population genetics with qs

11

Population

Genetics

22

The Gene PoolThe Gene Pool

•Members of a species can interbreed & produce fertile offspring

•Species have a shared gene pool

•Gene pool – all of the alleles of all individuals in a population

33

The Gene PoolThe Gene Pool

•Different species do NOT exchange genes by interbreeding

•Different species that interbreed often produce sterile or less viable offspring e.g. Mule

44

Populations

•A group of the same species living in an area

•No two individuals are exactly alike (variations)

•More Fit individuals survive & pass on their traits

55

Speciation

•Formation of new species

•One species may split into 2 or more species

•A species may evolve into a new species

•Requires very long periods of time

6

Modern Evolutionary Thought

77

Modern Synthesis TheoryModern Synthesis Theory

•Combines Combines Darwinian Darwinian selectionselection and and Mendelian Mendelian inheritanceinheritance

•Population Population geneticsgenetics - study of - study of genetic variation genetic variation within a populationwithin a population

•Emphasis on Emphasis on quantitative quantitative characterscharacters

88

Modern Synthesis TheoryModern Synthesis Theory

•1940s – 1940s – comprehensive comprehensive theory of evolution theory of evolution (Modern Synthesis (Modern Synthesis Theory)Theory)

•Introduced by Fisher Introduced by Fisher & Wright& Wright

•Until thenUntil then, many did , many did not accept that not accept that Darwin’s theory of Darwin’s theory of natural selection natural selection could drive evolutioncould drive evolution

S. Wright

A. Fisher

99

Modern Synthesis Theory

•Today’s theory on evolution

•Recognizes that GENES are responsible for the inheritance of characteristics

•Recognizes that POPULATIONS, not individuals, evolve due to natural selection & genetic drift

•Recognizes that SPECIATION usually is due to the gradual accumulation of small genetic changes

1010

Microevolution

•Changes occur in gene pools due to mutation, natural selection, genetic drift, etc.

•Gene pool changes cause more VARIATION in individuals in the population

•This process is called MICROEVOLUTION

•Example: Bacteria becoming unaffected by antibiotics (resistant)

1111

Allele Frequencies Define Gene Pools

As there are 1000 copies of the genes for color, the allele frequencies are (in both males and females):

320 x 2 (RR) + 160 x 1 (Rr) = 800 R; 800/1000 = 0.8 (80%) R160 x 1 (Rr) + 20 x 2 (rr) = 200 r; 200/1000 = 0.2 (20%) r

500 flowering plants

480 red flowers 20 white flowers

320 RR 160 Rr 20 rr

1212

Species & Populations

•PopulationPopulation - a localized group of individuals of the same species.

•SpeciesSpecies - a group of populations whose individuals have the ability to breed and produce fertile offspring.

•Individuals near a population Individuals near a population centercenter are, on average, more closely related to one another than to members of other populations.

1414

Gene Pools

•A population’s gene poolgene pool is the total of all genes in the population at any one time.

•If all members of a population are homozygous for a particular allele, then the allele is fixed in the gene pool.

1515

The Hardy-Weinberg TheoremThe Hardy-Weinberg Theorem

•Used to describe a non-non-evolving population.evolving population.

•Shuffling of alleles by meiosis and random fertilization have no effect on the overall gene pool.

• Natural populations are NOT expected to actually be in Hardy-Weinberg equilibrium.

1616

.

The Hardy-Weinberg TheoremThe Hardy-Weinberg Theorem

•Deviation from Hardy-Weinberg equilibrium usually results in evolution

•Understanding a non-evolving population, helps us to understand how evolution occurs

1717

Assumptions of the H-W TheoremAssumptions of the H-W Theorem

1.Large population size - small populations can have chance fluctuations in allele frequencies (e.g., fire, storm).

2.No migration- immigrants can change the frequency of an allele by bringing in new alleles to a population.

3.No net mutations- if alleles change from one to another, this will change the frequency of those alleles

1818

Assumptions of the H-W TheoremAssumptions of the H-W Theorem

3.Random mating- if certain traits are more desirable, then individuals with those traits will be selected and this will not allow for random mixing of alleles.

4.No natural selection- if some individuals survive and reproduce at a higher rate than others, then their offspring will carry those genes and the frequency will change for the next generation.

