Mendelism

Let's say you do a cross of a white pea plant with a purple pea plant. In the F2 generation, you get 78 plants with purple flowers, and 27 plants with white flowers. The ratio of purple to white in this cross is 2.89:1. This is not exactly the 3:1 ratio predicted by Mendel, but is it close enough that we can consider it a 3:1 ratio? This question is answered by doing a chi-square test. The chi-square test determines whether the difference between what we expect and what we observe is small enough to allow us to conclude that we observed what we expected. To calculate the chi-square (X²) value, take each phenotypic class, subtract the expected number from the observed number, square the result, and divide by the expected number. Then add together the results for all of the phenotypic classes, and the total is the chi-square value. This may seem confusing, but it's fairly straightforward once you become familiar with it. To illustrate, let's use the example above. We got 105 flowers in the F2 generation. For a perfect 3:1 ratio, we would expect to see 78.75 purple-flowered plants and 26.25 white-flowered plants. The chisquare calculation therefore becomes:

So what does this number tell us? You look up a table of chi-square values (such as the one on p. 271 of your textbook), and select the appropriate degrees of freedom. The number of degrees of freedom is one less than the number of phenotypic classes. We have two phenotypic classes, so the degrees of freedom in this case would be 1. Compare the calculated chi-square value to the "critical value" for one degree of freedom, and if the chi-square is less than the critical value, then we can accept the observed ratio as being close enough to the expected ratio. In our example, the critical value is 3.841. 0.02854 is clearly less than that, so our observed F2 ratio is close enough to 3:1 that we can say it is effectively 3:1.

How can we apply the rules of Mendelian inheritance to humans? It is impossible, for ethical reasons, to do crosses using human subjects. It would also take at nearly 40 years, maybe longer, to take the cross through to the F2 generation!

Human genetics is studied by doing something called pedigree analysis. A pedigree is like a family history of a genetic trait. For a particular trait, the phenotypes of as many family members as possible are recorded and the relationships of those family members are also documented. This is like recreating the results of a series of genetic crosses begun generations ago. By looking at the prevalence of a trait in a family, and its pattern of inheritance, it is often possible to determine the mode of inheritance of a trait (in other words, how the trait is passed from one generation to another).

Pedigrees are generally presented diagrammatically, using several conventions that allow them to be easily understood. For example, males are portrayed as squares while females are represented by circles. As shown in the diagram below, a horizontal line directly connecting a male and female indicates a mating. A vertical line is used to connect the parents to their offspring. Roman numerals (like those shown in the left column of the diagram) are used to indicate different generations of the family, and arabic numerals (like those along the bottom) are used to indicate different individuals within each generation.

Individuals in a pedigree that exhibit the phenotype of interest are indicated by a shaded (or sometimes colored) symbol. In the pedigree below, for example, the male in generation I, both females in generation II, and two of the three in generation III exhibit the phenotypic trait of interest. This type of pattern, with individuals exhibiting the trait in every generation, is representative of a dominant trait.

In the pedigree below, the male in generation I and the female in generation III exhibit the phenotypic trait . This pattern of inheritance, where few individuals exhibit the trait, and the trait often skips a generation, is typical of a recessive trait. If this pedigree represented albinism, for example, then the two shaded individuals would be albino, whereas the unshaded symbols would represent normally pigmented individuals.

In this pedigree, we can't tell for sure in some cases whether an individual with the dominant phenotype is homozygous or heterozygous. The parents of the children in generation III must both be heterozygous, because one of their children is homozygous recessive. The other female in generation II must also be heterozygous, because her father is homozygous recessive, and can therefore only pass on a recessive allele. But what about the males in generation III? Are they homozygous or heterozygous? We can't tell, because they have no offspring listed. This illustrates one property of pedigree analysis: in a sense pedigrees are worked out by working backwards, because we often determine the genotype of an individual by examining the phenotypes of their children. Regarding the males in generation III, even though we can't say for sure what their phenotype is, we can work out probabilities. As already mentioned, both of their parents are heterozygous. They obviously got a dominant allele from one parent, but what did they get from the other parent? For each, there is a 50% chance that he got a dominant allele and a 50% that he got a recessive allele.