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Deep mutational scanning (DMS) is a high-throughput experimental technique that measures the effects of thousands of mutations to a protein. These experiments can be performed on multiple homologs of a protein or on the same protein selected under multiple conditions. It is often of biological interest to identify mutations with shifted effects across homologs or conditions. However, it is challenging to determine if observed shifts arise from biological signal or experimental noise. Here, we describe a method for jointly inferring mutational effects across multiple DMS experiments while also identifying mutations that have shifted in their effects among experiments. A key aspect of our method is to regularize the inferred shifts, so that they are nonzero only when strongly supported by the data. We apply this method to DMS experiments that measure how mutations to spike proteins from SARS-CoV-2 variants (Delta …