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. 2021 Sep 16;6(1):bpab017.
doi: 10.1093/biomethods/bpab017. eCollection 2021.

OptM: estimating the optimal number of migration edges on population trees using Treemix

Robert R Fitak  1
Affiliations

OptM: estimating the optimal number of migration edges on population trees using Treemix

Robert R Fitak. Biol Methods Protoc. .

Abstract

The software Treemix has become extensively used to estimate the number of migration events, or edges (m), on population trees from genome-wide allele frequency data. However, the appropriate number of edges to include remains unclear. Here, I show that an optimal value of m can be inferred from the second-order rate of change in likelihood (Δm) across incremental values of m. Repurposed from its original use to estimate the number of population clusters in the software Structure (ΔK), I show using simulated populations that Δm performs equally as well as current recommendations for Treemix. A demonstration of an empirical dataset from domestic dogs indicates that this method may be preferable in large, complex population histories and can prioritize migration events for subsequent investigation. The method has been implemented in a freely available R package called "OptM" and as a web application (https://rfitak.shinyapps.io/OptM/) to interface directly with the output files of Treemix.

Keywords: SNPs; likelihood; population genomics; structure.

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Figures

Figure 1:
Figure 1:
The output produced by OptM for the simulated dataset with m = 3 migration edges. (a) The mean and standard deviation (SD) across 10 iterations for the composite likelihood L(m) (left axis, black circles) and proportion of variance explained (right axis, red “x”s). The 99.8% threshold (horizontal dotted line) is that recommended by Pickrell and Pritchard [2]. (b) The second-order rate of change (Δm) across values of m.
Figure 2:
Figure 2:
The output produced by OptM for an empirical dataset of domestic dogs. A total of 10 iterations were run for each possible number of migration edges, m = 1–40. (a) The mean and standard deviation (SD) for the composite likelihood L(m) (left axis, black circles) and proportion of variance explained (right axis, red “x”s). The 99.8% threshold is that recommended by Pickrell and Pritchard [2], but not visible here because the threshold is still not met at m = 40 edges. OptM produces a warning to notify the user that this threshold is not visible. (b) The second-order rate of change (Δm) across values of m. The arrow indicates the peak in Δm at m = 5 edges.
Figure 3:
Figure 3:
The tree structure of the graph inferred by Treemix for the 34 dog breeds and gray wolf populations. Five migration edges were allowed as inferred by OptM. The migration edges are colored according to their weight (w^). The scale bar indicates ten times the average standard error of the values in the covariance matrix.
See this image and copyright information in PMC

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