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BioA414Population Genetics

Handout VIII

Migration• Migration in genetic terms equates to gene flow

• Two major effects– Introduces and spreads unique alleles to new

populations

– If allelic frequencies of migrants and recipient populations differ, gene flow changes allele frequencies of the recipient population

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• The change in allelic freq. p

• Can be written

Allelic frequency after migration

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Migration• Increases the effective size of a population

• Prevents allelic fixation• Migration rate (m) >> mutation rate of ( )

• Especially important to conservation biology because habitat fragmentation can prevent gene flow, and thus reduce effective population size of isolated populations

Distribution of Monarch Butterfly Danaus plexippus

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Overwintering Monarchs clustering on Oyamel trees

Natural selection• Populations growth occurs exponentially more individuals

are produced than can be supported by available resources in

a struggle for existence

• No two individuals are the same, natural populations display

enormous variation, and variation is heritable

• Survival is not random, but depends in part on the hereditary

makeup of offs pring

• Over generations, this process leads to gradual change of

populations and evolution of new s pecies

• Alfred Russel Wallace and Charles Darwin should be given

equal credit for developing the theory of evolution through

natural selection

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Alfred WallaceCharles Darwin

Theory of evolution

Biston betulariathe peppered moth

Countryside Polluted areas

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Features of life• The expression of genes within

cells leads to an organism’s traits– Different alleles encode slightly

different proteins e.g., Enzymes producing different amounts of pigment

– Different alleles different forms of a given trait e.g., Dark- or light-pigmented moths

– Different forms of a trait can influence survival e.g., Differential predation

Natural Selection Natural selection works because some

genotypes are more successful in a given environment than others Successful (adaptive) genotypes become

more common in subsequent generations, causing an alteration in allele frequency over time that leads to a consequent increase in fitness

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Three Forms of Natural Selection

Natural selection• Natural selection equates to the

differential survival of genotypes• Darwinian fitness (W) = relative

reproductive ability of a genotype • Selection coefficient (s) = 1 - W• Contribution of each genotype to the

next generation

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Fitness and selection coefficient

aaAaAA

q2 Waa /WMEAN2pq WAa /WMEANp2 WAA/WMEANRelative frequency after selection

q2 Waa2pq WAap2 WAAFrequency after selection

WaaWAaWAAFitness

q22pqp2Initial genotypic frequencies

General method

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Calculations of allelic frequencies

• Consider a population– One locus, two alleles A1 and A2

– Let p = f(A1) = 0.6 and q = f(A2) = 0.4– Initial genotypic frequencies under HWE:

Calculations of allelic frequencies

• The fitness associated with each genotype– W11 = 0, W12 = 0.4 and W22 = 1

• Frequency after selection:

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• The mean fitness of the populationW = p2W11 + 2pqW12 + q2W22W = 0 + 0.19 + 0.16 = 0.35

• The relative genotypic frequency after selection:

Calculations of allelic frequencies

• Allelic frequency after selection

• Change in allelic frequency caused by selection

Calculations of allelic frequencies

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Effect of selection• WAA = WAa = Waa no natural selection• WAA = WAa < 1.0 and Waa = 1.0 natural

selection and complete dominance operate against a dominant allele

• WAA = WAa = 1.0 and Waa < 1.0 natural selection and complete dominance operate against a recessive allele

Natural selection• WAA < WAa < 1.0 and Waa = 1.0

heterozygote shows intermediate fitness• WAA and Waa < 1.0 and WAa = 1.0

heterozygote has the highest fitness natural selection/codominance favor the heterozygote overdominance or heterosis

• WAa < WAA and Waa = 1.0 heterozygote has lowest fitness natural selection favors either homozygote

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Selection against recessive alleles

• Recessive traits in reduced fitness• If so, there is selection against

homozygous recessives ↓ the frequency of the recessive allele

• Recessive allele is not eliminated (rare) lethal recessive alleles occur in the heterozygote (protected polymorphism)

Selection against a recessive trait

• Consider a population, one locus, one gene, two alleles A and a

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• Genotypes are initially in HWE

• Mean fitness = 1 – sq2

Selection against a recessive trait

• The normalized genotypic frequencies after selection

Selection against a recessive trait

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• Calculate allele frequency after selection– q' = f(aa) + ½ f(Aa)

Selection against a recessive trait

Selection against a recessive trait

• The change in the frequency of a allele after one generation of selection:– q = q' – q =

– q

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Selection against a recessive lethal genotype

Effect of dominance on changes in allelic frequency

• Fitnesses of the genotypes AA, Aa, and aa– I (dominant case) 1.0, 0.5, and 0.5

– II (additive case) 1.0. 0.75, and 0.5

– III (recessive case) 1.0, 1.0, and 0.5

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Frequency of the (a) allele is plotted

• Type of selection against aa

• Calculation of change in allelic frequency

Formulas

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• Type of selection against A

• Calculation of change in allelic frequency

Formulas

• Type of selection no dominance

• Calculation of change in allelic frequency

Formulas

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• Type of selection overdominance

• Calculation of change in allelic frequency

Formulas

• Type of selection against Aa

• Calculation of change in allelic frequency

Formulas

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• Type of selection general

• Calculation of change in allelic frequency

Formulas

Heterozygote superiority• If a heterozygote has higher fitness than

the homozygotes– Both alleles are maintained in the population– Because both are favored by the

heterozygote genotype– Sickle cell trait

• known as heterosis or overdominance

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Hybrid Vigor• Hybrids superior in

performance• Result from the

hybridization• Heterozygote advantage

as in sickle cell anemia is an alternative explanation

Balance between mutation and selection

• When an allele becomes rare, changes in frequency due to natural selection are small

• Mutation occurs at the same time and produces new rare alleles

• Balance between mutation and selection results in evolution

• For a complete recessive allele at equilibrium– q = √ (/s)– If homozygote is lethal (s = 1) then q = √

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• Consider a recessive gene for which the mutation rate is 10-6 and s = 0.1 q = √10-6/0.1 = 0.0032

• Consider a dominant allele u = 10-6

and s = 0.1

p = u/s p = 10-6/0.1 = 0.00001

Balance between mutation and selection