding purple-flowered plant with a true-breeding white-flowered one. All the offspring are purple. Under blending inheritance they should have been pale violet. The white has not been diluted; it has vanished.

Now let those purple offspring self-fertilise. The white reappears, in about one quarter of the next generation. Mendel counted 705 purple to 224 white — a ratio of 3.15 to 1.

Something that vanished completely in one generation and came back unchanged in the next cannot have been blended. It must have been present but hidden. From that, Mendel deduced:

1. Each plant carries two factors for each trait.
2. One factor can mask the other. He called the masking one dominant and the masked one recessive.
3. The two factors separate when gametes are made, so each gamete gets one.
4. Fertilisation restores the pair, one from each parent.

We now know the factors are alleles, and that the separation in point 3 is meiosis I from Chapter 1.7 — which is remarkable, because Mendel had no way to know that chromosomes existed in pairs or that they separated.

The vocabulary, defined once

Gene — a stretch of DNA specifying a product. Allele — one version of that gene. Genotype — which alleles you carry. Written with letters: capital for dominant, lowercase for recessive. Phenotype — what you actually show. Homozygous — two identical alleles (BB or bb). Heterozygous — two different alleles (Bb). Carrier — heterozygous for a recessive condition: you carry it, you do not have it.

Dominant does not mean common, strong, or better. It means only that one copy is enough to show the trait. Polydactyly — extra fingers — is dominant and rare. Having five fingers is recessive and near-universal. Huntington's disease is dominant and is not in any sense an advantage.

The Punnett square

A Punnett square for two heterozygous parents. Each parent's two alleles go along one edge; each box is one possible combination, and all four are equally likely. Three boxes show the dominant phenotype and one shows the recessive — the 3:1 ratio Mendel counted. Image: Wikimedia Commons.

Reginald Punnett's grid is simply an organised way of listing every combination. Put one parent's possible gametes along the top and the other's down the side, fill each box with the combination, and count.

For Bb × Bb the four boxes are BB, Bb, Bb, bb. Three of the four show the dominant phenotype, one shows the recessive. 3:1 in phenotype, 1:2:1 in genotype.

Each box is a probability, not a quota. This is the single most misunderstood point in clinical genetics, and it matters when talking to a family. Two carriers have a 25 percent chance per pregnancy of an affected child. Having one affected child does not "use up" the risk — the next pregnancy is still 25 percent, exactly like a coin that has just come up heads. It is entirely possible for two carriers to have four affected children out of four, and it is entirely possible for them to have none.

Mendel's two laws

Segregation. The two alleles of a gene separate during gamete formation, so each gamete carries one. This is meiosis I.

Independent assortment. The alleles of different genes separate independently of each other, so inheriting your mother's allele for one gene does not affect which allele you get for another. This is only true for genes on different chromosomes, or far apart on the same one — and Mendel was lucky that the seven traits he studied happened to behave this way. Chapter 2.7 covers linkage, which is what happens when they do not.

The inheritance patterns a doctor recognises

There are five main patterns, and each has a distinctive shape in a family tree. Being able to read that shape is genuinely useful — it tells you the risk to the next generation before any test is done.

Autosomal recessive

Autosomal recessive inheritance. Both parents are unaffected carriers; on average one child in four is affected, and males and females equally often. The condition typically appears with no family history at all, which is what makes it so often unexpected. Image: Wikimedia Commons.

Autosomal means the gene is on one of the 22 non-sex chromosomes, so males and females are affected equally.

Two copies are needed to be affected. Carriers are healthy. Two carriers have a 25 percent risk per child, and two thirds of their unaffected children will themselves be carriers.

The pattern in a family tree is horizontal — affected siblings, with unaffected parents, and often no earlier cases at all. This is why these conditions so often arrive as a complete surprise.

Examples: cystic fibrosis, sickle cell disease, thalassaemia, Tay–Sachs, phenylketonuria, most inborn errors of metabolism, and the commonest form of congenital deafness.

Cousin marriage raises the risk, and the reason is arithmetic rather than anything mystical. Everyone carries several recessive disease alleles — the usual estimate is one to two lethal-equivalent alleles each. If your partner is unrelated, the chance you both carry a fault in the same gene is small. First cousins share about one eighth of their DNA, so the chance rises. Concretely, the risk of a serious birth defect goes from roughly 2 to 3 percent in the general population to roughly 4 to 6 percent for first cousins. That is a real doubling and it is worth knowing, and it is also far smaller than the number usually assumed. It also compounds across generations where cousin marriage is repeated, which is the situation that matters most clinically.

