Population Genetics. 1859: Darwin and the birth of modern biology (explaining why living things are...

Population Genetics

1859: Darwin and the birth of modern biology(explaining why living things are as they are) – Heritable Traits and Environment Evolution

Review:

Mendel: Heredity works by the transmission of particles (genes) that influence the expression of traits

Review:

Avery, McCarty, and MacLeod: Genes are DNA

Review:

Watson and Crick: Here’s the structure of DNA

Review:

Modern Genetics: Here’s how DNA influences the expression of traits from molecule to phenotype throughout development

Review:

How does evolution work at a genetic level? Population Genetics and the Modern Synthesis

Review:

How does evolution work at a genetic level? Population Genetics and the Modern Synthesis

How can we describe the patterns of evolutionary change through DNA analyses? Evolutionary Genetics

Review:

The Modern Synthesis

The Darwinian Naturalists

Ernst Mayr

Selection is the only mechanism that can explain adaptations; mutations are random and cannot explain the non-random ‘fit’ of organisms to their environment

The Mutationists

T. H. Morgan R. Goldschmidt

The discontinuous variation between species can only be explained by the discontinuous variation we see expressed as a function of new mutations; the probabilistic nature of selection is too weak to cause the evolutionary change we see in the fossil record

The Modern Synthesis

R. A. Fisher

Multiple genes can produce continuous variation, and selection can act on this variation and cause change in a population

Sewall Wright

Random chance was an important source of change in small populations

J. B. S. Haldane

Developed mathematical models of population genetics

with Fisher and Wright

Theodosius Dobzhansky

Described genetic differences between natural populations; described evolution as a change in allele frequencies.

Population Genetics

I. Basic Principles

Population Genetics

I. Basic Principles

A. Definitions:- Population: a group of interbreeding organisms that share a

common gene pool; spatiotemporally and genetically defined - Gene Pool: sum total of alleles held by individuals in a population - Gene/Allele Frequency: % of genes at a locus of a particular allele - Gene Array: % of all alleles at a locus: must sum to 1. - Genotypic Frequency: % of individuals with a particular genotype - Genotypic Array: % of all genotypes for loci considered = 1.

Population Genetics

I. Basic Principles

A. Definitions: B. Basic computations:

1. Determining the Gene and Genotypic Array:AA Aa aa

Individuals 60 80 60 (200)

Population Genetics

I. Basic Principles

Genotypic Array

60/200 = 0.30

80/200 = .40 60/200 = 0.30

Population Genetics

I. Basic Principles

Genotypic Array

60/200 = 0.30

80/200 = .40 60/200 = 0.30

''A' alleles 120 80 0 200/400 = 0.5

Population Genetics

I. Basic Principles

Genotypic Array

60/200 = 0.30

80/200 = .40 60/200 = 0.30

''A' alleles 120 80 0 200/400 = 0.5

'a' alleles 0 80 120 200/400 = 0.5

Population Genetics

I. Basic Principles

1. Determining the Gene and Genotypic Array

2. Short Cut Method:

- Determining the Gene Array from the Genotypic Array

a. f(A) = f(AA) + f(Aa)/2 = .30 + .4/2 = .30 + .2 = .50

b. f(a) = f(aa) + f(Aa)/2 = .30 + .4/2 = .30 + .2 = .50

KEY: The Gene Array CAN ALWAYS be computed from the genotypic array; the process just counts alleles instead of genotypes. No assumptions are made when you do this.

Population Genetics

I. Basic Principles

A. Definitions: B. Basic computations: C. Hardy-Weinberg Equilibrium:

1. If a population acts in a completely probabilistic manner, then: - we could calculate genotypic arrays from gene arrays - the gene and genotypic arrays would equilibrate in one generation

Population Genetics

I. Basic Principles

1. If a population acts in a completely probabilistic manner, then: - we could calculate genotypic arrays from gene arrays - the gene and genotypic arrays would equilibrate in one generation

2. But for a population to do this, then the following assumptions must be met (Collectively called Panmixia = total mixing)

- Infinitely large (no deviation due to sampling error) - Random mating (to meet the basic tenet of random mixing) - No selection, migration, or mutation (gene frequencies must not change)

Population GeneticsI. Basic Principles A. Definitions: B. Basic computations: C. Hardy-Weinberg Equilibrium:

Sources of Variation Agents of Change

Mutation N.S.

