Stability and response of polygenic traits to stabilizing selection and mutation

When polygenic traits are under stabilizing selection, many different combinations of alleles allow close adaptation to the optimum. If alleles have equal effects, all combinations that result in the same deviation from the optimum are equivalent. Furthermore, the genetic variance that is maintained by mutation-selection balance is $2 \mu/S$ per locus, where $\mu$ is the mutation rate and $S$ the strength of stabilizing selection. In reality, alleles vary in their effects, making the fitness landscape asymmetric, and complicating analysis of the equilibria. We show that that the resulting genetic variance depends on the fraction of alleles near fixation, which contribute by $2 \mu/S$, and on the total mutational effects of alleles that are at intermediate frequency. The interplay between stabilizing selection and mutation leads to a sharp transition: alleles with effects smaller than a threshold value of $2\sqrt{\mu / S}$ remain polymorphic, whereas those with larger effects are fixed. The genetic load in equilibrium is less than for traits of equal effects, and the fitness equilibria are more similar. We find that if the optimum is displaced, alleles with effects close to the threshold value sweep first, and their rate of increase is bounded by $\sqrt{\mu S}$. Long term response leads in general to well-adapted traits, unlike the case of equal effects that often end up at a sub-optimal fitness peak. However, the particular peaks to which the populations converge are extremely sensitive to the initial states, and to the speed of the shift of the optimum trait value.Comment: Accepted in Genetic

The statistical mechanics of a polygenic characterunder stabilizing selection, mutation and drift

By exploiting an analogy between population genetics and statistical mechanics, we study the evolution of a polygenic trait under stabilizing selection, mutation, and genetic drift. This requires us to track only four macroscopic variables, instead of the distribution of all the allele frequencies that influence the trait. These macroscopic variables are the expectations of: the trait mean and its square, the genetic variance, and of a measure of heterozygosity, and are derived from a generating function that is in turn derived by maximizing an entropy measure. These four macroscopics are enough to accurately describe the dynamics of the trait mean and of its genetic variance (and in principle of any other quantity). Unlike previous approaches that were based on an infinite series of moments or cumulants, which had to be truncated arbitrarily, our calculations provide a well-defined approximation procedure. We apply the framework to abrupt and gradual changes in the optimum, as well as to changes in the strength of stabilizing selection. Our approximations are surprisingly accurate, even for systems with as few as 5 loci. We find that when the effects of drift are included, the expected genetic variance is hardly altered by directional selection, even though it fluctuates in any particular instance. We also find hysteresis, showing that even after averaging over the microscopic variables, the macroscopic trajectories retain a memory of the underlying genetic states.Comment: 35 pages, 8 figure

Wolbachia in the Culex pipiens group mosquitoes: introgression and superinfection.

Wolbachia bacteria in mosquitoes induce cytoplasmic incompatibility (CI), where sperm from Wolbachia-infected males can produce inviable progeny. The wPip strain in the Culex pipiens group of mosquitoes produces a complexity of CI crossing types. Several factors are thought to be capable of influencing the expression of CI including Wolbachia strain type and host genotype. In this study, the unidirectional CI that occurs between 2 C. pipiens complex laboratory strains, Col and Mol, was further investigated by nuclear genotype introgression. The unidirectional CI between Col and Mol was not found to be influenced by host genetic background, in contrast to a previous introgression study carried out using bidirectionally incompatible C. pipiens group strains. A line containing both wPip strain variants superinfection was also generated by embryonic cytoplasmic transfer. The same crossing type as the parental Col strain was observed in the superinfected line. Quantitative polymerase chain reaction demonstrated a low density of the injected wPipMol variant in the superinfected line after 18 generations, which was considered likely to be responsible for the crossing patterns observed. The Wolbachia density was also shown to be lower in the parental Mol strain males compared with Col strain males, and no inverse relationship between WO phage and Wolbachia density could be detected

The genetics of mate preferences in hybrids between two young and sympatric Lake Victoria cichlid species

The genetic architecture of mate preferences is likely to affect significant evolutionary processes, including speciation and hybridization. Here, we investigate laboratory hybrids between a pair of sympatric Lake Victoria cichlid fish species that appear to have recently evolved from a hybrid population between similar predecessor species. The species demonstrate strong assortative mating in the laboratory, associated with divergent male breeding coloration (red dorsum versus blue). We show in a common garden experiment, using DNA-based paternity testing, that the strong female mate preferences among males of the two species are fully recovered in a large fraction of their F2 hybrid generation. Individual hybrid females often demonstrated consistent preferences in multiple mate choice trials (more than or equal to five) across a year or more. This result suggests that female mate preference is influenced by relatively few major genes or genomic regions. These preferences were not changed by experience of a successful spawning event with a male of the non-preferred species in a no-choice single-male trial. We found no evidence for imprinting in the F2 hybrids, although the F1 hybrid females may have been imprinted on their mothers. We discuss this nearly Mendelian inheritance of consistent innate mate preferences in the context of speciation theory

Cryo-EM structures and binding of mouse and human ACE2 to SARS-CoV-2 variants of concern indicate that mutations enabling immune escape could expand host range.

