Strong Selection is Necessary for Evolution of Blindness in Cave Dwellers

Blindness has evolved repeatedly in cave-dwelling organisms, and investigating the loss of sight in cave dwellers presents an opportunity to understand the operation of fundamental evolutionary processes, including drift, selection, mutation, and migration. The observation of blind organisms has prompted many hypotheses for their blindness, including both accumulation of neutral, loss-of-function mutations and adaptation to darkness. Here we model the evolution of blindness in caves. This model captures the interaction of three forces: (1) selection favoring alleles causing blindness, (2) immigration of sightedness alleles from a surface population, and (3) loss-of-function mutations creating blindness alleles. We investigated the dynamics of this model and determined selection-strength thresholds that result in blindness evolving in caves despite immigration of sightedness alleles from the surface. Our results indicate that strong selection is required for the evolution of blindness in cave-dwelling organisms, which is consistent with recent work suggesting a high metabolic cost of eye development.

"neutral-mutation hypothesis" -random mutations can accumulate in genes or regulatory regions related 23 to sight when, as in caves, there is no purifying selection to eliminate them. However, the accumulation 24 of mutations causing blindness due to mutation pressure would take a long time to result in fixation of 25 blindness in populations on its own (Barr, 1968). Thus, genetic drift has been proposed to accelerate 26 the evolution of blindness due to mutation pressure (Kimura and King, 1979;Borowsky, 2015;Wilkens, 27 1988). This hypothesis of relaxed selection appears to be supported by the observation of a high number 28 of substitutions in putative eye genes in the blind forms of cavefishes (Hinaux et al., 2013;Protas et al., 29 2006; Gross et al., 2009). However, repeatedly developing blindness in cave populations simply by drift in 30 isolation seems unlikely. 31 Relaxing selection that maintains the eye, however, also allows for other agents of selection to act on 32 this trait (Lahti et al., 2009). The "adaptation hypothesis" suggests that there is a cost to an eye; thus, 33 individuals without eyes have greater fitness when eyes are are not helpful, resulting in the eventual 34 elimination of seeing individuals. This cost may either come from the energy required to develop a complex 35 structure or due to the vulnerability of the eye (Barr, 1968;Strickler et al., 2007;Jeffery, 2005 Moran et al., 2015). Alternatively, positive selection 37 may act on genes related to the eye if these genes act pleiotropically on traits that are beneficial in the 38 dark. For example, in the Mexican tetra (Astyanax mexicanus) increased expression of Hedgehog (Hh) 39 affects feeding structures, allowing better foraging in low light conditions (Jeffery, 2001(Jeffery, , 2005. Increased 40 Hh signaling also inhibits pax6 expression, which results in eye loss during development (Yamamoto 41 et al., 2004;Jeffery, 2005). Alternatively, cryptic variation may be maintained in normal conditions and 42 expressed as blindness only in case of stress, such as entry into the cave (Rohner et al., 2013). When the 43 cryptic variation is "unmasked", it is then exposed to selection and could become fixed in the population. 44 Given that there is often gene flow from surface populations into caves, it seems that blind phenotypes 45 should be lost unless selection for blindness is large (Avise and Selander, 1972). Recent work suggests a 46 very high cost to developing neural tissue, including eyes (Moran et al., 2015). This cost, combined with pleiotropic effects, could lead to blindness despite immigration. However, the level of selection required 48 to induce blindness in cave populations has not been quantified. 49 Here, we model the effects of migration, selection, and mutation to determine the conditions required for 50 the evolution of blindness. This model allows us to explore migration-selection-mutation balance. Where 51 previous theory have explored this balance more generally (Haldane, 1930;Wright, 1931Wright, , 1969Hedrick, 52 2011; Nagylaki, 1992;Yeaman and Otto, 2011;Yeaman and Whitlock, 2011;Bulmer, 1972), we address cavefish 53 evolution specifically. The amount of selection required to oppose the force of immigration is high, but 54 consistent with previous work on metabolic costs in novel environments and selection in other species. 55 Interestingly, drift only impacts blindness in the cave population in a limited range of combinations of 56 selection, dominance, and migration.

