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 biodesign.asu.edu RA Cartwright cartwrig.ht/lab/ Research Overview: Computational Evolutionary Genomics Evolutionary Bioinformatics Mutational Biology Pathogen Genomics Human Population Genetics Statistical Genetics biodesign.asu.edu RA Cartwright cartwrig.ht/lab/ Dramatis personæ Alex biodesign.asu.edu Rachel RA Cartwright Megan cartwrig.ht/lab/ Model Organisms for Evolution Thousands of cave-dwelling species Repeated across taxa Neotrogla curvata Yoshizawa et al. 2014 biodesign.asu.edu RA Cartwright cartwrig.ht/lab/ 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. biodesign.asu.edu RA Cartwright cartwrig.ht/lab/ 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 biodesign.asu.edu RA Cartwright cartwrig.ht/lab/ Astyanax mexicanus: Mexican Tetra For phenotypes to evolve repeatedly in the face of migration requires strong selection. Bradic et al. 2012 biodesign.asu.edu RA Cartwright cartwrig.ht/lab/ 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. biodesign.asu.edu Blindness allele maintained on the surface via mutationselection balance. RA Cartwright cartwrig.ht/lab/ Modeling Cavefish Evolution Variables and Parameters 𝑞 Frequency of blindness allele, b, in the cave 𝑝 Frequency of seeing allele, B, in the cave 𝑞 ̃ Frequency of blindness allele on the surface 𝑠 Strength of selection favoring blindness 𝑚 Fraction of immigrants in the adult population 𝑢 Mutation rate of 𝐵 → 𝑏 (per-generation) Genotype: bb bB Fitness: 1 + 𝑠 1 biodesign.asu.edu RA Cartwright BB 1 cartwrig.ht/lab/ Modeling Cavefish Evolution Life Cycle Stage Zygotes biodesign.asu.edu Allele Frequency 𝑞 RA Cartwright Event Birth cartwrig.ht/lab/ Modeling Cavefish Evolution Life Cycle Stage Zygotes Allele Frequency 𝑞 Juveniles 𝑞u� = biodesign.asu.edu (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 𝑞 Juveniles 𝑞u� = Adults biodesign.asu.edu (1+u�)u�2 +1u�(1−u�) u�̄ Event Birth Selection 𝑞u� = 𝑞u� (1 − 𝑚) + 𝑞𝑚 ̃ Immigration RA Cartwright cartwrig.ht/lab/ Modeling Cavefish Evolution Life Cycle Stage Zygotes Allele Frequency 𝑞 Juveniles 𝑞u� = Adults Gametes biodesign.asu.edu (1+u�)u�2 +1u�(1−u�) u�̄ Event Birth Selection 𝑞u� = 𝑞u� (1 − 𝑚) + 𝑞𝑚 ̃ Immigration 𝑞′ = 𝑞u� + (1 − 𝑞u� )𝑢 RA Cartwright Mutation cartwrig.ht/lab/ Modeling Cavefish Evolution Life Cycle Stage Zygotes Allele Frequency 𝑞 Juveniles 𝑞u� = Adults Gametes Offspring biodesign.asu.edu (1+u�)u�2 +1u�(1−u�) u�̄ Event Birth Selection 𝑞u� = 𝑞u� (1 − 𝑚) + 𝑞𝑚 ̃ Immigration 𝑞′ = 