Horizontal Gene Transfer Phylogenetics: A Random Walk Approach

Abstract

The dramatic decrease in time and cost for generating genetic sequence data has opened up vast opportunities in molecular systematics, one of which is the ability to decipher the evolutionary history of strains of a species. Under this fine systematic resolution, the standard markers are too crude to provide a phylogenetic signal. Nevertheless, among prokaryotes, genome dynamics in the form of horizontal gene transfer (HGT) between organisms and gene loss seem to provide far richer information by affecting both gene order and gene content. The “synteny index” (SI) between a pair of genomes combines these latter two factors, allowing comparison of genomes with unequal gene content, together with order considerations of their common genes. Although this approach is useful for classifying close relatives, no rigorous statistical modeling for it has been suggested. Such modeling is valuable, as it allows observed measures to be transformed into estimates of time periods during evolution, yielding the “additivity” of the measure. To the best of our knowledge, there is no other additivity proof for other gene order/content measures under HGT. Here, we provide a first statistical model and analysis for the SI measure. We model the “gene neighborhood” as a “birth–death–immigration” process affected by the HGT activity over the genome, and analytically relate the HGT rate and time to the expected SI. This model is asymptotic and thus provides accurate results, assuming infinite size genomes. Therefore, we also developed a heuristic model following an “exponential decay” function, accounting for biologically realistic values, which performed well in simulations. Applying this model to 1,133 prokaryotes partitioned to 39 clusters by the rank of genus yields that the average number of genome dynamics events per gene in the phylogenetic depth of genus is around half with significant variability between genera. This result extends and confirms similar results obtained for individual genera in different manners.

Relation between two evolutionary clocks reveal new insights in bacterial evolution

“…For 16S gene distance we used the Jukes Cantor model [ 32 ] for distance between sequences. For gene order we used the model developed in [ 33 ], which declares the expected SI value for a proper number of recombination events:…”

“…where is neighbourhood size, n is genome size and is number of recombination events. We note that is the expected SI after infinite number of translocation events (see [ 33 ] for proof). This model enables the translation of the observed SI to the expected number of recombination events:…”

“…We analyse this pattern and detect that the phase transition point occurs where . In our previous work [ 33 ], we developed a statistical model, which can be used to translate to the number of recombination events [i.e. to a real distance function, equations (1,2)] [ 33 ].…”

“…In our previous work [ 33 ], we developed a statistical model, which can be used to translate to the number of recombination events [i.e. to a real distance function, equations (1,2)] [ 33 ]. Based on this model we can see that the point of phase transition occurs where (since this leads to ), which means that at this point each gene in the genome undergoes, on average, one translocation.…”

“…n−1 is the expected SI after infinite number of translocation events (see [33] for proof). This model enables the translation of the observed SI to the expected number of recombination events:…”