# tips vs nodes

Edna Huelsenbeck huelsen at brahms.biology.rochester.edu
Thu Jun 8 18:34:54 EST 2000

```I am not certain that a relative rates test is what you want
to do, as that tests the molecular clock assumption. It seems
to me that you want to test the null hypothesis that:

H0:

D
1
+-C
5
+--B
6
A

where the branches 1, 5, and 6 are free parameters. The alternative
hypothesis has a more tree-like structure with three additional
parameters (the lengths of branches 2, 3, and 4; these branch lengths
are fixed to be 0.0 under H0):

H1:

D   C   B   A
1   2   !   !
+-+-+   3   !
5     !   4
+--+--+   !
6      !
+------+

I am assuming that the topology of the tree is fixed.

Calculate the maximum likelihood under each hypothesis and denote
the likelihoods L0 and L1 for the null and alternative hypotheses,
respectively. The null hypothesis can be tested using a likelihood
ratio test. The test statistic is -2 (lnL0 - lnL1). The null hypothesis
is a special case of the alternative, and it is tempting to think that
-2 (lnL0 - lnL1) follows a chi-square distribution with three degrees
of freedom. I suspect that the chi-square approximation would be
quite good, although technically the null hypothesis is at the
edge of the parameter space. If you are concerned about the
quality of the chi-square approximation, you can simulate the
null distribution of the test statistic (i.e., using parametric
bootstrapping).

John

In article <8hoj1c\$j7m\$1 at mercury.hgmp.mrc.ac.uk>, Guy Hoelzer
<hoelzer at unr.edu> wrote:

:  In article <8hmopn\$l61\$1 at mercury.hgmp.mrc.ac.uk>, Dmitri Sherbakov
:  <sherb at srv01.lin.irk.ru> wrote:
:
:  > I came across a dataset of 18S rRNA sequences of algae, where phylogenetic
:  > analysis suggests the following:
:  >
:  > A->B->C->D            (1)
:  >
:  >
:  > A   B   C   D         (2)
:  > !   !   !   !
:  > +-+-+   !   !
:  >   !     !   !
:  >   +--+--+   !
:  >      !      !
:  >      +------+
:  >
:  > due to zero or almost zero lengths of some branches.
:  > Since the case (1) may be describe realistic evolutionary events, the
:  > questions are:
:  >
:  > Is it possible to built a test distinguishing between (1) and (2)?
:
:  The only difference between cases (1) and (2) is branch lengths, not
:  topology; so the test would be one comparing branch lengths.  Relative
:  rate tests should do the trick.
:
:  > Did anybody meet and not discard stuation like that?
:
:  The kind of topology you describe is typical of many viruses in nature
:  (see the papers by Stuart Nichol and Walter Fitch).  It is usually
:  interpretted as evidence of selection dominated evolution; evolution stops
:  when the organism becomes optimally adapted to a particular environment
:  and bursts ahead when some individuals successfully colonize a new
:  environment.
:
:  --
:  Guy Hoelzer
:  Department of Biology
:  Reno, NV  89557

---|)---------------------------------------------------------
---|---- Edna Huelsenbeck ------------------------------------
--/|---- huelsen at brahms.biology.rochester.edu ----------------
-| |')-- http://brahms.biology.rochester.edu/edna/edna.html --
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'

```