1919

Hardy-Weinberg Equilibrium The gene pool of a non-evolving population remains constant over multiple generations; i.e., the allele frequency does not change over generations of time. The Hardy-Weinberg Equation: 1.0 = p2 + 2pq + q2

where p2 = frequency of AA genotype; 2pq = frequency of Aa plus aA genotype; q2 = frequency of aa genotype

2222

But we know that evolution does occur within populations.

Evolution within a species/population = microevolution.

Microevolution refers to changes in allele frequencies in a gene pool from generation to generation. Represents a gradual change in a population.

Causes of microevolution: 1) Genetic drift

2) Natural selection (1 & 2 are most important)

3) Gene flow

4) Mutation

2323

1) Genetic drift

Genetic drift = the alteration of the gene pool of a small population due to chance.

Two factors may cause genetic drift: a) Bottleneck effect may lead to reduced genetic

variability following some large disturbance that removes a large portion of the population. The surviving population often does not represent the allele frequency in the original population.

b) Founder effect may lead to reduced variability when a few individuals from a large population colonize an isolated habitat.

2626

*Yes, I realize that this is not really a cheetah.

2727

2) Natural selection As previously stated, differential success in reproduction based on heritable traits results in selected alleles being passed to relatively more offspring (Darwinian inheritance).

The only agent that results in adaptation to environment.

3) Gene flow -is genetic exchange due to the migration of fertile individuals or gametes between populations.

2929

4) Mutation Mutation is a change in an organism’s DNA and is represented by changing alleles. Mutations can be transmitted in gametes to offspring, and immediately affect the composition of the gene pool.

The original source of variation.

3030

Genetic Variation, the Substrate for Natural Selection Genetic (heritable) variation within and between populations: exists both as what we can see (e.g., eye color) and what we cannot see (e.g., blood type). Not all variation is heritable.

Environment also can alter an individual’s phenotype [e.g., the hydrangea we saw before, and…

…Map butterflies (color changes are due to seasonal difference in hormones)].

3232

Variation within populations

Most variations occur as quantitative characters (e.g., height); i.e., variation along a continuum, usually indicating polygenic inheritance.

Few variations are discrete (e.g., red vs. white flower color).

Polymorphism is the existence of two or more forms of a character, in high frequencies, within a population. Applies only to discrete characters.

3333

Variation between populations

Geographic variations are differences between gene pools due to differences in environmental factors.

Natural selection may contribute to geographic variation.

It often occurs when populations are located in different areas, but may also occur in populations with isolated individuals.

3434

Geographic variation between isolated populations of house mice.

Normally house mice are 2n = 40. However, chromosomes fused in the mice in the example, so that the diploid number has gone down.

3535

Cline, a type of geographic variation, is a graded variation in individuals that correspond to gradual changes in the environment.

Example: Body size of North American birds tends to increase with increasing latitude. Can you think of a reason for the birds to evolve differently? Example: Height variation in yarrow along an altitudinal gradient. Can you think of a reason for the plants to evolve differently?

3737

Mutation and sexual recombination generate genetic variation a. New alleles originate only by mutations (heritable only in gametes; many kinds of mutations; mutations in functional gene products most important). - In stable environments, mutations often result in little or no benefit to an organism, or are often harmful. - Mutations are more beneficial (rare) in changing environments. (Example: HIV resistance to antiviral drugs.)

b. Sexual recombination is the source of most genetic differences between individuals in a population. - Vast numbers of recombination possibilities result in varying genetic make-up.

3838

Diploidy and balanced polymorphism preserve variation a. Diploidy often hides genetic variation from selection in the form of recessive alleles.

Dominant alleles “hide” recessive alleles in heterozygotes. b. Balanced polymorphism is the ability of natural selection to maintain stable frequencies of at least two phenotypes. Heterozygote advantage is one example of a balanced polymorphism, where the heterozygote has greater survival and reproductive success than either homozygote (Example: Sickle cell anemia where heterozygotes are resistant to malaria).

4040

Frequency-dependent selection = survival of one phenotype declines if that form becomes too common.

(Example: Parasite-Host relationship. Co-evolution occurs, so that if the host becomes resistant, the parasite changes to infect the new host. Over the time, the resistant phenotype declines and a new resistant phenotype emerges.)

4343

Neutral variation is genetic variation that results in no competitive advantage to any individual. - Example: human fingerprints.

4444

A Closer Look: Natural Selection as the Mechanism of Adaptive Evolution Evolutionary fitness - Not direct competition, but instead the difference in reproductive success that is due to many variables.

