Introduction to Population Genetics Flashcards
Genotypes and the Hardy-Weinberg Equilibrium
Terminology reminder
A sexual, diploid organism has two alleles at each locus
One inherited from its mother, and one from its father
Locus: a position within the genome – like an ‘address’
Allele: the DNA at that locus, and there can be many alleles at a given locus (variation among individuals within a population)
Genetic variation within and among populations is the basis of evolutionary change
In asexual populations genetic change is reflected in ‘lineages’ that may survive or go to extinction.
In sexual populations diversity is spread out among individuals in the population according to the rules of Mendelian segregation
Greater potential for variation in sexual reproduction due to recombination. Variation only occurs in asexual organisms due to mutation
DNA sequence comparisons reveal a great deal of variation among individuals
what evolutionary forces could have led to so much divergence among individuals within a species?
ADH (alchohol dehydrogenase) gene from Drosophila – Kreitman (1983) Nature 304:412-417
Krietman identified more vairation than was expected as previously allozyme processing only showed that one variation caused a change in the AA whereas there were infact far more base viariations in the sequence that did not change the AA outcome and therefore were not observable by allozyme gel electrophoresis
Population genetics is concerned with alleles that differ from one another.
In diploid organisms there are three ways they can differ:
1) by origin: alleles that differ by origin are from the same locus, but on different chromosomes.
2) by state: alleles are identical by state if they have the same genotype (but context important).
3) by descent: Usual concern is with alleles that are recently different by decent. Because of mutation, alleles that are identical by decent, may or may not be different by state
see diagram: N-2 (AAC) all were the same and in n-1 (AAC) however in n generation there is a mutation that causes one to be different by state (AAG) even though both are the same by descent
Alleles in Populations: Calculating allele frequencies
see diagram for allele estimations within populations
For now, we’ll assume two alleles in a population of
sexual, diploid organisms.
There are two alleles at a locus in a diploid organism,
so the genotypes could be: A1A1,A2A2 or A1A2
and the relative genotype frequencies will be
x11, x22 and x12
^x values refer to the genotype frequency of each of the 3 genotypes
Given the genotype frequencies, we can calculate the
allele frequencies as follows:
Let the frequency of A1 = p, and A2 = q
p= x11 + 1/2 (x12)
q= 1-p
= x22 + 1/2 (x12)
So if genotypes frequencies are as follows
Homozygote: 0.60
Heterozygote:0.30
Homozygote: 0.10
Given the genotype frequencies, we can calculate the
allele frequencies as follows:
A1 = p
A2 = q
p= 0.60+1/2(0.30)
q= I-p = 0.10+1/2 (0.30)
Because X11 is 100% A1 and X12 is ½ A1
q= 1-p
= X22 100% A2 + ½ X12 which is 50% A2
p= 0.60+1/2(0.30)
q= I-p = 0.10+1/2 (0.30)
Two ways to think of the allele frequency p:
l) the relative frequency ofAl in the population
among all A alleles
2) the probability that an allele picked at random from
the population is an Al allele can be broken down into
a series of paired actions: picking the genotype at
random, and then picking an allele at random from the
chosen genotype
p = x l) + x 1/2) + (x22 x O)
Hardy Weinburg law (as defined by George Hardy & Wilhelm Weinberg)
describes the equilibrium state of a single locus in a randomly mating, infinitely large diploid population, free from other evolutionary forces (mutation, migration, genetic drift & selection).
Because of the independent assortment of gametes, and the multiplicative rule for the probability of combining independent events:
genotype AIAI AIA2 AIAI
HWfreq p^2 + 2pq + q^2 = 1
p = 0.10
q = 0.90 (= 1 – p)
To understand the probability of two independent events happening at the same time multiply together (mutiplicative)
(AA = P^2 Aa=2pq aa=q^2 )
Important assumptions for Hardy Weinburg law
When forming a zygote, the probability of choosing a male gamete that is A1 is the same as the probability of choosing a female gamete that is A1 = p.
