chapter 24-population genetics
DESCRIPTION
Population GeneticsTRANSCRIPT
Population genetics is the study of the genetic composition of a population and the forces that determine and change that composition
INTRODUCTION
Let us begin with a few definitions
Species = A group of organisms potentially capable of interbreeding
Population = A group of individuals of the same species that exist together in time and space
Gene pool = The totality of genetic information possessed by reproductive members of a population
Kaibab squirrelAbert squirrel
A mathematical model developed independently in 1908 by Godfrey H. Hardy and Willhelm Weinberg
It relates allelic and genotypic frequencies in a population
The HARDY-WEINBERG LAW
The HW law has three important aspects 1. Allele frequencies in a population
do not change over time 2. Allele frequencies predict
genotypic frequencies 3. Equilibrium is achieved in one
generation of random mating
It disproved the assumption that dominant traits would become more common, while recessive traits would become rarer
The assumptions for the HW law
1. The organisms are diploid and sexually-reproducing
2. The population has a large size 3. Mating within the population is
random 4. There is no natural selection 5. There is no mutation or
migration
Calculating Allele Frequencies
For a gene with two alleles, the frequency of one allele is designated p , while that of the other allele is designated q p and q do NOT represent the
allelic frequencies in an individual, but in the population at large
p and q are assigned arbitrarily p + q = 1
Example = MN blood group in humans
One gene = L
Two alleles = LM and LN
Three genotypes = LNLN LMLM
LMLN
Calculating Allele Frequencies
Consider a population of 200 individuals where M = 114 MN = 76 N = 10
Allelic frequencies can be measured in two ways 1) By counting alleles 2) By using genotypic frequencies
Frequency of M allele = # of M alleles
total # of alleles
Method 1 = Counting Alleles
f(M) = p = [2(114) + 1(76)]/400 304/400 0.76
f(N) = q = [2(10) + 1(76)]/400 96/400 0.24
Alternatively, p + q = 1 q = 1 - p q = 1 - 0.76 q = 0.24
Method 1 = Counting Alleles
f(MM) = 114/200 = 0.57
f(MN) = 76/200 = 0.38
f(NN) = 10/200 = 0.05
Method 2 = Using Genotypic Frequencies
p = f(M) = f(MM) + (1/2)f(MN) 0.57 + 0.38/2 = 0.76
q = f(N) = f(NN) + (1/2)f(MN) 0.05 + 0.38/2 = 0.24
Method 2 = Using Genotypic Frequencies
Consider a population of individuals segregating the A and a alleles at the A locus What are the possible
genotypes of each individual? p = f(A) q = f(a)
Calculating Allele Frequencies
FemaleMale
A f(A)=p
a f(a)=q
A f(A)=p
a f(a)=q
Calculating Allele Frequencies
AA Aa
Aa aa
f(AA)=p2 f(Aa)=pq
f(Aa)=pq f(aa)=q2
=> The distribution of the three possible genotypes is given by the binomial expansion
(p + q)2
p2 + q2 + 2pq
Calculating Allele Frequencies
18
p + q = 1
p = allele frequency of one alleleq = allele frequency of a second allele
p2 + 2pq + q2 = 1
p2 and q2 Frequencies for each homozygote
2pq Frequency for heterozygotes
All of the allele frequencies together equals 1
All of the genotype frequencies together equals 1
Hardy-Weinberg Equation
NOW consider a population in which the frequency of the A allele is 0.7 and that of the a allele is 0.3 Then p = 0.7 and q = 0.3 Therefore, frequency of genotypes
produced by random mating f(AA) =
p2 = (0.7)2 = 0.49 f(Aa) =
2pq = 2(0.7)(0.3) = 0.42 f(aa) =
q2 = (0.3)2 = 0.09
What are the frequencies of alleles in the new generation?
f(A) = f(AA) + (1/2)f(Aa) 0.49 + 0.42/2 0.7
f(a) = f(aa) + (1/2)f(Aa) 0.09 + 0.42/2 0.3
=> Frequencies of the A and a alleles in the new generation are the same as those in the previous generation
Therefore, the population is in HW equilibrium
Important points to consider:
This genetic equilibrium explains why recessive alleles do not disappear
When a population is in equilibrium, genetic variability is maintained
If any of the assumptions made above are not true, then the population will not be in HW equilibrium
X-linked Genes Can we still calculate allelic frequencies
using HWL? We sure can! First of all, it is easy to calculate
frequency of X-linked alleles in males, because it is the same as the phenotypic frequency
If we assume identical allele frequencies and random mating, we can use the HW equation to calculate frequency of genotypes in the female
EXTENSIONS OF THE HW LAW
In other words, here’s how X-linked traits are handled:
For females, the standard Hardy-Weinberg equation applies
p2 + 2pq + q2 = 1
However, in males the allele frequency is the phenotypic frequency
p + q = 1
Problem In a particular population, the frequency of
color blindness in males is 8%. What is the expected frequency in females?
