Inferring number of populations and changes in connectivity under the n-island model.

Inferring the demographic history of species is one of the greatest challenges in populations genetics. This history is often represented as a history of size changes, ignoring population structure. Alternatively, when structure is assumed, it is defined a priori as a population tree and not inferred. Here we propose a framework based on the IICR (Inverse Instantaneous Coalescence Rate). The IICR can be estimated for a single diploid individual using the PSMC method of Li and Durbin (2011). For an isolated panmictic population, the IICR matches the population size history, and this is how the PSMC outputs are generally interpreted. However, it is increasingly acknowledged that the IICR is a function of the demographic model and sampling scheme with limited connection to population size changes. Our method fits observed IICR curves of diploid individuals with IICR curves obtained under piecewise stationary symmetrical island models. In our models we assume a fixed number of time periods during which gene flow is constant, but gene flow is allowed to change between time periods. We infer the number of islands, their sizes, the periods at which connectivity changes and the corresponding rates of connectivity. Validation with simulated data showed that the method can accurately recover most of the scenario parameters. Our application to a set of five human PSMCs yielded demographic histories that are in agreement with previous studies using similar methods and with recent research suggesting ancient human structure. They are in contrast with the view of human evolution consisting of one ancestral population branching into three large continental and panmictic populations with varying degrees of connectivity and no population structure within each continent.

Coalescence times for three genes provide sufficient information to distinguish population structure from population size changes.

The increasing amount of genomic data currently available is expanding the horizons of population genetics inference. A wide range of methods have been published allowing to detect and date major changes in population size during the history of species. At the same time, there has been an increasing recognition that population structure can generate genetic data similar to those generated under models of population size change. Recently, Mazet et al. (Heredity 116(4):362-371, 2016) introduced the idea that, for any model of population structure, it is always possible to find a panmictic model with a particular function of population size-change having an identical distribution of [Formula: see text] (the time of the first coalescence for a sample of size two). This implies that there is an identifiability problem between a panmictic and a structured model when we base our analysis only on [Formula: see text]. In this paper, based on an analytical study of the rate matrix of the ancestral lineage process, we obtain new theoretical results about the joint distribution of the coalescence times [Formula: see text] for a sample of three haploid genes in a n-island model with constant size. Even if, for any [Formula: see text], it is always possible to find a size-change scenario for a panmictic population such that the marginal distribution of [Formula: see text] is exactly the same as in a n-island model with constant population size, we show that the joint distribution of the coalescence times [Formula: see text] for a sample of three genes contains enough information to distinguish between a panmictic population and a n-island model of constant size.

Inferring Population Size History from Large Samples of Genome-Wide Molecular Data - An Approximate Bayesian Computation Approach.

Inferring the ancestral dynamics of effective population size is a long-standing question in population genetics, which can now be tackled much more accurately thanks to the massive genomic data available in many species. Several promising methods that take advantage of whole-genome sequences have been recently developed in this context. However, they can only be applied to rather small samples, which limits their ability to estimate recent population size history. Besides, they can be very sensitive to sequencing or phasing errors. Here we introduce a new approximate Bayesian computation approach named PopSizeABC that allows estimating the evolution of the effective population size through time, using a large sample of complete genomes. This sample is summarized using the folded allele frequency spectrum and the average zygotic linkage disequilibrium at different bins of physical distance, two classes of statistics that are widely used in population genetics and can be easily computed from unphased and unpolarized SNP data. Our approach provides accurate estimations of past population sizes, from the very first generations before present back to the expected time to the most recent common ancestor of the sample, as shown by simulations under a wide range of demographic scenarios. When applied to samples of 15 or 25 complete genomes in four cattle breeds (Angus, Fleckvieh, Holstein and Jersey), PopSizeABC revealed a series of population declines, related to historical events such as domestication or modern breed creation. We further highlight that our approach is robust to sequencing errors, provided summary statistics are computed from SNPs with common alleles.

