Mendelian genetics

Genes, alleles and your two copies

A gene is a stretch of DNA that affects a trait, such as flower colour. A gene can come in different versions, called alleles. For flower colour in peas there's a purple allele (written P) and a white allele (written p).

You carry two copies of most genes, one from each parent, because chromosomes come in matching pairs. If both copies are the same allele (PP or pp), you're homozygous for that gene. If they're different (Pp), you're heterozygous.

Your combination of alleles is your genotype. The trait you can actually observe, like purple flowers, is your phenotype.

Dominant and recessive

A heterozygous Pp plant has purple flowers. The P allele is dominant: it shows up in the phenotype even when there's only one copy. The p allele is recessive: white flowers appear only in pp plants, which have no P at all.

Here's what's usually happening underneath. The P allele codes for a working enzyme that makes purple pigment, and the p allele codes for a version that doesn't work. One working copy makes enough pigment to colour the flower. The recessive allele isn't destroyed or switched off by the dominant one; it just doesn't make a working product.

The law of segregation

Mendel's first law says that the two alleles of a gene separate when eggs and sperm (gametes) are made. Each gamete gets just one allele, and it's equally likely to be either one. So a Pp plant makes gametes that are half P and half p.

Today we know why. During meiosis I, the two chromosomes of each matching pair are pulled into different cells, taking their alleles with them. At fertilisation, an egg and a sperm each bring one allele, restoring the pair.

Predicting a cross with a Punnett square

A Punnett square is a grid that shows every way the parents' gametes can combine. Here's how to use one for two heterozygous parents, Pp × Pp:

1. 1Write out each parent's gametes: P or p, each with a ½ chance.
2. 2Draw a 2 × 2 grid. Put one parent's gametes across the top and the other's down the side.
3. 3Fill in each box by combining the allele above it with the allele beside it.
4. 4Count the genotypes: 1 PP, 2 Pp and 1 pp, a genotype ratio of 1 : 2 : 1.
5. 5Turn the genotypes into phenotypes: PP and Pp are purple and pp is white, so the ratio is 3 purple : 1 white.

That's the pattern Mendel saw. From one such cross he counted 705 purple plants and 224 white ones, a ratio of 3.15 : 1. It isn't exactly 3 : 1 because these ratios are probabilities, not guarantees, a bit like flipping a coin. With large numbers the result lands close to the prediction. In a small family of four children, anything can happen.

The test cross: revealing a hidden genotype

A purple plant could be PP or Pp; you can't tell by looking. To find out, cross it with a white pp plant. This is a test cross. If any white offspring appear, the purple parent must have been carrying a p, so it's Pp, and you'd expect roughly half purple and half white. If many offspring are all purple, the parent is almost certainly PP.

Two genes at once: independent assortment

Now follow two genes: seed colour (yellow Y is dominant over green y) and seed shape (round R is dominant over wrinkled r). Mendel's second law, the law of independent assortment, says that the alleles of different genes are sorted into gametes independently of each other. Which colour allele a gamete gets tells you nothing about which shape allele it gets.

The reason is again in meiosis. In metaphase I, each pair of chromosomes lines up on its own, facing either way, independently of the other pairs. So a YyRr plant makes four kinds of gametes in equal numbers: YR, Yr, yR and yr.

Cross two YyRr plants and a 4 × 4 Punnett square gives the famous 9 : 3 : 3 : 1 ratio: 9 yellow round, 3 yellow wrinkled, 3 green round and 1 green wrinkled.

A faster way: the probability rules

Punnett squares get unwieldy quickly: three genes would need a 64-box grid. Two simple rules of probability do the same job much faster.

The product rule: the chance that two independent events both happen is their probabilities multiplied. For example, in a YyRr × YyRr cross, the chance of a green wrinkled (yyrr) seed is ¼ (for yy) × ¼ (for rr) = 1/16.

The sum rule: the chance that one or the other of two outcomes happens, when they can't both happen, is their probabilities added. In a Pp × Pp cross, the chance of a purple plant is P(PP) + P(Pp) = ¼ + ½ = ¾.

Key terms

Gene / allele

A stretch of DNA that affects a trait / one version of that gene.

Genotype / phenotype

The alleles an organism carries / the traits you can observe.

Homozygous / heterozygous

Two identical alleles / two different alleles for a gene.

Dominant / recessive

Shows up with one copy / shows up only with two copies.

Law of segregation

The two alleles of a gene separate into different gametes, each with equal chance.

Law of independent assortment

Alleles of different (unlinked) genes are sorted into gametes independently.

Test cross

Crossing an individual with a homozygous recessive to reveal its genotype.

Product rule / sum rule

Multiply the chances for "and" (independent events); add them for "or" (outcomes that can't both happen).

Check yourself

Try answering in your head before you open each answer.

• 1.Cystic fibrosis is caused by a recessive allele (a). Two parents are both carriers (Aa). What is the chance that their child has cystic fibrosis? And the chance the child is a carrier?Show answerHide

  An aa child has a ¼ chance. A carrier (Aa) has a ½ chance: from the Punnett square, 2 of the 4 boxes are Aa.

• 2.Tall (T) is dominant over short (t) in peas. A tall plant crossed with a short plant gives 48 tall and 52 short offspring. What was the tall parent's genotype?Show answerHide

  Tt. The roughly 1 : 1 ratio is what a test cross gives with a heterozygote. A TT parent would have given only tall offspring.

• 3.Which event in meiosis explains independent assortment?Show answerHide

  In metaphase I, each pair of chromosomes lines up at the middle of the cell with its own random orientation. So alleles on different chromosomes end up in gametes in every combination equally often.