The process of amino acid replacement in proteins is contextdependent, with substitution rates influenced by local structure, functional role, and amino acids at other locations. Predicting how these differences affect replacement processes is difficult. To make such inference easier, it is often assumed that the acceptabilities of different amino acids at a position are constant. However, evolutionary interactions among residue positions will tend to invalidate this assumption. Here, we use simulations of purple acid phosphatase evolution to show that amino acid propensities at a position undergo predictable change after an amino acid replacement at that position. After a replacement, the new amino acid and similar amino acids tend to become gradually more acceptable over time at that position. In other words, proteins tend to equilibrate to the presence of an amino acid at a position through replacements at other positions. Such a shift is reminiscent of the spectroscopy effect known as the Stokes shift, where molecules receiving a quantum of energy and moving to a higher electronic state will adjust to the new state and emit a smaller quantum of energy whenever they shift back down to the original ground state. Predictions of changes in stability in real proteins show that mutation reversals become less favorable over time, and thus, broadly support our results. The observation of an evolutionary Stokes shift has profound implications for the study of protein evolution and the modeling of evolutionary processes.A major focus of modern evolutionary studies is to understand how structural and functional contexts determine the patterns of evolutionary change at different positions in a biological macromolecule. Such an understanding is important to phylogenetics, partially because the position-specific processes of evolution are known to determine our ability to reconstruct deep nodes in the tree of life (1) but also because features of the evolutionary process such as convergence can deterministically mislead phylogenetic reconstruction (2). Understanding patterns of evolution and how they respond to details of structure and function can also potentially help us to better decode the evolutionary record, allowing us to distinguish between structural and functional constraints and identify the signatures of positive selection. This finding can lead to improved understanding of a biomolecule's structure, dynamics, thermodynamics, functionality, and physiological context. Key questions concern how evolutionary processes vary among sites and over time and particularly, how the evolution at different locations influences each other. For example, coevolution between different locations in a protein can slow the amino acid replacement process, allowing phylogenetic inference at deep nodes that would otherwise have been swamped by recurrent neutral changes. Furthermore, coevolution tends to depend on proximity in the 3D structure of proteins, leading to the hope that, if properly understood, it could improve our ability...