AP Biology · Natural Selection · free lesson

Population Genetics

The idea, then worked examples solved step by step, then practice questions whose numbers change every time you try them.

The idea

Population genetics: evolution as a change in allele frequencies

Population genetics is the study of how forces change the allele frequencies in a population over time. A population here means the members of one species living in the same place. The gene pool is the sum of all the alleles in that population, and the allele frequency of one allele is the number of copies of it divided by all the copies of that gene in the population. Picture a jar of marbles: each marble is one copy of a gene, and the allele frequency is the share of the marbles that are one color.

Evolution, in population genetics, is a change in the frequency of an allele in a population. That is the whole definition, and it brings a first misconception to drop: an individual does not evolve. Your genotype does not change to suit your surroundings in your lifetime; what changes, from one generation to the next, is the mix of alleles in the gene pool of the whole population.

Here is a count. A population of 50 plants has 20 with genotype AA, 20 with Aa and 10 with aa. Each plant carries two copies of the gene, so the gene pool holds 100 copies; the script counts them.

Of the 100 copies, 60 are A, so the frequency of A is 0.6 (call it p) and the frequency of a is 0.4 (call it q). With two alleles, p and q together make 1. If the next generation shows p = 0.5, then the population has evolved, whatever the cause. A change in allele frequencies is evidence that evolution has occurred in a population. Natural selection is one force that can cause it. The others in this topic are random: mutation, genetic drift (with its two special cases, the bottleneck effect and the founder effect), and gene flow.

Mutation: new variation, made by chance

A mutation is a change in DNA. Mutation is a random process that adds new genetic variation to a population: a new allele can appear that no member carried before. Random here means chance, not aimed. A mutation does not appear because the organism needs it, and the environment does not steer which mutations arise. Mutation does something else of great importance: it makes the raw material. Mutations result in genetic variation, which provides phenotypes on which natural selection acts. Selection sorts among the alleles and phenotypes that exist, and mutation is the ultimate source of new ones.

Genetic drift: chance in who has offspring

Natural selection means that some individuals leave more offspring because of an inherited trait. Genetic drift is a change in allele frequencies that comes from chance instead: a nonselective process. By chance, some individuals have more offspring than others, not because of an advantage from some genetically encoded trait, but because one happened to be in the right place at the right time, and another was in the wrong place when a fox was hunting.

The effect of chance depends on the size of the population. Take a population of 10 individuals. If one dies young before it has offspring, all of its genes, one tenth of the gene pool, are suddenly lost. In a population of 100 the same death removes just one percent. So small populations are more affected by genetic drift, and in large populations its effect is much weaker. Think of tossing a coin: ten tosses often give a split such as 7 heads to 3 tails, while ten thousand tosses stay very close to half and half.

The graph shows that idea. Each line follows the frequency of one allele over 30 generations in a population that starts at 0.5, where each new generation is a random draw of alleles from the one before. No allele is better than the other in this model; the gold lines come from populations of 10 individuals and the blue lines from populations of 250.

The blue lines (large populations) wander a little around 0.5. The gold lines (small populations) swing widely, and a line that reaches 0 or 1 stays there: that allele was eliminated by chance or, for the other allele, is now carried by all the members. Genetic drift can eliminate an allele from a population by chance, and because the lines of different small populations go different ways, it can also lead the populations of one species to diverge from each other.

Warning.

Drift does not favor the fitter. An allele can rise or vanish through drift even if it helps survival, and drift has no direction. Selection, by contrast, tends to push an allele the same way in each generation.

The bottleneck effect: a disaster that samples at random

The bottleneck effect is a type of genetic drift. It occurs when the population size is reduced to a small number of individuals for at least one generation, for example by a natural disaster that kills a large portion of the population at random. The survivors are a small, chance sample of the original population, and their genetic structure becomes the genetic structure of the whole population as it recovers. That structure may be very different from the one before the disaster, and variation is usually lost. In the picture, each circle is one copy of the gene, with its color showing which of two alleles it is, so two copies stand for one diploid individual. The script counts the colors.