Natural Selection can be defined in two ways: a. Darwinian fitness- Contribution of an individual to the gene pool, relative to the contributions of other individuals.

And,

4545

b. Relative fitness

- Contribution of a genotype to the next generation, compared to the contributions of alternative genotypes for the same locus.

- Survival doesn’t necessarily increase relative fitness; relative fitness is zero (0) for a sterile plant or animal.

Three ways (modes of selection) in which natural selection can affect the contribution that a genotype makes to the next generation. a. Directional selection favors individuals at one end of the phenotypic range. Most common during times of environmental change or when moving to new habitats.

4646

Directional selection

4747

Diversifying selection favors extreme over intermediate phenotypes.

- Occurs when environmental change favors an extreme phenotype.

Stabilizing selection favors intermediate over extreme phenotypes.

- Reduces variation and maintains the current average.

- Example = human birth weights.

4848

Diversifying selection

5050

Natural selection maintains sexual reproduction

-Sex generates genetic variation during meiosis and fertilization.

-Generation-to-generation variation may be of greatest importance to the continuation of sexual reproduction.

-Disadvantages to using sexual reproduction: Asexual reproduction produces many more offspring.

-The variation produced during meiosis greatly outweighs this disadvantage, so sexual reproduction is here to stay.

5151

All asexual individuals are female (blue). With sex, offspring = half female/half male. Because males don’t reproduce, the overall output is lower for sexual reproduction.

5252

Sexual selection leads to differences between sexes

a. Sexual dimorphism is the difference in appearance between males and females of a species.

-Intrasexual selection is the direct competition between members of the same sex for mates of the opposite sex.

-This gives rise to males most often having secondary sexual equipment such as antlers that are used in competing for females.

-In intersexual selection (mate choice), one sex is choosy when selecting a mate of the opposite sex.

-This gives rise to often amazingly sophisticated secondary sexual characteristics; e.g., peacock feathers.

5555

Natural selection does not produce perfect organisms a. Evolution is limited by historical constraints (e.g., humans have back problems because our ancestors were 4-legged). b. Adaptations are compromises. (Humans are athletic due to flexible limbs, which often dislocate or suffer torn ligaments.) c. Not all evolution is adaptive. Chance probably plays a huge role in evolution and not all changes are for the best. d. Selection edits existing variations. New alleles cannot arise as needed, but most develop from what already is present.

56

Genes Within Populations

Chapter 21

5757

Gene Variation is Raw Material

Natural selection and evolutionary changeSome individuals in a population possess certain

inherited characteristics that play a role in producing more surviving offspring than individuals without those characteristics.

The population gradually includes more individuals with advantageous characteristics.

5858

Gene Variation In Nature

Measuring levels of genetic variationblood groups – 30 blood grp genesEnzymes – 5% heterozygous

Enzyme polymorphismA locus with more variation than can be explained by

mutation is termed polymorphic.Natural populations tend to have more polymorphic loci

than can be accounted for by mutation.15% Drosophila5-8% in vertebrates

5959

Hardy-Weinberg Principle

Population genetics - study of properties of genes in populationsblending inheritance phenotypically intermediate

(phenotypic inheritance) was widely acceptednew genetic variants would quickly be diluted

6060


Hardy-Weinberg - original proportions of genotypes in a population will remain constant from generation to generationSexual reproduction (meiosis and fertilization) alone

will not change allelic (genotypic) proportions.

6161

Hardy-Weinberg Equilibrium

Population of cats n=10016 white and 84 blackbb = whiteB_ = black

Can we figure out the allelic frequencies of individuals BB and Bb?

6262


Necessary assumptionsAllelic frequencies would remain constant if…population size is very largerandom matingno mutationno gene input from external sourcesno selection occurring

6363


Calculate genotype frequencies with a binomial expansion

(p+q)2 = p2 + 2pq + q2

p2 = individuals homozygous for first allele2pq = individuals heterozygous for allelesq2 = individuals homozygous for second allele

6464

p2 + 2pq + q2

and

p+q = 1 (always two alleles)

16 cats white = 16bb then (q2 = 0.16)This we know we can see and count!!!!!If p + q = 1 then we can calculate p from q2

Q = square root of q2 = q √.16 q=0.4p + q = 1 then p = .6 (.6 +.4 = 1)P2 = .36All we need now are those that are

heterozygous (2pq) (2 x .6 x .4)=0.48

.36 + .48 + .16


6565

Hardy-Weinberg Equilibrium

6666

Five Agents of Evolutionary Change

MutationMutation rates are generally so low they have little

effect on Hardy-Weinberg proportions of common alleles.

ultimate source of genetic variation

Gene flowmovement of alleles from one population to another

tend to homogenize allele frequencies

6767


Nonrandom matingassortative mating - phenotypically similar individuals

mateCauses frequencies of particular genotypes to

differ from those predicted by Hardy-Weinberg.

