Long branch attraction (LBA) is a phenomenon in phylogenetic analyses (most commonly those employing maximum parsimony) when rapidly evolving lineages are inferred to be closely related, regardless of their true evolutionary relationships. The problem arises when the DNA of two (or more) lineages evolve rapidly. There are only four possible nucleotides and when DNA substitution rates are high, the probability that two lineages will convergently evolve the same nucleotide at the same site increases. When this happens, parsimony erroneously interprets this similarity as a synapomorphy (i.e., evolving once in the common ancestor of the two lineages).
This problem can be minimized by using methods that incorporate differential rates of substitution among lineages (e.g., maximum likelihood) or by breaking up long branches by adding taxa that are related to those with the long branches.
References
Bergsten, J. (2005): A review of long-branch attraction. Cladistics21(2): 163-193. PDF fulltext
Felsenstein, J. (2004): Inferring Phylogenies. Sinauer Associates, Sunderland, MA.
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