The effectiveness of selection in a species affects the direction of amino acid frequency evolution

Nearly neutral theory predicts that species with higher effective population size $\left(N_e\right)$ are better at purging slightly deleterious mutations. We compare evolution in high- $N_e$ vs. low- $N_e$ vertebrates to reveal subtle selective preferences among amino acids. We take three complementary approaches. First, we fit non-stationary substitution models using maximum likelihood, comparing the high- $N_e$ clade of rodents and lagomorphs to its low- $N_e$ sister clade of primates and colugos. Second, we compared evolutionary outcomes across a wider range of vertebrates, via correlations between amino acid frequencies and $N_e$ . Third, we dissected which amino acids substitutions occurred in human, chimpanzee, mouse, and rat, as scored by parsimony - this also enabled comparison to a historical paper. All methods agree on amino acid preference under more effective selection. Preferred amino acids are less costly to synthesize and use GC-rich codons, which are hard to maintain under AT-biased mutation. These factors explain 85% of the variance in amino acid preferences. Parsimony-induced bias in the historical study produces an apparent reduction in structural disorder, perhaps driven by slightly deleterious substitutions in rapidly evolving regions. Within highly exchangeable pairs of amino acids, arginine is strongly preferred over lysine, aspartate over glutamate, and valine over isoleucine, consistent with more effective selection preferring a marginally larger free energy of folding. Two of these preferences (K→R and I→V), but not a third (E→D) match differences between thermophiles and mesophilic relatives. These results reveal the biophysical consequences of mutation-selection-drift balance, and demonstrate the utility of nearly neutral theory for understanding protein evolution.