Applied Maths Seminar: Jermiin -- New methods of detecting violated phylogenetic assumptions: Implications on comparative genomics

Most phylogenetic methods assume that the sequences of nucleotides or amino acids have
evolved under stationary, reversible and homogeneous conditions.  When these assumptions
are violated by the data, as would be the case if there is compositional heterogeneity
across the sequences, the phylogenetic estimates are obtained under an incorrect model
and thus subject to error.  Methods to examine aligned sequences for violation of these
assumptions have been available for years, but they are rarely used, presumably because
they are not widely known or because they are poorly understood.  Here we describe and
compare matched-pairs tests for symmetry of two-dimensional contingency tables from
homologous sequences and show that the tests of symmetry, marginal symmetry and internal
symmetry can be used not only to detect violation of the assumption of stationarity,
reversibility and homogeneity, but also to identify what may underpin this violation.
Under the assumption that the sequences evolved under stationary, reversible and
homogeneous conditions, the tests are unaffected by invariant sites and divergence
between the pairs of sequences, implying that they may be used to identify suitable
substitution models for estimation of evolutionary relationships under a Markovian
model.