Principles of Inheritance and Variation

1Mendel's method and his three laws

Mendel spent seven years crossing the garden pea, Pisum sativum, because it gave him true-breeding varieties, seven pairs of sharply contrasting traits and flowers he could pollinate by hand. His real innovation was arithmetic: he counted every plant in the F2 instead of describing the typical one, and the counts came back as small whole-number ratios.

Three statements came out of that counting. The Law of Dominance: of a pair of alleles, one expresses itself in the hybrid while the other stays hidden. The Law of Segregation: the two alleles of a pair separate cleanly during gamete formation, so every gamete carries one and only one — this one follows straight from meiosis, and unlike the other two it is not broken by any of the deviations in this chapter. The Law of Independent Assortment: alleles of different gene pairs are dealt into gametes independently of one another.

Figure. The dwarf form vanishes completely in the F1 and returns in a quarter of the F2. That reappearance is the evidence that the two alleles stay separate inside the hybrid instead of blending.

How the cross is set up

1. Start true-breedingChoose lines that give only the parental form generation after generation — TT tall, tt dwarf.
2. Cross them (P)Remove one parent's anthers and dust its stigma with the other's pollen. Every F1 plant is Tt.
3. Let the F1 selfThe hybrid pollinates itself, so the cross is Tt × Tt and the two alleles get a second chance to meet.
4. Count the F2The dwarf form returns in about a quarter of the plants — proof it was never lost, only masked.

2The monohybrid cross: 3 : 1 and 1 : 2 : 1

Tt × Tt is the whole of Mendelism in one line. Each parent makes two kinds of gamete in equal numbers, T and t, so the four combinations in the grid are equally likely: TT, Tt, Tt, tt. Three of the four carry at least one T and stand tall; only tt is dwarf. The same four cells therefore read two different ways — 3 : 1 if you count what you can see, 1 : 2 : 1 if you count what the plants actually carry — and a question will always be asking for one of them, not both.

Figure. Every cell of the grid is one fertilisation, and all four are equally likely because both gametes of each parent are made in equal numbers. Count the cells one way for the phenotype, another way for the genotype.

3The test cross

A tall pea is either TT or Tt, and nothing about its appearance will tell you which. Cross it with a dwarf, tt. The tester can only contribute t, so whatever the unknown parent puts into a gamete shows up directly in the offspring's phenotype: an all-tall progeny points to TT, while a 1 : 1 split of tall and dwarf proves the parent was Tt. The same trick checks a dihybrid, where RrYy × rryy gives four classes in 1 : 1 : 1 : 1 — and it is how recombinants get counted in linkage work.

Figure. Both testers are the same dwarf, so the two progenies differ only because of what the unknown parent could put into a gamete. One column is all the tester ever offers, which is exactly what makes the result readable.

4Independent assortment and the product rule

Two gene pairs on different chromosomes are dealt into gametes independently, so RrYy makes four kinds of gamete — RY, Ry, rY, ry — in equal numbers, and the F2 of RrYy × RrYy comes out 9 : 3 : 3 : 1. You almost never need to draw those sixteen cells. Each gene taken by itself still gives 3 : 1, so you can simply multiply: the fraction in any combined class is the product of its single-gene fractions. A forked-line diagram is that multiplication drawn out, and it scales to three or four genes where a grid does not.

Figure. Branch on one gene, then on the other, and multiply along each path. The upper branches are yellow (3/4) and the lower ones green (1/4); R_ means RR or Rr. Four paths, four products, and they are the 9 : 3 : 3 : 1 ratio.

5When one allele does not simply win

Dominance is a property of a particular pair of alleles, not a law of nature, and two patterns break it. In incomplete dominance the heterozygote is intermediate: a red snapdragon (RR) crossed with a white one (rr) gives pink F1 plants, and the F2 comes out 1 red : 2 pink : 1 white — the phenotypic ratio has collapsed onto the genotypic one, because now every genotype looks different. In codominance neither allele is diluted; both are expressed fully and at the same time.

The ABO blood groups show codominance and multiple allelism together. One gene has three alleles in the population — I^A, I^B and i — though any one person still carries only two of them. I^A and I^B are codominant, so an I^AI^B person builds both A and B antigens on the same red cell rather than something in between, while i is recessive to both.

Figure. Four cells, four different blood groups — the cross that most cleanly separates the three alleles. Only the AB cell shows codominance; the A and B cells show ordinary dominance of I^A or I^B over i, and the O cell has no dominant allele present to express.

6Linkage, recombination and map distance

Independent assortment quietly assumes the two genes ride on different chromosomes. Genes on the same chromosome travel together, and Morgan's crosses in Drosophila melanogaster showed it plainly: parental combinations came back far more often than recombinant ones. Crossing over in meiosis I is what breaks the association, and the further apart two genes sit, the likelier a crossover falls between them.

That makes recombination frequency a measure of distance. One per cent recombinants is defined as one map unit, or centimorgan, and Sturtevant used exactly this to build the first genetic maps. Morgan found white eye and yellow body so tightly linked that only 1.3 per cent of the progeny were recombinant, while white and miniature wing gave 37.2 per cent.

Recombinants can never exceed half the progeny. Once two genes are far enough apart for a crossover to fall between them almost every time, the four classes even out, and 50 per cent recombination is indistinguishable from independent assortment. That is also why short intervals add along a map but long ones read short: a second crossover in a long interval puts the parental combination back together, and goes uncounted.

Figure. Three of Morgan's X-linked genes drawn to scale: y is yellow body, w white eye, m miniature wing. y and w are so close that a crossover almost never separates them, while w and m are far enough apart that more than a third of the progeny come back recombinant. Map distances add, which is how 1.3 and 37.2 place y and m 38.5 units apart — and why that sum is a better estimate of the separation than a single y-to-m cross, which would score lower for the reason the text gives.

7Sex determination and X-linked traits

In humans the female is XX and the male XY, so it is the sperm that decides the sex of a child: half carry an X, half a Y, and the ratio of boys to girls is expected to be 1 : 1. Grasshoppers manage with XX/XO, and in birds and butterflies the arrangement is reversed — the female is the heterogametic sex, ZW against the male's ZZ.

A gene on the X has no partner on the Y, so a male carries only one copy of it and a single recessive allele is enough to show. That is why haemophilia and red-green colour blindness are far commoner in men, why they reach half the sons of a carrier mother, and why a father can never pass one to his son — what he gives a son is a Y.

Figure. The father's two gametes are not two versions of one thing: the X^H column is his daughters and the Y column is his sons. Reading down a single column is what turns one in four of the children into one in two of the sons.

8Reading pedigrees, and the disorders they trace

You cannot arrange crosses in humans, so human genetics is read backwards, off a family tree. A pedigree draws each male as a square and each female as a circle, joins a couple with a horizontal line, hangs their children beneath it, fills in the symbol of anyone affected, half-fills a circle for a known carrier and numbers the generations I, II, III down the left margin. What you are hunting for is a pattern, and each mode of inheritance leaves its own signature.

Not everything inherited is an allele, though. Down's syndrome comes from non-disjunction in meiosis: the two copies of chromosome 21 fail to separate, a gamete carries both, and the child ends up with three — a trisomy, 47 chromosomes in all, and the risk of that error rises with the mother's age. Klinefelter's syndrome (47, XXY) and Turner's syndrome (45, X0) arise the same way from the sex chromosomes. None of these segregates as a Mendelian allele, so none of them gives a Mendelian ratio.