reweighting characters, few and many

John Trueman trueman at RSBS.ANU.EDU.AU
Sat Oct 30 11:38:37 CDT 1999

Congratulations to Thomas Schlemmermeyer for providing a real example of
phylogenetics in action.

>From his post it is clear that Thomas's data are insufficient to provide a
fully resolved and robustly determined tree. As well, his "intuitive" tree
is somewhat similar to the most-parsimonious tree (mpt) in that at least
some nodes are common to both trees. Neither of these features should
surprise us. First, any good taxonomist will have a reasonably good idea of
how their data may pan out, at least most of the time. The informed
observer is not likely to be totally wrong when it comes to "intuiting" a

Second, any dataset created to address a real problem in phylogeny
estimation (as opposed to some "demo" problem concerning already
well-determined relationships) typically will produce one or both of two
(1) Some nodes will be undetermined, either because no data addresses the
relevant split(s) among taxa or what data there are suggest mutually
incompatible solutions. A likely result under the parsimony method is
multiple mpts.
(2) Some nodes are underdetermined. Although they appear determined in the
parsimony (or likelihood, lets not be partisan here) analysis, they are not
determined with sufficient rigor to achieve statistical significance.

To expand on point (2), if there are N taxa there are N-1 internal nodes.
Supposing we want to establish only the topology of the tree not the branch
lengths, we have to put in enough information to determine these. Now, in a
typical statistics problem where we are estimating a single parameter,
conventional random sampling schemes would have us seek not one or two but
at least 20 data points in order to get a robust solution. The nodes in a
tree are not independent so we don't need 20x(N-1) observations but we do
still need many (it's almost impossible to say how many) items of data,
including some which bear on each node. Unfortunately, our data selection
criterion in phylogenetics is a scattergun with respect to nodes and
potential nodes. We simply grab what characters we can which vary across
the whole taxon set. In any real data set some nodes typically will get to
be supported more strongly than others.

Put these two features together and we arrive at what should be the nub of
any phylogenetic analysis. It is not sufficient to stop when our selected
method applied to our selected data gives this, that or the other tree.
Sure, to get such a tree is the first step. However, the really interesting
question, and the only place where scientific method (as opposed to an
ability with technological button-pressing) comes in, is when we start to
ask "What does this analysis tell us which we did not know before?"

Strong support for an expected node or set of nodes (pre-existing tree
hypothesis) can be seen as a test of that hypothesis. It provides us with
corroboration sensu Popper. Support for a rival node may amount to
refutation. Support (perhaps less strong) for whatever arrangement also may
send our research off in some entirely new direction. So far so good, we
have learned something. A mere weak failure to establish the pre-existing
hypothesis is, in and of itself, nowhere near so exciting.

Thomas's example will be all too familiar to many of us. We may not have
met it in quite the same way, but we all know the feeling when our data
gives a tree on which the key branches are unresolved, or else they appear
at first to be resolved but later collapse in a bootstrap resampling of the
data or when we tweak the parsimony or likelihood model in some trivial
way. If we can show that the presence/absence of our favourite group is
reliant on whether we treated character "X" as ordered or unordered,
whether we downweighted 3rd positions 2:1 or 3:1, whether we assumed that
all or only 60% of positions are free to vary, etc., we don't have much of
a leg to stand on when it comes to asserting that the data do or do not
corroborate/refute our favourite tree.

Thomas tweaked his tree-estimation method in a (novel) trivial way. The
resulting change in tree indicates that his data are not strongly
supportive either of the "intuitive" tree or any from a number of plausible

A cladist might say "the untweaked method is the one true method and the
untweaked tree is the best estimate of the true phylogeny" (or, more
charitably,  "of the tree which this method gives" -- since some take the
getting of that tree itself as their goal).

But a scientist would be asking "Do these data corroborate my prior
(intuitive) hypothesis?", "Do they refute it?", and "What does this mean
for my research program/what do I look to next?"  The answer to both the
first and the second of these scientific questions is that all-too-familiar

John Trueman

John Trueman
Faculties Research Fellow
Bioinformatics Group
Research School of Biological Sciences
Australian National University
Canberra, ACT 0200,  AUSTRALIA

ph: +61 2 6249 4840
fax: +61 2 6279 8525
email: trueman at

Reason is a tool. Try to remember where you left it.

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