A practical introduction to sequentially Markovian coalescent methods for estimating demographic history from genomic data

Abstract

A common goal of population genomics and molecular ecology is to reconstruct the demographic history of a species of interest. A pair of powerful tools based on the sequentially Markovian coalescent have been developed to infer past population sizes using genome sequences. These methods are most useful when sequences are available for only a limited number of genomes and when the aim is to study ancient demographic events. The results of these analyses can be difficult to interpret accurately, because doing so requires some understanding of their theoretical basis and of their sensitivity to confounding factors. In this practical review, we explain some of the key concepts underpinning the pairwise and multiple sequentially Markovian coalescent methods (PSMC and MSMC, respectively). We relate these concepts to the use and interpretation of these methods, and we explain how the choice of different parameter values by the user can affect the accuracy and precision of the inferences. Based on our survey of 100 PSMC studies and 30 MSMC studies, we describe how the two methods are used in practice. Readers of this article will become familiar with the principles, practice, and interpretation of the sequentially Markovian coalescent for inferring demographic history.

Keywords: coalescent; demographic history; mutation rate; population genomics; population size.

Figure 1

The sequentially Markovian coalescent. The colored circles represent nucleotide states belonging to the alleles at each locus. Double gray lines denote recombination breakpoints, which separate the loci along the genome. The time to the most recent common ancestor of the two alleles at each locus is reflected in the local tree. (a) In PSMC, there are only two haplotypes. Thus, the topology of the local tree is fixed, but the time to the most recent common ancestor differs among loci. (b) In MSMC, there are multiple haplotypes. MSMC ignores most of the local tree topology, focusing only on the most recent coalescence event at each locus

Figure 2

Illustrations of two different uses of PSMC and MSMC methods. (a) Dating speciation events using the PSMC (Li & Durbin, 2011). The solid lines represent PSMC plots from the genomes of two modern humans: Yoruba (red) and Chinese (blue). Looking backwards in time, the plots become identical from about 100–120 thousand years ago, indicating a shared population history. The dotted line shows a PSMC plot from a hybrid genome constructed from the X chromosomes of the Yoruba and Chinese genomes, scaled by 0.75. Looking forwards in time, the infinite population size at about 20 thousand years ago suggests cessation of gene flow between the two populations. (b) Estimating the mutation rate using PSMC (Fu et al., 2014). The two thick lines are plots for a 45,000‐year‐old modern human from Ust'‐Ishim in western Siberia, either uncorrected (red) or shifted horizontally (blue) to align with the plots from present‐day non‐African modern humans (thin gray lines). The magnitude of the horizontal shift indicates the number of mutations that have occurred in 45,000 years, providing a means of estimating the mutation rate

Figure 3

Data from random samples of 100 studies that implemented the pairwise sequentially Markovian coalescent (PSMC) method and 30 studies that implemented the multiple sequentially Markovian coalescent (MSMC) method. (a) Taxonomic affiliations of the organisms studied. (b) Source of mutation rates used to scale the demographic plots. The choice of mutation rate affects the scale of the horizontal axis and the estimate of the effective population size, but does not affect the qualitative shape of the plot. For example, a higher mutation rate will cause the estimated population size to be scaled down linearly and will shift the curve closer to the present. Details of the 130 studies surveyed are provided in Appendix S1 on Dryad (https://doi.org/10.5061/dryad.0vt4b8gv2)