Strong Selection is Necessary for Repeated Evolution of Blindness in Cavefish

Strong Selection is Necessary for
Repeated Evolution of Blindness in
Cavefish
Alexandra L. Merry and Reed A. Cartwright
School of Life Sciences and
Center for Human and Comparative Genomics
The Biodesign Institute
Arizona State University
SCalE 2014
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RA Cartwright
cartwrig.ht/lab/
Research Overview: Computational
Evolutionary Genomics
Evolutionary Bioinformatics
Mutational Biology
Pathogen Genomics
Human Population Genetics
Statistical Genetics
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RA Cartwright
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Dramatis personæ
Alex
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Rachel
RA Cartwright
Megan
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Model Organisms for Evolution
Thousands of cave-dwelling species
Repeated across taxa
Neotrogla curvata
Yoshizawa et al. 2014
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RA Cartwright
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Why do Cave Populations go Blind?
Mutation Pressure: Relaxation of purifying selection allows
mutations to accumulate.
•
•
Darwin: eyes would be lost by “disuse”.
Lots of mutations observed in putative eye genes in A.
mexicanus (Hinaux et al. 2013)
Genetic Drift: Without selection blindness alleles can go to
fixation.
Adaptation: individuals without eyes have greater fitness,
resulting in the eventual elimination of seeing fish.
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RA Cartwright
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Astyanax mexicanus: Mexican Tetra
Multiple colonization events
Phenotypic convergence /
repeated evolution of cave
phenotype
Cave populations receive
migrants
Repeated loss of functional
constraint
Bradic et al. 2012
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RA Cartwright
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Astyanax mexicanus: Mexican Tetra
For phenotypes to evolve
repeatedly in the face of
migration requires strong
selection.
Bradic et al. 2012
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RA Cartwright
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Modeling Cavefish Evolution
Assumptions
Small, but infinite, cave
population of diploid fish.
A single biallelic locus with
recessive blindness allele.
Discrete, overlapping
generations.
Blindness favored in the cave
via constant viability selection.
Random mating in the cave.
Loss-of-function mutations
occur the the seeing allele at a
constant rate.
Immigration occurs from the
surface.
Emigration does not influence
the surface.
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Blindness allele maintained on
the surface via mutationselection balance.
RA Cartwright
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Modeling Cavefish Evolution
Variables and Parameters
 Frequency of blindness
allele, b, in the cave
 Frequency of seeing allele, B,
in the cave
 ̃ Frequency of blindness
allele on the surface
 Strength of selection
favoring blindness
 Fraction of immigrants in the
adult population
 Mutation rate of  → 
(per-generation)
Genotype: bb bB
Fitness: 1 +  1
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RA Cartwright
BB
1
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Modeling Cavefish Evolution
Life Cycle
Stage
Zygotes
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Allele Frequency

RA Cartwright
Event
Birth
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Modeling Cavefish Evolution
Life Cycle
Stage
Zygotes
Allele Frequency

Juveniles u� =
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(1+u�)u�2 +1u�(1−u�)
u�̄
RA Cartwright
Event
Birth
Selection
cartwrig.ht/lab/
Modeling Cavefish Evolution
Life Cycle
Stage
Zygotes
Allele Frequency

Juveniles u� =
Adults
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(1+u�)u�2 +1u�(1−u�)
u�̄
Event
Birth
Selection
u� = u� (1 − ) + 
̃
Immigration
RA Cartwright
cartwrig.ht/lab/
Modeling Cavefish Evolution
Life Cycle
Stage
Zygotes
Allele Frequency

Juveniles u� =
Adults
Gametes
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(1+u�)u�2 +1u�(1−u�)
u�̄
Event
Birth
Selection
u� = u� (1 − ) + 
̃
Immigration
′ = u� + (1 − u� )
RA Cartwright
Mutation
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Modeling Cavefish Evolution
Life Cycle
Stage
Zygotes
Allele Frequency

