Chapter 24-Population Genetics

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


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)


FemaleMale

A f(A)=p

a f(a)=q

A f(A)=p

a f(a)=q


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


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


Population

MM MN NN M N

NEW 0.430 0.230 0.340 0.545 0.455


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

Chapter 24-Population Genetics

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