Population Genetics

A gene pool is every copy of every allele in a population. In DNA and Genetics you followed one family through a Punnett square. Here we count a whole population at once.

Take one gene with two alleles, A and a. Each person carries two copies, so a population of 100 holds 200 copies. If 60 of those copies are a, the allele frequency of a is 60 ÷ 200 = 0.3. We call it q, and the frequency of A is p. Since every copy is one or the other, p + q = 1.

Genotype frequencies count people instead of copies: the share who are AA, Aa or aa. They add up to 1 as well.

In 1908 a British mathematician, G. H. Hardy, and a German physician, Wilhelm Weinberg, each showed independently that in a large, randomly mating population the frequencies of alleles tend to stay the same from one generation to the next unless outside forces act on them (see Britannica). In this way even the rarest alleles are kept rather than dying out (see Britannica).

If alleles combine at random, the chance of AA is p × p, of aa is q × q, and of Aa is 2pq, since a child can get A from either parent. So the genotype frequencies are

p² + 2pq + q² = 1

The law holds only if five conditions are met (see Britannica):

1. The population is very large, so chance does not shift frequencies.
2. Mating is random.
3. There is no natural selection.
4. There is no mutation.
5. There is no migration in or out, which is to say no gene flow.

Real populations never meet all five. That is the point: if measured frequencies drift away from p², 2pq and q², one of these forces is at work. Medical geneticists also use the law to estimate how many people carry a recessive allele (see Britannica).

Worked example. About 1 in 400 Black people worldwide has sickle cell anemia, which needs two copies of the HbS allele (see Britannica). So q² = 1 ÷ 400 = 0.0025, and q = √0.0025 = 0.05. Then p = 1 − 0.05 = 0.95, and carriers make up 2pq = 2 × 0.95 × 0.05 = 0.095, about 1 in 11. Britannica gives about 1 in 12 as carriers (see Britannica). The two are close but not identical: Hardy-Weinberg gives an idealized estimate, and real populations break its conditions, here through selection, as section 5 shows, and through mixing between groups.

Genetic drift is change in a gene pool by chance alone. The alleles passed to the next generation are a sample of the parents' alleles, and a small sample can be far from typical. The smaller the population, the bigger the swings. Drift can make an allele common or wipe it out whether it helps survival or not; once only one allele is left, that allele is fixed (see Britannica). The Evolution simulator showed drift as a wobble on top of selection. Here it is on its own.

Bottlenecks. When a population crashes, the survivors carry only part of the old gene pool. Northern elephant seals fell to 20 to 100 animals in the 1890s, and now number over 175,000. Old museum seals from before the crash had four mitochondrial DNA types in just five animals, but more than 150 seals from 1892 on have only two (see Weber and others).

Founder effect. When a few people start a new, closed population, their alleles become that population's gene pool. Ellis-van Creveld syndrome, a recessive condition causing short limbs, extra fingers and heart defects, affects about 1 in 60,000 to 200,000 newborns in most places (see MedlinePlus). It is far more common among the Old Order Amish of Lancaster County, Pennsylvania, where the parents of nearly all early cases trace back to one immigrant couple from the mid-1700s (see Alahmadi and Sharma).

Besides drift, three outside forces break the Hardy-Weinberg balance: selection, mutation and migration (see Britannica).

• Gene flow is migration of alleles, as when individuals or pollen move between populations. It makes neighbouring gene pools more alike.
• Mutation makes new alleles. DNA and Genetics shows how a single base change does it.
• Natural selection changes frequencies when one genotype leaves more offspring than another. Over many generations the alleles it favours become commoner (see Britannica).

Drift and selection can work together. Fisher, Haldane and Wright each built mathematical arguments using mutation rates, population size and patterns of reproduction to tie Darwin's selection to Mendel's genes (see Britannica).

Sickle cell anemia comes from a variant hemoglobin, HbS. People with two copies have red cells that bend into stiff sickles when oxygen is low and block small blood vessels. People with one copy carry the sickle cell trait and mostly have no symptoms (see Britannica).

So why is a harmful allele common in a broad belt across Africa? Carriers resist malaria. When a malaria parasite invades a carrier's red cell, the cell sickles and is destroyed, and the parasite with it (see Britannica). Where malaria is common, carriers survive better than people with no HbS, while people with two copies suffer from the disease. This is heterozygote advantage: selection favours the Aa genotype, so both alleles stay in the gene pool. Anthony Allison reported this protection in 1954 (see Allison).

The field began with two short papers and grew into the maths behind modern evolution.