Lee Altenberg

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.

The evolution and function of imitation have always been placed within the confines of animal learning and associated with its crucial role in cultural transmission and cultural evolution. Can imitation evolve as a form of phenotypic plasticity in the absence of cultural transmission, in phenotypes beyond behavior? We investigate a model in which imitation is unbundled from cultural transmission: an organism's adult phenotype is plastically altered by its experiences as a juvenile of other juveniles' genetically determined traits. The only information transmitted between generations is genetic. We find that during a period of directional selection towards a phenotypic optimum, natural selection favors modifiers which cause an organism to bias its plastic phenotype in the direction opposite to the mean phenotype of the population -- anti-imitation. As the population approaches the phenotypic optimum and shifts into stabilizing selection, selection on the modifier reverses and favors strong imitation of the population mean. Imitation can evolve to overshoot the target and produce an evolutionary pathology where mean fitness decreases. When purifying selection for an extreme phenotype is modeled, only selection for anti-imitation occurs, even at a mutation-selection balance. Imitation and anti-imitation emerge from these models in the absence of any goal representation, cognitive understanding of its purpose, or discernment of any kind. These theoretical outcomes are all novel evolutionary and biological phenomena, and we discuss their implications.

Significance: Evolution by Darwinian natural selection can not only shape how organisms survive and reproduce, but also affect transmission of genetic and other information between generations. Modifier-gene models for the evolution of information transmission have revealed a universal tendency for more faithful transmission to evolve in populations at equilibrium where natural selection is balanced by errors in information transmission. This is shown to be a very general property of models that include mutation and migration under selection and recombination under selection on diploids. The breadth of this reduction principle focuses attention on the departures from its mathematical assumptions, which may explain those biological phenomena of information transmission between generations for which the reduction principle fails.

The mathematical symbol for the norm, which is heavily overloaded with multiple definitions that have both universal and specific properties, lends itself to confusion. This is manifest in the proof of an important theorem for population dynamics by Schreiber and Li on how dispersal increases population growth in a periodic environment. Here the theorem is placed in context, the proof is clarified, and the confusing but inconsequential errors corrected.