Analysis and rejection sampling of Wright–Fisher diffusion bridges

We investigate the properties of a Wright–Fisher diffusion process starting at frequency xx at time 0 and conditioned to be at frequency yy at time TT. Such a process is called a bridge. Bridges arise naturally in the analysis of selection acting on standing variation and in the inference of selection from allele frequency time series. We establish a number of results about the distribution of neutral Wright–Fisher bridges and develop a novel rejection-sampling scheme for bridges under selection that we use to study their behavior.