# RASA

James Francis Lyons-Weiler weiler at ERS.UNR.EDU
Thu Mar 6 06:30:22 CST 1997

```        I'm responding to Tom's request that I explain my
probabilistic approach.  This is rather serendipitous,
for I am close to releasing RASA 2.1, and I can take
full advantage of this forum to explain in some
detail the workings and my understanding of RASA theory
to date.  Most of the extensions are currently under peer
review, but most of this has been presented in verbal
form elsewhere.  Given the informal nature of this list,
I'll not cite literature when I should.

Signal:
RASA provides a measure of how much cladistic hierarchy is present
in a matrix of character state beyond that which is expected by
chance alone.  It is similar in it goal to g1 and PTP, but
quite different in its implementation and flexibility.

It does this by taking advantage of the observable consequence
that random data produces no differences between an observed
and null rate of increase in apparent cladistic similarity
(RAS) among pairs of taxa as a function of overall similarity, but
data with signal produces a statistically significant difference
between the slopes.

[note that some folk balk at the use of the term
cladistic similarity;  I don't really care what
one calls the metric; for me, it's a semantic issue.]

Cladistic similarity is defined for each taxon pair as the
number of times that pair shares a character state to the
exclusion of other taxa, all characters considered.
Semantics aside, this metric incorporates all of the
(A,B),X comparisons where A is taxon A, B is taxon B, and
X is any other taxon, for all characters.  As a measure of
unique similarity, the metric contains ALL of the information
in the matrix.  Invariant sites are trivial.

the phenetic used (on the x-axis) is the number of characters
that are putatively informative for a taxon pair; i.e., the
number of characters that contribute to the cladistic
metric for that pair.  This two metric will positively
covary EVEN with random data, so a test of this slope
against zero is trivial.

The test statistic (trasa) incorporates three parameters, each
observed directly from the matrix: the observed slope, the
null slope, and an error term (a function of scatter and slope
in the observed model).  The null slope can either be
determined by permutations to the matrix, or by an analytical
procedure. Each matrix has a characteristic null slope.  Details
on the process that determines the null slope (reciprocal
equiprobable redistribution) are as follows:

Each taxon pair contributes a particular amount of information
to each axis.  If no cladistic hierarchy is present, there is
nothing remarkable about any the three-taxon comparisons (ie.,
no synapomorphic information is represented).  To
determine the expected rate of increase in the cladistic metric as
a function of the phenetic, the total amount of information on
each axis is summed, and the "matrix rate" is the ratio of the sum
of the cladistic metric values to the sum of the phenetic values
(D. Colless pointed out that my eq. in the RASA I paper was
inelegant).  I am at present exploring the effects of a variety
of factor other than randomness and phylogeny on the null.

Simulated and empirical test of the test for signal have
been conducted.  trasa has predictive power for the accuracy
of methods of phylogenetic inference.  It tracks the decay
of signal as internodal nodes become long.  It, like
mp, is sensitive to long branches, to outgroup selection,
and other pathologies that can reduce the accuracy of
evolutionary trees.

This sensitivity has been turned to an advantage.  But first,
assumptions, falsifiability, and limitations

The assumptions of the test are that past processes of evolution
may or may not produce pattern in the data that
looks like signal, and that other processes only produce
signal-like pattern rarely (explicitly, ca. 5% of the time).
This makes the method falsifiable.  If other conditions can be
shown to produce signal > 5% of the time, the test statistic

On the other hand, the method assumes that processes of
evolution that produce distributions of character states
among taxa and cause methods of phylogenetic inference
to retrieve accurate trees will result in a difference
between the slopes.  Often there is a complex interplay
between the cladistic hierarchy in a matrix, caused
by the processes of the evolution, and localized
violations of the assumptions of phylogenetic
methods.  This turns out to not be a problem, and
because these influences are readily identifiable..

The method is falsifiable.  Specifically, some rather bold
predictions can be made.  For example, anything one does to the
matrix that increases tRASA will increase the accuracy of the
phylogenetic inference.  This includes taxon sampling,
and character sampling. tRASA therefore provides a ready
criterion for determining the implications of things like
removing apparent autapomorphies.

