Population Genetics
Useful Reading
Campbell, Biology 6th Ed - Chapter 23, pgs 445-463
Campbell, Biology 7th Ed - Chapter 23, pgs 454-471
Vocabulary
Evolution – changes in population allele frequencies over time. The population is the smallest unit which can evolve.
Population – any group of organisms coexisting at the same time and place that are capable of interbreeding with one another.
Gene Pool – all of the alleles at all loci in the population.
Natural Selection – differential survival and reproduction of individuals in a population due to trait differences.
Genetic Drift – changes in the gene pool of a small population due to chance. Random changes due to sampling errors in propagation of alleles.
Bottleneck Effect – population undergoes a drastic reduction in size as a result of chance events. A cause of genetic drift.
Founder Effect – a small group of individuals becomes separated from the larger population. A cause of genetic drift.
Gene flow – movement of genes between populations. Gain or loss of alleles from a population due to migration of fertile individuals, or from the transfer of gametes.
Allele fixation – when a gene has only one allele. When one allele of a gene becomes the only allele, while the alternatives are eliminated from the population.
Population Genetics
Population genetics is a useful tool for studying evolution and quantifying how evolution operates. It emphasizes counting allele and genotype frequencies to understand how phenotype frequencies in a population change over time.
Models can be built that incorporate the varied effects of selection, genetic drift, migration, etc. For example, with population genetics, you can ask:
How long would it take for a given allele to be fixed given a certain selective force for it?
How strong would migration of the alternative allele into the population have to be to counteract the effects of selection and maintain the alternative allele at the original frequency?
Hardy-Weinberg
The Hardy-Weinberg Theorem states that the allele frequencies of a gene in a population will remain constant, as long as evolutionary forces are not acting. H-W therefore provides a baseline (a null expectation) for a population that is not evolving. For a population to be in H-W equilibrium, the following conditions or assumptions must be met:
1. The population is very large; there is no genetic drift
2. Matings are random
3. There is no mutation
4. There is no migration
5. There is no selection
If one of these conditions is broken, an evolutionary force is acting to change allele frequencies, and the population may not be in H-W equilibrium. Natural populations probably seldom meet all of these conditions; H-W provides a nice model to study evolution via deviations from H-W equilibrium.
Hardy Weinberg Equation
Basic Relations
A = dominant
allele
a = recessive allele
p + q = 1
Where p = frequency of A allele
q = frequency of a allele
p2 +
2pq + q2 = 1
Where p2 = frequency of AA genotype
2pq = frequency of Aa genotype
q2 = frequency of aa genotype
Example Problem – when a population is in H-W
You are studying the gene that regulates interlocking fingers in a small isolated village with a population of 2500 individuals. It is already known that a dominant allele (F) causes one to interlock their fingers in such a way that the left thumb is nearly always on top, while a recessive allele (f) in the homozygous conditions results in the right thumb being on top. You have asked the entire village to gather at the town hall one Saturday afternoon so that you can run your experiment and collect the data all at once. After everyone is seated you ask them to each clasp their hand together in front of them, interlocking their fingers. Then you ask them to look down at their hands and note which thumb is on top. With the help of your trusty assistant, you are able to collect all the data that afternoon. Now your only job left is to calculate all the related frequencies and determine how many homozygous dominant and heterozygous individuals for your trait of interest are in this population.
Data
Collected: Left thumb over right = 2275 individuals = FF, Ff genotypes
Right thumb over left = 225 individuals = ff
genotype
1. Since there are 2500 individuals in the population, it is understood that there are 5000 alleles in the population.
2. Given the data and basic relations, the frequencies for the recessive genotype and allele can be calculated.
Recessive genotype frequency:
q2
= (ff)/(totalpop) = (225)/(2500) =
0.09 Right thumb over left
represent 9% of the population.
9% are homozygous
recessive = aa
Recessive allele frequency:
q = (q2)1/2 = (0.09)1/2 = 0.3 The frequency of the recessive (f) allele is 30%.
3. Now the frequencies for the dominant allele and homozygous dominant and heterozygous genotypes can be calculated.
Dominant allele frequency:
p = 1 - q = 1 - 0.3 = 0.7 The frequency of the dominant (F) allele is 70%.
Homozygous dominant genotype frequency:
p2 = (0.7)2 = 0.49
Heterozygous genotype frequency:
2pq =
2(0.07)(0.03) = 0.42
Left thumb over right represent 91% of the population.
