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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
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