C. Blair/The Ain Ghazal Archaeological Project

C. Blair/The Ain Ghazal Archaeological Project Direc8onal selec8on fully recessive h = 0
Relative fitness wij
1
additive h = 0.5
fully dominant h = 1
0
wij
A1A1
A1A2
A2A2
1
1 – hs
1 – s
w1 = w11 pt + w12qt = pt + (1 − hs)qt
w 2 = w12 pt + w 22qt = (1 − hs) pt + (1 − s)qt
1
Δpt =
w 1 −w 2
w
pt hs + qt s(1 − h) h = 2 1
pt qt =
pt ≈
spt qt
s<< 1 2
w
w 2 = w12 pt + w 22qt = (1 − hs) pt + (1 − s)qt
1
Δpt =
w 1 −w 2
w
pt hs + qt s(1 − h) h = 2 1
pt qt =
pt ≈
spt qt
s<<
1
w
2
Freq. of A1 allele, pt w1 = w11 pt + w12qt = pt + (1 − hs)qt
A1 dominant A1 addi8ve A1 recessive Genera8on t Δp Time for an allele to move from frequency A new advantageous addi8ve allele takes p0 to pt if h= ½ and s<<1 on average 2ln(2N)/s genera8ons to reach (near) fixa8on, where N is the popula8on t 0
size. t 0
If p0=1/(2N) & pt =1-‐1/(2N) t⇡
Freq. of A1 allele, pt 2
log
s
✓
pq
qp
4
t ⇡ log(2N )
s
◆
Beneficial dominant alleles are quick to spread but slow to fix. Red Morph: Homozygotes rr and heterozygotes rR Silver fox pelts were par8cularly valuable to hunters Silver fox morph :RR homozygote Why is there so much polymorphism? •  The paradox of varia8on in popula8on gene8cs: Selec8on quickly fixes alleles that are beneficial so why is there so much gene8c polymorphism within natural popula8ons? Three broad explana8ons: •  Selec8on some8mes acts to maintain varia8on, balancing selec8on •  Muta8on-‐selec8on balance •  Muta8on-‐dri\ balance (Neutral theory). Selec8on can act to maintain polymorphism within a popula8on •  Selec8on can maintain balanced polymorphisms in the popula8on •  Balancing selec8on can result when: •  The heterozygotes for an allele are fi]er than either homozygote (termed heterozygote advantage or overdominance) (Heterozygote superiority) 1
Relative fitnnes wij
Overdominance s1
s2
0
A1A1
1 – s1
A1A2
1
A2A2
1 – s2
Selec8ve maintenance of gene8c varia8on Sickle allele dist
Malaria dist Data on sickle genotype frequencies in infants and adults in Tanzania (Allison 1956) Genotype AA AS SS Freq S allele Freq infant 0.66 0.31 0.03 0.186 Freq adult
0.61 0.38 0.007 0.198 Fitness 0.93 1.23 0.24 Rel fitness
0.76 1 0.18 Heterozygote has highest fitness = heterozygote advantage = overdominance Anemia and malaria are opposing selec8ve factors See also Haldane 1949 Selec8ve maintenance of gene8c varia8on q Frequency through 8me Genotype AA AS SS Rel fitness
0.76 1 0.18 qeq Freq S allele= 0.4 Freq infant 0.36 0.48 0.16 Rel fit xFreq.
0.76x0.36 1 x0.48 0.18x0.16 Genera8on =0.274 =0.48
=0.028 Rela8ve w=Sum=0.782 Freq adult
0.35 0.61 0.037 New S frequency = fSS+ (fAS/2) = 0.34 Freq. S allele = 0.1 Freq infant 0.81 0.18 0.01 Freq. x Rel fit
0.76x0.81 1 x0.18 0.01x0.18 =0.616 =0.18
=0.0018 Rela8ve w=Sum=0.797 Freq adult
0.772 0.225 0.0023 New S frequency = fSS+ (fAS/2) = 0.115 Frequency through 8me q Heterozygote advantage (Over dominance) A1A1 A1A2 A2A2 1-‐s1 1 1-‐s2 Rel fitness 0.76 1 0.18 s1=1-‐0.76=0.24 s2=1-‐0.18=0.82 At equilibrium Δp =0 Δp = pq( w1 -‐ w2) w qeq Genera8on i.e.( w1 -‐ w2) = pw11+qw12-‐pw12 – qw22 = 0 At equilibrium, freq A1 =peq= s2/(s1+s2) freq A2 =qeq= s1/(s1+s2) the mean fitness of pop. Is maximized at this frequency. qeq= 0.24 = 0.226 0.24+0.82 Overdominance (heterozygote advantage) A1A1 A1A2 A2A2 1 – s1 1 1 – s2 s1 > 0, s2 > 0 w1 = (pw11 + qw12) w2 = (pw12 + qw22) Δp = pq( w1 -‐ w2) w At equilibrium Δp = 0 Two boring eq. p = 0, q = 0 Polymorphic eq. pw11 + qw12= pw12 + qw22 Over-‐dominance results in a balanced polymorphism Addi8ve effect of alleles 1
2
1.4
1.0
0.8
0.4
0.2
0.4
●
0.2
0
●
●
0.4
●
●
0.6
●
range(a) * c(0.5, 1.5)
1.2
1.4
1.2
1.0
0.8
●
0.6
0.6
●
range(a) * c(0.5, 1.5)
1.2
1.0
0.8
●
0.2
Mean pheno. of each geno. 1.4
The addi8ve/marginal effect on an allele is the effect of an allele averaged over the gene8c backgrounds it can occur in. What is gain in phenotype for extra copy of allele A? 0
1
2
0
1
2
The addi8ve/marginal effect of an allele, is the effect of an allele averaged across the possible genotypes it could occur in. Addi8ve effect of A allele = αA = p X2 + q X1 Addi8ve effect of a allele = αa = p X1 + q X0 The contribu8on of locus to the addi8ve variance is = 2pq (αA -‐ αa)2 However, unless the allele is truly addi8ve in its effect there is unexplained variance Balancing Selec8on Modes of selec8on maintaining varia8on are collec8vely referred to as balancing selec9on Heterozygote advantage is just one form of balancing selec8on A broad class of balancing selec8on is nega9ve frequency dependent selec9on •  Fitness nega8vely correlated with frequency •  Occurs in many systems due to interac8ons between individuals or species •  e.g. prey/predator or pathogen/host dynamics

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