We study the effect of natural selection on the performance of phylogeny reconstruction algorithms using Avida, a software platform that maintains a population of digital organisms (self-replicating computer programs) that evolve subject to natural selection, mutation, and drift. We compare the performance of neighbor-joining and maximum parsimony algorithms on these Avida populations to the performance of the same algorithms on randomly generated data that evolve subject only to mutation and drift. Our results show that natural selection has several specific effects on the sequences of the resulting populations, and that these effects lead to improved performance for neighbor-joining and maximum parsimony in some settings. We then show that the effects of natural selection can be partially achieved by using a non-uniform probability distribution for the location of mutations in randomly generated genomes.