The disaster did not target the gold allele, yet its frequency moved from 0.3 to 0.5, a change from chance alone. Had the two surviving individuals (four copies) all carried blue, the gold allele would have disappeared from the population. The same bottleneck, repeated on the same population, would give a different result each time.

The founder effect: a small group starts a new population

The founder effect is a type of genetic drift that occurs when a population is separated from other members of the population, as when a few individuals leave to start a new population in a new place or a physical barrier divides a population. These founders are unlikely to be representative of the whole, so the frequency of genes and traits in the new population shifts to match the genes the founders happened to carry. A real case: the Afrikaner population of Dutch settlers in South Africa shows unusually high rates of Huntington's disease and Fanconi anemia, attributed to a higher-than-normal share of the founding colonists carrying those alleles.

Both effects are drift, and both come from a small sample of the original gene pool. In a bottleneck the sample is the survivors of a disaster in the same place; in the founder effect the sample is the group that leaves or is cut off. In both, the sample need not be typical of the whole.

Gene flow: alleles move between populations

Migration can result in gene flow, the addition or removal of alleles from a population. When individuals move in, or pollen or other gametes arrive from another population of the species, the arriving alleles are added; when individuals leave, their alleles are removed. Gene flow can bring new genetic variation into a population, and so can mutation, though by a different route: mutation makes an allele new to the species, while gene flow brings in one that already exists elsewhere.

Gene flow and drift pull in opposite directions. Genetic drift can allow a small population to diverge from other populations of the same species, since each small population drifts by chance on its own. Gene flow between two populations prevents them from diverging into separate species, because the exchange keeps their gene pools alike. The more gene flow, the less the divergence.

Random processes in specific populations

Put together, random occurrences change real populations in these ways. Mutation adds a new allele and so supplies new phenotypes for selection to act on. Drift, the bottleneck effect and the founder effect change allele frequencies by chance, most strongly when the population is small. Migration moves alleles between populations. Natural populations are constantly changing in genetic makeup because of drift, mutation, possibly migration, and selection. Drift and mutation are not aimed at any goal, and they need not make a population better adapted; natural selection is the process that tends to do that.

Warning.

Four traps to leave behind. First, individuals do not evolve; populations do. Second, mutations are not caused by need: a population does not mutate because it would benefit. Third, drift is not selection; a chance change can lower the frequency of a helpful allele. Fourth, a bottleneck and the founder effect are different events: one is a drop in the size of a population in place; the other is a new population begun by a small group that is separated from the rest, whether by leaving or by a barrier that divides the population.

Adapted from Biology by OpenStax (Rice University), licensed under CC BY 4.0. Access for free at https://openstax.org/details/books/biology

Worked examples

Each example is the kind of question the AP exam asks on this topic, worked the way a teacher would talk it through.

Example.

1. Did the population evolve? In one generation a population of 100 beetles has 30 with genotype BB, 40 with Bb and 30 with bb. Ten generations later the population is 200 beetles, with 20 BB, 60 Bb and 120 bb. Find the frequency of the B allele in each generation and say whether the population evolved.

The allele frequency is the copies of the allele divided by all the copies of the gene. Each beetle carries two copies, and each BB beetle has two copies of B while each Bb beetle has one. The script gives 200 copies in the first generation and 100 of them are B, so the frequency of B is 0.5.
In the later generation there are 400 copies and 100 are B, so the frequency of B is 0.25.
The frequency of B fell from 0.5 to 0.25. A change in allele frequencies in a population is evidence that evolution has occurred.

Result.

The frequency of B fell from 0.5 to 0.25, so the population evolved. The data do not say why; selection, drift, mutation or gene flow could each produce such a change.

Example.

2. A bottleneck and a rare allele. A large population of snails carries a rare allele at a frequency of 0.2. A flood kills most of the snails at random and leaves 10 survivors, which then breed. Each of the 10 snails carries two copies of the gene, so the survivors hold 20 copies. Treat each copy as an independent draw from the old gene pool. What is the chance that the rare allele is absent from the survivors, and what does that show about the bottleneck effect?

