Complex adaptations can drive the evolution of the capacitor [PSI], even with realistic rates of yeast sex

Abstract

The [PSI(+)] prion may enhance evolvability by revealing previously cryptic genetic variation, but it is unclear whether such evolvability properties could be favored by natural selection. Sex inhibits the evolution of other putative evolvability mechanisms, such as mutator alleles. This paper explores whether sex also prevents natural selection from favoring modifier alleles that facilitate [PSI(+)] formation. Sex may permit the spread of "cheater" alleles that acquire the benefits of [PSI(+)] through mating without incurring the cost of producing [PSI(+)] at times when it is not adaptive. Using recent quantitative estimates of the frequency of sex in Saccharomyces paradoxus, we calculate that natural selection for evolvability can drive the evolution of the [PSI(+)] system, so long as yeast populations occasionally require complex adaptations involving synergistic epistasis between two loci. If adaptations are always simple and require substitution at only a single locus, then the [PSI(+)] system is not favored by natural selection. Obligate sex might inhibit the evolution of [PSI(+)]-like systems in other species.

Figure 1. Different mechanisms of readthrough translation.

Either the presence of [PSI⁺] (B) or an agp ⁺ point mutation (C) can lead to readthrough of the wild-type stop codon (A).

Figure 2. Alternative pathways, with and without [PSI⁺], leading to the same readthrough adaptation.

Adaptation in environment 2 can proceed either via: (1) [PSI⁺] appearance followed by point mutation at agp loci (genetic assimilation) and finally reversion to [psi ⁻] (left) and (2) direct adaptation at agp loci without involvement of [PSI⁺] (right). The fitness of an individual is given to the right of its genotype, calculated using s ₂ = 0.001. Only homozygous states are shown because inbreeding quickly leads to homozygosity. The genetic assimilation pathway typically occurs more often because [PSI⁺] individuals appear far more often than [psi⁻] individuals who carry the “+” allele at both agp loci.

Figure 3. An example of two-locus adaptation mediated by [PSI⁺].

ε = 0.01, Ω₁₂ = Ω₂₁ = 10⁻⁵, s ₂ = 0.001, h = 1.

Figure 4. prf⁺ is maintained in the two-locus but not the one-locus model.

The y-axis gives the probability that the frequency of prf⁺ after 5×10⁵ generations is greater than its starting frequency of 0.5. The strength of selection s₂ for adaptation in environment 2 affects the cutoff frequency of sex. ε = 0.01, Ω₁₂ = Ω₂₁ = 10⁻⁵. prf⁺ is maintained in the two-locus model unless sex is very frequent.

Figure 5. If environment 2 is too short-lived (high Ω₂₁), then prf⁺ is not maintained.

This is because there is insufficient time for the selective sweeps shown in Figure 3 to be completed. ε = 0.01, Ω₁₂ = 10⁻⁵, h = 1.

Figure 6. Very rare opportunities for adaptation (low Ω₁₂) cause prf⁺ to be lost.

ε = 0.01, Ω₂₁ = 10⁻⁵.

Figure 7. Fixation probabilities starting from a single copy.

prf⁺ fixes more often than the neutral expectation (10⁻⁷), except when selection is weak (s ₂≤0.001) and sex is common p_sex≥0.1. All parameters are equal to values in Figure 3, with the additional parameter μ_prf+ equal to 10⁻⁹. For p_sex = 0.001 and p_sex = 0.01, results are based on 10⁶ replicates. For p_sex = 0.1 and s₂ = 0.001, the number of replicates is 3.5×10⁷. Otherwise the number of replicates is 6×10⁶.

Figure 8. Fixation probabilities starting from a single copy.

prf⁺ allele fixes above neutral expectations (10⁻⁷) when the transition probability to environment 2 is greater than 10⁻⁸. All parameters are equal to values in Figure 6, with the additional parameter μ_prf+ = 10⁻⁹. Results are based on 10⁶ replicates (Ω₁₂ = 10⁻⁵), 5×10⁶ replicates (Ω₁₂ = 10⁻⁶), 2×10⁷ replicates (Ω₁₂ = 10⁻⁷) and 2×10⁷ replicates (Ω₁₂ = 10⁻⁸).