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Two broad paradigms exist for inferring dN/dS,the ratio of nonsynonymous to synonymous substitution rates, from coding sequences: (i) a one-rate approach, where dN/dSis represented with a single parameter, or (ii) a two-rate approach, where dNand dSare estimated separately. The performances of these two approaches have been well studied in the specific context of proper model specification, i.e., when the inference model matches the simulation model. By contrast, the relative performances of one-rate vs.two-rate parameterizations when applied to data generated according to a different mechanism remain unclear. Here, we compare the relative merits of one-rate and two-rate approaches in the specific context of model misspecification by simulating alignments with mutation–selection models rather than with dN/dS-based models. We find that one-rate frameworks generally infer more accurate dN/dSpoint estimates, even when dSvaries among sites. In other words, modeling dSvariation may substantially reduce accuracy of dN/dSpoint estimates. These results appear to depend on the selective constraint operating at a given site. For sites under strong purifying selection (dN/dS≲0.3), one-rate and two-rate models show comparable performances. However, one-rate models significantly outperform two-rate models for sites under moderate-to-weak purifying selection. We attribute this distinction to the fact that, for these more quickly evolving sites, a given substitution is more likely to be nonsynonymous than synonymous. The data will therefore be relatively enriched for nonsynonymous changes, and modeling dScontributes excessive noise to dN/dSestimates. We additionally find that high levels of divergence among sequences, rather than the number of sequences in the alignment, are more critical for obtaining precise point estimates.

It has long been recognized that certain sites within a protein, such as sites in the protein core or catalytic residues in enzymes, are evolutionarily more conserved than other sites. However, our understanding of rate variation among sites remains surprisingly limited. Recent progress to address this includes the development of a wide array of reliable methods to estimate site-specific substitution rates from sequence alignments. In addition, several molecular traits have been identified that correlate with site-specific mutation rates, and novel mechanistic biophysical models have been proposed to explain the observed correlations. Nonetheless, current models explain, at best, approximately 60% of the observed variance, highlighting the limitations of current methods and models and the need for new research directions.

Transition metal cofactors are crucial for many biological processes. Despite being primarily considered to be toxic, the transition metal cadmium (Cd) was discovered to be a substitute cofactor for zinc (Zn) in photosynthetic carbon fixation pathways of marine diatoms. However, it is not known how conditions in the geosphere impacted Cd availability and its incorporation as an alternative metal cofactor for phytoplankton. We employed mineral chemistry network analysis to investigate which geochemical factors may have influenced the availability of Cd and Zn during the putative time period that the alternative Cd‐based pathway evolved. Our results show that Zn minerals are more chemically diverse than are Cd minerals, but Zn‐ and Cd‐containing minerals have similar network centrality values when specifically considering sulfur (S)‐containing species. Cadmium and Zn sulfides are the most common Cd‐ and Zn‐containing mineral species over the past 500 million years. In particular, the Cd and Zn sulfides, respectively greenockite and sphalerite, were highly abundant during this time period. Furthermore, S‐containing Cd and Zn minerals are commonly co‐located in geologic time, allowing them to be weathered and transported to the ocean in tandem, rather than from separate sources. We suggest that the simultaneous weathering of Cd and Zn sulfides allowed for Cd to be a bioavailable direct substitute for Zn in protein complexes during periods of Zn depletion. The biogeochemical cycles of Zn and Cd exemplify the importance of the coevolution of the geosphere and biosphere in shaping primary production in the modern ocean. Cadmium (Cd) is a toxic heavy metal in biology, but the element is also used as an alternative cofactor for zinc (Zn) in carbon fixation proteins of productive marine phytoplankton called diatoms. It is not known how a toxic metal became available for biological utilization during periods of diatom evolution. In this study we used network analysis of the chemistry of Cd and Zn minerals over billions of years of Earth history to better understand how these elements are related. Our results show that the chemistry of Zn minerals is much more diverse than for Cd minerals, but the two elements are similar in terms of their sulfur‐containing mineral chemistry in geologic time. Cadmium sulfides are also commonly co‐located with Zn sulfides, which are both highly weatherable. Simultaneous weathering of Cd and Zn sulfides make Cd a bioavailable substitute for Zn in protein complexes during periods of Zn depletion. Cd and Zn share similar sulfide mineral chemistry and weatherabilitySulfur‐containing Cd minerals are often co‐located with sulfur‐containing Zn sulfide mineralsSimultaneous weathering of sulfur‐containing Cd and Zn minerals allows Cd to be a substitute for Zn in protein complexes during periods of Zn depletion Cd and Zn share similar sulfide mineral chemistry and weatherability Sulfur‐containing Cd minerals are often co‐located with sulfur‐containing Zn sulfide minerals Simultaneous weathering of sulfur‐containing Cd and Zn minerals allows Cd to be a substitute for Zn in protein complexes during periods of Zn depletion