This is true when genotype frequencies are the same for males and females, and males and females have an equal probability of mating (or most simply, when all individuals are hermaphrodites).
HW equilibrium is reached after 1 generation of random mating among hermaphrodites
or after up to 2 generations for dioecious species when allele frequencies differ for the two sexes.
Important implications of HW Law
1) Mating behaviour can affect genotype frequencies, but not allele frequencies. Once equilibrium has been reached, genotype frequencies will also remain the same.
2) To calculate genotype frequencies, we need only the allele frequencies.
Useful observation:
When an allele is rare, it is most likely to be found in a
heterozygote:
2pq/q2 = 2p/q 2/q
e.g. if q=0.01, then that allele (A2) is 200 times more
likely to be in a heterozygote than in a homozygote
Means that a rare ‘bad’ allele can hide in heterozygotes and wont be exposed to selection – therefore in large healthy population disfunctional alleles can be retained.
What happens if there are more than 2 alleles?
For loci with multiple alleles, the frequency of the
AiAi homozygote is Pi2, and the frequency of the
AiAJ heterozygote is 2p,pj
For example: ifthere are 3 alleles (a,b & c), then
this is determined by the binomial expansion
(p + q + = p2 + q 2 + r2 + 2pq + 2prH- 2qr
Quickly gets messy…
So, if there is more than two alleles we can use a short-cut instead:
The total freq of homozygotes (homozygosity) =
G= sum of Pi^2
(Homozygosity (G) = sum of all)
The frequency of heterozygotes (heterozygosity) =
H=1-G= 1- sum of Pi^2
Heterozygosity (H) = 1 – Homozygosity (G)
What about polyploids?
We can predict those frequencies as well, still using the binomial expansion.
For example for a triploid species:
For 2 alleles: (p + q)3
For 3 alleles: (p + q + r)3
(Simple binomial expansion)
Why is knowing all this useful?
One example – the Wahlund effect (named after Sten Gösta William Wahlund 1901-76)
Based on assumptions
e.g. assuming that all belong to one population when infact they are not:
An extreme example:
Two actual populations each with 40 individuals.
* There are 2 alleles (red and green) with equal frequencies in the overall (if single) population (p = q = 0.5)
* If it had been just one population, there should be
2pq x N = 2 x O.5 x O.5 x 80 = 40 Heterozygous individuals (H=0.50), but there are only 2 (H = 0.025), much fewer than expected.
Expected 40 heterozygotes but only 5 observed – this would be very low if 1 population but it is infact 2 populations
Real example of Wahlund effect:
Real example of Wahlund effect:
Cryptic population structure in a large, mobile mammalian
predator: the Scandinavian lynx
doi: 10.1046/j.1365-294x.2003.01952.x
Strong differentiation had been found between Russia, Finland. Czech Republic. Estonia and Norway/ Sweden.
Subdivision within Norway or Sweden was not known
or expected. Hovever, when Norwegian Or Swedish
subsamples were combined. there were too few heterozygotes — highly Significant for Norway (p<0.001)
Conclusions
Found that there was little heterozygosity across the whole group.
However once divided into subpopulations they found their populations did fit Hardy Weinburg law
Another example: Eastern mosquito fish
Temporal Population Genetic Structure Of Eastern Mosquitofish in a Dynamic Aquatic Landscape.
McElroy et al. (201 1) doi:IO.1093/jhered/esr088
Wahlund effect detected mixing when a drought forced
fish to move into the habitat of a neighbouring population.
Divide observed by expected heterozygosity predicted by HW. In drought a decrease of heterozygosity occurs due to population mixing
Genotype and the HW equilibrium: Summary
I) High levels of variation in natural populations revealed by DNA sequencing
2) population genetics is concerned with differences among alleles, and these differences can be by origin, by state and by descent.
3) Can estimate measures or population genetic structure based On allele frequencies, and larger sample give us better estimates.
4) Genotype frequencies can be calculated from allele frequencies according to the HW rule
Assumes random mating in a large diploid population free from evolutionary forces that affect allele frequency, such as mutation, migration, drift or selection.
