After domestication, during a process of widespread range extension, barley adapted to a broad spectrum of agricultural environments. To explore how the barley genome responded to the environmental challenges it encountered, we sequenced the exomes of a collection of 267 georeferenced landraces and wild accessions. A combination of genome-wide analyses showed that patterns of variation have been strongly shaped by geography and that variant-by-environment associations for individual genes are prominent in our data set. We observed significant correlations of days to heading (flowering) and height with seasonal temperature and dryness variables in common garden experiments, suggesting that these traits were major drivers of environmental adaptation in the sampled germplasm. A detailed analysis of known flowering-associated genes showed that many contain extensive sequence variation and that patterns of single- and multiple-gene haplotypes exhibit strong geographical structuring. This variation appears to have substantially contributed to range-wide ecogeographical adaptation, but many factors key to regional success remain unidentified.

The ability of the site-frequency spectrum (SFS) to reflect the particularities of gene genealogies exhibiting multiple mergers of ancestral lines as opposed to those obtained in the presence of population growth is our focus. An excess of singletons is a wellknown characteristic of both population growth and multiple mergers. Other aspects of the SFS, in particular, the weight of the right tail, are, however, affected in specific ways by the two model classes. Using an approximate likelihood method and minimum-distance statistics, our estimates of statistical power indicate that exponential and algebraic growth can indeed be distinguished from multiplemerger coalescents, even for moderate sample sizes, if the number of segregating sites is high enough. A normalized version of the SFS (nSFS) is also used as a summary statistic in an approximate Bayesian computation (ABC) approach. The results give further positive evidence as to the general eligibility of the SFS to distinguish between the different histories.KEYWORDS coalescent; multiple mergers; population growth; approximate maximum likelihood test; approximate Bayesian computation; sitefrequency spectrum T HE site-frequency spectrum (SFS) at a given locus is one of the most important and popular statistics based on genetic data sampled from a natural population. In combination with the postulation of the assumptions of the infinitelymany-sites mutation model (Watterson, 1975) and a suitable underlying coalescent framework, the SFS allows one to draw inferences about evolutionary parameters, such as coalescent parameters associated with multiple-merger coalescents or population-growth models.The Kingman coalescent, developed by Kingman (1982a, b,c), Hudson (1983a,b), and Tajima (1983), describing the random ancestral relations among DNA sequences drawn from natural populations, is a prominent and widely used model from which one can make predictions about genetic diversity. Many quantities of interest, such as the expected values and covariances of the SFS associated with the Kingman coalescent, are easily computed thanks to results by Fu (1995). The robustness of the Kingman coalescent is quite remarkable; indeed, a large number of genealogy models can be shown to have the Kingman coalescent or a variant thereof as their limit process (cf., e.g., Möhle 1998). A large volume of work is thus devoted to inference methods based on the Kingman coalescent [see, e.g., Donnelly and Tavaré (1995), Hudson (1990), Nordborg (2001), Hein et al. (2005), and Wakeley (2007) for reviews].However, many evolutionary histories can lead to significant deviations from the Kingman coalescent model. Such deviations can be detected using a variety of statistical tools, such as Tajima's D (Tajima 1989a), Fu and Li's D (Fu and Li 1993), and Fay and Wu 's H (Fay and Wu 2000), which are all functions of the SFS. However, they do not always allow one to identify the actual evolutionary mechanisms leading to such deviations. Developing statistical tools that allow one to dist...

The ability of the site-frequency spectrum (SFS) to reflect the particularities of gene genealogies exhibiting multiple mergers of ancestral lines as opposed to those obtained in the presence of exponential population growth is our focus. An excess of singletons is a well-known characteristic of both population growth and multiple mergers. Other aspects of the SFS, in particular the weight of the right tail, are, however, affected in specific ways by the two model classes. Using minimum-distance statistics, and an approximate likelihood method, our estimates of statistical power indicate that exponential growth can indeed be distinguished from multiple merger coalescents, even for moderate sample size, if the number of segregating sites is high enough. Additionally, we use a normalised version of the SFS as a summary statistic in an approximate bayesian computation (ABC) approach to distinguish multiple mergers from exponential population growth. The ABC approach gives further positive evidence as to the general eligibility of the SFS to distinguish between the different histories, but also reveals that suitable weighing of parts of the SFS can improve the distinction ability. The important issue of the difference in timescales between different coalescent processes (and their implications for the scaling of mutation parameters) is also discussed.

