Variation and Selection

Lessons

Senior 6 · Biology

Variation and Selection

5 lessons

Lesson 5 of 5

Gene pools, genetic drift, the founder effect and the Hardy-Weinberg principle

35 min

Counting alleles, not individuals

In the 1890s, hunting for their oil had reduced northern elephant seals to a few dozen animals, perhaps fewer, on one island off Mexico. Once protected, they recovered to well over a hundred thousand. Yet when biologists examined their DNA, they found almost no genetic variation: the seals alive today descend from the few that survived, and most of the alleles of the original population were lost for ever. Nothing about the lost alleles made them worse; they disappeared by chance. To understand events like this, and to measure evolution at all, we need to think about populations in terms of their alleles. This lesson introduces the gene pool, the random process of genetic drift, and the Hardy-Weinberg principle, which describes a population that is not evolving.

Definition

Population: a group of organisms of the same species living in the same area at the same time, which can interbreed.

Gene pool: all the alleles of all the genes in a population at a given time.

Allele frequency: the proportion of all the copies of a gene in a population that are one particular allele, from 0 to 1.

Genetic drift: random change in allele frequencies from one generation to the next, caused by chance in which individuals survive and reproduce and which alleles they pass on.

Bottleneck effect: loss of genetic variation when a population is reduced to a few individuals.

Founder effect: the difference in allele frequencies between a new population started by a few individuals and the population they came from.

Hardy-Weinberg principle: in a large, randomly mating population with no mutation, migration or selection, allele and genotype frequencies stay the same from generation to generation.

Allele frequencies

Each diploid individual carries two copies of each gene, so a population of $N$ individuals has $2 N$ copies. For a gene with alleles A and a, the frequency of A is

p = \frac{2 \times (\text{number of AA}) + (\text{number of Aa})}{2N}

and the frequency of a is $q = 1 - p$ . Evolution, in its simplest sense, is a change in allele frequencies in a population over time. Four processes cause it: natural selection (lesson 3), genetic drift, migration (gene flow) and mutation.

Genetic drift

In every generation, chance decides which individuals happen to reproduce and which of each parent's two alleles goes into each successful gamete. In a large population these chance effects nearly cancel out. In a small population they do not: allele frequencies wander randomly, and an allele can be lost (frequency 0) or fixed (frequency 1) within a few generations, whether it is useful, harmful or neutral.

Drift matters most in two situations:

Bottlenecks. When disease, hunting, drought or habitat loss reduces a population to a few individuals, the survivors carry only a small, random sample of the original alleles. Even if numbers recover, the lost variation does not return, except slowly by mutation. The elephant seals are an example, and many endangered species, which survive only in small, isolated populations, are losing variation by drift today.
The founder effect. When a few individuals start a new population, for example on an island or in a new settlement, their alleles are a chance sample of the source population. A rare allele carried by one founder can become common in the new population. Among the Old Order Amish of Lancaster County in Pennsylvania, USA, a community descended from a small group of eighteenth-century settlers who mostly married within the community, a rare recessive form of dwarfism with extra fingers (Ellis-van Creveld syndrome) is far more common than in the general population.

The Hardy-Weinberg principle

In 1908 Godfrey Hardy, a mathematician, and Wilhelm Weinberg, a physician, independently showed what happens to allele frequencies if nothing causes evolution. If the frequency of allele A is $p$ and of allele a is $q$ , then

p + q = 1

With random mating, the chance of a zygote receiving A from both parents is $p \times p$ , and so on, giving the genotype frequencies:

p^{2} + 2pq + q^{2} = 1

where $p^{2}$ is the frequency of AA, $2 p q$ of Aa and $q^{2}$ of aa. These frequencies stay the same generation after generation, provided that:

the population is very large, so there is no genetic drift;
mating is random;
there is no mutation;
there is no migration into or out of the population;
there is no selection: all genotypes survive and reproduce equally well.

No real population meets all of these conditions, which is exactly why the principle is useful. It gives a baseline: if observed genotype frequencies differ significantly from the Hardy-Weinberg expectation, at least one of the conditions is being broken, and the population may be evolving. It also lets us estimate how many people carry a recessive allele, which cannot be seen in their phenotype.

Worked example 1: is a population in equilibrium?

The MN blood group is controlled by two codominant alleles, M and N, so every genotype can be identified. In a sample of 500 people (illustrative data), 160 are MM, 230 are MN and 110 are NN. (a) Calculate the allele frequencies. (b) Calculate the genotype numbers expected under Hardy-Weinberg equilibrium and compare.

(a) Copies of M: $2 \times 160 + 230 = 550$ out of $2 \times 500 = 1\,000$ . So $p = 0.55$ and $q = 1 - 0.55 = 0.45$ .
(b) Expected MM: $p^{2} \times 500 = 0.3025 \times 500 = 151$ . Expected MN: $2pq \times 500 = 0.495 \times 500 = 248$ (to the nearest whole number). Expected NN: $q^{2} \times 500 = 0.2025 \times 500 = 101$ .
Observed 160, 230, 110 against expected 151, 248, 101: there are slightly fewer heterozygotes than expected.

