Branching Out to Speciation in a Model of Fractionation: The Malvaceae

Integrated synteny- and similarity-based inference on the polyploidization-fractionation cycle

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 unpaired 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.

Distinguishing successive ancient polyploidy levels based on genome-internal syntenic alignment

BACKGROUND

A basic tool for studying the polyploidization history of a genome, especially in plants, is the distribution of duplicate gene similarities in syntenically aligned regions of a genome. This distribution can usually be decomposed into two or more components identifiable by peaks, or local maxima, each representing a different polyploidization event. The distributions may be generated by means of a discrete time branching process, followed by a sequence divergence model. The branching process, as well as the inference of fractionation rates based on it, requires knowledge of the ploidy level of each event, which cannot be directly inferred from the pair similarity distribution.

RESULTS

For a sequence of two events of unknown ploidy, either tetraploid, giving rise to whole genome doubling (WGD), or hexaploid, giving rise to whole genome tripling (WGT), we base our analysis on triples of similar genes. We calculate the probability of the four triplet types with origins in one or the other event, or both, and impose a mutational model so that the distribution resembles the original data. Using a ML transition point in the similarities between the two events as a discriminator for the hypothesized origin of each similarity, we calculate the predicted number of triplets of each type for each model combining WGT and/or WGD. This yields a predicted profile of triplet types for each model. We compare the observed and predicted triplet profiles for each model to confirm the polyploidization history of durian, poplar and cabbage.

CONCLUSIONS

We have developed a way of inferring the ploidy of up to three successive WGD and/or WGT events by estimating the time of origin of each of the similarities in triples of genes. This may be generalized to a larger number of events and to higher ploidies.

A branching process for homology distribution-based inference of polyploidy, speciation and loss

BACKGROUND

The statistical distribution of the similarity or difference between pairs of paralogous genes, created by whole genome doubling, or between pairs of orthologous genes in two related species is an important source of information about genomic evolution, especially in plants.

METHODS

We derive the mixture of distributions of sequence similarity for duplicate gene pairs generated by repeated episodes of whole gene doubling. This involves integrating sequence divergence and gene pair loss through fractionation, using a branching process and a mutational model. We account not only for the timing of these events in terms of local modes, but also the amplitude and variance of the component distributions. This model is then extended to orthologous gene pairs.

RESULTS

We apply the model and inference procedures to the evolution of the Solanaceae, focusing on the genomes of economically important crops. We assess how consistent or variable fractionation rates are from species to species and over time.