Transcript GLYPHOSATE RESISTANCE Background / Problem
Lecture 8: Types of Selection September 17, 2012
Reminders
I will be gone Thursday and Friday. No office hours this week.
Monday Review Session Bring specific questions!
Exam next Wednesday Everything mentioned in lecture and lab fair game Formulas provided: see sample exam
Last Time
Introduction to selection Predicting allele frequency change in response to selection
Today
Dominance and types of selection Why do lethal recessives stick around?
Equilibrium under selection Stable equilibrium: overdominance Unstable equilibrium: underdominance
Putting it all together Relative Fitness (ω) Relative Fitness (hs) A 1 A 1 ω 11 1 A 1 A 2 ω 12 1-hs Δq =pq[q(ω 22 Reduces to: – ω 12 ) - p(ω 11 - ω 12 )] ω Δq =-pqs[ph + q(1-h)] 1-2pqhs-q 2 s A 2 A 2 ω 22 1-s
Modes of Selection on Single Loci
Directional – One homozygous genotype has the highest fitness
Purifying selection AND Darwinian/positive/adaptive selection
ω
1 0.8
0.6
0.4
0.2
0
Depends on your perspective!
0 ≤ h ≤ 1 A AA 1 A 1 A Aa 1 A 2 A 2 A 2
Overdominance – Heterozygous genotype has the highest fitness (balancing selection) h<0, 1-hs > 1
Underdominance – The heterozygous genotypes has the lowest fitness (diversifying selection) h>1, (1-hs) < (1 – s) < 1 for s > 0
ω
1 0.8
0.6
0.4
0.2
0 A AA 1 A 1 A Aa 1 A 2 A 2 A 2
ω
1 0.8
0.6
0.4
0.2
0 A AA 1 A 1 A Aa 1 A 2 A 2 A 2
Directional Selection Δq =-pqs[ph + q(1-h)] 1-2pqhs-q 2
s
0 ≤ h ≤ 1 Δq 0
q
0.5
q
1 h=0.5, s=0.1
Time
Lethal Recessives Relative Fitness (ω) A 1 A 1 ω 11 A 1 A 2 ω 12 Relative Fitness (hs) 1
For completely recessive case, h=0 1-hs
For lethality, s=1
ω
0.8
0.6
1 0.4
0.2
0 A 1 A A 1 1 1 A 1 1 A 1 A 1 2 1 A 2 2 A 2 A 2 2 2 A 2 2 A 2 A 2 ω 22 1-s
Lethal Recessive Δq = -pqs[ph + q(1-h)] = 1-2pqhs-q 2 s For q<1 -pq 2 1-q 2 =
0.0
h=0; s=1
-0.1
ω 11 =1; ω 12 =1-hs=1; ω 22 =1-s=0
q
-0.2
-0.3
-0.4
Δq more negative at large q
-0.5
0.0
Population moves toward maximum fitness
1.0
0.8
Rate of change decreases at low q
0.6
0.4
0.2
0.0
0.0
-q 2 1+q
0.2
0.2
0.4
q
0.6
0.4
q
0.6
0.8
0.8
1.0
1.0
Retention of Lethal Recessives
As p approaches 1, rate of change decreases
Very difficult to eliminate A population
2
, recessive deleterious allele from
Heterozygotes
“
hidden
”
from selection (ω 11 =1; ω 12 =1-hs=1)
12 10
2pq 2q
2
=
At low frequencies, most A
2
heterozygous state:
p p q q 0.5
0.1
0.01
q 1 9 99
are in Ratio of A2 alleles in heterozygotes versus homozygotes
8 6 4 2 0 0.0
0.2
0.4
q
0.6
0.8
1.0
Time to reduce lethal recessives
t
1
q t
q
1 0
See Hedrick 2011, p. 123 for derivation It takes a very large number of generations to reduce lethal recessive frequency once frequency gets low
Selection against Recessives ω s A 1 A 1 ω 11 1 A 1 A 2 ω 12 1-hs A 2 A 2 ω 22 1-s
For completely recessive case, h=0
For deleterious recessives, s<1
ω
0.8
0.6
1 0.4
0.2
0 A 1 A A 1 1 1 A 1 A 1 A 1 2 1 A 2 A 2 A 2 2 2 A 2
Selection Against Recessives Δq = -pqs[ph + q(1-h)] 1-2pqhs-q 2 s
h=0; 0
Maximum rate of change at intermediate allele frequencies
q
s=0.4
Location of maximum depends on s: q=2/3 for small s
Where is maximum rate of change in q for lethal recessive?
Lethal recessive, continues off chart
What is final value of q?
What is final average fitness of population?
Modes of Selection on Single Loci
Directional – One homozygous genotype has the highest fitness
Purifying selection AND Darwinian/positive/adaptive selection
ω
1 0.8
0.6
0.4
0.2
0
Depends on your perspective!
