## Why Dont We Observe 3 to 1 Ratios of Dominant Versus Recessive Traits in Populations

In chapter 3 we saw that the laws of Mendelian inheritance apply to people too. At first, many scientists did not easily accept this idea. The first case of a dominant trait discovered in humans, in 1903, was brachy-dactyly. This condition is characterized by shortened or fused fingers and toes. Based on the low frequency of this condition in the population at large, some scientists stated that Mendelian genetics did not apply to people. One wrote, "If Mendelian Laws of Genetics apply to people, and brachydactyly is a dominant trait, why don't 3 out of 4 people have

Figure 10.1 A Punnett Square Used to Predict the Offspring of Heterozygous Brachydactyly Parents. With these parents we would expect 75 percent brachydactyly children and 25 percent normal since brachydactyly is a dominant trait. However, this prediction is true only if both parents are heterozygous for brachydactyly.

Figure 10.1 A Punnett Square Used to Predict the Offspring of Heterozygous Brachydactyly Parents. With these parents we would expect 75 percent brachydactyly children and 25 percent normal since brachydactyly is a dominant trait. However, this prediction is true only if both parents are heterozygous for brachydactyly.

brachydactyly?" (Udny Yule, cited in G. H. Hardy, "Mendelian Proportions in a Mixed Population," Science n.s. 28 (1908): 49-50). You see, this scientist drew a Punnett square with two heterozygotes for brachydactyly as parents and saw that 75 percent of the offspring must have the brachydactyly trait (figure 10.1). Since 75 percent of the population doesn't have brachydactyly, he claimed that Mendelian laws of genetics do not apply to people! Can you see what is wrong with his logic? The prediction of 75 percent brachydactyly only applies if two heterozygotes for brachydactyly have children, in which case the prediction is absolutely correct. Since most people do not have brachydactyly, most parents are normal and do not expect to have any brachydactyly children. The flaw in the logic was pointed out by an English mathematician, Godfrey H. Hardy, and by Wilhelm Weinberg, a German physician. Both provided the correct explanation as to why a dominant trait does not appear three times more frequently than a recessive trait in a population. Thus, predictions regarding genotype frequencies in populations is called the Hardy-Weinberg law. This law is useful for calculating approximate frequencies of genes and genotypes in populations.