Most phylogenetic reconstructions using sequence data eitehr ignore natural selection or incorporate it in a heuristic manner such as Yang and Nielsen's ω term for describing either stabilizing or diversifying selection. Here we present an alternative approach in which fixation probabilities are explicitly based on the Wright-Fisher model of population genetics undergoing gene specific, stabilizing selection the amino acid sequence of a given protein. Further, the mechanistic nature of our approach means our model is easier to justify biologically and the parameters estimated describe explicit biological processes such as a gene's average protein production rate or the predicted effect of an amino acid substitution on protein function. Despite being more parameter rich than traditional, heuristic models used in phylogenetics, our model consistently provides astronomically better AIC values when applied to a wide range of test datasets. Finally, because it is mechanistically derived, it is relatively straight forward to expand our model to incorporate additional or alternative biological processes.