Juveniles u� =
Adults
Gametes
Offspring
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(1+u�)u�2 +1u�(1−u�)
u�̄
Event
Birth
Selection
u� = u� (1 − ) + 
̃
Immigration
′ = u� + (1 − u� )
′
RA Cartwright
Mutation
Fertilization
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Migration-Selection Balance Theory
Wright (1969), Hedrick (1985), Nagalaki (1992), etc.
0.015
0.010
s
∆q
0.005
u
0.000
m
−0.005
−0.010
0.0
biodesign.asu.edu
0.2
0.4
q
RA Cartwright
0.6
0.8
1.0
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Migration-Selection Balance Theory
Wright (1969), Hedrick (1985), Nagalaki (1992), etc.
0.015
0.010
∆q
0.005
0.000
−0.005
0.11
0.0021
0.88
−0.010
0.0
biodesign.asu.edu
0.2
0.4
q
RA Cartwright
0.6
0.8
1.0
cartwrig.ht/lab/
Migration-Selection Balance Theory
Wright (1969), Hedrick (1985), Nagalaki (1992), etc.
0.015
0.010
~ = 0.001
q
∆q
0.005
0.000
−0.005
0.11
0.0021
0.88
−0.010
0.0
biodesign.asu.edu
0.2
0.4
q
RA Cartwright
0.6
0.8
1.0
cartwrig.ht/lab/
Equilibria Analysis
Δ = 0 ⟹ 3 + 2 +  +  = 0
 = −
 =  ((1
̃
− ) − (1 − ) + 1)
 = −(1 − ) − 
 = (1
̃
− ) + 
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RA Cartwright
cartwrig.ht/lab/
Equilibria Analysis
Setting  ̃ = 0 and  = 0 makes analysis tractable.
Δ = 0 ⟹ 3 + 2 +  +  = 0
 = −
 = (1 − )
 = −
=0
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RA Cartwright
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Equilibria Analysis: Approximating is Okay
0.015
0.010
∆q
0.005
0.000
−0.005
−0.010
0.0
biodesign.asu.edu
0.2
0.4
q
RA Cartwright
0.6
0.8
1.0
cartwrig.ht/lab/
Equilibria Analysis
Three possible equilibria:
•
u� = 0 is stable.
And if  >
4u�
:
(1−u�)2
•
u� =
1
2
(1 − u� −
√(1−u�)2 u�−4u�
) is unstable.
•
u� =
1
2
(1 − u� +
√(1−u�)2 u�−4u�
) is stable.
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√u�
√u�
RA Cartwright
cartwrig.ht/lab/
Increasing Immigration Lowers Δ
0.015
0.010
∆q
0.005
0.000
−0.005
−0.010
0.0
biodesign.asu.edu
0.2
0.4
q
RA Cartwright
0.6
0.8
1.0
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Increasing  ̃ Raises Δ
0.015
0.010
∆q
0.005
0.000
−0.005
−0.010
0.0
biodesign.asu.edu
0.2
0.4
q
RA Cartwright
0.6
0.8
1.0
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Increasing  ̃ Raises Δ
We can approximate Δ near  = 0 as
Δ ≈ (1 − )2 − ( + ) + ( ̃ + )
This quadratic has two roots if
( + )2
<
4(1 − )( ̃ + )
Otherwise Δ > 0 when  is near 0.
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RA Cartwright
cartwrig.ht/lab/
Dynamics and Equilibria Summary
0<<
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4u�
:
(1−u�)2
one stable equilibrium near  = .̃
RA Cartwright
cartwrig.ht/lab/
Dynamics and Equilibria Summary
0<<
4u�
(1−u�)2
biodesign.asu.edu
4u�
:
(1−u�)2
<<
one stable equilibrium near  = .̃
(u�+u�)2
:
4(1−u�)(u�u�+u�)
̃
=
two stable and one unstable near
√(1 − )2  − 4 ⎞
1⎛
⎜
⎟
⎜1 −  −
⎟
2
√

