The monohybrid cross

A monohybrid cross follows a single trait. It is the founding experiment, and it produces a ratio Mendel was the first to see.

Mendel's experiment

GENERATION P   (parents, pure lines)

   PURPLE flowers     ×   WHITE flowers
       V//V                    w//w
            |
            v
GENERATION F1

   100 % PURPLE flowers             all V//w
   -> the white trait has DISAPPEARED
            |
            |  self-fertilisation of F1
            v
GENERATION F2

   3/4 purple  and  1/4 white
   -> the white trait REAPPEARS

On Mendel's actual data: 705 purple and 224 white, a ratio of 3.15 to 1. On another trait, seed shape: 6022 round and 2001 wrinkled, a ratio of 3.01 to 1.

The explanation via the Punnett square

Each F1 parent is heterozygous V//w and produces two kinds of gametes in equal proportions: V and w.

                 gametes of parent 2
                     V          w
              +-----------+-----------+
   gametes  V |   V//V    |   V//w    |
   of         |  purple   |  purple   |
   parent 1   +-----------+-----------+
            w |   V//w    |   w//w    |
              |  purple   |   WHITE   |
              +-----------+-----------+

   genotypes : 1 V//V  +  2 V//w  +  1 w//w       ->  1 : 2 : 1
   phenotypes: 3 purple             1 white       ->  3 : 1

The observed 3 : 1 ratio is therefore a direct consequence of the 1 : 2 : 1 genotypic ratio, two different genotypes giving the same phenotype.

The first law: segregation

Law of segregation. The two alleles of a gene separate during gamete formation, and each gamete receives only one.

Mendel deduced it from his counts, knowing nothing of chromosomes. We now know what physically realises it: meiosis, where homologous chromosomes separate in the first division. The correspondence between Mendel's "factors" and chromosome behaviour was only established in 1902, by Sutton and Boveri.

Probability enters biology

Mendel's proportions are probabilities, not guarantees. A V//w × V//w couple has a one-in-four chance of a w//w child — but may perfectly well have four w//w in a row, just as a coin can give four heads.

   each offspring:  P(white) = 1/4, independently of the previous ones

This is why Mendel had to count thousands of plants: it is the law of large numbers that makes the theoretical ratio appear. On ten plants, nothing would have been visible.

Summary

• Crossing two pure lines → a uniform F1 carrying the dominant trait.
• Self-fertilising the F1 gives an F2 in the ratio 3 : 1.
• F2 genotypes: 1 : 2 : 1; two of them give the same phenotype.
• The Punnett square predicts these proportions.
• First law: the two alleles separate at gamete formation (meiosis).
• The proportions are probabilities: they appear only in large numbers.