0 ≤ h ≤ 1 A AA 1 A 1 A Aa 1 A 2 A aa 2 A 2
Overdominance – Heterozygous genotype has the highest fitness (balancing selection) h<0, 1-hs > 1
Underdominance – The heterozygous genotypes has the lowest fitness (diversifying selection) h>1, (1-hs) < (1 – s) < 1 for s > 0
ω
1 0.8
0.6
0.4
0.2
0 A AA 1 A 1 A Aa 1 A 2 A aa 2 A 2
ω
1 0.8
0.6
0.4
0.2
0 A 1 A 1 A 1 A 2 A aa 2 A 2
Equilibrium
The point at which allele frequencies become constant through time
Two types of equilibria
Stable
Unstable
The question: stable or unstable?
What happens if I move q a little bit away from equilibrium?
Stable Equilibria
•
Perturbations from equilibrium cause variable to move toward equilibrium railslide.com
Unstable Equilibria
•
Perturbations from equilibrium cause variable to move away from equilibrium
Does selection always cause average fitness to approach 1?
Under what conditions do we reach an equilibrium while polymorphisms still exist in the population?
Heterozygote Advantage (Overdominance)
ω
1 0.8
0.6
0.4
0.2
0
New notation for simplicity (hopefully):
Fitness Fitness in terms of
s
and
h q
1 = 1 2 2
p
0
q
0 w 12 w +
q
2 w 22 w =
p
0
q
0 w 12 w +
q
0 2 w 22
AA A 1 A 1 Aa A 1 A 2 aa A 2 A 2
Genotype A 1 A 1
ω
11 1 –
s
1 A
ω
1 1 A 12 2 A
ω
2 1 – A 22
s
2 2
q
1 =
p
0 2
p
0
q
0 +
q
2 0 (1 -
s
2 ) (1 -
s
1 ) + 2
p
0
q
0 +
q
2 0 (1 -
s
2 )
Equilibrium under Overdominance
Equilibrium occurs under three conditions: q=0, q=1 (trivial), and
s 1 p – s 2 q = 0
s
1
p eq
s
2
q eq
0
s
2
q eq
s
1 ( 1
q eq
)
s
2
q eq
s
1
q eq
s
1
q eq
s
1
s
1
s
2
q eq
(
s
1
s
2 )
s
1
Equilibrium under Overdominance
Allele frequency always approaches same value of q when perturbed away from equilibrium value
Stable equilibrium
Allele frequency change moves population toward maximum average fitness
q eq
s
1
s
1
s
2
Heterozygote Disadvantage (Underdominance) 1 0.8
ω
0.6
0.4
0.2
0 A 1 A 1 A 1 A 2 A aa 2 A 2
Fitness Fitness in terms of
s
and
h
A 1 A 1
ω
11 1 +
s
1 Genotype A 1 A 2
ω
12 1 A 2 A 2
ω
22 1 +
s
2
q eq
s
1
s
1
s
2
Heterozygote Disadvantage (Underdominance)
Fitness Fitness in terms of
s
and
t
A 1 A 1
ω
11 1 +
s
Genotype A 1 A 2
ω
12 1 A 2 A 2
ω
22 1 +
t
s = 0.1
t = 0.1
Equilibrium under Underdominance
Allele frequency moves away from equilibrium point and to extremes when perturbed
Unstable equilibrium
Equilibrium point is at local minimum for average fitness
Population approaches trivial equilibria: fixation of one allele
Where are equilibrium points?
ω 11
=1.1 ω
12
= 1 ω
22
= 1.1
Underdominance Revisited
Genotype Fitness Fitness in terms of
s 1
and
s 2
Fitness in terms of
s h
1 and
h
A 1 A 1
ω
11 1 +
s
1 1 A 1 A 2
ω
12 1 1-
hs
A 2 A 2
ω
22 1 +
s
2 1-
s s
1
hs s
2
s
(
h hs
1 )
s ω
s 1
hs
s s 2
A 1 A 1 A 1 A 2 A 2 A 2
Why does
“
nontrivial
”
equilibrium occur with underdominance?
Why doesn always go to fixation if
A 1 A 1
genotype?
’
t A
1
is most fit allele
ω
Proportion of A 1 alleles in heterozygous state:
pq
(pq+p 2 )
= q
A 1 A 1 A 1 A 2 A 2 A 2
What determines the equilibrium point with underdominance?
ω 11 =1; ω 12 =0.8; ω 22 =1 ω 11 =0.85; ω 12 =0.8; ω 22 =1
Why does equilibrium point of A
1
allele frequency increase when selection coefficient decreases?
A 1 A 1 A 1 A 2 A 2 A 2 p eq s
1
p eq
s
1
s
2
s
2
s
2
q eq
Example: Kuru in Fore Tribespeople
Prion disease in Fore tribesmen
Transmitted by cannibalism of relatives by women/children
Cannibalism stopped in 1950
’
s
Older people exposed to selection, younger are
‘
controls
’
Identified locus that causes susceptibility: Prion Protein Gene, PRNP
MM and VV are susceptible, MV are resistant http://learn.genetics.utah.edu/features/prions/kuru.cfm
Kuru and Heterozygote Advantage
Selection coefficient (
s
1 2
v
)
(only females)
0.403
0.2985
0.373
q eq
s MM s MM
s VV
0 .
483
Tremendous selective advantage in favor of heterozygotes
Balancing selection maintains polymorphism in human populations