Robustness and epistasis in mutation-selection models

We investigate the fitness advantage associated with the robustness of a phenotype against deleterious mutations using deterministic mutation-selection models of quasispecies type equipped with a mesa shaped fitness landscape. We obtain analytic results for the robustness effect which become exact in the limit of infinite sequence length. Thereby, we are able to clarify a seeming contradiction between recent rigorous work and an earlier heuristic treatment based on a mapping to a Schr\"odinger equation. We exploit the quantum mechanical analogy to calculate a correction term for finite sequence lengths and verify our analytic results by numerical studies. In addition, we investigate the occurrence of an error threshold for a general class of epistatic landscape and show that diminishing epistasis is a necessary but not sufficient condition for error threshold behavior.Comment: 20 pages, 14 figure

Exploring the effect of sex on empirical fitness landscapes

The nature of epistasis has important consequences for the evolutionary significance of sex and recombination. Recent efforts to find negative epistasis as a source of negative linkage disequilibrium and associated long-term advantage to sex have yielded little support. Sign epistasis, where the sign of the fitness effects of alleles varies across genetic backgrounds, is responsible for the ruggedness of the fitness landscape, with several unexplored implications for the evolution of sex. Here, we describe fitness landscapes for two sets of strains of the asexual fungus Aspergillus niger involving all combinations of five mutations. We find that 30% of the single-mutation fitness effects are positive despite their negative effect in the wild-type strain and that several local fitness maxima and minima are present. We then compare adaptation of sexual and asexual populations on these empirical fitness landscapes by using simulations. The results show a general disadvantage of sex on these rugged landscapes, caused by the breakdown by recombination of genotypes on fitness peaks. Sex facilitates movement to the global peak only for some parameter values on one landscape, indicating its dependence on the landscape’s topography. We discuss possible reasons for the discrepancy between our results and the reports of faster adaptation of sexual population

Multiple-line inference of selection on quantitative traits

Trait differences between species may be attributable to natural selection. However, quantifying the strength of evidence for selection acting on a particular trait is a difficult task. Here we develop a population-genetic test for selection acting on a quantitative trait which is based on multiple-line crosses. We show that using multiple lines increases both the power and the scope of selection inference. First, a test based on three or more lines detects selection with strongly increased statistical significance, and we show explicitly how the sensitivity of the test depends on the number of lines. Second, a multiple-line test allows to distinguish different lineage-specific selection scenarios. Our analytical results are complemented by extensive numerical simulations. We then apply the multiple-line test to QTL data on floral character traits in plant species of the Mimulus genus and on photoperiodic traits in different maize strains, where we find a signatures of lineage-specific selection not seen in a two-line test.Comment: 21 pages, 11 figures; to appear in Genetic

Biological evolution through mutation, selection, and drift: An introductory review

Motivated by present activities in (statistical) physics directed towards biological evolution, we review the interplay of three evolutionary forces: mutation, selection, and genetic drift. The review addresses itself to physicists and intends to bridge the gap between the biological and the physical literature. We first clarify the terminology and recapitulate the basic models of population genetics, which describe the evolution of the composition of a population under the joint action of the various evolutionary forces. Building on these foundations, we specify the ingredients explicitly, namely, the various mutation models and fitness landscapes. We then review recent developments concerning models of mutational degradation. These predict upper limits for the mutation rate above which mutation can no longer be controlled by selection, the most important phenomena being error thresholds, Muller's ratchet, and mutational meltdowns. Error thresholds are deterministic phenomena, whereas Muller's ratchet requires the stochastic component brought about by finite population size. Mutational meltdowns additionally rely on an explicit model of population dynamics, and describe the extinction of populations. Special emphasis is put on the mutual relationship between these phenomena. Finally, a few connections with the process of molecular evolution are established.Comment: 62 pages, 6 figures, many reference

IAMBEE : a web-service for the identification of adaptive pathways from parallel evolved clonal populations

IAMBEE is a web server designed for the Identification of Adaptive Mutations in Bacterial Evolution Experiments (IAMBEE). Input data consist of genotype information obtained from independently evolved clonal populations or strains that show the same adapted behavior (phenotype). To distinguish adaptive from passenger mutations, IAMBEE searches for neighborhoods in an organism-specific interaction network that are recurrently mutated in the adapted populations. This search for recurrently mutated network neighborhoods, as proxies for pathways is driven by additional information on the functional impact of the observed genetic changes and their dynamics during adaptive evolution. In addition, the search explicitly accounts for the differences in mutation rate between the independently evolved populations. Using this approach, IAMBEE allows exploiting parallel evolution to identify adaptive pathways. The web-server is freely available at http://bioinformatics.intec.ugent.be/iambee/ with no login requirement

The evolution of genetic architectures underlying quantitative traits

In the classic view introduced by R. A. Fisher, a quantitative trait is encoded by many loci with small, additive effects. Recent advances in QTL mapping have begun to elucidate the genetic architectures underlying vast numbers of phenotypes across diverse taxa, producing observations that sometimes contrast with Fisher's blueprint. Despite these considerable empirical efforts to map the genetic determinants of traits, it remains poorly understood how the genetic architecture of a trait should evolve, or how it depends on the selection pressures on the trait. Here we develop a simple, population-genetic model for the evolution of genetic architectures. Our model predicts that traits under moderate selection should be encoded by many loci with highly variable effects, whereas traits under either weak or strong selection should be encoded by relatively few loci. We compare these theoretical predictions to qualitative trends in the genetics of human traits, and to systematic data on the genetics of gene expression levels in yeast. Our analysis provides an evolutionary explanation for broad empirical patterns in the genetic basis of traits, and it introduces a single framework that unifies the diversity of observed genetic architectures, ranging from Mendelian to Fisherian.Comment: Minor changes in the text; Added supplementary materia

Cancer initiation with epistatic interactions between driver and passenger mutations

We investigate the dynamics of cancer initiation in a mathematical model with one driver mutation and several passenger mutations. Our analysis is based on a multi type branching process: We model individual cells which can either divide or undergo apoptosis. In case of a cell division, the two daughter cells can mutate, which potentially confers a change in fitness to the cell. In contrast to previous models, the change in fitness induced by the driver mutation depends on the genetic context of the cell, in our case on the number of passenger mutations. The passenger mutations themselves have no or only a very small impact on the cell's fitness. While our model is not designed as a specific model for a particular cancer, the underlying idea is motivated by clinical and experimental observations in Burkitt Lymphoma. In this tumor, the hallmark mutation leads to deregulation of the MYC oncogene which increases the rate of apoptosis, but also the proliferation rate of cells. This increase in the rate of apoptosis hence needs to be overcome by mutations affecting apoptotic pathways, naturally leading to an epistatic fitness landscape. This model shows a very interesting dynamical behavior which is distinct from the dynamics of cancer initiation in the absence of epistasis. Since the driver mutation is deleterious to a cell with only a few passenger mutations, there is a period of stasis in the number of cells until a clone of cells with enough passenger mutations emerges. Only when the driver mutation occurs in one of those cells, the cell population starts to grow rapidly