Genetics, the study of inheritance and hereditary traits, is strongly based on the work of Gregor Mendel. In 1866, Mendel published his theory on how traits are inherited. It was dismissed at the time as being too simple, as the commonly accepted theories were extremely complex. In 1900, his work was rediscovered, and it was at that time, after Mendel’s death, that his theories were accepted.

Mendel worked with garden peas. These peas had a number of alleles, or variations of traits, and the same alleles were always observed in plants: the offspring of each plant. Here are some of the traits found in pea

These pea plants usually self-pollinate, creating almost identical offspring. However, it is possible to cross-polinate two plants by using the pollen from one and putting it on the other. In one experiment, Mendel crossed one pure red-flowered plant with a pure white-flowered plant. The result was what is known as a hybrid, with some genes from each plant. However, all of the offspring had red flowers. Mendel then allowed these hybrid offspring to self-pollinate. The result was over 900 plants, most of which had red flowers, but about one fourth of which had white flowers!

This experiment demonstrated the characteristic of dominance. Each offspring of any animal or plant has one set of genes from the mother and one set of genes from the father. Some genes are dominant over others, which are recessive. In this case, the genes for red flowers are dominant over the genes for the white flowers. Here is a chart that will help explain why only red flowers were shown in the F1, or first, generation, and why some white flowers appeared in the F2, or second, generation. Usually, dominant traites are indicated wuth a capital letter, and recessive traits with a lowercase of that letter. Therefore, the gene for red flowers will be known as "R". Because the gene for white flowers is recessive to the gene for red flowers, it will be known as "r". This kind of diagram is called a Punnett Square:

Along the top is the white flowered parent, which has two genes for white flowers (r). Along the left is the red flowered parent, which has two genes for red flowers (R). You can see from the animation how the results are acquired. All Punnett squares work like this. The center four squares represent the offspring and show all the possible combinations of genes. According to the diagram, all of the offspring with have one gene for red flowers and one gene for white flowers. When an organism’s genes are not the same for a specific trait, it is said to be heterozygous for that trait. The opposite, when an organism’s genes are the same for a specific trait, is said to be homozygous, or pure, for that trait. However, because the red is dominant, all of the offspring will have red flowers. Let’s now look at the F2 generation:

This generation is a little more complicated. About half of the offspring are going to be heterozygous (Rr). One quarter of the offspring are going to homozygous for red (RR). The last quarter will be homozygous for white (rr). This ratio, 1 RR : 2 Rr : 1 rr, is the genotype of the offspring. This means that for every "RR" offspring, there will be an offspring with "rr" and two with "Rr". A gene or allele is said to be expressed when it can be seen in the organism. In heterozygous organisms, it is the dominant trait that is expressed. The recessive gene still exists, but is not expressed, since it can not be seen on the organism. The phenotype of an organism is the expressed genes of that organism. The phenotype ratio of this F2 generation is 3 red : 1 white.

We can now see how Mendel got his results with the pea plants. It was from this, and other experiments, that he devised his theory of genetics.

A Punnett Square can also be larger. This allows for more traits to be considered. Here is an example. In addition to the red (R) and white (r) flowers, another trait in pea plants is having a tall (T) or short (t) stem. If we were to cross a homozygous tall, red-flowered plant (TTRR) with a homozygous short, white-flowered plant (ttrr), all of the offspring would be heterozygous in both traits (TtRr), and therefore their phenotype would be tall, red-flowered, which are the dominant genes. You can test this for yourself, and you’ll find that whenever you cross two organisms that are homozygous in all of the compared traits, but have different genes for those traits, the offspring will be heterozygous in all of those traits. The following Punnett Square demonstrates the results of the F2 generation:

You will notice a few differences in this Punnett Square. It is four by four instead of two by two, and along the top and left are pairs of genes instead of just a single gene. The pairs simply represent all of the combinations of the genes that can be passed on to the offspring. Other than that, the Punnett Square works the same way. You will notice that there are different genotype and phenotype ratios as well. The phenotype ratio is 9 tall, red : 3 short, red : 3 tall, white : 1 short, white.

You can then figure out what the probability of a certain outcome is by putting the possibilities of that outcome over the total possibilities. That sounds confusing, but is really quite simple. For example, there are a total of 16 squares in the Punnett Square, so there are 16 possibilities. If you wanted to know the chances of getting a tall, white-flowered pea plant, you would put the number of possibilities (3) over the total possibilities (16) in a fraction. So, there is a 3/16 chance of getting a tall, white-flowered plant. This also means that 3 out of 16 of the offspring will be tall and white-flowered. These numbers are only probabilities, and are not always entirely correct. They are only good approximations of what will happen.

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