Gregor Mendel is known as the "father of modern genetics. " In breeding experiments between 1856 and 1865, Gregor Mendel first traced inheritance patterns of certain traits in pea plants and showed that they obeyed simple statistical rules. Although not all features show these patterns of "Mendelian Inheritance," his work served as a proof that application of statistics to inheritance could be highly useful. Since that time, many more complex forms of inheritance have been demonstrated.
In 1865, Mendel wrote the paper Experiments on Plant Hybridization. Mendel read his paper to the Natural History Society of Brünn on February 8 and March 8, 1865. It was published in the Proceedings of the Natural History Society of Brünn the following year. In his paper, Mendel compared seven discrete characters (as diagramed in ):
Mendel's Seven Characters
This diagram shows the seven genetic "characters" observed by Mendel.
- color and smoothness of the seeds (yellow and round or green and wrinkled)
- color of the cotyledons (yellow or green)
- color of the flowers (white or violet)
- shape of the pods (full or constricted)
- color of unripe pods (yellow or green)
- position of flowers and pods on the stems
- height of the plants (short or tall)
Mendel's work received little attention from the scientific community and was largely forgotten. It was not until the early 20th century that Mendel's work was rediscovered, and his ideas used to help form the modern synthesis.
The Experiment
Mendel discovered that when crossing purebred white flower and purple flower plants, the result is not a blend. Rather than being a mixture of the two plants, the offspring was purple-flowered. He then conceived the idea of heredity units, which he called "factors", one of which is a recessive characteristic and the other of which is dominant. Mendel said that factors, later called genes, normally occur in pairs in ordinary body cells, yet segregate during the formation of sex cells. Each member of the pair becomes part of the separate sex cell. The dominant gene, such as the purple flower in Mendel's plants, will hide the recessive gene, the white flower.
When Mendel grew his first generation hybrid seeds into first generation hybrid plants, he proceeded to cross these hybrid plants with themselves, creating second generation hybrid seeds. He found that recessive traits not visible in the first generation reappeared in the second, but the dominant traits outnumbered the recessive by a ratio of 3:1.
After Mendel self-fertilized the F1 generation and obtained the 3:1 ratio, he correctly theorized that genes can be paired in three different ways for each trait: AA, aa, and Aa. The capital "A" represents the dominant factor and lowercase "a" represents the recessive. Mendel stated that each individual has two factors for each trait, one from each parent. The two factors may or may not contain the same information. If the two factors are identical, the individual is called homozygous for the trait. If the two factors have different information, the individual is called heterozygous. The alternative forms of a factor are called alleles. The genotype of an individual is made up of the many alleles it possesses.
An individual possesses two alleles for each trait; one allele is given by the female parent and the other by the male parent. They are passed on when an individual matures and produces gametes: egg and sperm. When gametes form, the paired alleles separate randomly so that each gamete receives a copy of one of the two alleles. The presence of an allele does not mean that the trait will be expressed in the individual that possesses it. In heterozygous individuals, the allele that is expressed is the dominant. The recessive allele is present but its expression is hidden
Relation to Statistics
The upshot is that Mendel observed the presence of chance in relation to which gene-pairs a seed would get. Because the number of pollen grains is large in comparison to the number of seeds, the selection of gene-pairs is essentially independent. Therefore, the second generation hybrid seeds are determined in a way similar to a series of draws from a data set, with replacement. Mendel's interpretation of the hereditary chain was based on this sort of statistical evidence.
In 1936, the statistician R.A. Fisher used a chi-squared test to analyze Mendel's data, and concluded that Mendel's results with the predicted ratios were far too perfect; this indicated that adjustments (intentional or unconscious) had been made to the data to make the observations fit the hypothesis. However, later authors have claimed Fisher's analysis was flawed, proposing various statistical and botanical explanations for Mendel's numbers. It is also possible that Mendel's results were "too good" merely because he reported the best subset of his data — Mendel mentioned in his paper that the data was from a subset of his experiments.
In summary, the field of genetics has become one of the most fulfilling arenas in which to apply statistical methods. Genetical theory has developed largely due to the use of chance models featuring randomized draws, such as pairs of chromosomes.