Cutter_Lecture_10 - PopulationGeneticsofNaturalSelection(2)...

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1 Population Genetics of Natural Selection (2)
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1 locus 2 alleles: A 2 A 2 individuals largest, A 1 A 1 individuals smallest Directional selection for large size Directional selection increases relative frequency of genotypes that encode the more extreme trait values Effects of directional selection on genotypes 2 size Breeding individuals NON breeding individuals
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Genotype ratios for adults AFTER SELECTION: p 2 w 11 : 2pqw 12 : q 2 w 22 Allele ratios for adults and their gametes (A 1 : A 2 ): [p 2 w 11 + ½(2pqw 12 )] : [½(2pqw 12 ) + q 2 w 22 ] =p(pw 11 + qw 12 ) : q(pw 12 + qw 22 ) Sum of alleles after selection = w Allele frequencies in adults (and next gen gametes) after selection (p’, q’): Change in allele frequencies between generations: Δ p= p’ p Simple model of directional selection 3 ( w ij ) w 11 w 12 w 22 (at birth) () w qw pw p p 12 11 ' + = Σ = 1 0 w ij 1 Σ 1 p’ + q’ = 1
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Change in allele frequencies between generations: Δ p= p’ p Simple model of directional selection 4 ( w ij ) w 11 w 12 w 22 (at birth) () ( ) () ( ) [] sq spq p w w w q w w p pq p w w p qw pw p p w qw pw p p = Δ + = Δ + = + = Δ 1 2 1 22 12 12 11 12 11 12 11 Δ p> 0 … only if p > 0 and s > 0 Provided s > 0… p will always increase until fixation (p=1) Allele A 1 can invade the population, even when rare Even if s is tiny (0.001)
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Change in allele frequencies between generations: Δ p= p’–p = Δ q Same equations apply to selection on disadvantageous allele Selection fixes A 1 Positive directional selection on A 1 A 1 Selection eliminates A 2 Purifying (negative) selection against A 1 A 2 and A 2 A 2 Selection against disadvantageous allele 5
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If Δ p> 0 in this model, eventually A 1 will be fixed How long will it take?
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Cutter_Lecture_10 - PopulationGeneticsofNaturalSelection(2)...

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