Recombination Drift

- crossing over Migration

- independent assortment Mutation

Non-random Mating

VARIATION

So, if NO AGENTS are acting on a population, then it will be in equilibrium and WON'T change.

Population Genetics

I. Basic Principles

3. PROOF: - Given a population with p + q = 1. - If mating is random, then the AA, Aa and aa zygotes will be formed at p2 + 2pq + q2 - They will grow up and contribute genes to the next generation: - All of the gametes produced by AA individuals will be A, and they will be produced at a frequency of p2 - 1/2 of the gametes of Aa will be A, and thus this would be 1/2 (2pq) = pq - So, the frequency of A gametes in the “gamete/gene pool” will be p2 + pq = p(p + q) = p(1) = p - Likewise for the 'a' allele (remains at frequency of q). - Not matter what the gene frequencies, if panmixia occurs then the population will reach an equilibrium after one generation of random mating...and will NOT change (no evolution)

Population Genetics

I. Basic Principles

AA Aa aa

Initial genotypic freq.

0.4 0.4 0.2 1.0

Gene freq.

Genotypes, F1

Gene Freq's

Genotypes, F2

Population Genetics

I. Basic Principles

AA Aa aa

0.4 0.4 0.2 1.0

Gene freq. f(A) = p = .4 + .4/2 = 0.6 f(a) = q = .2 + .4/2 = 0.4

Genotypes, F1

Gene Freq's

Genotypes, F2

Population Genetics

I. Basic Principles

AA Aa aa

0.4 0.4 0.2 1.0

Gene freq. f(A) = p = .4 + .4/2 = 0.6 f(a) = q = .2 + .4/2 = 0.4

Genotypes, F1 p2 = .36 2pq = .48 q2 = .16 = 1.00

Gene Freq's

Genotypes, F2

Population Genetics

I. Basic Principles

AA Aa aa

0.4 0.4 0.2 1.0

Gene freq. f(A) = p = .4 + .4/2 = 0.6 f(a) = q = .2 + .4/2 = 0.4

Genotypes, F1 p2 = .36 2pq = .48 q2 = .16 = 1.00

Gene Freq's f(A) = p = .36 + .48/2 = 0.6 f(a) = q = .16 + .48/2 = 0.4

Genotypes, F2

Population Genetics

I. Basic Principles

AA Aa aa

0.4 0.4 0.2 1.0

Gene freq. f(A) = p = .4 + .4/2 = 0.6 f(a) = q = .2 + .4/2 = 0.4

Genotypes, F1 p2 = .36 2pq = .48 q2 = .16 = 1.00

Gene Freq's f(A) = p = .36 + .48/2 = 0.6 f(a) = q = .16 + .48/2 = 0.4

Genotypes, F2 .36 .48 .16 1.00

Population Genetics

I. Basic Principles

A. Definitions: B. Basic computations: C. Hardy-Weinberg Equilibrium: D. Utility

Population Genetics

I. Basic Principles

1. If no real populations can explicitly meet these assumptions, how can the model be useful?

Population Genetics

I. Basic Principles

1. If no real populations can explicitly meet these assumptions, how can the model be useful? It is useful for creating an expected model that real populations can be compared against to see which assumption is most likely being violated.

Example:

CCR5 – a binding protein on the surface of white blood cells, involved in the immune response.

CCR5-1 = functional alleleCCR5 – 32 = mutant allele – 32 base deletion

Curiously, homozygotes for 32 are resistant to HIV, and heterozygotes show slower progression to AIDS.

Mutant allele interrupts virus’s ability to infect cells.

Example:

CCR5 – a binding protein on the surface of white blood cells, involved in the immune response.

