Punnett squares in code

Mendel on a computer

In the Heredity chapter you met Mendel's pea plants. A tall plant crossed with a short one gave only tall plants. When those plants were crossed with each other, about one plant in four came out short.

A Punnett square explains this. It lists every way a gamete of one parent can meet a gamete of the other. Here you build it in Python, so the computer does the listing and the counting.

Plant height in peas is set by one gene with two forms:

• T, tall, is dominant;
• t, short, is recessive.

A plant carries two letters. TT and Tt plants are tall; only tt is short.

Gametes are letters

Each gamete gets one of the parent's two letters. In Python, a genotype is a string, and list() splits it into its letters:

It prints ['T', 't']: the two kinds of gamete a Tt plant makes, in equal numbers.

Joining two gametes

A child gets one letter from each parent. Adding two strings joins them, but the order can come out either way: "t" + "T" gives "tT". Biologists always write the dominant letter first, so "tT" and "Tt" are the same genotype.

sorted() fixes this. Capital letters come before small ones, so the dominant letter always lands first:

It prints Tt. Without sorting, a count would treat tT and Tt as two different genotypes.

The square

Two loops visit every pair of gametes, one from each parent. That is exactly what the square does.

It prints ['TT', 'Tt', 'Tt', 'tt']: the four boxes, read row by row.

From genotype to phenotype

The phenotype is what you see. A small function turns a genotype into it:

One T is enough for a tall plant, so the test is simply whether "T" is in the string.

Counting with Counter

Counter from the collections module counts how often each item appears in a list:

It prints Counter({'Tt': 2, 'TT': 1, 'tt': 1}): the 1:2:1 ratio of genotypes. Counting phenotypes instead gives 3 tall to 1 short, the 3:1 ratio. Mendel saw nearly this: $787$ tall and $277$ short plants, about $2.84$ to 1.

Practise with new numbers

Try it in Python

The program builds the square for Tt with Tt, prints it as a grid, and counts the genotypes and the phenotypes.

Common mistakes

• Forgetting to sort. Then tT and Tt are counted apart, and the genotype count shows four kinds instead of three.
• Testing the first letter only. g[0] == "T" works only when every genotype is sorted. "T" in g always works.
• Calling a TT plant and a Tt plant different in looks. Both are tall. The genotype differs; the phenotype does not.
• Forgetting the import. Counter needs from collections import Counter, or Python stops with NameError.

Remember these

• A gamete is one letter: list("Tt") gives ['T', 't'].
• A child is "".join(sorted(a + b)), so the dominant letter comes first.
• Two loops over the parents' letters fill the Punnett square.
• Counter(kids) gives the 1:2:1 genotype ratio; counting phenotypes gives 3:1.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. Why does a Tt plant make two kinds of gamete in equal numbers?

2. What does "".join(sorted("t" + "T")) give, and why is the sort needed?

3. A cross of TT with tt gives which children, and what do they look like?

4. Why does phenotype test "T" in genotype and not genotype == "TT"?

5. Counter gives {'Tt': 2, 'TT': 1, 'tt': 1}. What is the ratio of phenotypes?