  Terraces are potentially large sets of trees with precisely the same
likelihood or parsimony score, which can be induced by missing sequences in
partitioned multi-locus phylogenetic data matrices. The set of trees on a
terrace can be characterized by enumeration algorithms or consensus methods
that exploit the pattern of partial taxon coverage in the data, independent of
the sequence data themselves. Terraces add ambiguity and complexity to
phylogenetic inference particularly in settings where inference is already
challenging: data sets with many taxa and relatively few loci. In this paper we
present five new findings about terraces and their impacts on phylogenetic
inference. First we clarify assumptions about model parameters that are
necessary for the existence of terraces. Second, we explore the dependence of
terrace size on partitioning scheme and indicate how to find the partitioning
scheme associated with the largest terrace containing a given tree. Third, we
highlight the impact of terraces on bootstrap estimates of confidence limits in
clades, and characterize the surprising result that the bootstrap proportion
for a clade can be entirely determined by the frequency of bipartitions on a
terrace, with some bipartitions receiving high support even when incorrect.
Fourth, we dissect some effects of prior distributions of edge lengths on the
computed posterior probabilities of clades on terraces, to understand an
example in which long edges "attract" each other in Bayesian inference. Fifth,
we show that even if data are not partitioned, patterns of missing data studied
in the terrace problem can lead to instances of apparent statistical
inconsistency when even a small element of heterotachy is introduced to the
model generating the sequence data. Finally, we discuss strategies for
remediation of some of these problems.