CCR5-1 = functional alleleCCR5 – 32 = mutant allele – 32 base deletion

Curiously, homozygotes for 32 are resistant to HIV, and heterozygotes show slower progression to AIDS.

32 base-pair deletion, shortening one of the fragments digested with a restriction enzyme

GENOTYPES

GENOTYPE

OBSERVED EXPECTED O - E (O – E)2 (O – E)2/E

1/1 223 224.2 -1.2 1.44 0.006

32/1 57 55.4 1.6 2.56 0.046

32/32 3 3.4 -0.4 0.16 0.047

283 X2 = 0.099

1/1 = 223/283 = 0.788 p = 0.788 + 0.201/2 = 0.8932/1 = 57/283 = 0.20132/32 = 3/283 = 0.011 q = 0.011 + 0.201/2 = 0.11

Expected 1/1 = p2 x 283 = (0.792) x 283 = 224.2Expected 1/32 = 2pq x 283 = (0.196) x 283 = 55.4Expected 32/32 = q2 x 283 = (0.0121) x 283 = 3.4

So this population is in HWE at this locus. HIV is still rare, and is exerting too small a selective pressure on the whole population to change gene frequencies significantly.

This is the percentage of CCR5 delta 32 in different ethnic populations:

European Descent: 16% African Americans: 2% Ashkenazi Jews: 13% Middle Eastern: 2-6%

Why does the frequency differ in different populations? Drift or Selection?

Galvani, Alison P. , and John Novembre. 2005. The evolutionary history of the CCR5-D32 HIV-resistance mutation. Microbes and Infection 7 (2005) 302–309

Allelic frequency of CCR5-d32 in Europe

Why Europe?

- the allele is a new mutation - was it selected for in the past?

Spread of the Bubonic Plague

“In the 18th century in Europe, 400,000 people died annually of smallpox, and one third of the survivors went blind (4). The symptoms of smallpox, or the “speckled monster” as it was known in 18th-century England, appeared suddenly and the sequelae were devastating. The case-fatality rate varied from 20% to 60% and left most survivors with disfiguring scars. The case-fatality rate in infants was even higher, approaching 80% in London and 98% in Berlin during the late 1800s.” Reidel (2005).

The WHO certified that smallpox was eradicated in 1979

Why Europe?

- the allele is a new mutation - was it selected for in the past?

Smallpox in Europe

Smallpox and CCR5

1. “Smallpox, on the other hand, was a continuous presence in Europe for 2,000 years, and almost everyone was exposed by direct person-to-person contact. Most people were infected before the age of 10, with the disease's 30 percent mortality rate killing off a large part of the population before reproductive age.” ScienceDaily (Nov. 20, 2003)

2.The HIV epidemic in Africa began as vaccination against smallpox waned in the 1950’s – 1970’s. Perhaps vaccinations for smallpox were working against HIV, too.

3.In vitro studies of wbc’s from vaccinated people had a 5x reduction in infection rate of HIV compared to unvaccinated controls. Weinstein et al. 2010

Relationships Between Smallpox and HIV

So, it may have been selected for in Europe, and now confer some resistance to HIV.

Population Genetics

I. Basic Principles

1. If no real populations can explicitly meet these assumptions, how can the model be useful? It is useful for creating an expected model that real populations can be compared against to see which assumption is most likely being violated.

2. Also, If HWCE is assumed and the frequency of homozygous recessives can

be measured, then the number of heterozygous carriers can be estimated.

Example:

Cystic fibrosis (cc) has a frequency of 1/2500 = 0.0004 in people of northern European ancestry.

Water follows salt flow by osmosis and dilutes mucus

More than 1,000 different mutations in the CFTR gene have been identified in cystic fibrosis patients. The most common mutation (observed in 70% of cystic fibrosis patients) is a three-base deletion in the DNA sequence, causing an absence of a single amino acid in the protein. = 0.0004 x 0.7 = 0.00028

Example:

Cystic fibrosis (cc) has a frequency of 1/2500 = 0.0004 in people of northern European ancestry; common allele = 0.00028.

