BUSTED and BUSTED-E applied to the UROD gene alignment of 40 bird sequences from Shultz and Sackton Shultz and Sackton (2019) which used a sophisticated alignment curation and masking procedure to remove artifacts.

BUSTED infers three ω classes, including a class with ω > 1, and deduces the presence of episodic diversifying selection (EDS), p = 0.006. BUSTED-E introduces an additional error class (ω > 100, maximum weight f 1%). This changes improves model fit (small sample AIC), places a 0.1% fraction of the alignment in the error class, removes the distribution class with 1 < ω < 100, and eliminates evidence for EDS (p = 0.50). The error attribution procedure of BUSTED-E highlights (red colors) one problematic part of this alignment, located at the 3’ end of the gene, in the Apteryx rowi (aptHaa) sequence. BUSTED misinterprets such local misalignments as evidence of rapid diversification, whereas BUSTED-E has the option to correctly treat them as “noise”. Blue and yellow backgrounds represent low error probability.

Figure 1—figure supplement 1. Apparent local misalignment at the 3’ end of the PXDNL gene from Shultz and Sackton (Shultz and Sackton, 2019). The color palette indicates empirical Bayes factor support for assignment to the error class.

The large scale datasets used for BUSTED-E evaluation.

For all per-alignment quantities (sequences, codons, tree length, gaps per) we report the median value and the [2.5% : 97.5%] range. Gaps per sequence are normalized per 1000 codons. Tree length is the cumulative branch length (expected substitutions/nucleotide) under the simple (MG94xREV) codon model. Abbreviations for the Alignment column are as follows. P2C: translated protein sequences are aligned, then mapped back to codon sequences; P&C: protein based homology and filtering, codon-level alignment; MNM : multi-nucleotide mutations.

Comparative Method Performance on Genome-Scale Datasets.

BUSTED (Std.) and BUSTED-E (-E) performance on empirical data sets; both original and filtered using BUSTED-E (see text). MA: model average. *: estimates between BUSTED-E and BUSTED have a Mann-Whitney test p < 0.0001. (1) Per lineage branch-site tests using PAML at FDRf0.05 following the Rom correction. (2) No direct dN/dS ë 1 tests were done. (3) FDRf0.01 corrected clade branch-site tests using PAML for different clades. (4). p f 0.05 for different PAML model pairs and the original BUSTED method. The study used a 0.14 rate by requiring unanimous method consent.

The rate at which genes are found to be subject to EDS as function of the nominal p-value cutoff.

The grey line shows the expectation under the strict null (no positive selection, at most neutral evolution).

Enrichment/depletion analysis using top 5% LRT genes (BUSTED-E) as the foreground set, at FDR f 0.2.

Each bar is colored by the AUC of a simple predictive model which uses alignment length to predict BUSTED LRT model ranking (see text).

The distribution of ω3 (positive selection class estimate) estimated by BUSTED and BUSTED-E from individual genes in the Shultz and Sackton dataset Shultz and Sackton (2019).

Genes are separated into groups by how the two methods classify EDS: both ‘no selection’, both ‘yes’, or ‘discordant’ top, middle and last row respectively. (Corresponding fractions of genes are shown.) The first columns shows the ω3 values the second column shows the corresponding weight of the ω3 class. For readability, values are capped at log10(ω3) = 5 and log10 Pr(ω = ω3) = –5 The rectangles show areas of the parameter space where BUSTED estimates are “error-like” (high ω, low weight) and BUSTED-E estimates lie in the more nominal range. These ranges are more densely represented among the discordant genes (last row).

Rates of EDS selection on data simulated with the BUSTED model (Supplementary Table 6).

A LRT test with pf0.05 constitutes a positive result. Horizontal reference lines demarcate 0.05 and 0.90 rates. The datasets are sorted by the number of characters, smallest to largest. Circles are of different sizes to eliminate overlap, and sizes have no specific meaning.

Figure 5—figure supplement 1. Rates of EDS selection on data simulated with the BUSTED model (Supplementary Table 6). A LRT test with pf0.05 constitutes a positive result. Horizontal reference lines demarcate 0.05 and 0.90 rates. The datasets are sorted by the number of characters, smallest to largest. Circles are of different sizes to eliminate overlap.

BUSTED-E filtering procedure statistics.

Unaffected alignments are those where no filtering is deemed necessary. All the following statistics are computed only over those alignments where some filtering was done. Masked codons per is the median [2.5% - 97.5%] number of codons masked per: alignment (raw counts), a single column (normalized), 1000 codons of sequence (normalized). As fraction of total gaps, refers to the median [2.5% - 97.5%] percentage of the gaps in the filtered alignment that are due to those added by filtering (the others were already there). *Input datasets for this reference contained no gaps.

The effects of various data filtering approaches on BUSTED and BUSTED-E performance; the “original data” row also includes filtering metrics using BUSTED-E.

Key BUSTED-E rate variation parameters.

Point estimates of multiple-nucleotide substitution rates (under BUSTED-MH) stratified by BUSTED/BUSTED-E (without MH support) EDS classification at pf0.05, e.g. +-: detected as EDS by BUSTED, but not by BUSTED-E.

Examples of codon sites filtered and retained by the heuristic filtering procedures based on the empirical Bayes factors for error class membership and for positive selection.