6868


Genetic drift – statistical accidents.Frequencies of particular alleles may change by chance

alone.important in small populations

founder effect - few individuals found new population (small allelic pool)

bottleneck effect - drastic reduction in population, and gene pool size

6969

Genetic Drift - Bottleneck Effect

7070


Selection – Only agent that produces adaptiveevolutionary changeartificial - breeders exert selection natural - nature exerts selection

variation must exist among individualsvariation must result in differences in numbers of

viable offspring producedvariation must be genetically inherited

natural selection is a process, and evolution is an outcome

7171


Selection pressures:avoiding predatorsmatching climatic conditionpesticide resistance

7272

Measuring Fitness

Fitness is defined by evolutionary biologists as the number of surviving offspring left in the next generation.relative measure

Selection favors phenotypes with the greatest fitness.

7373

Interactions Among Evolutionary Forces

Levels of variation retained in a population may be determined by the relative strength of different evolutionary processes.

Gene flow versus natural selectionGene flow can be either a constructive or a

constraining force.Allelic frequencies reflect a balance between

gene flow and natural selection.

7474

Natural Selection Can Maintain Variation

Frequency-dependent selectionPhenotype fitness depends on its frequency within the

population.Negative frequency-dependent selection favors rare

phenotypes.Positive frequency-dependent selection eliminates

variation.

Oscillating selectionSelection favors different phenotypes at different times.

7575

Heterozygote Advantage

Heterozygote advantage will favor heterozygotes, and maintain both alleles instead of removing less successful alleles from a population.Sickle cell anemia

Homozygotes exhibit severe anemia, have abnormal blood cells, and usually die before reproductive age.

Heterozygotes are less susceptible to malaria.

7676

Sickle Cell and Malaria

7777

Forms of Selection

Disruptive selectionSelection eliminates intermediate types.

Directional selectionSelection eliminates one extreme from a phenotypic

array.

Stabilizing selectionSelection acts to eliminate both extremes from an

array of phenotypes.

7878

Kinds of Selection

7979

Selection on Color in Guppies

Guppies are found in small northeastern streams in South America and in nearby mountainous streams in Trinidad.Due to dispersal barriers, guppies can be found in

pools below waterfalls with high predation risk, or pools above waterfalls with low predation risk.

8080

Evolution of Coloration in Guppies

8181

Selection on Color in Guppies

High predation environment - Males exhibit drab coloration and tend to be relatively small and reproduce at a younger age.

Low predation environment - Males display bright coloration, a larger number of spots, and tend to be more successful at defending territories.In the absence of predators, larger, more colorful fish

may produce more offspring.

8282

Evolutionary Change in Spot Number

8383

Limits to Selection

Genes have multiple effectspleiotropy

Evolution requires genetic variationIntense selection may remove variation from a

population at a rate greater than mutation can replenish.

thoroughbred horses

Gene interactions affect allelic fitnessepistatic interactions

85

Variations in genotype arise by random fusion of gametes, mutation, and ______.

85

25% 25%25%25%

201 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

1.Recombination2.Translation3.Transcription4.Sorting by

phenotype

86

The total genetic information in a population is called the

86

Allele fr

equency

Phenotype fr

equency

Gene pool

Dist

ribution of t

raits

25% 25%25%25%

201 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

1.Allele frequency2.Phenotype

frequency3.Gene pool4.Distribution of

traits

87

Saint Bernards and Chihuahuas can’t mate normally owing to great differences in size. What type of reproductive isolationg mechanism is operating here?

87

Deve

lopmental

Prezy

gotic

Postzygo

tic

Geogra

phic

25% 25%25%25%

201 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

1.Developmental2.Prezygotic3.Postzygotic4.Geographic

88

If a population is in genetic equilibrium,

88

Evolution is

occurin

g

Specia

tion is occ

uring

Allelic

frequencie

s are c.

..

Allelic

frequencie

s are r.

..