Interpretation. The differences are small. A chi-squared test would show whether they are larger than chance would explain. If they were significant, a shortage of heterozygotes would suggest that mating is not random, for example because people tend to marry within small communities.

Worked example 2: how many carriers?

Illustrative value. In a population, 1 baby in 10 000 is born with a recessive genetic disorder. Assuming Hardy-Weinberg equilibrium, estimate the proportion of people who are carriers.

Affected people are aa: $q^{2} = \frac{1}{10\,000} = 0.0001$ , so $q = \sqrt{0.0001} = 0.01$ .
$p = 1 - 0.01 = 0.99$ .
Carriers are Aa: $2pq = 2 \times 0.99 \times 0.01 = 0.0198$ , about 1 person in 50.

Interpretation. There are $\frac{0.0198}{0.0001} = 198$ carriers for every affected person. Most copies of a rare recessive allele are hidden in healthy heterozygotes, where selection cannot act on them, which is why harmful recessive alleles persist in populations and why marriages between relatives raise the risk of affected children.

The founder effect, step by step

The founders' allele frequencies are set by chance, not by fitness, and drift continues while the new population is small. Founder populations therefore often differ from their source populations in the frequencies of particular alleles, including those for some genetic disorders.

Warning

Common mistakes

Using $q^{2}$ for carriers. $q^{2}$ is the frequency of homozygous recessive individuals; carriers are $2 p q$ ; $q$ is the frequency of the allele.
Taking $q$ straight from the proportion showing the dominant phenotype. Dominant phenotypes include both AA and Aa, so start from the recessive phenotype, $q^{2}$ , and take the square root.
"Drift only removes harmful alleles." Drift is random: it can fix harmful alleles and lose useful ones, especially in small populations.
"Dominant alleles become more common." Dominance does not change allele frequency; without selection or drift, a dominant allele can stay rare.

Amoeba Sisters: "Genetic Drift". Watch for the bottleneck and founder effects and why small populations are more affected by chance.

✦

Practice: gene pools and Hardy-Weinberg

Define (a) gene pool, (b) allele frequency.
In a population of 200 plants, 72 are RR, 96 are Rr and 32 are rr. Calculate the frequencies of R and r.
State the five conditions under which Hardy-Weinberg equilibrium holds.
In a population, 4% of people show a recessive characteristic. Calculate the percentage of (a) carriers, (b) homozygous dominant people.
Explain why genetic drift has a larger effect in small populations.
Distinguish between the bottleneck effect and the founder effect.
A rare allele has a frequency of 0.001 in a large population. A new island population is founded by 20 people, one of whom is heterozygous for it. Calculate the allele's frequency among the founders, and how many times greater it is.
Explain why conservation biologists try to keep endangered populations large and connected, rather than in small isolated reserves.

Show answersHide answers

(a) All the alleles of all the genes in a population at a given time. (b) The proportion of all copies of a gene in a population that are a particular allele.
R: $\frac{2 \times 72 + 96}{400} = \frac{240}{400} = 0.6$ ; r: $1 - 0.6 = 0.4$ .
Very large population (no drift); random mating; no mutation; no migration; no selection.
$q^{2} = 0.04$ , so $q = 0.2$ and $p = 0.8$ . (a) $2pq = 2 \times 0.8 \times 0.2 = 0.32$ , 32%. (b) $p^{2} = 0.64$ , 64%.
Each generation carries only a small sample of the parents' alleles; in a small sample, chance differences make up a large proportion, so frequencies change more, and alleles are fixed or lost quickly. In a large population, chance effects average out.
Bottleneck: an existing population is drastically reduced in size, and the survivors carry a random subset of its alleles. Founder effect: a few individuals leave to found a new population elsewhere, carrying a random subset of the source population's alleles. Both reduce variation and change frequencies by chance.
20 people carry 40 copies; 1 is the rare allele: $\frac{1}{40} = 0.025$ . $\frac{0.025}{0.001} = 25$ times greater.
Small, isolated populations lose genetic variation by drift and inbreeding, so they become less able to adapt to disease or change. Large, connected populations keep their variation, and gene flow between them replaces alleles lost by drift.

Key points

A gene pool is all the alleles in a population; evolution is a change in allele frequencies, caused by selection, drift, migration and mutation.
Genetic drift is random change in allele frequency, strongest in small populations; it can fix or lose alleles regardless of fitness.
Bottlenecks and founder effects reduce variation and change allele frequencies by chance.
Hardy-Weinberg: $p + q = 1$ and $p^{2} + 2pq + q^{2} = 1$ , in a large, randomly mating population with no mutation, migration or selection.
Use $q^{2}$ (recessive phenotype) to find $q$ , then carriers $= 2 p q$ .

1Counting alleles, not individuals

2Allele frequencies

3Genetic drift

4The Hardy-Weinberg principle

5The founder effect, step by step

Counting alleles, not individuals

Allele frequencies

Genetic drift

The Hardy-Weinberg principle

The founder effect, step by step