Our focus here is on the infinitesimal model. In this model, one or several quantitative traits are described as the sum of a genetic and a non-genetic component, the first being distributed as a normal random variable centred at the average of the parental genetic components, and with a variance independent of the parental traits. We first review the long history of the infinitesimal model in quantitative genetics. Then we provide a definition of the model at the phenotypic level in terms of individual trait values and relationships between individuals, but including different evolutionary processes: genetic drift, recombination, selection, mutation, population structure, … We give a range of examples of its application to evolutionary questions related to stabilising selection, assortative mating, effective population size and response to selection, habitat preference and speciation. We provide a mathematical justification of the model as the limit as the number M of underlying loci tends to infinity of a model with Mendelian inheritance, mutation and environmental noise, when the genetic component of the trait is purely additive. We also show how the model generalises to include epistatic effects. In each case, by conditioning on the pedigree relating individuals in the population, we incorporate arbitrary selection and population structure. We suppose that we can observe the pedigree up to the present generation, together with all the ancestral traits, and we show, in particular, that the genetic components of the individual trait values in the current generation are indeed normally distributed with a variance independent of ancestral traits, up to an error of order M^{-1/2}. Simulations suggest that in particular cases the convergence may be as fast as 1/M.

The packaging of eukaryotic genomes into nucleosomes plays critical roles in all DNA-templated processes, and chromatin structure has been implicated as a key factor in the evolution of gene regulatory programs. While the functions of many histone modifications appear to be highly conserved throughout evolution, some well-studied modifications such as H3K9 and H3K27 methylation are not found in major model organisms such as Saccharomyces cerevisiae, while other modifications gain/lose regulatory functions during evolution. To study such a transition we focused on H3K9 methylation, a heterochromatin mark found in metazoans and in the fission yeast S. pombe, but which has been lost in the lineage leading to the model budding yeast S. cerevisiae. We show that this mark is present in the relatively understudied yeast Kluyveromyces lactis, a Hemiascomycete that diverged from S. cerevisiae prior to the whole-genome duplication event that played a key role in the evolution of a primarily fermentative lifestyle. We mapped genome-wide patterns of H3K9 methylation as well as several conserved modifications. We find that well-studied modifications such as H3K4me3, H3K36me3, and H3S10ph exhibit generally conserved localization patterns. Interestingly, we show H3K9 methylation in K. lactis primarily occurs over highly-transcribed regions, including both Pol2 and Pol3 transcription units. We identified the H3K9 methylase as the ortholog of Set6, whose function in S. cerevisiae is obscure. Functionally, we show that deletion of KlSet6 does not affect highly H3K9me3-marked genes, providing another example of a major disconnect between histone mark localization and function. Together, these results shed light on surprising plasticity in the function of a widespread chromatin mark.

Microbial populations often rely on the cooperative production of extracellular public goods molecules. The cooperative nature of public good production may lead to minimum viable population sizes, below which populations collapse. In addition, cooperator public goods producing cells face evolutionary competition from non-producing mutants, or freeloaders. Thus, public goods cooperators have to be stable not only to the invasion of freeloaders, but also to ecological perturbations that may push their numbers too small to be sustainable. Through a combination of experiments with microbial populations and mathematical analysis of the Ecological Public Goods Game, we show that game parameters and experimental conditions that improve the evolutionary stability of cooperators also lead to a low ecological stability of the cooperator population. Complex regulatory strategies mimicking those used by microbes in nature may allow cooperators to beat this eco-evolutionary stability tradeoff and become resistant to freeloaders while at the same time maximizing their ecological stability. Our results thus identify the coupled eco-evolutionary stability as being key for the long-term viability of microbial public goods cooperators.

We present IMP, an automated pipeline for reproducible integrated analyses of coupled metagenomic and metatranscriptomic data. IMP incorporates preprocessing, iterative co-assembly of metagenomic and metatranscriptomic data, analyses of microbial community structure and function as well as genomic signature-based visualizations. Complementary use of metagenomic and metatranscriptomic data improves assembly quality and enables the estimation of both population abundance and community activity while allowing the recovery and analysis of potentially important components, such as RNA viruses. IMP is containerized using Docker which ensures reproducibility. IMP is available at http://r3lab.uni.lu/web/imp/.

Many approaches for inferring adaptive molecular evolution analyze the unfolded site frequency spectrum (SFS), a vector of counts of sites with different numbers of copies of derived alleles in a sample of alleles from a population. Accurate inference of the high copy number elements of the SFS is difficult, however, because of misassignment of alleles as derived versus ancestral. This is a known problem with parsimony using outgroup species. Here, we show that the problem is particularly serious if there is variation in the substitution rate among sites brought about by variation in selective constraint levels. We present a new method for inferring the SFS using one or two outgroups, which attempts to overcome the problem of misassignment. We show that two outgroups are required for accurate estimation of the SFS if there is substantial variation in selective constraints, which is expected to be the case for nonsynonymous sites of protein-coding genes. We apply the method to estimate unfolded SFSs for synonymous and nonsynonymous sites from Phase 2 of the Drosophila Population Genomics Project. We use the unfolded spectra to estimate the frequency and strength of advantageous and deleterious mutations, and estimate that ~50% of amino acid substitutions are positively selected, but that less than 0.5% of new amino acid mutations are beneficial, with a scaled selection strength of Nes ≈ 12.

Background: A number of large genomic datasets are being generated for studies of human ancestry and diseases. The ADMIXTURE program is commonly used to infer individual ancestry from genomic data. Results: We describe two improvements to the ADMIXTURE software. The first enables ADMIXTURE to infer ancestry for a new set of individuals using cluster allele frequencies from a reference set of individuals. Using data from the 1000 Genomes Project, we show that this allows ADMIXTURE to infer ancestry for 10,920 individuals in a few hours (a 5x speedup). This mode also allows ADMIXTURE to correctly estimate individual ancestry and allele frequencies from a set of related individuals. The second modification allows ADMIXTURE to correctly handle X-chromosome (and other haploid) data from both males and females. We demonstrate increased power to detect sex-biased admixture in African-American individuals from the 1000 Genomes project using this extension. Conclusions: These modifications make ADMIXTURE more efficient and versatile, allowing users to extract more information from large genomic datasets.