49% are homozygous
dominant = AA
42% are
heterozygous = Aa
4. Finally the actual numbers of people that are homozygous dominant and heterozygous can be calculated.
Known: 225 individuals (9%) are homozygous recessive =
aa
49% are homozygous dominant = AA
42% are heterozygous = Aa
Number of homozygous dominant individuals:
(0.49)(2500) = 1225
Number of heterozygous individuals:
(0.42)(2500) = 1050
Testing and establishing Hardy-Weinberg equilibrium
We can test if populations are in H-W equilibrium by seeing if the genotypes match H-W predictions, given the allele frequencies (AA=p2, Aa=2pq, aa=q2).
For example, imagine we know that 4% of a population (4/100) has sickle-cell anemia (aa), 60% (60/100) are heterozygous for sickle-cells (Aa), and 36% (36/100) do not have the sickle-cell allele (AA).
If we do the calculations the way we did in the previous example:
1. Determine the allele frequencies:
q: q2 (aa freq) = .04 , p = (.04)1/2 = 0.2
p: p = 1-q = 0.8
2. Predict the genotype frequencies under H-W equilibrium
aa: q2 = 0.04
Aa: 2pq = 0.32
AA: p2 = 0.64
We see something is wrong – the predicted genotype frequencies do not match what we observed. The population must not be in H-W equilibrium!
To see why is happening, let’s actually count up the allele frequencies (we can do this because we know the frequency of the heterozygote) and see what the genotype frequencies should be. In our population of 100 individuals, there are 200 alleles.
1. Determine the true p and q by counting alleles:
q: all alleles in aa individuals and half of the alleles in Aa individuals
2 x 4 + 60 = 68 “a” alleles.
q = 68 / 200 = 0.34
p: all alleles in AA individuals and half of the alleles in Aa individuals
2 x 36 + 60 = 132
p = 132 / 200 = 0.66
2. Determine the expected genotype frequencies under H-W
AA: p2 = (0.66)2 = 0.44 or 44% of individuals (36% observed)
Aa: 2pq = 2(0.34)(0.66) = 0.45 or 45% of individuals (60% observed)
aa: q2 = (0.34)2 = 0.12 or 12% or individuals (4% observed)
Conclusion: there are more Aa individuals and fewer aa and AA than expected given the allele frequencies! Determining the frequency of “a” though (q2)1/2 led us to underestimate the frequency of the “a” allele, because there are more heterozygotes carrying “a” than a population in H-W equilibrium would have.
Given what we know about the selective advantage that Aa individuals have in resistance to malaria, perhaps this population is under selection for heterozygotes. One of the assumptions of H-W is broken (no selection).
To establish H-W equilibrium in the offspring of a population, only one generation of random-mating is needed (Note: if selection continues, the offspring will soon fall out of H-W equilibrium).
1. In the example above, we determined the allele frequencies in the population:
p = 0.34
q = 0.66 (see step 1 above)
2. After one generation of random mating, the genotype frequencies are given by the H-W equation (see step 2 above):
AA = p2 = 0.44
Aa = 2pq = 0.45
aa = q2 = 0.12
Forces of evolution / Violations of H-W assumptions
Genetic drift
Drift is important for small populations, where chance events may eliminate or change the frequency of alleles. Drift produces evolutionary change, but there is no guarantee that the new population will be more fit than the original one. Evolution by drift is aimless, not adaptive, because it is chance alone (not phenotype) which changes allele frequencies. Drift is common in two population events: Genetic bottlenecks and Founder events.
In bottlenecks, the population is vastly reduced in number (e.g. a hurricane kills most individuals in the population). It is completely arbitrary and unrelated to phenotype who lives (contributes to the future populations) and who dies. In your lab, you simulated bottlenecks by randomly pulling a few alleles from a bag. Most likely, the few alleles pulled from the pool will not represent the same allele frequency as in the bag. The population allele frequencies have changed!
In founder events, a few individuals leave the original population and found a new population (e.g. colonize an island). As with bottlenecks, the founders are likely not representative of the original population.
Under drift, the chance that an allele will be eliminated (lost) in the population is equal to its initial frequency. The chance that it will be fixed is equal to 1 – (initial frequency). The rate of change of gene frequency by random drift depends on the size of the population.
This figure shows the results of computer simulations of genetic drift in stoneflies. Both graphs had a starting population where the frequency of allele “A” was 0.5. Nine groups of stoneflies were allowed to “breed” randomly for 50 generations (in simulation). In the left graph, 25 flies bred in each generation. In roughly half of the groups, the A allele went extinct. In the other half, A was fixed. In the graph on the right, 500 flies bred in each generation. Although the frequency of A fluctuated over time, it had not become fixed or extinct in any line after 50 generations. This figure demonstrates 1) the chance of an allele becoming lost from the population is equal to its initial frequency, and 2) the larger the population size, the slower (weaker) drift is.