Multiple-merger coalescents, e.g. Λ-n-coalescents, have been proposed as models of the genealogy of n sampled individuals for a range of populations whose genealogical structures are not captured well by Kingman's n-coalescent. Λ-n-coalescents can be seen as the limit process of the discrete genealogies of Cannings models with fixed population size, when time is rescaled and population size N → ∞. As established for Kingman's n-coalescent, moderate population size fluctuations in the discrete population model should be reflected by a time-change of the limit coalescent. For Λ-n-coalescents, this has been explicitly shown for only a limited subclass of Λ-n-coalescents and exponentially growing populations. This article gives a general construction of time-changed Λ-n-coalescents as limits of specific Cannings models with rather arbitrary time changes.

The Kingman coalescent and its developments are often considered among the most important advances in population genetics of the last decades. Demographic inference based on coalescent theory has been used to reconstruct the population dynamics and evolutionary history of several species, including Mycobacterium tuberculosis (MTB), an important human pathogen causing tuberculosis. One key assumption of the Kingman coalescent is that the number of descendants of different individuals does not vary strongly, and violating this assumption could lead to severe biases caused by model misspecification. Individual lineages of MTB are expected to vary strongly in reproductive success because 1) MTB is potentially under constant selection due to the pressure of the host immune system and of antibiotic treatment, 2) MTB undergoes repeated population bottlenecks when it transmits from one host to the next, and 3) some hosts show much higher transmission rates compared to the average (“super-spreaders”). Here we used an Approximate Bayesian Computation approach to test whether multiple merger coalescents (MMC), a class of models that allow for large variation in reproductive success among lineages, are more appropriate models to study MTB populations. We considered eleven publicly available whole genome sequence data sets sampled from local MTB populations and outbreaks, and found that MMC had a better fit compared to the Kingman coalescent for ten of the eleven data sets. These results indicate that the null model for analyzing MTB outbreaks should be reassessed, and that past findings based on the Kingman coalescent need to be revisited.

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The reproductive mechanism of a species is a key driver of genome evolution. The standard Wright-Fisher model depict reproduction of individuals in a population and assumes that each individual produces a number of offspring negligible compared to the total population size. Yet many species of plants, invertebrates, prokaryotes or fish exhibit neutrally skewed offspring distribution or strong selection events yielding few individuals to produce a number of offspring of up to the same magnitude as the population size. As a result, the genealogy of a sample is characterized by multiple individuals (more than two) coalescing simultaneously to the same common ancestor. The current methods developed to detect such multiple merger events do not account for complex demographic scenarios or recombination, and require large sample sizes. We tackle these limitations by developing two novel and different approaches to infer multiple merger events from the ancestral recombination graph (ARG): a sequentially Markovian coalescent (SMβC) and a graph neural network (GNNcoal). We first give proof of the accuracy of our methods to estimate the multiple merger parameter and past demographic history using simulated data under the β-coalescent model. Secondly, we show that our approaches can also recover the effect of a positive selective sweeps along the genome. Finally, we are able to distinguish skewed offspring distribution from selection while simultaneously inferring the past variation of population size. Our findings stress the aptitude of neural networks to leverage information from the ARG for inference, and the added value of comparing ad hoc SMC and GNN methods.

In this paper, we consider Beta(2 − α, α) (with 1 < α < 2) and related Λcoalescents. If T (n) denotes the length of an external branch of the n-coalescent, we prove the convergence of n α−1 T (n) when n tends to ∞, and give the limit. To this aim, we give asymptotics for the number σ (n) of collisions which occur in the n-coalescent until the end of the chosen external branch, and for the block counting process associated with the n-coalescent.