Mucus in lungs reduces respiration, increases bacterial infection

In pancreas/liver, reduces flow/efficacy of digestive enzymes

In intestine, reduces nutrient uptake

Example:

Cystic fibrosis (cc) has a frequency of 1/2500 = 0.0004 in people of northern European ancestry, common allele = 0.00028

How many carriers are there?

q2 = 0.00028, so q2 = q = 0.017.

p + q = 1, so p = 0.983

So, the frequency of heterozygous carriers for this allele = 2pq = 0.033

This calculation can only be performed if HWE is assumed.

Population Genetics

I. Basic Principles

II. Deviations from HWE

A. Mutation

1. Basics:

A. Mutation

1. Basics:a. Consider a population with:

f(A) = p = .6

f(a) = q = .4

A. Mutation

1. Basics:

a. Consider a population with:

f(A) = p = .6

f(a) = q = .4

b. Suppose ‘A' mutates to ‘a' at a realistic rate of:

μ = 1 x 10-5

A. Mutation

f(A) = p = .6

f(a) = q = .4

μ = 1 x 10-5

c. Well, what fraction of alleles will change?

‘A' will decline by: μp = .6 x 0.00001 = 0.000006

‘a' will increase by the same amount.

A. Mutation

f(A) = p = .6

f(a) = q = .4

μ = 1 x 10-5

c. Well, what fraction of alleles will change?

‘A' will decline by: μp = .6 x 0.00001 = 0.000006

‘a' will increase by the same amount.

d. So, the new gene frequencies will be:

q1 = q + μp = .400006

p1 = p - μp = p(1-μ) = .599994

At this realistic rate, it takes thousands of generations to cause appreciable change. Mutation is the source of new alleles, but it does not change the frequency of alleles very much. Were the mutationists wrong?

A. Mutation

1. Basics:

2. Other Considerations:

A. Mutation

1. Basics:

- Selection:

Selection can BALANCE mutation... so a deleterious allele might not accumulate as rapidly as mutation would predict, because it is eliminated from the population by selection each generation.

A. Mutation

1. Basics:

- Selection:

- Drift:

The probability that a new allele (produced by mutation) becomes fixed (q = 1.0) in a population = 1/2N (basically, it's frequency in that population of diploids). In a small population, this chance becomes measureable and likely. So, NEUTRAL mutations have a reasonable change of becoming fixed in small populations... and then replaced by new mutations.

A. MutationB. Migration 1. Basics:

- Consider two populations:

p1 = 0.2

q1 = 0.8

p2 = 0.7

q2 = 0.3

p1 = 0.2

q1 = 0.8

p2 = 0.7

q2 = 0.3

suppose migrants immigrate at a rate such that the new immigrants represent 10% of the new population

p2 = 0.7

q2 = 0.3

p1 = 0.2

q1 = 0.8

p2 = 0.7

q2 = 0.3

p1 = 0.2

q1 = 0.8

p(new) = p1(1-m) + p2(m)

P(new) = (0.2).9 + (0.7)0.1 = 0.25

IMPORTANT EFFECT, BUT MAKES POPULATIONS SIMILAR AND INHIBITS DIVERGENCE AND ADAPTATION TO LOCAL CONDITIONS (EXCEPT IT MAY INTRODUCE NEW ADAPTIVE ALLELES)

Frequency of the ‘B’ allele of the ABO blood group locus, largely as a result of the Mongol migrations following the fall of the Roman Empire

A. MutationB. MigrationC. Non-Random Mating 1. Positive Assortative Mating "like phenotype mates with like phenotype"

a. Pattern:

AA Aa aa

.2 .6 .2

offspring

a. Pattern:

AA Aa aa

.2 .6 .2

offspring ALL AA 1/4AA:1/2Aa:1/4aa ALL aa

a. Pattern:

AA Aa aa

.2 .6 .2

.2 .15 + .3 + .15 .2

F1 .35 .3 .35

a. Pattern:

AA Aa aa

.2 .6 .2

.2 .15 + .3 + .15 .2

F1 .35 .3 .35

b. Effect: - reduction in heterozygosity at this locus; increase in homozygosity.

