Spectral landscape theory for genetic load

Sewall Wright touched on 2 phenomena when he introduced the concept of fitness landscapes: the evolutionary traversal of the landscape, and the population at a fitness peak. Here, the property of fitness peaks is investigated, specifically the mathematical structures underlying mutation-selection balance. The genetic load at a mutation-selection balance is found to depend on the relationship between the fitnesses, and the eigenvalues and eigenvectors of its mutation matrix. This is an extension of spectral landscape theory into the regime of strong mutation and strong selection dynamics. The classical Haldane–Muller principle is the finding that the loss of fitness in a population due to mutations is nearly independent of selection strength, but instead is dominated by the mutation rate. Departures from the Haldane–Muller principle, where mutation-selection balance produces a mean fitness greater than Haldane’s limits, have been documented in models of multilocus selection where there is threshold selection, truncation selection, synergistic epistasis, or evolution on neutral networks. The key finding here is that the departures from Haldane’s limits may be estimated by how the fitnesses and reproductive values align with the eigenvectors of the mutation matrix: the closer the alignment with eigenvectors corresponding to the largest eigenvalues of the mutation matrix, the greater the equilibrium mean fitness will be. This yields a deep relationship: perturbations of haplotype frequencies that converge fastest to mutational equilibrium will, when used to perturb fitnesses, result in the greatest genetic loads at mutation-selection balance. The results are obtained for a haploid model with arbitrary fitnesses and reversible mutation patterns. The theory is applied to specific models from the literature, including house-of-cards mutation, threshold selection, and neutral networks. House-of-cards mutation is proven to remain close to the Haldane–Muller principle.