We develop criteria to detect neighborhood selection effects on gene loss following whole genome duplication, and apply them to the recently sequenced poplar (Populus trichocarpa) genome. We improve on guided genome halving algorithms so that several thousand gene sets, each containing two paralogs in the descendant T of the doubling event and their single ortholog from an undoubled reference genome R, can be analyzed to reconstruct the ancestor A of T at the time of doubling. At the same time, large numbers of defective gene sets, either missing one paralog from T or missing their ortholog in R, may be incorporated into the analysis in a consistent way. We apply this genomic rearrangement distance-based approach to the poplar and grapevine (Vitis vinifera) genomes, as T and R respectively. We conclude that, after chromosome doubling, the "choice" of which paralogous gene pairs will lose copies is random, but that the retention of strings of single-copy genes on one chromosome versus the other is decidedly non-random.