Inference of gene flow in the process of speciation: Efficient maximum-likelihood implementation of a generalised isolation-with-migration model

The 'isolation with migration' (IM) model has been extensively used in the literature to detect gene flow during the process of speciation. In this model, an ancestral population split into two or more descendant populations which subsequently exchanged migrants at a constant rate until the present. Of course, the assumption of constant gene flow until the present is often over-simplistic in the context of speciation. In this paper, we consider a 'generalised IM' (GIM) model: a two-population IM model in which migration rates and population sizes are allowed to change at some point in the past. By developing a maximum-likelihood implementation of this model, we enable inference on both historical and contemporary rates of gene flow between two closely related populations or species. The GIM model encompasses both the standard two-population IM model and the 'isolation with initial migration' (IIM) model as special cases, as well as a model of secondary contact. We examine for simulated data how our method can be used, by means of likelihood ratio tests or AIC scores, to distinguish between the following scenarios of population divergence: (a) divergence in complete isolation; (b) divergence with a period of gene flow followed by isolation; (c) divergence with a period of isolation followed by secondary contact; (d) divergence with ongoing gene flow. Our method is based on the coalescent and is suitable for data sets consisting of the number of nucleotide differences between one pair of DNA sequences at each of a large number of independent loci. As our method relies on an explicit expression for the likelihood, it is computationally very fast

A Genealogical Interpretation of Principal Components Analysis

Principal components analysis, PCA, is a statistical method commonly used in population genetics to identify structure in the distribution of genetic variation across geographical location and ethnic background. However, while the method is often used to inform about historical demographic processes, little is known about the relationship between fundamental demographic parameters and the projection of samples onto the primary axes. Here I show that for SNP data the projection of samples onto the principal components can be obtained directly from considering the average coalescent times between pairs of haploid genomes. The result provides a framework for interpreting PCA projections in terms of underlying processes, including migration, geographical isolation, and admixture. I also demonstrate a link between PCA and Wright's fst and show that SNP ascertainment has a largely simple and predictable effect on the projection of samples. Using examples from human genetics, I discuss the application of these results to empirical data and the implications for inference

GENOMEPOP: A program to simulate genomes in populations

<p>Abstract</p> <p>Background</p> <p>There are several situations in population biology research where simulating DNA sequences is useful. Simulation of biological populations under different evolutionary genetic models can be undertaken using backward or forward strategies. Backward simulations, also called coalescent-based simulations, are computationally efficient. The reason is that they are based on the history of lineages with surviving offspring in the current population. On the contrary, forward simulations are less efficient because the entire population is simulated from past to present. However, the coalescent framework imposes some limitations that forward simulation does not. Hence, there is an increasing interest in forward population genetic simulation and efficient new tools have been developed recently. Software tools that allow efficient simulation of large DNA fragments under complex evolutionary models will be very helpful when trying to better understand the trace left on the DNA by the different interacting evolutionary forces. Here I will introduce GenomePop, a forward simulation program that fulfills the above requirements. The use of the program is demonstrated by studying the impact of intracodon recombination on global and site-specific <it>dN/dS </it>estimation.</p> <p>Results</p> <p>I have developed algorithms and written software to efficiently simulate, forward in time, different Markovian nucleotide or codon models of DNA mutation. Such models can be combined with recombination, at inter and intra codon levels, fitness-based selection and complex demographic scenarios.</p> <p>Conclusion</p> <p>GenomePop has many interesting characteristics for simulating SNPs or DNA sequences under complex evolutionary and demographic models. These features make it unique with respect to other simulation tools. Namely, the possibility of forward simulation under General Time Reversible (GTR) mutation or GTR×MG94 codon models with intra-codon recombination, arbitrary, user-defined, migration patterns, diploid or haploid models, constant or variable population sizes, etc. It also allows simulation of fitness-based selection under different distributions of mutational effects. Under the 2-allele model it allows the simulation of recombination hot-spots, the definition of different frequencies in different populations, etc. GenomePop can also manage large DNA fragments. In addition, it has a scaling option to save computation time when simulating large sequences and population sizes under complex demographic and evolutionary situations. These and many other features are detailed in its web page <abbrgrp><abbr bid="B1">1</abbr></abbrgrp>.</p

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

International audienceSeveral 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 T 2 (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