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BioA414Population Genetics

Handout I

References• Hartl, D. and Clark, A. Principles of Population Genetics.

2006, Fourth Edition Sinauer Associates: Sunderland. • Hedrick, P.W. Genetics of Populations, Third Edition. 2005,

Jones and Bartlett Publishers, Sudbury, MA.• Kartavtsev, Y. Molecular Evolution and Population

Genetics for Marine Biologists. 2015, CRC Press.• Peng, B., Kimmel, M. and Amos, C.I. Forward-Time

Population Genetics Simulations: Methods, Implementation, and Applications. 2012, John Wiley & Sons.

• Templeton, A.R. Population Genetics and Microevolutionary Theory. 2006, John Wiley and Sons.

http://yeastwonderfulworld.wordpress.com/

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Definition• Population Genetics genetic structure

of a population– Population group of individuals of the

same species that can interbreed– Genetic structure alleles and genotypes

• Patterns of genetic variation in populations

• Changes in genetic structure through time genetic evolution

200 white

500 pink

300 red

• genotype frequencies• allele frequencies

200/1000 = 0.2 rr

500/1000 = 0.5 Rr

300/1000 = 0.3 RR

total = 1000 flowers

Genotypefrequencies:

Describing genetic structure

200 rr

500 Rr

300 RR

• genotype frequencies• allele frequencies

900/2000 = 0.45 r

1100/2000 = 0.55 R

total = 2000 alleles

Allelefrequencies:

= 400 r

= 500 r= 500 R

= 600 R

Describing genetic structure Four disciplines in Genetics• Transmission Genetics genetic

processes within individuals• Molecular Genetics molecular nature

of genes• Population Genetics heredity in

groups of individuals• Quantitative Genetics polygenetic

traits

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Some facts• Population and Quantitative Genetics

– Mendelian principles– Amenable to mathematical models– Development rediscovery of Mendel’s

work– Mendelian theory and Darwinian theory

neo-Darwinian synthesis foundation of modern biology

Modern synthesis• Integration of Darwin’ natural selection and Mendelian

genetics• Natural selection acting on mutations new

adaptations and new s pecies• Fundamental basis for evolutionary biology

– Natural selection is the driving force of evolution– Evolution in terms of mutations and recombination

• A rigorous and testable natural science• Dobzhansky, Simpson, Mayr, Ford, Stebbins, and R. A.

Fisher

Mendelian population• Investigate how genetic variation

change over time• A group of interbreeding individuals

who share a common set of genes gene pool

• Evolutionary process gene pool rather than individual genotypes

Mathematical models…How much genetic variation is found in natural population? What processes control the

amount of variation observed?

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Mathematical models…What processes are

responsible for producing genetic divergence among

populations?

Mathematical models…

How do biological characteristics of a

population influence the gene pool?

Hardy-Weinberg law• Set of equations influence of random

mating on the allele and genotype frequencies of an infinitely large population

• What assumptions models• Violation of one assumption effect on

genetic structure

Genetic structure of populations

• Calculate frequencies• Frequency between 0 and 1• Consider a locus the pattern of spots

in the scarlet tiger moth, Callimorphadominula (formerly Panaxia dominula)– Three genotypes in most populations– BB, Bb, and bb

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BB

Bb

Bb

bb

out of 497 moths collectedBB appears 452 timesBb appears 43 timesbb appears 2 times

FrequenciesBB 452/497 = 0.909Bb 43/497 = 0.087bb 2/497 = 0.004Total 1.000

Allelic frequencies

p = f(G) = (2 x count of GG) + (count of Gg)2 x total number of individuals

q = f(g) = (2 x count of gg) + (count of Gg)2 x total number of individuals

q = f(g) = 1 - p

for a populationwith genotypes:

100 GG

160 Gg

140 gg

Genotype frequencies

Phenotype frequencies

Allele frequencies

100/400 = 0.25 GG160/400 = 0.40 Gg140/400 = 0.35 gg

260/400 = 0.65 green140/400 = 0.35 brown

360/800 = 0.45 G440/800 = 0.55 g

0.65260

calculate:

400

another way to calculateallele frequencies:

Genotype frequencies

Allele frequencies

0.25 GG

0.40 Gg

0.35 gg

360/800 = 0.45 G440/800 = 0.55 gOR [(0.25x2 + 0.40)/2] = 0.45

[(0.35x2 + 0.40)/2] = 0.55

G

g

Gg

2 x 0.250.400.402 x 0.35

100 GG

160 Gg

140 gg

400

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Allelic frequencies

p = f(G) = frequency of the GG homozygote+ ½ frequency of the Gg heterozygote

q = f(g) = 1 - p

q = f(g) = frequency of the gg homozygote+ ½ frequency of the Gg heterozygote

another way to calculateallele frequencies:

