  With advances in sequencing technologies, there are now massive amounts of
genomic data from across all life, leading to the possibility that a robust
Tree of Life can be constructed. However, "gene tree heterogeneity", which is
when different genomic regions can evolve differently, is a common phenomenon
in multi-locus datasets, and reduces the accuracy of standard methods for
species tree estimation that do not take this heterogeneity into account. New
methods have been developed for species tree estimation that specifically
address gene tree heterogeneity, and that have been proven to converge to the
true species tree when the number of loci and number of sites per locus both
increase (i.e., the methods are said to be "statistically consistent"). Yet,
little is known about the biologically realistic condition where the number of
sites per locus is bounded. We show that when the sequence length of each locus
is bounded (by any arbitrarily chosen value), the most common approaches to
species tree estimation that take heterogeneity into account (i.e., traditional
fully partitioned concatenated maximum likelihood and newer approaches, called
summary methods, that estimate the species tree by combining gene trees) are
not statistically consistent, even when the heterogeneity is extremely
constrained. The main challenge is the presence of conditions such as long
branch attraction that create biased tree estimation when the number of sites
is restricted. Hence, our study uncovers a fundamental challenge to species
tree estimation using both traditional and new methods.
