genetics

The fundamental information about genetics for any individual is her genotype — the alleles that she has. But genes in populations can be considered in other ways as well.

For instance, a population consists of individuals, so a geneticist may count the number of individuals with every possible genotype. Comparing these numbers with the total number of individuals, the geneticist may calculate the genotype frequencies, the proportion of individuals who have each possible genotype.

Cystic fibrosis (CF) is a very rare disorder. Among Americans of European ancestry, only around 1 in 2500 people will develop CF during her lifetime. The disorder is even rarer among people of non-European origin. Geneticists have surveyed many people to discover how many of them carry the disorder, and today a number of states screen newborns for cystic fibrosis as a way of directing affected children to early medical treatment (AAP Newborn Screening Task Force 2000). From this information, geneticists have determined that while only around 0.04 percent of the population is affected by cystic fibrosis, with a genotype of ff, approximately 2.5 percent of people are carriers of the allele, with a genotype of Ff. This leaves some 97.5 percent of the population with the genotype FF. These proportions are the frequencies of the three possible genotypes for this gene: 0.04% ff, 2.5% Ff and 97.5% FF.

The frequency of an allele is the proportion of copies of that allele compared to the total number of copies of all alleles in a population.

When geneticists know the frequencies of genotypes in a population, they can estimate how many copies of each allele are in the population as a whole. One recent study used genetic techniques to assess the genotypes of a group of colorectal cancer patients for the two possible alleles (A and B) of the p73 gene on chromosome 1 (Pfeifer et al. 2004). In this sample, 113 people (63 percent) were AA, 54 people (30 percent) were AB, and 12 people (7 percent) were BB. Each AA person has two copies of the A allele and each AB person has one copy, so the total sample included 280 copies of the A allele and 78 copies of the B allele. The allele frequency of the A allele is then 280/358, or 78 percent. The frequency of the B allele in this sample is 22 percent.

Hardy-Weinberg proportions

While geneticists can determine the frequency of an allele from the proportions of genotypes in a population, they may also do the same calculation in reverse — figuring out the expected proportions of genotypes from the frequencies of alleles. For example, if the cystic fibrosis f allele is found at a frequency of 5 percent in a population, then the chance that an individual will have two copies of this allele is simply the 5 percent chance for each of the two alleles, multiplied by each other. Five percent times five percent is 0.0025, which is 0.25% twenty-five chances out of 10,000.

The Hardy-Weinberg genotype proportions are p² + 2pq + q² for a two-allele gene.

The proportion of both homozygotes in the population may be determined in the same way. The probability that an individual will be a homozygote for either allele equals the frequency of the allele times itself, or squared. Thus, in the example above, the chance of f homozygotes is equal to the frequency of f squared. The proportion of heterozygotes is equal to the chance that one allele is F times the chance that the other allele is f, plus the chance that the first allele is f times the chance that the other allele is F. Since these likelihoods are the same, the total chance of an individual being a heterozygote is 2 times the frequency of one allele times the frequency of the other allele. Thus, the proportions of genotypes are p² and q² homozygotes, and 2pq heterozygotes.

These proportions are called the Hardy-Weinberg proportions, after the British mathematician G. H. Hardy and German physician Wilhelm Weinberg, who independently formulated the relation in 1908. The proportions come from simple probability of sampling copies from a population with given allele frequencies. These proportions are expected to form an equilibrium. That is, they should stay the same over time, as long as the allele frequencies stay the same. When individuals mate without regard to the alleles they carry, every generation of a population should have genotype frequencies in approximately the Hardy-Weinberg proportions.

The Hardy-Weinberg proportion is important for two reasons. First, the proportions of genotypes in a population may diverge from the expected ones for many reasons, including natural selection, division of populations into different subgroups, or mating that is not entirely random. Comparing the expected and observed proportions of genotypes allows biologists to determine whether these evolutionary forces may be contributing to a population.

The heterozygosity of a population is the expected proportions of heterozygotes, given the allele frequencies in the population.

