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zoology, botany, physics, and chemistry at the University of Vienna. Upon returning to Brno, he began an active experimentation with pea plants, with strong support from the abbot of the Augustinian monastery. Mendel focused his research on pea plants because they were easy to grow, and also because they have both male and female reproductive organs. Consequently, pea plants can be either self-pollinated or cross-pollinated with another plant. By cross-pollinating plants that produce only green seeds with plants that produce only yellow seeds, Mendel obtained results that at first glance appeared to be very puzzling (figure 34). The first offspring generation had only yellow seeds. However, the following generation consistently had a 3:1 ratio of yellow to green seeds! From these surprising findings, Mendel was able to distill three conclusions that became important milestones in genetics:

The inheritance of a characteristic involves the transmittance of certain “factors” (what we call genes today) from parents to offspring.

Every offspring inherits one such “factor” from each parent (for any given trait).

A given characteristic may not manifest itself in an offspring but it can still be passed on to the following generation.

But how can one explain the quantitative results in Mendel’s experiment? Mendel argued that each of the parent plants must have had two identical “factors” (what we would call alleles, varieties of a gene), either two yellow or two green (as in figure 35). When the two were mated, each offspring inherited two different alleles, one from each parent (according to rule 2 above). That is, each offspring seed contained a yellow allele and a green allele. Why then were the peas of this generation all yellow? Because, Mendel explained, yellow was the dominant color and it masked the presence of the green allele in this generation (rule 3 above). However (still according to rule 3), the dominant yellow did not prevent the recessive green from being passed on to the next generation. In the next mating round, each plant containing one yellow allele and one green allele was pollinated with another plant containing the same combination of alleles. Since the offspring contain one allele from each parent, the seeds of the next generation may contain one of the following combinations (figure 35): green-green, green-yellow, yellow-green, or yellow-yellow. All the seeds with a yellow allele become yellow peas, because yellow is dominant. Therefore, since all the allele combinations are equally likely, the ratio of yellow to green peas should be 3:1.

Figure 34

Figure 35

You may have noticed that the entire Mendel exercise is essentially identical to the experiment of tossing two coins. Assigning heads to green and tails to yellow and asking what fraction of the peas would be yellow (given that yellow is dominant in determining the color) is precisely the same as asking what is the probability of obtaining at least one tails in tossing two coins. Clearly that is 3/4, since three of the possible outcomes (tails-tails, tails-heads, heads-tails, heads-heads) contain a tails. This means that the ratio of the number of tosses that do contain at least one tails to the number of tosses that do not should be (in the long run) 3:1, just as in Mendel’s experiments.

In spite of the fact that Mendel published his paper “Experiments on Plant Hybridization” in 1865 (and he also presented the results at two scientific meetings), his work went largely unnoticed until it was rediscovered at the beginning of the twentieth century. While some questions related to the accuracy of his results have been raised, he is still regarded as the first to have laid the mathematical foundations of modern genetics. Following in the path cleared by Mendel, the influential British statistician Ronald Aylmer Fisher (1890–1962) established the field of population genetics—the mathematical branch that centers on modeling the distribution of genes within a population and on calculating how gene frequencies change over time. Today’s geneticists