Robust model selection between population growth and multiple merger coalescents

A general and efficient representation of ancestral recombination graphs

As a result of recombination, adjacent nucleotides can have different paths of genetic inheritance and therefore the genealogical trees for a sample of DNA sequences vary along the genome. The structure capturing the details of these intricately interwoven paths of inheritance is referred to as an ancestral recombination graph (ARG). Classical formalisms have focused on mapping coalescence and recombination events to the nodes in an ARG. However, this approach is out of step with some modern developments, which do not represent genetic inheritance in terms of these events or explicitly infer them. We present a simple formalism that defines an ARG in terms of specific genomes and their intervals of genetic inheritance, and show how it generalizes these classical treatments and encompasses the outputs of recent methods. We discuss nuances arising from this more general structure, and argue that it forms an appropriate basis for a software standard in this rapidly growing field.

Determinants of rapid adaptation in species with large variance in offspring production

The speed of population adaptation to changing biotic and abiotic environments is determined by the interaction between genetic drift, positive selection and linkage effects. Many marine species (fish, crustaceans), invertebrates and pathogens of humans and crops, exhibit sweepstakes reproduction characterized by the production of a very large amount of offspring (fecundity phase) from which only a small fraction may survive to the next generation (viability phase). Using stochastic simulations, we investigate whether the occurrence of sweepstakes reproduction affects the efficiency of a positively selected unlinked locus, and thus, the speed of adaptation since fecundity and/or viability have distinguishable consequences on mutation rate, probability and fixation time of advantageous alleles. We observe that the mean number of mutations at the next generation is always the function of the population size, but the variance increases with stronger sweepstakes reproduction when mutations occur in the parents. On the one hand, stronger sweepstakes reproduction magnifies the effect of genetic drift thus increasing the probability of fixation of neutral allele and decreasing that of selected alleles. On the other hand, the time to fixation of advantageous (as well as neutral) alleles is shortened by stronger sweepstakes reproduction. Importantly, fecundity and viability selection exhibit different probabilities and times to fixation of advantageous alleles under intermediate and weak sweepstakes reproduction. Finally, alleles under both strong fecundity and viability selection display a synergistic efficiency of selection. We conclude that measuring and modelling accurately fecundity and/or viability selection are crucial to predict the adaptive potential of species with sweepstakes reproduction.

Sweepstakes reproduction facilitates rapid adaptation in highly fecund populations

Adaptation enables natural populations to survive in a changing environment. Understanding the mechanics of adaptation is therefore crucial for learning about the evolution and ecology of natural populations. We focus on the impact of random sweepstakes on selection in highly fecund haploid and diploid populations partitioned into two genetic types, with one type conferring selective advantage. For the diploid populations, we incorporate various dominance mechanisms. We assume that the populations may experience recurrent bottlenecks. In random sweepstakes, the distribution of individual recruitment success is highly skewed, resulting in a huge variance in the number of offspring contributed by the individuals present in any given generation. Using computer simulations, we investigate the joint effects of random sweepstakes, recurrent bottlenecks and dominance mechanisms on selection. In our framework, bottlenecks allow random sweepstakes to have an effect on the time to fixation, and in diploid populations, the effect of random sweepstakes depends on the dominance mechanism. We describe selective sweepstakes that are approximated by recurrent sweeps of strongly beneficial allelic types arising by mutation. We demonstrate that both types of sweepstakes reproduction may facilitate rapid adaptation (as defined based on the average time to fixation of a type conferring selective advantage conditioned on fixation of the type). However, whether random sweepstakes cause rapid adaptation depends also on their interactions with bottlenecks and dominance mechanisms. Finally, we review a case study in which a model of recurrent sweeps is shown to essentially explain population genomic data from Atlantic cod.

A general and efficient representation of ancestral recombination graphs

As a result of recombination, adjacent nucleotides can have different paths of genetic inheritance and therefore the genealogical trees for a sample of DNA sequences vary along the genome. The structure capturing the details of these intricately interwoven paths of inheritance is referred to as an ancestral recombination graph (ARG). Classical formalisms have focused on mapping coalescence and recombination events to the nodes in an ARG. This approach is out of step with modern developments, which do not represent genetic inheritance in terms of these events or explicitly infer them. We present a simple formalism that defines an ARG in terms of specific genomes and their intervals of genetic inheritance, and show how it generalises these classical treatments and encompasses the outputs of recent methods. We discuss nuances arising from this more general structure, and argue that it forms an appropriate basis for a software standard in this rapidly growing field.

Estimating the Lambda measure in multiple-merger coalescents

Multiple-merger coalescents, also known as Λ-coalescents, have been used to describe the genealogy of populations that have a skewed offspring distribution or that undergo strong selection. Inferring the characteristic measure Λ, which describes the rates of the multiple-merger events, is key to understand these processes. So far, most inference methods only work for some particular families of Λ-coalescents that are described by only one parameter, but not for more general models. This article is devoted to the construction of a non-parametric estimator of the density of Λ that is based on the observation at a single time of the so-called Site Frequency Spectrum (SFS), which describes the allelic frequencies in a present population sample. First, we produce estimates of the multiple-merger rates by solving a linear system, whose coefficients are obtained by appropriately subsampling the SFS. Then, we use a technique that aggregates the information extracted from the previous step through a kernel type of re-construction to give a non-parametric estimation of the measure Λ. We give a consistency result of this estimator under mild conditions on the behavior of Λ around 0. We also show some numerical examples of how our method performs.

