Evolution of genetic potential

Abstract

Organisms employ a multitude of strategies to cope with the dynamical environments in which they live. Homeostasis and physiological plasticity buffer changes within the lifetime of an organism, while stochastic developmental programs and hypermutability track changes on longer time-scales. An alternative long-term mechanism is "genetic potential"--a heightened sensitivity to the effects of mutation that facilitates rapid evolution to novel states. Using a transparent mathematical model, we illustrate the concept of genetic potential and show that as environmental variability decreases, the evolving population reaches three distinct steady state conditions: (1) organismal flexibility, (2) genetic potential, and (3) genetic robustness. As a specific example of this concept we examine fluctuating selection for hydrophobicity in a single amino acid. We see the same three stages, suggesting that environmental fluctuations can produce allele distributions that are distinct not only from those found under constant conditions, but also from the transient allele distributions that arise under isolated selective sweeps.

Figure 1. Evolution of Genetic Potential

The gray regions represent neutral networks—sets of genotypes that give rise to each phenotype. The degree of shading indicates the likelihood that mutations will impact phenotype, where darker regions are robust to mutations. Under constant conditions, populations evolve toward the most robust regions of neutral networks. Under variable conditions, populations may evolve toward genotypes that easily mutate from one phenotype to the other. These regions of genetic potential do not always lie on the evolutionary path between the equilibrium states for constant environments (arrow).

Figure 2. Mutational Networks

(A) Five alleles lie on a mutational pentagon with genetic degeneracy for the A phenotype. Colors indicate phenotypes with blue for A, yellow for B, and gray for V. Edges indicate that an allele on one side can mutate to the allele on the other side. Arrows illustrate the dynamics in equation 2. (B) Each vertex represents an amino acid. The size of the vertex indicates the number of codons coding for the amino acid. Edges indicate point mutations between hydrophobicity classes. Mutations that preserve hydrophobicity class, including those that preserve the amino acid, are included in the model but not depicted here. The color of the vertex corresponds to the hydrophobicity class: blue indicates hydrophobic, yellow indicates hydrophilic, green indicates intermediate, and red indicates stop codons [21]. This network was drawn with PAJEK [50].

Figure 3. Allele Distributions under Environmental Fluctuations

The graphs show the stationary allele distributions averaged over an E_A epoch (top) and an E_B epoch (bottom) as a function of the variability of the environment. As environmental variability decreases, the population moves from the intermediate phenotype to the genetic boundary between the A and B phenotypes, and eventually to an oscillation between the center of the network for A and the gene for B. Diagrams above the graphs illustrate the frequency distributions in each of the three phases. Vertex areas are proportional to the average frequencies for each allele. (For the data depicted in this figure, s = 1, k = 0.5, and μ = 0.01.)

Figure 4. Codon Distributions under Environmental Fluctuations

(A) gives the robustness for each codon, that is, the fraction of all possible point mutations that leave the hydrophobicity class unchanged. The codons have been ordered to reflect roughly the mutational adjacency of the hydrophobicity classes. (B–D) show the average codon frequency distribution for each epoch type after the population has reached stationary oscillation. These show frequencies for environmental epochs of exactly λ generations (thick lines) and epochs of random duration—Poisson distributed with mean λ (thin lines). Black corresponds to epochs favoring hydrophobicity and gray corresponds to epochs favoring hydrophilicity. The rate of environmental fluctuations is decreasing from (B) to (D) (λ = 10, 10², and 10⁶, respectively).

Figure 5. Faster Environmental Fluctuations Yield Greater Genetic Potential

Genetic potential is the likelihood that a mutation to a gene coding for the currently favored phenotype will produce the intermediate or unfavored phenotype. Thick lines correspond to populations that have reached stable oscillations when λ = 100, and thin lines correspond to populations that experience a single environmental shift after having equilibrated in a constant environment. The maximum genetic potential after a single shift is significantly less than the minimum under persistent fluctuations.

Figure 6. Amino Acid Distributions Reflect Genetic Potential

The left figure illustrates amino acid distribution in the generations with greatest genetic potential during each of the two epochs for λ = 100. Vertex area is proportional to the relative frequency of an amino acid. The right figure gives the amino acid distributions at equilibrium in the two environments (far left and right networks), and the transitional amino acid distributions that are most similar to those depicted for λ = 100 (left). Similarity is measured as mean squared difference in frequencies across all amino acids. The amino acid networks were drawn with PAJEK [50].

Figure 7. Pentagonal Mutational Networks

These are the 14 possible pentagonal mutational networks consisting of five alleles producing phenotypes A, B, or V, with at least one encoding A and one encoding B.