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MIP-relaxations may be formulated with alternative methods, for instance with a convex combination model that introduces only a number of extra binary variables and constraints that is logarithmic in the number of breakpoints [18].
The output from cBrother analyzed was the MAP number of breakpoints and mosaic structure, namely the most frequent combination of topologies and breakpoints.
These results suggest that advanced-stage and metastatic CRC could be associated with a greater number of breakpoints and higher chromosomal instability.
This approach is essentially a simplified version of the method of Davis and coworkers, in which an a priori unknown number of breakpoints is estimated [67].
The mode values inferred the true number of SPR operations in 71% of the datasets and correctly predicted the number of breakpoints in 84% of the simulations with eight taxa.
Moreover, since each SPR represents at least one recombination, the total number of approximate SPR moves is higher than the number of breakpoints (modal values of d̂SPR = 65 distributed among 37 locations).
Many of the sequences contained multiple breakpoints so that the number of breakpoints on each graph is typically larger than the number of recombinant sequences listed in Tables 1 7.
The convergence was accessed by visual inspection of the time series of the samples, posterior distribution and the scaled reduction factor [34] for the posterior probability, the number of breakpoints and the total estimated number of SPR moves.
If we consider only the detection of recombination, cBrother retrieved the correct number of breakpoints in 55% of the datasets with eight taxa, much lower than the 84% reported by our procedure (not shown).
The average number of breakpoints per chromosome was 35.
These outliers showed many small aberrations along the genome, and a very large number of breakpoints.
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