On the estimation of genome-average recombination rates.

The rate at which recombination events occur in a population is an indicator of its effective population size and the organism's reproduction mode. It determines the extent of linkage disequilibrium along the genome and, thereby, the efficacy of both purifying and positive selection. The population recombination rate can be inferred using models of genome evolution in populations. Classic methods based on the patterns of linkage disequilibrium provide the most accurate estimates, providing large sample sizes are used and the demography of the population is properly accounted for. Here, the capacity of approaches based on the sequentially Markov coalescent (SMC) to infer the genome-average recombination rate from as little as a single diploid genome is examined. SMC approaches provide highly accurate estimates even in the presence of changing population sizes, providing that (1) within genome heterogeneity is accounted for and (2) classic maximum-likelihood optimization algorithms are employed to fit the model. SMC-based estimates proved sensitive to gene conversion, leading to an overestimation of the recombination rate if conversion events are frequent. Conversely, methods based on the correlation of heterozygosity succeed in disentangling the rate of crossing over from that of gene conversion events, but only when the population size is constant and the recombination landscape homogeneous. These results call for a convergence of these two methods to obtain accurate and comparable estimates of recombination rates between populations.

Inference of recombination maps from a single pair of genomes and its application to ancient samples.

Understanding the causes and consequences of recombination landscape evolution is a fundamental goal in genetics that requires recombination maps from across the tree of life. Such maps can be obtained from population genomic datasets, but require large sample sizes. Alternative methods are therefore necessary to research organisms where such datasets cannot be generated easily, such as non-model or ancient species. Here we extend the sequentially Markovian coalescent model to jointly infer demography and the spatial variation in recombination rate. Using extensive simulations and sequence data from humans, fruit-flies and a fungal pathogen, we demonstrate that iSMC accurately infers recombination maps under a wide range of scenarios-remarkably, even from a single pair of unphased genomes. We exploit this possibility and reconstruct the recombination maps of ancient hominins. We report that the ancient and modern maps are correlated in a manner that reflects the established phylogeny of Neanderthals, Denisovans, and modern human populations.

Ancestral Population Genomics.

Borrowing both from population genetics and phylogenetics, the field of population genomics emerged as full genomes of several closely related species were available. Providing we can properly model sequence evolution within populations undergoing speciation events, this resource enables us to estimate key population genetics parameters such as ancestral population sizes and split times. Furthermore we can enhance our understanding of the recombination process and investigate various selective forces. With the advent of resequencing technologies, genome-wide patterns of diversity in extant populations have now come to complement this picture, offering an increasing power to study more recent genetic history.We discuss the basic models of genomes in populations, including speciation models for closely related species. A major point in our discussion is that only a few complete genomes contain much information about the whole population. The reason being that recombination unlinks genomic regions, and therefore a few genomes contain many segments with distinct histories. The challenge of population genomics is to decode this mosaic of histories in order to infer scenarios of demography and selection. We survey modeling strategies for understanding genetic variation in ancestral populations and species. The underlying models build on the coalescent with recombination process and introduce further assumptions to scale the analyses to genomic data sets.

Hidden Markov Models in Population Genomics.

With the advent of sequencing techniques population genomics took a major shift. The structure of data sets has evolved from a sample of a few loci in the genome, sequenced in dozens of individuals, to collections of complete genomes, virtually comprising all available loci. Initially sequenced in a few individuals, such genomic data sets are now reaching and even exceeding the size of traditional data sets in the number of haplotypes sequenced. Because all loci in a genome are not independent, this evolution of data sets is mirrored by a methodological change. The evolutionary processes that generate the observed sequences are now modeled spatially along genomes whereas it was previously described temporally (either in a forward or backward manner). Although the spatial process of sequence evolution is complex, approximations to the model feature Markovian properties, permitting efficient inference. In this chapter, we introduce these recent developments that enable the modeling of the evolutionary history of a sample of several individual genomes. Such models assume the occurrence of meiotic recombination, and therefore, to date, they are dedicated to the analysis of eukaryotic species.

Ancestral population genomics.