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Assumptions 59 We consider two populations: surface-dwelling and cave-dwelling. We are interested in determining 60 when the cave population will evolve blindness, i.e. become mostly comprised of blind individuals, as 61 has occurred in numerous natural systems. We first assume that the surface and cave populations do 62 not experience drift (i.e. populations are of infinite size). Additionally, immigration from the surface 63 population into the cave affects the allele frequency in the cave, but emigration from the cave to the 64 surface does not affect the surface population, as we assume that the surface population is significantly 65 larger than the cave. Generations are discrete and non-overlapping, and mating is random. We track a 66 single biallelic locus, where is the seeing allele and where is blindness allele. The frequency of is 67 denoted by ∈ [0, 1] on the surface and ∈ [0, 1] in the cave. On the surface, we assume that blindness 68 is strongly selected against, and is dictated by mutation-selection balance. Identifying equilibrium allele frequencies 88 The model we have developed is an example of migration-selection balance (Wright, 1969;Hedrick, 2011;89 Nagylaki, 1992), extended to also include mutation. An equilibrium exists for this model when Δ = 0. . 119 We can also estimate the amount of selection required such that is an equilibrium ( ( ) = 0, Equation 120 3): This equation is not valid for all ∈ [0, 1]. If the migration rate is low, < , no level of 122 selection will make an equilibrium, as all equilibria will be greater than . Similarly, if the migration rate 123 is high, no level of selection will make an equilibrium, as all equilibria will be less than .

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Dynamics and the evolution of blindness. The dynamics of the evolution of the cave population 126 depend on the parameter values and the starting allele frequency, 0 . If there is one equilibrium, then the 127 frequency of will evolve monotonically towards it, i.e. →âs → ∞. If there are three equilibria, then 128 the frequency of will evolve monotonically tôif 0 <̂and tôif 0 >̂.

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When the cave population is founded, its initial allele frequency will likely match the equilibrium frequency 130 on the surface ( 0 = ). Because <(Equation 2), the allele frequency in the cave will increase due 131 to selection until it reaches the lowest equilibrium, i.e. ∞ = inf{ ∶ 0 ≤ ≤ 1 and Δ = 0}. Whether 132 blindness evolves in the cave depends on whether ∞ ≥ * , where * is a researcher-chosen threshold 133 for determining that the cave population is a "blind" population. For example, * = 0.5 would specify 134 that the blindness allele is the majority allele, and * = 0.99 would determine that the blindness allele is 135 approximately fixed. We can also focus on phenotypes, and let = 2 + 2 (1 − )ℎ measure the average 136 blind phenotype in the cave; then We define * as the minimum level of selection required for cave population to become blind, given the 138 other parameters, i.e. 139 * = inf{ ∶ > 0 and ∞ ≥ * ≫ } For simplicity, we will only consider values of * much higher than the surface allele frequency. If there 140 is one equilibrium, * = * ( , ℎ, , ); however, if there are three equilibria, will evolve to the lower 141 equilibrium and ∞ ≈ ≠ * (typically). Thus selection needs to be strong enough such that there is 142 only one equilibrium; therefore, 143 * ≈ inf{ ∶ > 0 and ≥ * ( , ℎ, , ) and Δ( , , ℎ, , ) < 0} where Δ( , , ℎ, , ) is the discriminant of Equation 3. Figure 2 plots analytical solutions for * based on 144 different thresholds. When ≫ , the ratio * / is roughly constant such that if ∞ ≥ * then See Appendix for derivation.

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In order to study the equilibria in more detail we limit subsequent work to a model where blindness is 148 recessive (ℎ = 0). As we have previously shown the effects of varying ℎ, its impact on subsequent results 149 can be inferred generally. First, we will simplify our model by assuming that ≪ 1 such that 1 − ≈ 1 Furthermore if 0 = , the selection-threshold for blindness to be established in the cave is where * is the allele-frequency threshold. would provide more opportunities for drift to assist the evolution of blindness in caves. 270 We conclude that in most cases strong selection is necessary for the evolution of blind populations in caves.