Fig. 1

Different sites are expected to evolve differently, but d N/d S methods ignore this fact and so have limited power to detect positive selection. a The amino-acid preferences of five sites in TEM-1 β-lactamase as measured by deep mutational scanning (using the data measured with the highest concentration of ampicillin in [14]; letter heights are proportional to amino-acid preferences). Three sites experience mutations that confer extended-spectrum antibiotic or inhibitor resistance [15]. The two sites not involved in resistance are evolving in a way that seems roughly compatible with the experimentally measured amino-acid preferences, while the three sites implicated in resistance are evolving in ways that clearly deviate from the preferences (for instance, site 238 mutates from highly preferred glycine to the very low preference amino-acid serine). b A standard d N/d S model (the M0 variant [4] of the Goldman-Yang model [23], abbreviated GY94) assumes all sites evolve under uniform constraints. When this model is used to fit a site-specific d N/d S, no sites are deemed under diversifying selection (d N/d S>1) at a FDR of 0.05 for testing all sites, although the non-resistance site 242 is deemed under purifying selection (d N/d S<1). The violin plot shows the distribution of P-values for sites having d N/d S> or <1. All sites below the bottom dotted blue line are deemed to have d N/d S<1 at an FDR of 0.05. No sites have d N/d S>1 at this FDR, so the top dotted blue line indicate the P-value that would be needed for a site to have d N/d S>1 at a significance level of 0.05 using a Bonferroni correction. A full analysis of all sites and further details are later in the paper. See Additional file 16 for subtleties about amino-acid preferences versus equilibrium frequencies