Thesis (M.S., Bioinformatics & Computational Biology) -- University of Idaho, 2015 | Parallel phenotypic or genetic evolution is often assumed to result from strong repeated natural selection associated with adaptation to particular environments. Here we develop and analyze a mathematical model that predicts the probability of parallel genetic evolution as a function of the strength of phenotypic selection and constraints imposed by genetic architecture. We then develop a Bayesian approach that uses our model, along with estimates of genetic parameters derived from QTL scans, to estimate the strength of parallel phenotypic natural selection. Using extensive individual based simulations we then evaluate the performance of our Bayesian estimator across a wide range of genetic and evolutionary scenarios. These simulations demonstrate that our Bayesian approach provides a useful tool for estimating the strength of parallel phenotypic selection from genomic data. In addition, our analyses of simulated data allows us to compare the utility of two commonly used experimental methodologies and generate guidelines for future empirical studies of parallel genetic evolution.