Population genetics with qs

Population

Genetics

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

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

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

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

Modern Evolutionary Thought

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

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

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

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)

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

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.

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.

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.

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

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

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.

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

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

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.

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

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.

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.

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)].

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.

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.

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.

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?

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.

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).

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.)

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

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.

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.

Directional selection

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.

Diversifying selection

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.

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.

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.

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.

Genes Within Populations

Chapter 21

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.

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

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

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.

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?

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

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

p2 + 2pq + q2

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

Hardy-Weinberg Equilibrium

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

Nonrandom matingassortative mating - phenotypically similar individuals

mateCauses frequencies of particular genotypes to

differ from those predicted by Hardy-Weinberg.

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

Genetic Drift - Bottleneck Effect

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

Selection pressures:avoiding predatorsmatching climatic conditionpesticide resistance

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.

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.

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.

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.

Sickle Cell and Malaria

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.

Kinds of Selection

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.

Evolution of Coloration in Guppies

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.

Evolutionary Change in Spot Number

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

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

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

The total genetic information in a population is called the

Allele fr

equency

Phenotype fr

equency

Gene pool

ribution of t

25% 25%25%25%

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21 22 23 24 25 26 27 28 29 30

1.Allele frequency2.Phenotype

frequency3.Gene pool4.Distribution of

traits

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

lopmental

Postzygo

Geogra

25% 25%25%25%

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21 22 23 24 25 26 27 28 29 30

1.Developmental2.Prezygotic3.Postzygotic4.Geographic

If a population is in genetic equilibrium,

Evolution is

occurin

Specia

tion is occ

Allelic

frequencie

s are c.

Allelic

frequencie

s are r.

25% 25%25%25%

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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

Mutations affect genetic equilibrium by

Maintai

ning it

ducing n

Causing im

migr...

Causing emigr

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

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

Genetic e

quilibriu

election

Specia

25% 25%25%25%

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21 22 23 24 25 26 27 28 29 30

1.Genetic equilibrium

2.Natural selection3.Mutation4.Speciation

The most common way for new species to form is through

Stabiliz

ing selecti

Geogra

phic and re

prod...

Genetic e

quilibriu

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

selection3.Geographic and

reproductive isolation

4.Genetic equilibrium

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21 22 23 24 25 26 27 28 29 30

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

Describing genetic structure

• genotype frequencies

• allele frequencies

rr = white

Rr = pink

RR = red

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:

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

for a populationwith genotypes:

100 GG

160 Gg

140 gg

Genotype frequencies

Phenotype frequencies

Allele frequencies

calculate:

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:

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

0.250.40/2 = 0.200.40/2 = 0.200.35

Population genetics – Outline

What is population genetics?

Calculate

Why is genetic variation important?

- genotype frequencies

- allele frequencies

How does genetic structure change?

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Genetic variation in space and time

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

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

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

• adaptation to environmental change- conservation

•divergence of populations- biodiversity

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variation

no variation

EXTINCTION!!

globalwarming survival

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variation

no variation

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variation

no variation

divergence

NO DIVERGENCE!!

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Natural selection

Resistance to antibacterial soap

Generation 1: 1.00 not resistant 0.00 resistant

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Natural selection

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Natural selection

mutation!

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Natural selection

110110

Natural selection

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Natural selection can causepopulations to diverge

divergencenorth

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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

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• sampling error

genetic change by chance alone

• misrepresentation• small populations

• mutation

• migration

• natural selection

• genetic drift

• non-random mating

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Genetic drift

8 RR8 rr

Before:

After:2 RR6 rr

0.50 R0.50 r

0.25 R0.75 r

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• mutation

• migration

• genetic drift

cause changes inallele frequencies

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• mutation

• migration

• genetic drift

non-random allele combinations

mating combines alleles into genotypes

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AA x AA

aa x aa

AA0.8 x 0.8

Aa0.8 x 0.2

aA0.2 x 0.8

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

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Example: Coat color

B__ = blackbb = red

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

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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

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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

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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)

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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

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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).

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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

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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

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Expected frequencies in offspring

Genotypic

.35 BB

.50 Bb

.15 bb

Phenotypic

.85 brown

.15 platinum

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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

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

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

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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*)

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Assumptions for equilibrium

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

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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!!!!!

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Therefore:It can be used to estimate frequencies when the

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

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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.

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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%

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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

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Example use of H-W theorem

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

910 white (B_)90 black (bb)

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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

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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)

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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

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