25% 25%25%25%

201 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

1.Evolution is occuring

2.Speciation is occuring

3.Allelic frequencies are changing

4.Allelic frequencies are remaining stable

89

Mutations affect genetic equilibrium by

89

Maintai

ning it

Intro

ducing n

e...

Causing im

migr...

Causing emigr

a...

25% 25%25%25%

201 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

1.Maintaining it2.Introducing new

alleles3.Causing

immigration4.Causing

emigration

90

Directional selection, disruptive selection, and stabilizing selection are all examples of

90

Genetic e

quilibriu

m

Natu

ral s

election

Muta

tion

Specia

tion

25% 25%25%25%

201 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

1.Genetic equilibrium

2.Natural selection3.Mutation4.Speciation

91

The most common way for new species to form is through

91

Muta

tion

Stabiliz

ing selecti

on

Geogra

phic and re

prod...

Genetic e

quilibriu

m

25% 25%25%25%1.Mutation2.Stabilizing

selection3.Geographic and

reproductive isolation

4.Genetic equilibrium

201 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

9292

Population genetics

• genetic structure of a population

group of individualsof the same speciesthat can interbreed

• alleles

• genotypes

Patterns of genetic variation in populations

Changes in genetic structure through time

9393

Describing genetic structure

• genotype frequencies

• allele frequencies

rr = white

Rr = pink

RR = red

9494

200 white

500 pink

300 red



200/1000 = 0.2 rr

500/1000 = 0.5 Rr

300/1000 = 0.3 RR

total = 1000 flowers

genotypefrequencies:


9595

200 rr

500 Rr

300 RR



900/2000 = 0.45 r

1100/2000 = 0.55 R

total = 2000 alleles

allelefrequencies:

= 400 r

= 500 r= 500 R

= 600 R


9696

for a populationwith genotypes:

100 GG

160 Gg

140 gg

Genotype frequencies

Phenotype frequencies

Allele frequencies

calculate:

9797

for a populationwith genotypes:

100 GG

160 Gg

140 gg


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:

9898

another way to calculateallele frequencies:

100 GG

160 Gg

140 gg


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] = 0.65

G

g

Gg

0.250.40/2 = 0.200.40/2 = 0.200.35

9999

Population genetics – Outline

What is population genetics?

Calculate

Why is genetic variation important?

- genotype frequencies

- allele frequencies

How does genetic structure change?

100100

Genetic variation in space and time

Frequency of Mdh-1 alleles in snail colonies in two city blocks

101101

Changes in frequency of allele F at the Lap locusin prairie vole populations over 20 generations


102102

Why is genetic variation important?potential for change in genetic structure

• adaptation to environmental change- conservation


•divergence of populations- biodiversity

103103


variation

no variation

EXTINCTION!!

globalwarming survival

104104


variation

no variation

north

south

north

south

105105


variation

no variation

divergence

NO DIVERGENCE!!

north

south

north

south

106106

Natural selection

Resistance to antibacterial soap

Generation 1: 1.00 not resistant 0.00 resistant

107107

Natural selection



108108

Natural selection


mutation!



109109

Natural selection





110110

Natural selection






111111

Natural selection can causepopulations to diverge

divergencenorth

south

112112

Selection on sickle-cell allele

aa – abnormal ß hemoglobin sickle-cell anemia

very lowfitness

intermed.fitness

highfitness

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

Aa – both ß hemoglobins resistant to malaria

AA – normal ß hemoglobin vulnerable to malaria

113113

• sampling error

genetic change by chance alone

• misrepresentation• small populations


• mutation

• migration

• natural selection

• genetic drift

• non-random mating

114114

Genetic drift

8 RR8 rr

Before:

After:2 RR6 rr

0.50 R0.50 r

0.25 R0.75 r

115115

• mutation

• migration


• genetic drift


cause changes inallele frequencies


116116

• mutation

• migration


• genetic drift



non-random allele combinations

mating combines alleles into genotypes


117117

AA x AA

AA

aa x aa

aa

AA0.8 x 0.8

Aa0.8 x 0.2

aA0.2 x 0.8

A0.8

A0.8

a0.2

a0.2

aa0.2 x 0.2

genotype frequencies:AA = 0.8 x 0.8 = 0.64Aa = 2(0.8 x0.2) = 0.32aa = 0.2 x 0.2 = 0.04

allele frequencies:A = 0.8A = 0.2

A

AA A

AA

A A

a

a

118118

Example: Coat color

B__ = blackbb = red

Herd of 200 cows: 100 BB, 50 Bb and 50 bb

119119

Allele frequency

No. B alleles = 2(100) + 1(50) = 250No. b alleles = 2(50) + 1(50) = 150Total No. = 400