q = 0.08
=> Expected f(aa) in females = q2 = (0.08)2
0.0064
Example = ABO blood group in humans
One gene = I Three alleles = IA ; IB ; IO
Six genotypes = IAIA ; IAIB ; IAIO ; IBIB ; IBIO ; IOIO
Four phenotypes = A ; B ; AB ; O
Multiple Alleles
To calculate allelic and genotypic frequencies, we simply add another term to the binomial expansion
=> p + q + r = 1
p = IA q = IB r = IO
=> genotypes in a population under random mating will be given by (p + q + r)2
p2 + q2 + r2 + 2pq + 2pr + 2qr
IAIA IBIB IOIO IAIB IAIO IBIO
Blood Type
Number
A 199
B 53
AB 17
O 231
Consider a population of 500 individuals
f(OO) =
=> r2 = => r = =
Blood types A and O only include genotypes
=> The frequency of A and O phenotypes is given by
231/500= 0.462
0.462√0.462 0.680
IAIA , IAIO and IOIO
(p + r)2
The frequency of A and O phenotypes =
Therefore, (p + r)2 =
=> p + r =
=> p =
=> p =
=> p =
(199 + 231)/500 = 0.860
√0.860= 0.927
0.927 – r
0.927 – 0.680
0.247
0.860
q, the frequency of allele IB , can be obtained by similar logic with blood types B and O
or simply from the equation p + q + r = 1
=> q = 1 – (p + r) => q = 1 – 0.927 => q = 0.073
We can also use the HWL to calculate heterozygote frequency in a population
Example: Albinism In some populations, frequency of
albinism is 1/10,000 or 0.0001 Therefore, q2 = 0.0001 => q = √0.0001 => q = 0.01
Since p + q =1 => p = 1 – q = 1 – 0.01 => p = 0.99
Heterozygote frequency = 2pq = 2 (0.99)(0.01) ~ 0.02
So, while albinism is rare (1/10,000), being a carrier is not 1/50
How do we know if a population is in equilibrium?
If the calculated frequencies and the observed frequencies are the same
Example:
Population
MM MN NN M N
Eskimo 0.835 0.156 0.009 0.913 0.087
Aborigines 0.024 0.304 0.672 0.176 0.824
Genotypic FrequenciesAllelic Frequencies
Are the populations currently in equilibrium? They sure are!
Calculated Frequency
Observed Frequency
MM
0.835
MN 0.156
NN 0.009
0.833
0.159
0.008
(0.913)2 =
2(0.913)(0.087) =
(0.087)2 =
The same is true for the Aborigine population
But what if population is NOT in equilibrium? What if a hypothetical population that
was 50% Eskimo and 50% Aborigine was formed on an uninhabited island?
The initial frequencies will be:
Population
MM MN NN M N
Eskimo 0.835 0.156 0.009 0.913 0.087
Aborigines 0.024 0.304 0.672 0.176 0.824
Genotypic FrequenciesAllelic Frequencies
Population
MM MN NN M N
NEW 0.430 0.230 0.340 0.545 0.455
Genotypic FrequenciesAllelic Frequencies
Calculated Frequency
Observed Frequency
p2
MM 0.430
2pq MN
0.230
q2 NN
0.340
0.297
0.496
0.207
(0.545)2 =
2(0.545)(0.455) =
(0.455)2 =
=> population is NOT in equilibrium BUT, if mating is random, population
will reach equilibrium in one generation
Note: Hardy-Weinberg equilibrium is rare for protein-encoding genes that seriously affect the phenotype
However, it does apply to portions of the genome that do not affect phenotype
These include repeated DNA segments Not subject to natural selection
In natural populations, it is difficult to meet all the assumptions of the HW law
When one of the assumptions is not met, the population is in disequilibrium
This leads to evolutionary change
WHAT ARE THE FACTORS THATCAN AFFECT EQUILIBRIUM?
