Darwin, Mendel and statistical fluctuations

Freeman Dyson discusses Darwin's failure to discover Mendelian inheritance. Had Darwin a stronger grasp of statistics (then under development by his cousin Francis Galton), he might have discovered the properties of the basic units of inheritance, so central to his theory of natural selection. See also Bounded cognition.

NYBooks: ... Seven years after Darwin published The Origin of Species, without any satisfactory explanation of hereditary variations, the Austrian monk Gregor Mendel published his paper “Experiments in Plant Hybridization” in the journal of the Brünn Natural History Society. Mendel had solved Darwin’s problem. He proposed that inheritance is carried by discrete units, later known as genes, that do not blend but are carried unchanged from generation to generation. The Mendelian theory of inheritance fits perfectly with Darwin’s theory of natural selection. Mendel had read Darwin’s book, but Darwin never read Mendel’s paper.

The essential insight of Mendel was to see that sexual reproduction is a system for introducing randomness into inheritance. In sweet peas as in humans, each plant is either male or female, and each offspring has one male and one female parent. Inherited characteristics may be specified by one gene or by several genes. Single-gene characteristics are the simplest to calculate, and Mendel chose them to study. For example, he studied the inheritance of pod color, determined by a single gene that has a version specifying green and a version specifying yellow. Each plant has two copies of the gene, one from each parent. There are three kinds of plants, pure green with two green versions of the gene, pure yellow with two yellow versions, and mixed with one green and one yellow. It happens that only one green gene is required to make a pod green, so that the mixed plants look the same as the pure green plants. Mendel describes this state of affairs by saying that green is dominant and yellow is recessive.

Mendel did his classic experiment by observing three generations of plants. The first generation was pure green and pure yellow. He crossed them, pure green with pure yellow, so that the second generation was all mixed. He then crossed the second generation with itself, so that the third generation had all mixed parents. Each third-generation plant had one gene from each parent, with an equal chance that each gene would be green or yellow. On the average, the third generation would be one-quarter pure green, one-quarter pure yellow, and one-half mixed. In outward appearance the third generation would be three-quarters green and one-quarter yellow.

This ratio of 3 between green and yellow in the third generation was the new prediction of Mendel’s theory. Most of his experiments were designed to test this prediction. But Mendel understood very well that the ratio 3 would only hold on the average. Since the offspring chose one gene from each parent and every choice was random, the numbers of green and yellow in the third generation were subject to large statistical fluctuations. To test the theory in a meaningful way, it was essential to understand the statistical fluctuations. Fortunately, Mendel understood statistics.

Mendel understood that to test the ratio 3 with high accuracy he would need huge numbers of plants. It would take about eight thousand plants in the third generation to be reasonably sure that the observed ratio would be between 2.9 and 3.1. He actually used 8,023 plants in the third generation and obtained the ratio 3.01. He also tested other characteristics besides color, and used altogether 17,290 third-generation plants. His experiments required immense patience, continuing for eight years with meticulous attention to detail. Every plant was carefully isolated to prevent any intruding bee from causing an unintended fertilization. A monastery garden was an ideal location for such experiments.

In 1866, the year Mendel’s paper was published, but without any knowledge of Mendel, Darwin did exactly the same experiment. Darwin used snapdragons instead of sweet peas, and tested the inheritance of flower shape instead of pod color. Like Mendel, he bred three generations of plants and observed the ratio of normal-shaped to star-shaped flowers in the third generation. Unlike Mendel, he had no understanding of statistical fluctuations. He used a total of only 125 third-generation plants and obtained a value of 2.4 for the crucial ratio. This value is within the expected statistical uncertainty, either for a true value of 2 or for a true value of 3, with such a small sample of plants. Darwin did not understand that he would need a much larger sample to obtain a meaningful result.

Mendel’s sample was sixty-four times larger than Darwin’s, so that Mendel’s statistical uncertainty was eight times smaller. Darwin failed to repeat his experiment with a larger number of plants, and missed his chance to incorporate Mendel’s laws of heredity into his theory of evolution. He had no inkling that a fundamental discovery was within his grasp if he continued the experiment with larger populations. The basic idea of Mendel was that the laws of inheritance would become simple when inheritance was considered as a random process. This idea never occurred to Darwin. That was why Darwin learned nothing from his snapdragon experiment. It remained a brilliant blunder.

Bonus: Social Darwinism discussed on BBC In Our Time.