The full genomes of several closely related species are now available, opening an emerging field of investigation borrowing both from population genetics and phylogenetics. Providing we can properly model sequence evolution within populations undergoing speciation events, this resource enables us to estimate key population genetics parameters, such as ancestral population sizes and split times. Furthermore, we can enhance our understanding of the recombination process and investigate various selective forces. We discuss the basic speciation models for closely related species, including the isolation and isolation-with-migration models. A major point in our discussion is that only a few complete genomes contain much information about the whole population. The reason being that recombination unlinks genomic regions, and therefore a few genomes contain many segments with distinct histories. The challenge of population genomics is to decode this mosaic of histories in order to infer scenarios of demography and selection. We survey different approaches for understanding ancestral species from analyses of genomic data from closely related species. In particular, we emphasize core assumptions and working hypothesis. Finally, we discuss computational and statistical challenges that arise in the analysis of population genomics data sets.

A new isolation with migration model along complete genomes infers very different divergence processes among closely related great ape species.

We present a hidden Markov model (HMM) for inferring gradual isolation between two populations during speciation, modelled as a time interval with restricted gene flow. The HMM describes the history of adjacent nucleotides in two genomic sequences, such that the nucleotides can be separated by recombination, can migrate between populations, or can coalesce at variable time points, all dependent on the parameters of the model, which are the effective population sizes, splitting times, recombination rate, and migration rate. We show by extensive simulations that the HMM can accurately infer all parameters except the recombination rate, which is biased downwards. Inference is robust to variation in the mutation rate and the recombination rate over the sequence and also robust to unknown phase of genomes unless they are very closely related. We provide a test for whether divergence is gradual or instantaneous, and we apply the model to three key divergence processes in great apes: (a) the bonobo and common chimpanzee, (b) the eastern and western gorilla, and (c) the Sumatran and Bornean orang-utan. We find that the bonobo and chimpanzee appear to have undergone a clear split, whereas the divergence processes of the gorilla and orang-utan species occurred over several hundred thousands years with gene flow stopping quite recently. We also apply the model to the Homo/Pan speciation event and find that the most likely scenario involves an extended period of gene flow during speciation.

Estimating divergence time and ancestral effective population size of Bornean and Sumatran orangutan subspecies using a coalescent hidden Markov model.

Due to genetic variation in the ancestor of two populations or two species, the divergence time for DNA sequences from two populations is variable along the genome. Within genomic segments all bases will share the same divergence-because they share a most recent common ancestor-when no recombination event has occurred to split them apart. The size of these segments of constant divergence depends on the recombination rate, but also on the speciation time, the effective population size of the ancestral population, as well as demographic effects and selection. Thus, inference of these parameters may be possible if we can decode the divergence times along a genomic alignment. Here, we present a new hidden Markov model that infers the changing divergence (coalescence) times along the genome alignment using a coalescent framework, in order to estimate the speciation time, the recombination rate, and the ancestral effective population size. The model is efficient enough to allow inference on whole-genome data sets. We first investigate the power and consistency of the model with coalescent simulations and then apply it to the whole-genome sequences of the two orangutan sub-species, Bornean (P. p. pygmaeus) and Sumatran (P. p. abelii) orangutans from the Orangutan Genome Project. We estimate the speciation time between the two sub-species to be thousand years ago and the effective population size of the ancestral orangutan species to be , consistent with recent results based on smaller data sets. We also report a negative correlation between chromosome size and ancestral effective population size, which we interpret as a signature of recombination increasing the efficacy of selection.

Ancestral population genomics: the coalescent hidden Markov model approach.

With incomplete lineage sorting (ILS), the genealogy of closely related species differs along their genomes. The amount of ILS depends on population parameters such as the ancestral effective population sizes and the recombination rate, but also on the number of generations between speciation events. We use a hidden Markov model parameterized according to coalescent theory to infer the genealogy along a four-species genome alignment of closely related species and estimate population parameters. We analyze a basic, panmictic demographic model and study its properties using an extensive set of coalescent simulations. We assess the effect of the model assumptions and demonstrate that the Markov property provides a good approximation to the ancestral recombination graph. Using a too restricted set of possible genealogies, necessary to reduce the computational load, can bias parameter estimates. We propose a simple correction for this bias and suggest directions for future extensions of the model. We show that the patterns of ILS along a sequence alignment can be recovered efficiently together with the ancestral recombination rate. Finally, we introduce an extension of the basic model that allows for mutation rate heterogeneity and reanalyze human-chimpanzee-gorilla-orangutan alignments, using the new models. We expect that this framework will prove useful for population genomics and provide exciting insights into genome evolution.