1. Mutation 2. Migration 3. Nonrandom mating 4. Genetic drift
It is the source of all new alleles => it provides the raw genetic
material upon which evolution acts Mutation rates are too low
=> in the absence of other forces, particularly selection, mutation is negligible in changing genefrequencies
1. Mutation
Mutations occur at random Are generally recessive Can be
Neutral Detrimental Beneficial
1. Mutation
Selection eliminates deleterious alleles
However, harmful recessive alleles are maintained in heterozygotes and are reintroduced by mutations
Genetic load is the collection of recessive deleterious alleles present in a population
Migration usually implies the movement of individuals between populations
In population genetics we are interested in the movement of genes, or gene flow
2. Migration
Gene flow has two major effects on a population It introduces new alleles into the
population It changes the allelic frequencies
in populations There is a larger effect of gene flow
with small population sizes
2. Migration
Deviations from random mating occur when the choice of mates is influenced by phenotypic resemblance or genetic relatedness
3. Nonrandom Mating
i. When non-random mating occurs based on phenotype, the population is engaged in assortative mating
Positive assortative mating occurs when individuals with similar phenotypes mate preferentially
Negative assortative mating occurs when individuals with dissimilar phenotypes mate preferentially
ii. When non-random mating is based on genotype, inbreeding or outbreeding is in force Inbreeding occurs when the mating
individuals are more closely related than mates drawn by chance
The most extreme form of inbreeding is
Outbreeding occurs when the mating individuals are less closely related than mates drawn by chance
Figure 24.6 A human pedigree containing inbreeding
Said to be inbred
Any change in gene frequency in a population due to chance
It is very significant for small populations, but not so important for large ones
4. Genetic Drift
Sampling error Large populations produce a large pool of
gametes More likely that all possible combinations are generated in the offspring
If the population is small, the gametes that unite to form the progeny constitute only a sample from the large pool of gametes
=> this sample could deviate from the larger pool by chance or “error”
All genetic drift is caused by sampling errors, which may arise in several ways in natural populations
i. Small population size Population size remains
continuously small over many generations
4. Genetic Drift
Small population size increases the probability of homozygosity This increases recessive phenotypes in
population Example
Amish and Mennonite populations of Pennsylvania marry predominantly within their religious groups
Maintain their original small genetic pool
Increased incidence of otherwise rare traits
58Figure 15.6Ellis-van Creveld syndrome
ii. Founder effect New population established by a small,
nonrepresentative sample of a larger population
The new colony may have different allele frequencies than the original population
It may, by chance, either lack some alleles or have high frequency of others
4. Genetic Drift
Example of a founder effect The Dunkers Community
Emigrated from Germany to Pennsylvania in the 1720s
They remained a small isolated group
Some allelic frequencies in the Dunkers differs significantly from the frequencies in the general US population and the German population
Allele Frequencies Phenotypic Frequencies
Population
IA IB IO
A
B
AB
O
Dunker 0.38 0.03 0.59 0.593 0.036 0.023 0.348
USA 0.26 0.04 0.70 0.431 0.058 0.021 0.490
Germany
0.29 0.07 0.64 0.455 0.095 0.041 0.410
iii. Bottleneck Effect Occurs when a population is
drastically reduced in size as a result of a disaster
Rebounds in population size occur with descendants of limited number of survivors
Therefore, new population has a much more restricted gene pool than the large ancestral population
Pingelap atoll
Lagoon
Example of a bottleneck effect
Pingelap atoll in the West. Pacific Ocean
Circa 1780, a typhoon and famine left only 30 survivors
One of the 9 male survivors was a Chief who was heterozygous forachromatopsia, an autosomal recessive disorder characterized by ocular disturbances and complete inability to see colors
Lengkieki
If the Chief was the only carrier => the allele frequency =
The current population consists of about 3000 individuals, whose ancestry can be traced to the typhoon survivors
About 7 % of the population is color blind from infancy => the allele frequency =
Effects of Genetic Drift
i. Allelic frequencies change over time Sometimes, by chance, allelic frequencies
may reach 1.0 , in which case the allele is said to be fixed in the population
0.0 , in which case the allele is said to be lost from the population
Which allele will be fixed or lost is a function of the original allelic frequency
Figure 25.7 A hypothetical simulation of random genetic drift
In smaller populations, allele frequency fluctuates substantially
from generation to generation
In larger populations, allele frequency fluctuates much
less
ii. Divergence of populations away from each other
Effects of Genetic Drift