Second, the proportions lead to a natural definition of genetic variation in a population: the heterozygosity. A population's heterozygosity is the expected proportion of heterozygotes from the Hardy-Weinberg formula, 2pq. Two populations may be compared by their heterozygosities: the one with the higher heterozygosity has a higher chance that any single individual will have two different alleles, which means the population is genetically more variable. Variation is a consequence of evolutionary history, including the patterns of selection and genetic drift, and the amount that individuals have moved from one population to another in the past. Thus, the Hardy-Weinberg proportions give an important way to study the evolution of populations over time.

Tall people tend to have tall parents. The height of the body, called stature, is one of the most obvious phenotypic traits in human populations. Anyone who knows very many families can see that some families tend to have a lot of tall members, and others tend to be relatively short.

Still, there is more to being tall than having tall parents. A child may grow to be taller than either of his parents, sometimes much taller. A very tall father and short mother don't always have children that are in between their statures: sometimes a daughter may match her mother's height, or even be shorter. Relatives resemble each other in height, but we cannot say that a woman's stature is determined by the statures of her parents.

There are two key reasons why most phenotypes are not inherited as simple Mendelian traits. Many traits are affected not by one, but by multiple genes. At present, more than 300 genes are known to influence the variation in stature within populations of European ancestry. Other genes may be responsible for differences within other populations and between very different populations such as the short-statured Biaka Pygmies and tall-statured Dinka of equatorial Africa. The combination of so many genes helps to explain why stature is not a Mendelian trait with only two or three distinct forms. Instead, stature is a \term{continuous} trait, in which a person may be 62 inches tall, 61.5 inches, 61.25 inches, 61.0003 inches, or any measurable value in between.

Another reason for variation is that different people may have experienced different environments. The effects of environmental variation are plain in many fields of corn. The corn plants in a single field generally have very little genetic variation: they are hybrids bred for their high yields with adequate fertilizer, pesticide, and water. But many fields have low spots where water pools, or drier spots on the edge of the field. Here, the plants do not grow as tall or yield as much, because their environment is not ideal for high yield by the planted strain. The variation in plant height visible in such fields is entirely the result of environmental variation, because the plants are genetically uniform.

Environmental variation may come in at many points during an individual's life, from early embryonic development to childhood nutrition and disease. At all stages, this environmental variation can have a major effect on some phenotypes --- sometimes more extensive than variation in genes.

\begin{figure}
\includegraphics[width=\textwidth]{female_stature_heritability.png}
\label{fig:female_stature_heritability}
\caption[Female stature heritability]{Relationship of student stature to midparent stature in a sample of 100 female college students. The midparent stature is the average of the mother's and father's heights. Taller parents tend to have taller offspring, although some women are taller than the average of their parents, and others are shorter. The slope of the line relating the two reflects the heritability of stature in the sample, which for these students is estimated at 0.89. }
\end{figure}

For a phenotype like stature, it can be important to know how much of the variation results from genetic variation, and how much of the variation results from the environment. This is important because genetic changes can affect a phenotype only to the degree that the phenotypic variation is influenced by those genes. Geneticists also want to discover if phenotypic similarities among people are the result of shared alleles, or whether instead they are the effect of shared environments. The concept that relates genetic variation and phenotypic variation is called \term{heritability}, which is the proportion of phenotypic variation that can be explained by genetic variation in the population (Falconer and Mackay 1996). Because it is a proportion, heritability varies between 0 and 1.

Phenotypic traits with heritabilities near zero are very weakly affected by genetic variation, while heritabilities near 1 indicate a very strong genetic influence. Very different traits can have similar heritabilities. For example, near-sighted, or myopic, parents are substantially more likely to have children with myopia. In Western populations, genetic variation accounts for more than 80 percent of the variation in juvenile-onset myopia (Gilmartin 2004). Likewise, variation in the many genes that influence stature accounts for approximately 80 percent of the phenotypic variation in stature, at least in Western societies with relatively stable childhood nutrition (Silventoinen 2003). Some human traits have heritabilities very near 1. One example is the mass of the brain, which has a heritability of approximately 0.94 (Bartley et al. 1997).