Whole-genome doubling, tripling or replicating to a greater degree, due to fixation of polyploidization events, is attested in almost all lineages of the flowering plants, recurring in the ancestry of some plants two, three or more times in retracing their history to the earliest angiosperm. This major mechanism in plant genome evolution, which generally appears as instantaneous on the evolutionary time scale, sets in operation a compensatory process called fractionation, the loss of duplicate genes, initially rapid, but continuing at a diminishing rate over millions and tens of millions of years. We study this process by statistically comparing the distribution of duplicate gene pairs as a function of their time of creation through polyploidization, as measured by sequence similarity. The stochastic model that accounts for this distribution, though exceedingly simple, still has too many parameters to be estimated based only on the similarity distribution, while the computational procedures for compiling the distribution from annotated genomic data is heavily biased against earlier polyploidization events-syntenic 'crumble'. Other parameters, such as the size of the initial gene complement and the ploidy of the various events giving rise to duplicate gene pairs, are even more inaccessible to estimation. Here, we show how the frequency of genes, identified via their embedding in stretches of duplicate pairs, together with previously established constraints among some parameters, adds enormously to the range of successive polyploidization events that can be analysed. This also allows us to estimate the initial gene complement and to correct for the bias due to crumble. We explore the applicability of our methodology to four flowering plant genomes covering a range of different polyploidization histories.