Autosomal dominant

Autosomal dominant inheritance. One affected parent, about half the children affected, males and females equally, and the condition present in every generation. The vertical line down the chart is the signature. Image: Wikimedia Commons.

One copy is enough. An affected person has a 50 percent chance of passing it to each child. The pattern is vertical — present in every generation, no skipping.

Examples: Huntington's disease, familial hypercholesterolaemia, Marfan syndrome, achondroplasia, polycystic kidney disease, neurofibromatosis, hereditary breast and ovarian cancer from BRCA faults.

Two complications appear here and both matter in a clinic.

Incomplete penetrance. Not everyone carrying the allele develops the condition. A BRCA1 fault gives a lifetime breast cancer risk of roughly 55 to 70 percent, not 100. So the condition can appear to skip a generation when it has not — the allele passed through someone who never developed it.

Variable expressivity. Everyone affected shows it differently. In neurofibromatosis one person may have only a few skin patches while their child has significant complications, from the identical mutation.

X-linked recessive

X-linked recessive inheritance. A carrier mother passes the affected X to half her sons, who have no second X to compensate and are therefore affected, and to half her daughters, who become carriers. An affected father passes his X to every daughter — making them all carriers — and to no son. Image: Wikimedia Commons.

The gene is on the X chromosome. Males have one X, so one faulty copy is enough; females have two, so a female needs both faulty to be affected, which is rare.

The pattern: mostly males affected, inherited through unaffected carrier mothers, and no father-to-son transmission ever — a father gives his son a Y, not an X. That last rule is diagnostic. If you see an affected father and an affected son in the same line, it is not X-linked recessive.

Examples: haemophilia A and B, Duchenne muscular dystrophy, red–green colour blindness (about 8 percent of males, under 0.5 percent of females), G6PD deficiency.

The haemophilia in European royalty is the textbook illustration. Queen Victoria was a carrier, and through her daughters the allele entered the Spanish, German and Russian royal families. Tsarevich Alexei of Russia had it, and his parents' desperation over his bleeding is a large part of how Rasputin gained influence at the Russian court — a fair claim that one recessive allele on one chromosome had a hand in the politics of a revolution.

X-linked dominant, and Y-linked

X-linked dominant is rarer. Affected fathers pass it to all daughters and no sons; affected mothers pass it to half of each. Some are lethal in males, so only girls survive to be born with it.

Y-linked conditions pass strictly father to son, and are almost entirely about male fertility, since the Y carries few genes.

Mitochondrial inheritance was covered in Chapter 1.5: strictly maternal, affecting both sexes, never passed on by an affected father.

Where simple Mendelian rules stop

Most human traits are not Mendelian, and pretending otherwise leads directly to bad genetics.

Incomplete dominance — the heterozygote is genuinely in between. A red snapdragon crossed with white gives pink.

Codominance — both alleles show fully. The AB blood group is this: an AB person makes both the A sugar and the B sugar on their red cells, not a blend. Chapter 13.7.

Multiple alleles — a gene can have more than two versions in a population, even though any one person has only two. The ABO gene has three common alleles.

One gene, many effects (pleiotropy). Sickle cell affects red cells, spleen, bones, kidneys, lungs and brain, all from one substitution.

Many genes, one trait (polygenic). Height, skin colour, blood pressure and intelligence are each influenced by hundreds to thousands of variants, each contributing a small amount, plus environment. This is why the school textbook claim that eye colour is a single dominant gene is wrong. At least a dozen genes contribute, which is why two blue-eyed parents can occasionally have a brown-eyed child — a fact that has caused genuine and unnecessary marital suspicion.

Genes plus environment. Phenylketonuria is the finest example in medicine. It is straightforwardly autosomal recessive: a missing enzyme means phenylalanine builds up and causes severe, permanent intellectual disability. And it is completely preventable by diet. A newborn heel-prick test detects it in the first days of life, a low-phenylalanine diet started immediately prevents essentially all the damage, and a child who would have been profoundly disabled develops normally. Same genotype, entirely different outcome, decided by what is in the bottle. It is the standard answer to anyone who claims genes are destiny, and it is why newborn screening exists at all. Chapter 21.8.

What the next page fixes

Mendel's second law assumed genes assort independently. Genes on the same chromosome do not — they travel together, and how often they separate depends on how far apart they sit. Chapter 2.7 covers chromosomes: how two metres of DNA is packed, what a karyotype shows, how sex is determined, why linkage was the tool that let genes be mapped before DNA was even known to be the genetic material, and what happens when whole chromosomes go wrong.