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

Abstract

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, thus ignoring population structure. Alternatively, structure is defined a priori as a population tree and not inferred. Here we propose a framework based on the IICR (Inverse Instantaneous Coalescence Rate), which can be estimated using the PSMC method of Li and Durbin (2011) for a single diploid individual. For an isolated population, the IICR matches the population size history, which 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. Our automated method fits observed IICR curves of diploid individuals with IICR curves obtained under piecewise-stationary symmetrical island models, in which we assume a fixed number of time periods during which gene flow is constant. 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 widely accepted 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.

Heterogeneity in effective size across the genome: effects on the Inverse Instantaneous Coalescence Rate (IICR) and implications for demographic inference under linked selection

“…The models described in the present study propose another direction for the development of demographic inference methods by accounting for linked selection through variable classes of N e along the genome, and using the IICR as summary statistic. An IICR-based inference framework was recently proposed for the estimation of non stationary n-island models and provided very encouraging results (Arredondo et al, 2021). Given the strong impact of linked selection on the IICR under panmixia, as described in the present study, we believe that a similar approach could allow to jointly infer parameters related to demographic history and to the N e distribution.…”

“…Considering a symmetrical n-island model, we observed for instance that even when a large proportion of the genome is influenced by selection reducing N e the effect on the IICR could be difficult to see for models with reduced migration rates between islands (Figure 4). Focusing on humans we also considered a simple but reasonable demographic scenario of variable population structure Arredondo et al (2021) together with a realistic genomic N e distribution for this species Gossmann et al (2011). We found that the largest and most visible effect of linked selection on the IICR was an ancient population size increase (backward in time) related to the presence of balancing selection (Figure 5, bottom).…”

“…To check whether these conclusions may still hold for more realistic demographic scenarios, we next assume that each genomic class evolves under the non stationary n-island model estimated by Arredondo et al (2021) to fit the observed PSMC of a modern human from Karitiana (Li and Durbin, 2011). This model includes 11 islands with symmetric migration and (diploid) deme size 1,380 and it assumes that these islands go through We find that large values of a 1 could have a significant impact on the IICR in the period ranging from 10,000 to 30,000 generations ago (corresponding to 200-300,000 to 600-900,000 years ago).…”

“…Whatever the complexity of the model considered, the associated IICR can be computed exactly in a very small time using the rate matrix approach described in (Rodríguez et al, 2018) or Arredondo et al (2021), which allows to efficiently explore a very large number of scenarios or parameter values. As previously mentioned, the main limitation of the IICR approach described in this study is that it focuses on pairs of sequences.…”

“…Indeed, the IICR is equivalent to the past temporal trajectory of N e , previously defined as the coalescent N e (Sjödin et al, 2005), in a panmictic population under neutrality, and it is the quantity estimated by the popular PSMC method of Li and Durbin (2011). The IICR was first defined by Mazet et al (2016) for a sample size of two and its properties were studied under several models of population structure (Chikhi et al, 2018, Rodríguez et al, 2018 and it has been shown that it can be used for demographic inference under neutrality and models of population structure Arredondo et al (2021), Chikhi et al (2018). These studies showed that the IICR will significantly change over time when populations are structured, even when population size is actually constant.…”