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Statistically consistent estimation of phylogenetic trees or gene trees ispossible if pairwise sequence dissimilarities can be converted to a set ofdistances that are proportional to the true evolutionary distances. Susko etal. (2004) reported some strikingly broad results about the forms ofinconsistency in tree estimation that can arise if corrected distances are notproportional to the true distances. They showed that if the corrected distanceis a concave function of the true distance, then inconsistency due to longbranch attraction will occur. If these functions are convex, then two "longbranch repulsion" trees will be preferred over the true tree -- though thesetwo incorrect trees are expected to be tied as the preferred true. Here weextend their results, and demonstrate the existence of a tree shape (which werefer to as a "twisted Farris-zone" tree) for which a single incorrect treetopology will be guaranteed to be preferred if the corrected distance functionis convex. We also report that the standard practice of treating gaps insequence alignments as missing data is sufficient to produce non-linearcorrected distance functions if the substitution process is not independent ofthe insertion/deletion process. Taken together, these results implyinconsistent tree inference under mild conditions. For example, if somepositions in a sequence are constrained to be free of substitutions andinsertion/deletion events while the remaining sites evolve with independentsubstitutions and insertion/deletion events, then the distances obtained bytreating gaps as missing data can support an incorrect tree topology even givenan unlimited amount of data.

Twisted trees and inconsistency of tree estimation when gaps are treated  as missing data -- the impact of model mis-specification in distance  corrections