Allele frequencies:f(B) = 250/400 = .625 f(b) = 150/400 = .375

120120

genotypic frequencies f(BB) = 100/200 = .5 f(Bb) = 50/200 = .25 f(bb) = 50/200 = .25

phenotypic frequenciesf(black) = 150/200 = .75f(red) = 50/200 = .25

121121

Previous example: counted alleles to compute

frequencies. Can also compute allele frequency

from genotypic frequency.

f(A) = f(AA) + 1/2 f(Aa)f(a) = f(aa) + 1/2 f(Aa)

122122

Previous example, we had f(BB) = .50, f(Bb) = .25, f(bb) = .25.

allele frequencies can be computed as:f(B) = f(BB) + 1/2 f(Bb)

= .50 + 1/2 (.25) = .625

f(b) = f(bb) + 1/2 f(Bb) = .25 + 1/2 (.25) = .375

123123

Mink color example:

B_ = brown bb = platinum (blue-gray)

Group of females (.5 BB, .4 Bb, .1 bb) bred toheterozygous males (0 BB, 1.0 Bb, 0 bb).

124124

Allele frequencies among the females?f(B) = .5 + 1/2(.4) = .7f(b) = .1 + 1/2(.4) = .3

Allele frequencies among the males?f(B) = 0 + 1/2(1) = .5f(b) = 0 + 1/2(1) = .5

125125

Expected genotypic, phenotypic and allele frequencies in the offspring?

sires .5 B .5 b

________________dams .7 B .35 BB .35 Bb

.3 b .15 Bb .15 bb

126126

Expected frequencies in offspring

Genotypic

.35 BB

.50 Bb

.15 bb

Phenotypic

.85 brown

.15 platinum

127127

Allele frequencies in offspring

f(B) = f(BB) + .5 f(Bb)= .35 + .5(.50) = .6

f(b) = f(bb) + .5 f(Bb)= .15 + .5(.50) = .4

128128

Also note: allele freq. of offspring = average of sire and dam

f(B) = 1/2 (.5 + .7) = .6f(b) = 1/2 (.5 + .3) = .4

129129

Hardy-Weinberg Theorem

Population gene and genotypic frequencies don’t change over generations if is at or near equilibrium.

Population in equilibrium means that the populations isn’t under evolutionary forces (Assumptions for Equilibrium*)

130130

Assumptions for equilibrium

large population (no random drift)Random matingno selectionno migration (closed population)no mutation

131131


Under these assumptions populations remains stable over generations.

It means: If frequency of allele A in a population is =.5, the sires and cows will generate gametes with frequency =.5 and the frequency of allele A on next generation will be =.5!!!!!

132132


Therefore:It can be used to estimate frequencies when the

genotypic frequencies are unknown.Predict frequencies on the next generation.

133133


If predicted frequencies differ from observed frequencies Population is not under Hardy-Weinberg Equilibrium.

Therefore the population is under selection, migration, mutation or genetic drift.

Or a particular locus is been affected by the forces mentioned above.

134134

Hardy-Weinberg Theorem (2 alleles at 1 locus)

Allele freq.

f(A) = pf(a) = q

p + q = 1

Sum of all alleles = 100%

Genotypic freq.

f(AA) = p2 Dominant homozygousf(Aa) = 2 pq Heterozgousf(aa) = q2 Recessive homozygous

p2 + 2 pq + q2 = 1

Sum of all genotypes = 100%

135135


Allele freq.f(A) = pf(a) = qp + q = 1Sum of all alleles = 100%

Genotypic freq.f(AA) = p2 Dominant homozygousf(Aa) = 2 pq Heterozgousf(aa) = q2 Recessive homozygousp2 + 2 pq + q2 = 1Sum of all genotypes = 100%

Gametes A (p) a(q)

A(p) AA (pp)

Aa(pq)

a(q) aA (qp)

aa (qq)

AA = p*p = p2

Aa = pq + qp = 2pqAa = q*q = q2

136136

Example use of H-W theorem

1000-head sheep flock. No selection for color. Closed to outside breeding.