⎝
⎠
RA Cartwright
cartwrig.ht/lab/
Dynamics and Equilibria Summary
0<<
4u�
(1−u�)2
>
4u�
:
(1−u�)2
<<
one stable equilibrium near  = .̃
(u�+u�)2
:
4(1−u�)(u�u�+u�)
̃
=
√(1 − )2  − 4 ⎞
1⎛
⎜
⎟
⎜1 −  −
⎟
2
√

⎝
⎠
(u�+u�)2
:
4(1−u�)(u�u�+u�)
̃
biodesign.asu.edu
=
two stable and one unstable near
one stable equilibrium near
√(1 − )2  − 4 ⎞
1⎛
⎜
⎟
1
−

+
⎜
⎟
2
√

⎝
⎠
RA Cartwright
cartwrig.ht/lab/
Dynamics with Three Equilibria
0.015
0.010
~ = 0.001
q
∆q
0.005
0.000
−0.005
0.11
0.0021
0.88
−0.010
0.0
biodesign.asu.edu
0.2
0.4
q
RA Cartwright
0.6
0.8
1.0
cartwrig.ht/lab/
Frequency of b at Equilibrium
u� = 0, u� ̃ = 0.001, u�0 = u� ̃
1
0.1
0.01
s
0.001
1e−04
1e−05
1e−06
Fixation
Extinction
1e−07
1e−08
1e−08
1e−07
1e−06
1e−05
1e−04
0.001
0.01
0.1
1
m
biodesign.asu.edu
RA Cartwright
cartwrig.ht/lab/
Frequency of b at Equilibrium
u� = 0, u� ̃ = 0.001, u�0 = 0.5
1
0.1
0.01
s
0.001
1e−04
1e−05
1e−06
Fixation
Extinction
1e−07
1e−08
1e−08
1e−07
1e−06
1e−05
1e−04
0.001
0.01
0.1
1
m
biodesign.asu.edu
RA Cartwright
cartwrig.ht/lab/
Frequency of b at Equilibrium
u� = 10−5 , u� ̃ = 0.001, u�0 = u� ̃
1
0.1
0.01
s
0.001
1e−04
1e−05
1e−06
Fixation
Extinction
1e−07
1e−08
1e−08
1e−07
1e−06
1e−05
1e−04
0.001
0.01
0.1
1
m
biodesign.asu.edu
RA Cartwright
cartwrig.ht/lab/
Importance of Genetic Drift
0.015
0.010
~ = 0.001
q
∆q
0.005
0.000
−0.005
0.11
0.0021
0.88
−0.010
0.0
biodesign.asu.edu
0.2
0.4
q
RA Cartwright
0.6
0.8
1.0
cartwrig.ht/lab/
Unreasonably Strong Selection
Clearly, really strong selection is needed for a cave population
to evolve blindness.
•
•
If u� = 0.001, u� ̃ = 0.001, and u� = 10−5 , then u� > 0.02 for
fixation.
If u� = 0.001, u� ̃ = 0.001, and u� = 10−6 , then u� > 0.12 for
fixation.
But is strong viability selection probable for the evolution of
blindness in cave fish?
Shouldn’t sight be a nearly neutral phenotype in darkness?
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RA Cartwright
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Sir E. Ray Lankester (1847–1929)
Director of the Natural History Museum
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RA Cartwright
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Sir E. Ray Lankester (1847–1929)
Director of the Natural History Museum
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RA Cartwright
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Phototaxis Could Produce Enough Selection
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RA Cartwright
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Evolutionary Predictions
If there is immigration, then
blindness will only evolve if there is
strong selection against sight.
Emigration of seeing fish produces
this selection pressure.
Cave phenotypes can only evolve via
neutral processes if cave populations
are isolated from the surface.
However, drift is probably important
to get selection started.
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RA Cartwright
cartwrig.ht/lab/
Acknowledgments
SCalE Organizers
Minions
•
•
•
Alexandra Merry
Rachel Schwartz
Megan Howell
Barrett Honors College at ASU
Funding
•
•
•
•
biodesign.asu.edu
ASU Startup Funds
NSF DBI-1356548
NIH R01-GM101352
NIH R01-HG007178
RA Cartwright
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