Who is the postivist?

[Ted Schultz]

Richard Zander wrote:
>I think they are both wrong. Parsimony eliminates grossly unreasonable
>trees, maximum likelihood eliminates grossly improbable trees. The pool
>of trees 1 step (or 2 steps) longer than the shortest tree and the pool
>of "credible trees" (with posterior probability adding to 95%, are
>similar. No one ever assumes that, say, a radiocarbon date with sigma
>values (e.g.
>6970+or-760), converges on the truth with the central value
>approximating the truth. The truth is, probably, somewhere in the range
>(probability density) indicated. Likewise, statistical phylogeneticists
>select one tree, the tree of maximum likelihood, in my opinion, solely
>because cladists are seemingly able to select one tree, and you are both
>competing for grants.
>Ideally, statistical phylogeneticists can demonstrate as a probabilistic
>hypotheses only where all the trees in at least the 50% credible zone
>agree (and 95% if they actually want "results" as a theory, not just a
>hypotheses). And cladists...I don't see a way to select one tree as a
>reconstruction. Every elimination from the set of reasonable trees is an
>ad hoc assumption of no convergence.
>
>What
>is important is that Realists have lower standards for hypotheses than
>Antirealists. As long as you can demonstrate an increase in probability
>(lower falsifiability, whatever), you can select the best example as
>best explanation and therefore asseverate one tree as "approximately the
>truth." Even when the one tree has a low probability of being the truth.
>This is scientifically unconscionable.
>

I think many good points are being made on all sides in this thread and I
hesitate to get too involved.  Nonetheless, I will say that there are any
number of reasons why Zander's critique of phylogenetic methods above is
not fully justified.  In a post long past, I described one of them: All
possible topologies for a given set of taxa are not a priori equally
probable, i.e., in a Bayesian sense the prior probability is not evenly
distributed across all possible trees.  Depending on how skewed this
distribution is, the posterior probability of a given tree may be quite
high.

Two other reasons that blunt Zander's critique are:

1. An entire tree is not really a single hypothesis.  Instead, it is the
conjunction of multiple hypotheses of monophyletic groups.  Some of these
monophyletic groups may appear in many of the suboptimal trees surrounding
the optimal (most likely/most parsimonious) tree, i.e., they may be very
well supported and thus highly "probable."  Judging the probability of
subtrees rather than trees is certainly more fair to phylogenetic
methodology.

2. This relates to the Bayesian reason given above, but is phrased in
20th-century statistical terms: When trees or subtrees are framed as a
priori null hypotheses, and when they are subsequently corroborated because
they appear in the optimal tree or in the "confidence-set" of
optimal+suboptimal trees in some specified confidence interval, then we
have failed to reject these null groupings and, again, a probability is
conferred upon them that is greater than what is implied by Zander above.

In non-statistical terms, impugning phylogenetics because complex trees
consisting of many taxa are rarely entirely "true" or "false" ignores the
fact that phylogeneticists have discovered and continue to discover real,
highly corroborated monophyletic groups.

___________________________________
Ted Schultz, Research Entomologist
Department of Entomology, MRC 165
National Museum of Natural History
Smithsonian Institution
Washington, DC 20560
U.S.A.

schultz at onyx.si.edu
Phone (voice and fax): 202-357-1311