Investigation of potential hosts of the severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) is crucial to understanding future risks of spillover and spillback. SARS-CoV-2 has been reported to be transmitted from humans to various animals after requiring relatively few mutations. There is significant interest in describing how the virus interacts with mice as they are well adapted to human environments, are used widely as infection models and can be infected. Structural and binding data of the mouse ACE2 receptor with the Spike protein of newly identified SARS-CoV-2 variants are needed to better understand the impact of immune system evading mutations present in variants of concern (VOC). Previous studies have developed mouse-adapted variants and identified residues critical for binding to heterologous ACE2 receptors. Here we report the cryo-EM structures of mouse ACE2 bound to trimeric Spike ectodomains of four different VOC: Beta, Omicron BA.1, Omicron BA.2.12.1 and Omicron BA.4/5. These variants represent the oldest to the newest variants known to bind the mouse ACE2 receptor. Our high-resolution structural data complemented with bio-layer interferometry (BLI) binding assays reveal a requirement for a combination of mutations in the Spike protein that enable binding to the mouse ACE2 receptor

A simple mathematical model of gradual Darwinian evolution: Emergence of a Gaussian trait distribution in adaptation along a fitness gradient

We consider a simple mathematical model of gradual Darwinian evolution in continuous time and continuous trait space, due to intraspecific competition for common resource in an asexually reproducing population in constant environment, while far from evolutionary stable equilibrium. The model admits exact analytical solution. In particular, Gaussian distribution of the trait emerges from generic initial conditions.Comment: 21 pages, 2 figures, as accepted to J Math Biol 2013/03/1

How Gaussian competition leads to lumpy or uniform species distributions

A central model in theoretical ecology considers the competition of a range of species for a broad spectrum of resources. Recent studies have shown that essentially two different outcomes are possible. Either the species surviving competition are more or less uniformly distributed over the resource spectrum, or their distribution is 'lumped' (or 'clumped'), consisting of clusters of species with similar resource use that are separated by gaps in resource space. Which of these outcomes will occur crucially depends on the competition kernel, which reflects the shape of the resource utilization pattern of the competing species. Most models considered in the literature assume a Gaussian competition kernel. This is unfortunate, since predictions based on such a Gaussian assumption are not robust. In fact, Gaussian kernels are a border case scenario, and slight deviations from this function can lead to either uniform or lumped species distributions. Here we illustrate the non-robustness of the Gaussian assumption by simulating different implementations of the standard competition model with constant carrying capacity. In this scenario, lumped species distributions can come about by secondary ecological or evolutionary mechanisms or by details of the numerical implementation of the model. We analyze the origin of this sensitivity and discuss it in the context of recent applications of the model.Comment: 11 pages, 3 figures, revised versio

High-Resolution Genome-Wide Dissection of the Two Rules of Speciation in Drosophila

Postzygotic reproductive isolation is characterized by two striking empirical patterns. The first is Haldane's rule—the preferential inviability or sterility of species hybrids of the heterogametic (XY) sex. The second is the so-called large X effect—substitution of one species's X chromosome for another's has a disproportionately large effect on hybrid fitness compared to similar substitution of an autosome. Although the first rule has been well-established, the second rule remains controversial. Here, we dissect the genetic causes of these two rules using a genome-wide introgression analysis of Drosophila mauritiana chromosome segments in an otherwise D. sechellia genetic background. We find that recessive hybrid incompatibilities outnumber dominant ones and that hybrid male steriles outnumber all other types of incompatibility, consistent with the dominance and faster-male theories of Haldane's rule, respectively. We also find that, although X-linked and autosomal introgressions are of similar size, most X-linked introgressions cause hybrid male sterility (60%) whereas few autosomal introgressions do (18%). Our results thus confirm the large X effect and identify its proximate cause: incompatibilities causing hybrid male sterility have a higher density on the X chromosome than on the autosomes. We evaluate several hypotheses for the evolutionary cause of this excess of X-linked hybrid male sterility

Predicting evolution and visualizing high-dimensional fitness landscapes

The tempo and mode of an adaptive process is strongly determined by the structure of the fitness landscape that underlies it. In order to be able to predict evolutionary outcomes (even on the short term), we must know more about the nature of realistic fitness landscapes than we do today. For example, in order to know whether evolution is predominantly taking paths that move upwards in fitness and along neutral ridges, or else entails a significant number of valley crossings, we need to be able to visualize these landscapes: we must determine whether there are peaks in the landscape, where these peaks are located with respect to one another, and whether evolutionary paths can connect them. This is a difficult task because genetic fitness landscapes (as opposed to those based on traits) are high-dimensional, and tools for visualizing such landscapes are lacking. In this contribution, we focus on the predictability of evolution on rugged genetic fitness landscapes, and determine that peaks in such landscapes are highly clustered: high peaks are predominantly close to other high peaks. As a consequence, the valleys separating such peaks are shallow and narrow, such that evolutionary trajectories towards the highest peak in the landscape can be achieved via a series of valley crossingsComment: 12 pages, 7 figures. To appear in "Recent Advances in the Theory and Application of Fitness Landscapes" (A. Engelbrecht and H. Richter, eds.). Springer Series in Emergence, Complexity, and Computation, 201