Mendel's trick: careful counting

While plant and animal breeders produced the many domesticated species we know today, their approach produced no deep understanding of the mechanism of heredity. 

This was the approach taken by the Austrian Gregor Mendel (1822-1884). 

In 1856, Mendel began a series of experiments on plant breeding.   He eventually settled on studies of the garden pea Pisum sativum.   In this plant, the flowers contain both male and female organs - if left to their own devices they often self-fertilize (self-pollinate). 

To simplify his studies (and scientific progress often requires such constraints), he established three criteria for deciding which plants would be the most suitable for his studies.

1. They should possess clearly distinguishable, that is discontinuous, traits.
2. It must be possible to strictly control the breeding process.
3. Hybrids between the various stains must be fully fertile

Mendel was able to exploit the structure of the pea flower to generate crosses in which he knew which plant was the maternal parent and which was the parental parent (see below).

Mendel obtained many varieties of P. sativum and spent a number of years determining which 'bred true" for specific traits, i.e. whether self-fertilized plants always produced offspring similar to the parent.

These varieties differed from one another in "length and color of the stem; in the size and form of the leaves; in the position, color, size of the flowers; in the length of the flower stalk; in the color, form, and size of the pods; in the form and size of the seeds; and in the color of the seed-coats and of the albumen (endosperm)" - G. Mendel

A particular plant was either tall or short, had white or purple flowers, etc.  Which traits an individual displayed could be determined unambiguously – they could be counted.

• Why did it matter to Mendel that a variety "breed true"?
• Why did it matter that traits were discontinuous?  Is it possible to analyze continuous traits?