  Consensus methods provide a useful strategy for combining information from a
collection of gene trees. An important application of consensus methods is to
combine gene trees to estimate a species tree. To investigate the theoretical
properties of consensus trees that would be obtained from large numbers of loci
evolving according to a basic evolutionary model, we construct consensus trees
from independent gene trees that occur in proportion to gene tree probabilities
derived from coalescent theory. We consider majority-rule, rooted triple (R*),
and greedy consensus trees constructed from known gene trees, both in the
asymptotic case as numbers of gene trees approach infinity and for finite
numbers of genes. Our results show that for some combinations of species tree
branch lengths, increasing the number of independent loci can make the
majority-rule consensus tree more likely to be at least partially unresolved
and the greedy consensus tree less likely to match the species tree. However,
the probability that the R* consensus tree has the species tree topology
approaches 1 as the number of gene trees approaches infinity. Although the
greedy consensus algorithm can be the quickest to converge on the correct
species tree when increasing the number of gene trees, it can also be
positively misleading. The majority-rule consensus tree is not a misleading
estimator of the species tree topology, and the R* consensus tree is a
statistically consistent estimator of the species tree topology. Our results
therefore suggest a method for using multiple loci to infer the species tree
topology, even when it is discordant with the most likely gene tree.