The flood kills at random, so it does not pick out snails by their alleles. The survivors are a small chance sample of the gene pool, and each of their 20 copies is the rare allele with probability 0.2.
On average the survivors carry the script's 4 copies of the rare allele, so the expected frequency in the survivors, 4 of 20, matches the old frequency of 0.2. Chance alone, however, can move a small sample away from the average.
The chance that a copy is not the rare allele is 1 - 0.2 = 0.8, so the chance that not one of the 20 is the rare allele is 0.8 raised to the power 20, about 0.0115 in the script, near one chance in 87.
So the rare allele is usually still present, but often at a frequency that is not 0.2, and now and then it is lost altogether. Any allele lost this way is gone from the population, which has lost variation, even though the flood did not "choose" it.

Result.

About a 1 percent chance of losing the rare allele outright; more often its frequency simply shifts by chance. The bottleneck effect is genetic drift magnified by a drop in population size.

Example.

3. Reading a drift experiment. A student simulates two populations of the same species, each starting with the two alleles of a gene at a frequency of 0.5 each. No allele is favored. One population has 10 individuals and the other has 250. She follows the allele frequency for 30 generations. Which population probably shows the larger swings in allele frequency, and why? What does the simulation predict if the experiment is repeated?

In the graph the gold line is the population of 10 and the blue line is the population of 250. The script gives the final frequency of each at generation 30.
The population of 10 swings much more. When a population is small, the chance that a few individuals leave more offspring, or no offspring, moves the allele frequencies a lot. In a large population genetic drift has a much weaker effect, because each individual is a small share of the gene pool.
No allele is favored, so selection cannot explain the swings; they are genetic drift, a change in allele frequencies from a nonselective process.
If the experiment is repeated, the prediction is that the blue lines stay close together near 0.5, while the gold lines go different ways each time. Small populations of one species can therefore diverge from each other by drift alone.

Result.

The population of 10 changes more, by genetic drift; repeats would give different paths for small populations and similar paths for large ones.

Example.

4. Gene flow between two populations. On an island the allele R has a frequency of 0.2 among 200 copies of a gene. Migrants arrive from the mainland and add 50 copies, of which the frequency of R is 0.8. After the migrants breed with the residents, what is the frequency of R on the island? Is the island population now more like the mainland population or less?

Count the copies of R. The residents hold 40 and the migrants bring 40, so the island now has the script's 80 copies of R among 250 copies in all.
The new frequency is 80 out of 250, which is 0.32.
Before the migrants came, the two populations differed by 0.6 in the frequency of R. Now they differ by 0.48, so the island population is more like the mainland population.

Result.

The frequency of R rises from 0.2 to 0.32. Gene flow moves the populations toward each other; steady gene flow between two populations prevents them from diverging into separate species.

Example.

5. Which process is it? For each case, name the process that explains the change in allele frequencies. (a) A single new allele for a fur color appears in a lizard's egg, a color no lizard in the population has carried. (b) A storm kills most of the mice on a small island at random; the few survivors carry a different mix of alleles from the original population. (c) Six birds are blown to an island, and the island's population later shows an allele that was rare on the mainland at a high frequency. (d) Pollen from a distant meadow of the same species fertilizes flowers in a field, adding alleles that the field's plants lacked.

Case (a) is mutation. It is a random process that adds new genetic variation, an allele the population did not have. Mutation, not any outside source, made it.
Case (b) is the bottleneck effect, a type of genetic drift: the population size was reduced to a small number of individuals, and the survivors were a chance sample.
Case (c) is the founder effect, a type of genetic drift: a few individuals separated from the rest of the species, and the new population's frequencies follow the genes those founders carried.
Case (d) is gene flow. Migration, here of gametes, added alleles to a population.

Result.

(a) mutation, (b) bottleneck effect, (c) founder effect, (d) gene flow. In (b) the size of the existing population fell; in (c) a new population began from a small group that was separated from the rest, here by leaving.

Practice

Answer AP-style questions on population genetics. Each answer is checked, with the full solution, and every try brings new numbers. Practice needs a free account: it keeps your progress.

Practise population genetics with new numbers