Mendel's Peas: Segregation and Independent Assortment

Gregor Mendel counted 7,324 seeds borne by his round-by-wrinkled pea hybrids: 5,474 round and 1,850 wrinkled.

That is 2.96 round for every wrinkled seed. The hybrids themselves had all been round. So the wrinkled form vanished for a generation and came back, unchanged, in about a quarter of the next one. Seed colour did the same: 6,022 yellow and 2,001 green among 8,023 seeds, or 3.01 to 1. This lesson asks what a plant must carry to give those numbers, then uses the answer to predict new crosses.

Why peas, and why counting

Mendel worked with the garden pea, Pisum sativum. A pea flower keeps its reproductive organs enclosed in its petals and sheds pollen early, so it normally fertilises itself and is protected from stray pollen. That makes two things easy. Left alone, a pea line stays pure. Opened by hand, it can be crossed: Mendel removed the stamens from an immature flower before they shed pollen and placed pollen from another variety on its stigma, so he knew the father of every seed.

He began by checking his materials. He grew 34 varieties for two years and kept 22 for crossing, lines that remained true to type: a true-breeding line is one whose offspring, when it self-pollinates, all show the parent’s form. He chose characters with two clear forms, such as round or wrinkled seeds and tall or short stems. He made each cross both ways, with each variety serving once as seed parent and once as pollen parent. These reciprocal crosses gave the same hybrid, so it did not matter which parent was the mother.

Then he counted. He held that a ratio should be estimated from the sum of many observations, since one plant is a small sample. Seed characters helped: the shape and colour of a seed belong to the embryo inside it, so a single hybrid plant carries dozens of offspring that can be scored on the vine. He scored seeds only once the pods were ripe and dry.

In modern labels, which Mendel did not use, the true-breeding parents are the P generation, their hybrids the F1, and the offspring of selfed F1 plants the F2.

One character: a 3:1 that hides a 1:2:1

Cross round with wrinkled and every F1 seed is round. Mendel called round the dominant character, the one seen, wholly or nearly unchanged, in the hybrid, and wrinkled the recessive character, the one that becomes latent. In the F2, wrinkled returns at about one in four.

The F2 round seeds held a second surprise. Mendel grew 565 plants from them and let each self-pollinate. 193 gave only round seeds. 372 gave round and wrinkled seeds again, at about 3 to 1. So round plants that look alike come in two kinds, at 1.93 to 1. Wrinkled F2 plants, by contrast, bred true.

The model that fits: think of each plant as holding two cards for seed shape, one from each parent, and handing one card, at random, into each egg or pollen grain. In modern words:

• A locus is the place on a chromosome where a given gene lies; Mendel knew it only as a character.
• An allele is one version of the gene at that locus: R (round) or r (wrinkled).
• The genotype is the pair of alleles a plant carries; the phenotype is what you see.
• Homozygous means two identical alleles (RR or rr); heterozygous means two different ones (Rr).

An Rr plant makes R and r gametes in equal numbers. Selfed, its eggs and pollen meet at random:

Rr x Rr → 1/4 RR : 1/2 Rr : 1/4 rr, which shows as 3/4 round : 1/4 wrinkled

Because one R is enough to make a round seed, RR and Rr look the same, and the 1:2:1 genotype ratio shows as a 3:1 phenotype ratio. The F3 test exposed the hidden split: among round F2 plants, one third (RR) breed true and two thirds (Rr) segregate. This is the law of segregation: the two alleles of a plant separate into different gametes, each gamete carrying one.

Keep two things apart. 3:1 is a phenotype ratio; 1:2:1 is a genotype ratio. And dominance describes only what a heterozygote looks like. It does not mean an allele is stronger, better, or commoner in a population. A common reason an allele is recessive is that one working copy of an enzyme’s gene makes enough enzyme, which the lesson on how enzymes work helps explain.

Two characters: 9:3:3:1 is two 3:1 ratios multiplied

Mendel next crossed round yellow with wrinkled green. The F1 seeds were round and yellow, genotype RrYy. Fifteen F1 plants, self-pollinated, gave 556 seeds: 315 round yellow, 108 round green, 101 wrinkled yellow and 32 wrinkled green. Do shape and colour travel together, or separately?

Worked problem. Assume complete dominance at both loci, equal transmission of the two alleles at each, random union of gametes, and equal survival of all seed types.

Step 1. Look at each character alone. Round is 315 + 108 = 423 and wrinkled is 101 + 32 = 133, a ratio of 3.18 to 1. Yellow is 315 + 101 = 416 and green is 108 + 32 = 140, or 2.97 to 1. Each character on its own segregates near 3:1.