This figure shows the effect of population size, Ne, on the time for allele loss. Drift is stronger in smaller populations.
Gene flow
Gene flow occurs when alleles are exchanged between two populations. Gene flow occurs when individuals migrate (immigrate or emigrate) and breed in a new population (contributing their genes to that population). Gene flow can also occur through hybridization: when individuals from two separate populations (say, Pop A and Pop B) breed, their offspring carry genes from one population (Dad’s Pop A genes) into another (Pop B where the offspring lives). Gene flow increases the variability of the gene pool by adding new alleles.
Selection
If individuals having certain genes are better able to produce mature offspring than those without them, the frequency of those genes will increase. This is simply expressing Darwin's natural selection in terms of alterations in the gene pool. (Darwin knew nothing of genes.) Natural selection results from
1) differential mortality
and/or
2) differential fecundity
due to trait/phenotype differences.
Natural Selection is often used synonymously with Evolution; however, they have very different meanings. Here are some very important points about natural selection and evolution:
1)
Natural selection is a mechanism (differential reproductive success due to
traits)
2) Evolution is a process (change in allele frequencies over time)
3) Natural selection is one mechanism that can lead to evolution
4) Evolution can also be caused by all of the other forces mentioned here
(drift, migration, mutation, nonrandom mating)
5) Natural selection may not lead to evolution if the trait under selection
is not heritable.
No genetic component à
no evolution in response to selection
Although selection is not the only mechanism that can cause evolution, it is thought to be a major force of evolution and diversification. It is the only evolutionary force which can cause adaptive evolution. Evidence for the evolutionary effects of selection include:
1) Direct evidence: observation of allele / trait frequency change in response to natural and artificial selection. Examples include: moth melanism in England, selection for marbled meat in cows by agriculturalists.
2) Indirect evidence:
a) Adaptation of organisms to
their environment (form fits function), traits that are adaptively designed to
“solve a
problem”. Examples include: bugs that look like sticks cryptically avoid
predators, antelope
have long
legs to run fast.
b) Diversification of form / species to exploit new habitats or food. Examples include: Darwin’s Finches.
Nonrandom Mating
Nonrandom mating occurs when individuals have mating preferences rather than randomly mating with any other individual in the population. There are several ways nonrandom mating may occur:
1. Assortative mating – for example, when AA individuals preferentially mate with other AA individuals. This increases the probability that “A” gametes will combine with other “A” gametes, and decreases the probability of “A” combining with “a”. In humans, people often mate assortatively according to height (tall with tall, short with short).
2. Inbreeding – when close relatives mate.
3. Sexual selection. Female animals and plants frequently chose among many possible fathers for their offspring, selecting the father that has the best genes or is the best resource-provider. This increases the alleles contributing to the favored phenotype and decreases all alternative alleles.
Mutation
The frequency of “A” and “a” will not remain in Hardy-Weinberg equilibrium if the “A” mutates into “a” (or vice versa) or into any alternative alleles. By itself, this type of mutation probably plays only a minor role in evolution; the rates are simply too low. However, evolution depends on mutations because this is the only way that new alleles are created. After being shuffled in various combinations with the rest of the gene pool, these provide the raw material on which natural selection can act.
Good web resources:
Review Questions
- You surveyed 200 people for the presence of a widow's peak on their hairline. Widow's peak is due to the presence of a dominant gene, W. Suppose you obtained the following data:
Phenotype No. of people
Widow's peak 182
No widow's peak 18
1. Write out he
genotypes for each phenotype.
2. Calculate the frequency of each phenotype.
3. What is the frequency of the dominant allele?
4. What is the frequency of the recessive allele?
- If you had a widow's peak, how would you determine your exact genotype?
- How many generations of random-mating are needed for a population to be in H-W equilibrium?
- When trying to find allele frequencies, why do you focus on the homozygous recessive? Why can’t you use the individuals expressing the dominant trait to find the frequency of the dominant allele?
- In your lab experiments, why do you usually sample with replacement?
- If you sample 50 humans for the ability to taste PTC and get different allele frequencies than the known allele frequencies for the whole human population, what do you think is the cause? If a comet hit the earth and wiped out 99.9% of the human population, do you think the frequency of PTC tasters would remain the same? What is this process called?
- What are the conditions required for a population to be in H-W equilibrium?
- Explain the difference between natural selection and evolution.
- If you artificially selected flies for a trait whose variation was due entirely to environment (no genetic variation behind the trait), would the population evolve in response?
- How did drift, migration, and selection compare in their effect on your lab “populations” of beads? Did some forces have a stronger effect than others?