910 white (B_)90 black (bb)

137137

Start with known: f(black) = f(bb) = .09 =q2

Then, p = 1 – q = .7 = f(B)

f(BB) = p2 = .49f(Bb) = 2pq = .42f(bb) = q2 = .09

)(3.09.2 bfqq

138138

In summary:

Allele freq.f(B) = p = .7 (est.)f(b) = q = .3 (est.)

Phenotypic freq.f(white) = .91 (actual)f(black) = .09 (actual)

Genotypic freq.f(BB) = p2 = .49 (est.)f(Bb) = 2pq = .42 (est.)f(bb) = q2 = .09 (actual)

139139

Mink example using H-W

Group of 2000 (1920 brown, 80 platinum) in equilibrium. We know f(bb) = 80/2000 = .04 = q2

f(b) = (q2) = .04 = .2f(B) = p = 1- q = .8

f(BB) = p2 = .64f(Bb) = 2pq = .32

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Forces that affect allele freq.

1. Mutation2. Migration3. Selection4. Random (genetic) drift

Selection and migration most important for livestock breeders.

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Mutation

Change in base DNA sequence.Source of new alleles.Important over long time-frame.Usually undesirable.

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Migration

Introduction of allele(s) into a population from an outside source.

Classic example: introduction of animals into an isolated population.

others:new herd sire.opening herd books.“under-the-counter” addition to a breed.

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Change in allele freq. due to migration

pmig = m(Pm-Po) where

Pm = allele freq. in migrants

Po = allele freq. in original population

m = proportion of migrants in mixed pop.

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Migration example

100 Red Angus (all bb, p0 = 0)

purchase 100 Bb (pm = .5)

p = m(pm - po) = .5(.5 - 0) = .25

new p = p0 + p = 0 + .25 = .25 = f(B)

new q = q0 + q = 1 - .25 = .75 = f(b)

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Random (genetic) drift

Changes in allele frequency due to random segregation.

Aa .5 A, .5 a gametes

Important only in very small pop.

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Selection

Some individuals leave more offspring than others.

Primary tool to improve genetics of livestock.Does not create new alleles. Does alter freq.Primary effect change allele frequency of

desirable alleles.

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Example: horned/polled cattle

100-head herd (70 HH, 20 Hh, and 10 hh).

Genotypic freq.:f(HH) = .7, f(Hh) = .2, f(hh) = .1

Allele freq.:f(H) = .8, f(h) = .2

Suppose we cull all horned cows. Calculateallele and genotypic frequencies after

culling?

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After culling

f(HH) = .7/.9 = .778f(Hh) = .2/.9 = .222f(hh) = 0

f(H) = .778 + .5(.222) = .889f(h) = 0 + .5(.222) = .111

p = .889 - .8 = .089

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2nd example

Cow herd with 20 HH, 20 Hh, and 60 hh

Initial genotypic freq.: .2HH, .2Hh, .6hh

Initial allele frequencies:f(H) = .2 + 1/2(.2) = .3f(h) = .6 + 1/2(.2) = .7

Again, cull all horned cows.

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Genotypic Allele freq.

freq (HH) = .2/.4 = .5 f(H) = .5 + 1/2(.5) = .75freq (Hh) = .2/.4 = .5 f(h) = 0 + 1/2(.5) = .25freq (hh) = 0

p = .75 - .3 = .45

Note: more change can be made when the initial frequency of desirable gene is low.

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3rd example

initial genotypic freq. .2 HH, .2 Hh, .6 hh.

Initial allele freq. f(H) = .3 and f(h) = .7

Cull half of the horned cows.

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Genotypic Allele freq.f (HH) = .2/.7 = .2857 f(H) = .2857 + 1/2(.2857) = .429f (Hh) = .2/.7 = .2857 f(h) = .4286 + 1/2(.2857) = .571f (hh) = .3/.7 = .4286

p = .429 - .3 = .129

Note: the higher proportion that can be culled, the

more you can change allele freq.

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Selection Against Recessive Allele

Allele Freq. Genotypic Freq. A a AA Aa aa.1 .9 .01 .18 .81.3 .7 .09 .42 .49 .5 .5 .25 .50 .25.7 .3 .49 .42 .09.9 .1 .81 .18 .01

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Factors affecting response to selection

1. Selection intensity2. Degree of dominance

(dominance slows progress)

Initial allele frequency (for a one locus)

Genetic Variability (Bell Curve)

population genetics with qs

Technology

species populations

population centerare

surviving population

original population

ashared gene pool gene

gene pool members

overall gene pool

nonevolving population