𝑞u� + (1 − 𝑞u� )𝑢 𝑞′ RA Cartwright Mutation Fertilization cartwrig.ht/lab/ 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 cartwrig.ht/lab/ 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 Δ𝑞 = 0 ⟹ 𝐴𝑞3 + 𝐵𝑞2 + 𝐶𝑞 + 𝐷 = 0 𝐴 = −𝑠 𝐵 = 𝑠 (𝑞𝑚(1 ̃ − 𝑢) − 𝑚(1 − 𝑢) + 1) 𝐶 = −𝑚(1 − 𝑢) − 𝑢 𝐷 = 𝑞𝑚(1 ̃ − 𝑢) + 𝑢 biodesign.asu.edu RA Cartwright cartwrig.ht/lab/ Equilibria Analysis Setting 𝑞 ̃ = 0 and 𝑢 = 0 makes analysis tractable. Δ𝑞 = 0 ⟹ 𝐴𝑞3 + 𝐵𝑞2 + 𝐶𝑞 + 𝐷 = 0 𝐴 = −𝑠 𝐵 = 𝑠(1 − 𝑚) 𝐶 = −𝑚 𝐷=0 biodesign.asu.edu RA Cartwright cartwrig.ht/lab/ 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 𝑠 > 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. biodesign.asu.edu √u� √u� RA Cartwright cartwrig.ht/lab/ Increasing Immigration Lowers Δ𝑞 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/ Increasing 𝑞 ̃ Raises Δ𝑞 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/ Increasing 𝑞 ̃ Raises Δ𝑞 We can approximate Δ𝑞 near 𝑞 = 0 as Δ𝑞 ≈ 𝑠(1 − 𝑚)𝑞2 − (𝑚 + 𝑢)𝑞 + (𝑚𝑞 ̃ + 𝑢) This quadratic has two roots if (𝑢 + 𝑚)2 𝑠< 4(1 − 𝑚)(𝑚𝑞 ̃ + 𝑢) Otherwise Δ𝑞 > 0 when 𝑞 is near 0. biodesign.asu.edu RA Cartwright cartwrig.ht/lab/ Dynamics and Equilibria Summary 0<𝑠< biodesign.asu.edu 4u� : (1−u�)2 one stable equilibrium near 𝑞 = 𝑞.̃ RA Cartwright cartwrig.ht/lab/ Dynamics and Equilibria Summary 0<𝑠< 4u� (1−u�)2 biodesign.asu.edu 4u� : (1−u�)2 <𝑠< one stable equilibrium near 𝑞 = 𝑞.̃ (u�+u�)2 : 4(1−u�)(u�u�+u�) ̃ 𝑞= two stable and one unstable near √(1 − 𝑚)2 𝑠 − 4𝑚 ⎞ 1⎛ ⎜ ⎟ ⎜1 − 𝑚 − ⎟ 2 √ 𝑠 ⎝ ⎠ RA Cartwright cartwrig.ht/lab/ Dynamics and Equilibria Summary 0<𝑠< 4u� (1−u�)2 𝑠> 4u� : (1−u�)2 <𝑠< one stable equilibrium near 𝑞 = 𝑞.̃ (u�+u�)2 : 4(1−u�)(u�u�+u�) ̃ 𝑞= √(1 − 𝑚)2 𝑠 − 4𝑚 ⎞ 1⎛ ⎜ ⎟ ⎜1 − 𝑚 − ⎟ 2 √ 𝑠 ⎝ ⎠ (u�+u�)2 : 4(1−u�)(u�u�+u�) ̃ biodesign.asu.edu 𝑞= two stable and one unstable near one stable equilibrium near √(1 − 𝑚)2 𝑠 − 4𝑚 ⎞ 1⎛ ⎜ ⎟ 1 − 𝑚 + ⎜ ⎟ 2 √ 𝑠 ⎝ ⎠ 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? biodesign.asu.edu RA Cartwright cartwrig.ht/lab/ Sir E. Ray Lankester (1847–1929) Director of the Natural History Museum biodesign.asu.edu RA Cartwright cartwrig.ht/lab/ Sir E. Ray Lankester (1847–1929) Director of the Natural History Museum biodesign.asu.edu RA Cartwright cartwrig.ht/lab/ Phototaxis Could Produce Enough Selection biodesign.asu.edu RA Cartwright cartwrig.ht/lab/ 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. biodesign.asu.edu 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 cartwrig.ht/lab/
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