The IICR (inverse instantaneous coalescence rate) as a summary of genomic diversity: insights into demographic inference and model choice.

Several inferential methods using genomic data have been proposed to quantify and date population size changes in the history of species. At the same time an increasing number of studies have shown that population structure can generate spurious signals of population size change. Recently, Mazet et al. (2016) introduced, for a sample size of two, a time-dependent parameter, which they called the IICR (inverse instantaneous coalescence rate). The IICR is equivalent to a population size in panmictic models, but not necessarily in structured models. It is characterised by a temporal trajectory that suggests population size changes, as a function of the sampling scheme, even when the total population size was constant. Here, we extend the work of Mazet et al. (2016) by (i) showing how the IICR can be computed for any demographic model of interest, under the coalescent, (ii) applying this approach to models of population structure (1D and 2D stepping stone, split models, two- and three-island asymmetric gene flow, continent-island models), (iii) stressing the importance of the sampling strategy in generating different histories, (iv) arguing that IICR plots can be seen as summaries of genomic information that can thus be used for model choice or model exclusion (v) applying this approach to the question of admixture between humans and Neanderthals. Altogether these results are potentially important given that the widely used PSMC (pairwise sequentially Markovian coalescent) method of Li and Durbin (2011) estimates the IICR of the sample, not necessarily the history of the populations.

The IICR and the non-stationary structured coalescent: towards demographic inference with arbitrary changes in population structure.

In the last years, a wide range of methods allowing to reconstruct past population size changes from genome-wide data have been developed. At the same time, there has been an increasing recognition that population structure can generate genetic data similar to those produced under models of population size change. Recently, Mazet et al. (Heredity 116:362-371, 2016) showed that, for any model of population structure, it is always possible to find a panmictic model with a particular function of population size changes, having exactly the same distribution of T2 (the coalescence time for a sample of size two) as that of the structured model. They called this function IICR (Inverse Instantaneous Coalescence Rate) and showed that it does not necessarily correspond to population size changes under non-panmictic models. Besides, most of the methods used to analyse data under models of population structure tend to arbitrarily fix that structure and to minimise or neglect population size changes. Here, we extend the seminal work of Herbots (PhD thesis, University of London, 1994) on the structured coalescent and propose a new framework, the Non-Stationary Structured Coalescent (NSSC) that incorporates demographic events (changes in gene flow and/or deme sizes) to models of nearly any complexity. We show how to compute the IICR under a wide family of stationary and non-stationary models. As an example we address the question of human and Neanderthal evolution and discuss how the NSSC framework allows to interpret genomic data under this new perspective.

Demographic inference using genetic data from a single individual: Separating population size variation from population structure.

The rapid development of sequencing technologies represents new opportunities for population genetics research. It is expected that genomic data will increase our ability to reconstruct the history of populations. While this increase in genetic information will likely help biologists and anthropologists to reconstruct the demographic history of populations, it also represents new challenges. Recent work has shown that structured populations generate signals of population size change. As a consequence it is often difficult to determine whether demographic events such as expansions or contractions (bottlenecks) inferred from genetic data are real or due to the fact that populations are structured in nature. Given that few inferential methods allow us to account for that structure, and that genomic data will necessarily increase the precision of parameter estimates, it is important to develop new approaches. In the present study we analyze two demographic models. The first is a model of instantaneous population size change whereas the second is the classical symmetric island model. We (i) re-derive the distribution of coalescence times under the two models for a sample of size two, (ii) use a maximum likelihood approach to estimate the parameters of these models (iii) validate this estimation procedure under a wide array of parameter combinations, (iv) implement and validate a model rejection procedure by using a Kolmogorov-Smirnov test, and a model choice procedure based on the AIC, and (v) derive the explicit distribution for the number of differences between two non-recombining sequences. Altogether we show that it is possible to estimate parameters under several models and perform efficient model choice using genetic data from a single diploid individual.