Groth, J. 1993. Call matching and positive assortative mating in Red Crossbills. The Auk 110L: 398-401.

female

Type 1

Type 2

A. MutationB. MigrationC. Non-Random Mating 1. Positive Assortative Mating

2. Inbreeding - reduction of heterozygosity across the entire genome, at a rate that

correlates with the degree of relatedness. - full sibs, parent/offspring: lose 50%of heterozygosity each generation.

BigCatRescue

White tigers in the U.S. are all descendants of a brother-sister pair from the Cincinnati Zoo. The AZA has outlawed captive breeding of white tigers.

A. MutationB. MigrationC. Non-Random Mating 1. Positive Assortative Mating

2. Inbreeding - reduction of heterozygosity across the entire genome, at a rate that

correlates with the degree of relatedness. - full sibs, parent/offspring: lose 50%of heterozygosity each generation.

CAN INCREASE PROBABILITY OF DIVERGENCE BETWEEN POPULATIONS, AND CAN ALSO BE A WAY TO PURGE DELETERIOUS ALLELES (ALTHOUGH AT A COST TO REPRODUCTIVE OUTPUT).

A. MutationB. MigrationC. Non-Random MatingD. Genetic Drift - Sampling Error

1. The organisms that actually reproduce in a population may not be representative of the genetics structure of the population; they may vary just due to sampling error (chance).

D. Genetic Drift - Sampling Error1. The organisms that actually reproduce in a population may not be

representative of the genetics structure of the population; they may vary just due to sampling error (chance).

- most dramatic in small samples.

2. effects:

D. Genetic Drift - Sampling Error

1. The organisms that actually reproduce in a population may not be representative of the genetics structure of the population; they may vary just due to sampling error (chance).

2. effects:

1 - small pops will differ more, just by chance, from the original population

D. Genetic Drift - Sampling Error1. The organisms that actually reproduce in a population may not be

representative of the genetics structure of the population; they may vary just due to sampling error (chance).

2. effects:

1 - small pops will differ more, just by chance, from the original population

2 - small pops will vary more from one another than large populations

D. Genetic Drift - Sampling Error1. most dramatic in small samples.

2. effects

3. circumstances when drift is very important:

The Amish, a very small, close-knit group decended from an intial population of founders, has a high incidence of genetic abnormalities such as polydactyly

2. effects

- “Founder Effect”

- “Founder Effect” and Huntington’s Chorea

HC is a neurodegenerative disorder caused by an autosomal lethal dominant allele.

The fishing villages around Lake Maracaibo in Venezuela have the highest incidence of Huntington’s Chorea in the world, approaching 50% in some communities.

The gene was mapped to chromosome 4, and found the HC allele was caused by a repeated sequence of over 35 “CAG’s”. Dr. Nancy Wexler found homozygotes in Maracaibo and described it as the first truly dominant human disease (most are incompletely dominant and cause death in the homozygous condition).

By comparing pedigrees, she traced the incidence to a single woman who lived 200 years ago. When the population was small, she had 10 children who survived and reproduced. Folks with HC now trace their ancestry to this lineage. Also a nice example of “coalescence” – convergence of alleles on a common ancestral allele.

2. effects

- “Founder Effect”

- “Bottleneck”

- “Genetic Bottleneck”

If a population crashes (perhaps as the result of a plague) there will be both selection and drift. There will be selection for those resistant to the disease (and correlated selection for genes close to the genes conferring resistance), but there will also be drift at other loci simply by reducing the size of the breeding population.

European Bison, hunted to 12 individuals, now number over 1000.

Cheetah have very low genetic diversity, suggesting a severe bottleneck in the past. They can even exchange skin grafts without rejection.

Fell to 100’s in the 1800s, now in the 100,000’s

Population Genetics. 1859: Darwin and the birth of modern biology (explaining why living things are...

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