It has recently been claimed that certain amino acids have been increasing in frequency in all living organisms for most of the history of life on earth, while other amino acids have been decreasing in frequency. Three lines of evidence have been offered for this assertion, but each has a more plausible alternative interpretation. Here I show that unequal patterns of gains and losses for particular pairs of amino acids (such as more leucine --> phenylalanine than phenylalanine --> leucine substitutions in humans and chimpanzees since they split from a common ancestor) are consistent with a simple neutral model at equilibrium amino acid frequencies. Unequal numbers of gains and losses for particular amino acids (such as more gains than losses of cysteine) are shown by simulations to be consistent with a model of nearly neutral evolution. Unequal numbers of gains and losses for particular amino acids in human polymorphism data are shown by simulations to be explainable by the nearly neutral model as well. In a comparison of protein sequences from four strains of Escherichia coli, polarized by one outgroup strain of Salmonella, the disparity in number of gains and losses for particular amino acids is strong in terminal branches but weaker or nonexistent in internal branches, which is inconsistent with the universal trend model but as expected under the nearly neutral model.