Genotype frequencies

Allele frequencies

0.25 GG

0.40 Gg

0.35 gg

360/800 = 0.45 G440/800 = 0.55 g

OR [0.25 + 0.40/2] = 0.45[0.35 + 0.40/2] = 0.55

G

g

Gg

0.250.40/2 = 0.200.40/2 = 0.200.35

100 GG

160 Gg

140 gg

400

Genotype Number Number of A1

A1A1 4 2 x 4A1A2 41 41A2A2 84A1A3 25 25A2A3 88A3A3 32Total 274 548

p = f(A1) = 2(A1A1) + (A1A2) + (A1A3)…/2xTotal

What about multiple alleles? Allelic frequencies at X-linked locus

• Same principle• Males only have one X• f(one allele) = 2 x the homozygous

genotype + the number of heterozygotes+ the males with the phenotype all divided by the number of alleles in the population (2 x females + males )

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Allelic frequencies

p = f(XA) = (2 x XA XA) + (XAXa) + (XAY)2 x females + males

q = f(Xa) = 1 - p

q = f(Xa) = (2 x Xa Xa) + (XAXa) + (XaY)2 x females + males

Allelic frequencies

p = f(XA) = 2 f(XAXA) +1 f(XAXa) + 1 f(XAY)3 2 3

q = f(Xa) = 1 - p

q = f(Xa) = 2 f(XaXa) +1 f(XAXa) + 1 f(XaY)3 2 3

Hardy-Weinberg law• Frequencies of alleles and genotypes

within a population will remain in a particular balance or equilibrium

• Consider a monohybrid cross, Aa x Aa– Freq. of A in population will be defined as p– Freq. of a in population will be defined as q

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Frequency of AA offs pring is then p2

Frequency of aa offspring is then q2

Frequency of Aa offspring then 2pqp2 + 2pq + q2 = 1

f(aa) = q2f(Aa) = pqf(a) = q

f(Aa) = pqf(AA) = p2f(A) = p

f(a) = qf(A) = p

MalesFemales

Hardy-Weinberg Equation Hardy-Weinberg equilibrium

• The Hardy-Weinberg law frequencies in a population will remain the same over time

• Equilibrium Assumptions– The population follows the laws of Mendelian

genetics– The size of the population approaches infinity– There is no gene mutation– There is no natural selection– There is no migration into or out of the population– Mating is totally random

BB

Bb

Bb

bb

497 mothsBB appears 452 timesBb appears 43 timesbb appears 2 times

FrequenciesB (904 + 43)/994 = 0.953b (43 + 4)/994 = 0.047Total 1.000

FrequenciesBB 452/497 = 0.909Bb 43/497 = 0.087bb 2/497 = 0.004Total 1.000

p2 + 2pq + q2 = 1

Where p = frequency of “dominant” allele B = 0.953and q = frequency of “recessive” allele b = 0.047

For the moth example (0.953)2 + [2 X (0.953 X 0.047)] + (0.047)2 =

0.907 + (2 x 0.045) + 0.002 =0.907 + 0.09 + 0.002 = 0.999

At n+1 generation

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1

0.004

0.087

0.909

FreqAt n

4971497Total

10.0022bb

450.0943Bb

4510.907452BB

Nb. Ex.At n + 1

FreqAt n + 1

Nb. Ob.At n

At n+1 generation Evolution Changes in gene frequency

• Forces changesin gene frequency

– Mutation change gene frequencies

– Natural selection differential reproduction– Genetic drift sampling error– Migration immigration and emigration

gene flow into and out of the population

Genetic variation in space and time

• Why is genetic variation important?

– Adaptation to environmental change

conservation

– Divergence of populations

biodiversity

Why is genetic variation important?

variation

no variation

EXTINCTION!!

globalwarming survival

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variation

no variation

divergence

NO DIVERGENCE!!

north

south

north

south

Why is genetic variation important?

• mutation

• migration

• natural selection

• genetic drift

• non-random mating

How does genetic structure change?changes in allele frequencies and/or genotype frequencies through time

• mutation

• migration

• natural selection

• genetic drift

• non-random mating

spontaneous change in DNA

• creates new alleles

• ultimate source of allgenetic variation

How does genetic structure change?

• introduces new alleles

individuals move into population

How does genetic structure change?

• mutation

• migration

• natural selection

• genetic drift

• non-random mating

“gene flow”

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• differences in survivalor reproduction

certain genotypes producemore offspring

• leads to adaptation

differences in“fitness”

How does genetic structure change?

• mutation

• migration

• natural selection

• genetic drift

• non-random mating

Natural selection can causepopulations to diverge

divergencenorth

south

Sickle Cell Anemia Selection on sickle-cell allele

aa – abnormal ß hemoglobinsickle-cell anemia

very lowfitness

intermed.fitness

highfitness

Selection favors heterozygotes (Aa)Both alleles maintained in population (a at low level)

Aa – both ß hemoglobinsresistant to malaria

AA – normal ß hemoglobinvulnerable to malaria

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Incomplete dominance

• sampling error

genetic change by chance alone

• misrepresentation• small populations

How does genetic structure change?

• mutation

• migration

• natural selection

• genetic drift

• non-random mating

• mutation

• migration

• natural selection

• genetic drift

• non-random mating

cause changes inallele frequencies

How does genetic structure change?

• mutation

• migration

• natural selection

• genetic drift

• non-random mating

• non-random mating

non-randomallele combinations

mating combines allelesinto genotypes

How does genetic structure change?