Testing Homology

If a preponderance of hypotheses of homology are in err, then
an mp tree will likely be wrong, and inferred synapomorphies
will be erroneously adduced.  If a preponderance of hypotheses
of homology are wrong, phylogenetic signal is weak, tRASA
will not be significant, and the tree, which would have wrongly
been used to erroneously falsify correct hypotheses of
homology, would be recognized as a poor test, to be distrusted.

In contrast, tRASA tracks the proportion of erroneous
hypotheses of homology well, and can be applied to the
task of trying to falsify individual hypotheses of
homology.

The impact of individual hypotheses of homology
can be explored by comparing signal when they are
included or excluded.  This particalar application of
RASA is not well explored, but it appears to be justified.
I included here because it is most relevent to the
disucssion.  From my experience with empirical data, tree-based
indicators of accuracy can be improved dramatically by finding
and removing apparently misleading characters.  Once an
estimate of phylogeny is produce that uses apparently
accurate hypotheses of homology, the evolution of the
misleading characters can be better understood a posteriori.
Naturally, this is similar to previous approaches because it
has the same goal, but there are some fundamental differences
here; the RASA algorithm is solved in polynomial time (therefore,
the entire tree space doesn't have to be explored).

Long branches

Taxa at the end of long branches have undergone a great
amount of anagenetic evolution (not necessarily an increased
rate of evolution), without cladogenesis.  As a result,
autapomorphies accumulate.  This quite effectively randomizes the
charactre states _with respect to phylogenetic information).

This can be a result either of true evolutionary history (i.e.,
living fossils), or as result of taxon sampling.

Taxa (and clades) at the ends of long branches tend to be
not all that similar to other taxa in matrix (in the phenetic
sense); but for their low similarity, they tend to have a
high value of pairwise cladistic similarity with other
taxa in the matrix.  This tends to reduce the observed slope.
The contribution of each individual taxon to the variance
on each axis is summarized is a type of residual plot
(a taxon variance plot), in which taxa on long branches

Although such patterns are caused by long branch attraction,
this application makes no assumptions of evolutionary process,
for if ANY factor causes the characteristic pattern, the
algorithms for trees will respond similarly, and whatever
topologies are found to be optimal will be something other than
an accurate estimation of phylogeny.  A direct analogy is the
test for normality for parametric statistics; it is entirely
irrelevant to the functioning, accuracy and utility of the
test that a multitude of factors may causes a sample to be
non-normal

Although the cause of the observed pattern may be multifarious,
the method does not assume details of evolutionary processes
because all inferences are based on observed character states, not
on inferred transformations.  RASA does not assume homology;
it test for it.  For example, if an alignment of nucleotide is
wrong owing to a computer copy error, that matrix will be
innappropriate for phylogenetic inquiry; this type of error
will be observable in the signal, and in other ways (see below).

In another turn, I have found that when long branches have
influences the distribution of character states among
taxa (via simulation and some emprical data set as well),
a bootstrap power analysis that uses tRASA as a criterion
to ask the question "do I have enough characters?" has a
predictable and intuitive effect.  When signal is strong,
and there are o long branches, and characters are resampled
are various leves of Nc (number of characters), signal
increases and asymptotes.  This is a more classical and
better justified use of the boostrap (power analysis).  When
long branches are present, signal _decreases+ as one adds
more characters, just as Felsenstein predicted; obviously,
the taxon variance plot is direct evidence of which
taxa maybe problematic.   The efficiency of the algorithm
pays off here, too.

Outgroup Selection
In the calculation of RAS, comparisons of (A,B),X for a given
character are ignored if X is a putative outgroup and if
the state of that character is the same for A, B and X.
Similarly, a comparison of (A,B),Y is ignored if Y is not an
outgroup, but if A and B have the same state as X, which is a
putative outgroup.

When X is a poor outgroup choice (e.g., random data), the
constraints on the comparisons of (A,B),Y will includes (byt chance)
homoplasy, plesiomorphy, and synapomorphy.  When X has a sufficient
plesiomorphy content, MOSTLY plesiomorphy will be constrained, and that
plesiomorphy in the ingroup will include true plesiomorphy, and some
reversals.  When plesiomorphy is constrained, tRASA increases (i.e., less
noise in going into RASij and more signal (i.e., synapomorphy) is
incorporated.  This procedure can be used to choose among possible
outgroup candidates; this is important because of they PAUP and other
programs use outgroups, a poor outgroup selection can bend trees around,
and cause polarity inferences to be way off.

It is my hope that TAXACOMERS don't misread this post as