Step 2. Predict the combinations if the two are independent. If shape tells you nothing about colour, the probability of two outcomes together is the product of their separate probabilities:

P(round and yellow) = 3/4 x 3/4 = 9/16; round green = 3/16; wrinkled yellow = 3/16; wrinkled green = 1/16

Times 556 seeds, that predicts 312.75, 104.25, 104.25 and 34.75, close to the observed 315, 108, 101 and 32. Equivalently, an RrYy plant makes four gamete types, RY, Ry, rY and ry, at 1/4 each, and the 16 equally likely unions sort into 9, 3, 3 and 1.

Step 3. Check independence directly. Among yellow seeds the fraction round is 315/416 = 0.757. Among green seeds it is 108/140 = 0.771. Both are near 3/4. Knowing a seed’s colour does not change the odds on its shape.

Step 4. Read the gametes. If a round yellow plant of unknown genotype is crossed to wrinkled green (rryy) and gives all four classes in roughly equal numbers, it must be RrYy. The next section explains why.

This is the law of independent assortment: alleles at one locus enter gametes independently of alleles at another. Whether 315:108:101:32 is close enough to 9:3:3:1 needs a statistical test, which waits for probability and crosses. And the law has limits. It holds for these two characters; it does not hold for every pair of genes, as linkage and mapping will show.

The test cross: reading a genotype you cannot see

A round plant might be RR or Rr. Self it and wait a generation, as Mendel did, or cross it to a plant homozygous for the recessive allele. That is a test cross. The rr tester can give only r, so each seed’s phenotype reports which allele came from the unknown plant:

RR x rr → all Rr (round); Rr x rr → 1/2 Rr (round) : 1/2 rr (wrinkled)

One wrinkled seed proves the round parent carries r. All-round results are weaker evidence, because an Rr plant gives each seed a 1/2 chance of being round. Ten in a row from an Rr parent has probability (1/2)^10, about 1 in 1,000.

Mendel ran the two-character version both ways. With the RrYy hybrid as seed parent and wrinkled green as pollen parent, the seeds were 31 round yellow, 26 round green, 27 wrinkled yellow and 26 wrinkled green. With the hybrid as pollen parent they were 24, 25, 22 and 27. Both are close to 1:1:1:1, so the hybrid’s eggs and its pollen each carried the four allele combinations in about equal numbers.

What Mendel knew, and what the wrinkled allele turned out to be

Mendel was an Augustinian friar at St Thomas’s Abbey in Brünn, now Brno, and later its abbot. He presented the pea work to the town’s Natural History Society on 8 February and 8 March 1865, and the paper, “Versuche über Pflanzen-Hybriden”, was printed in 1866. He wrote of differing “elements” (Elemente) and of dominant and recessive characters. He did not know of chromosomes or meiosis, which explain his laws, and the word gene was coined by Wilhelm Johannsen in 1909. The paper was cited a few times before 1900, but it was not taken up.

In 1900 Hugo de Vries, in a French note that did not mention Mendel, and Carl Correns, who credited Mendel’s priority, both reported crosses that followed his rules. Erich von Tschermak is often named a third rediscoverer, though his place is disputed. In 1902 William Bateson published a defence of the paper, with an English translation of it reprinted in the book. The physical basis is the subject of chromosomes and meiosis.

Two later stories need correcting. A popular claim says each of Mendel’s seven characters sat on a different one of the pea’s seven chromosomes. It is false: several lie on the same chromosome, and seed shape (R) and pod colour (Gp) are weakly linked. And in 1936 Ronald Fisher argued that Mendel’s data fit too well, which began a statistical debate, not a finding of fraud; a 2019 reanalysis by Ellis and colleagues did not find remarkable disagreement with expectation.

The wrinkled allele has a molecular explanation. In 1990 Bhattacharyya, Smith, Ellis, Hedley and Martin reported that r carries an insertion resembling a transposable element in a gene for a starch-branching enzyme. Without the enzyme, rr embryos make less amylopectin, the branched form of starch (see carbohydrates), and hold more sugar. They take up more water as they develop and wrinkle as they dry. In Rr seeds, one working copy appears to be enough, which is why round is dominant.

Design problem

You have a tall pea plant with purple flowers from an unknown source. Tall (T) is dominant to short (t), and purple (P) to white (p). Design crosses to find its genotype at both loci and to test whether the two characters assort independently.