Interpreting the pervasive observation of U-shaped Site Frequency Spectra

The standard neutral model of molecular evolution has traditionally been used as the null model for population genomics. We gathered a collection of 45 genome-wide site frequency spectra from a diverse set of species, most of which display an excess of low and high frequency variants compared to the expectation of the standard neutral model, resulting in U-shaped spectra. We show that multiple merger coalescent models often provide a better fit to these observations than the standard Kingman coalescent. Hence, in many circumstances these under-utilized models may serve as the more appropriate reference for genomic analyses. We further discuss the underlying evolutionary processes that may result in the widespread U-shape of frequency spectra.

Sweepstakes reproductive success via pervasive and recurrent selective sweeps

Highly fecund natural populations characterized by high early mortality abound, yet our knowledge about their recruitment dynamics is somewhat rudimentary. This knowledge gap has implications for our understanding of genetic variation, population connectivity, local adaptation, and the resilience of highly fecund populations. The concept of sweepstakes reproductive success, which posits a considerable variance and skew in individual reproductive output, is key to understanding the distribution of individual reproductive success. However, it still needs to be determined whether highly fecund organisms reproduce through sweepstakes and, if they do, the relative roles of neutral and selective sweepstakes. Here, we use coalescent-based statistical analysis of population genomic data to show that selective sweepstakes likely explain recruitment dynamics in the highly fecund Atlantic cod. We show that the Kingman coalescent (modelling no sweepstakes) and the Xi-Beta coalescent (modelling random sweepstakes), including complex demography and background selection, do not provide an adequate fit for the data. The Durrett-Schweinsberg coalescent, in which selective sweepstakes result from recurrent and pervasive selective sweeps of new mutations, offers greater explanatory power. Our results show that models of sweepstakes reproduction and multiple-merger coalescents are relevant and necessary for understanding genetic diversity in highly fecund natural populations. These findings have fundamental implications for understanding the recruitment variation of fish stocks and general evolutionary genomics of high-fecundity organisms.

Efficient ancestry and mutation simulation with msprime 1.0

Stochastic simulation is a key tool in population genetics, since the models involved are often analytically intractable and simulation is usually the only way of obtaining ground-truth data to evaluate inferences. Because of this, a large number of specialized simulation programs have been developed, each filling a particular niche, but with largely overlapping functionality and a substantial duplication of effort. Here, we introduce msprime version 1.0, which efficiently implements ancestry and mutation simulations based on the succinct tree sequence data structure and the tskit library. We summarize msprime’s many features, and show that its performance is excellent, often many times faster and more memory efficient than specialized alternatives. These high-performance features have been thoroughly tested and validated, and built using a collaborative, open source development model, which reduces duplication of effort and promotes software quality via community engagement.

Evolutionary Genomics of High Fecundity

Natural highly fecund populations abound. These range from viruses to gadids. Many highly fecund populations are economically important. Highly fecund populations provide an important contrast to the low-fecundity organisms that have traditionally been applied in evolutionary studies. A key question regarding high fecundity is whether large numbers of offspring are produced on a regular basis, by few individuals each time, in a sweepstakes mode of reproduction. Such reproduction characteristics are not incorporated into the classical Wright-Fisher model, the standard reference model of population genetics, or similar types of models, in which each individual can produce only small numbers of offspring relative to the population size. The expected genomic footprints of population genetic models of sweepstakes reproduction are very different from those of the Wright-Fisher model. A key, immediate issue involves identifying the footprints of sweepstakes reproduction in genomic data. Whole-genome sequencing data can be used to distinguish the patterns made by sweepstakes reproduction from the patterns made by population growth in a population evolving according to the Wright-Fisher model (or similar models). If the hypothesis of sweepstakes reproduction cannot be rejected, then models of sweepstakes reproduction and associated multiple-merger coalescents will become at least as relevant as the Wright-Fisher model (or similar models) and the Kingman coalescent, the cornerstones of mathematical population genetics, in further discussions of evolutionary genomics of highly fecund populations.

Cannings models, population size changes and multiple-merger coalescents

Multiple-merger coalescents, e.g. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda $$\end{document}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. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda $$\end{document}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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N\rightarrow \infty $$\end{document}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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda $$\end{document}Λ-n-coalescents, this has been explicitly shown for only a limited subclass of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda $$\end{document}Λ-n-coalescents and exponentially growing populations. This article gives a more general construction of time-changed \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varLambda $$\end{document}Λ-n-coalescents as limits of specific Cannings models with rather arbitrary time changes.