I appreciate Patrick Martin's comments, but would like to point out where
his defense of "maximum likelihood" is problematic. Since I've not yet seen
his paper, I can't comment on how he dealt with sequence and morphological
data for inferring relationships.
Patrick makes a distinction between "maximum parsimony" and "maximum
likelihood," where the latter method "enables [one] to obtain the tree
which statistically optimizes the probability of observing the data given a
particular evolution model." First, no such distinction can be made between
"maximum parsimony" and "maximum likelihood." Maximum parsimony is not a
method, but a criterion of maximizing some parameter according to some
theory in the act of inference. What has been referred to as the "maximum
parsimony" method uses as its theory that of common ancestry. "Maximum
likelihood" simply uses a different theory. As such, BOTH methods employ
parsimony. Second, the term "maximum likelihood" has been misapplied in
making the schism between the two "methods." To reach a maximum likelihood
estimate is to maximize the probability of the observed data given some
hypothesis. Interestingly enough, any non-deductive inference that applies
the parsimony criterion to the fullest extent possible will lead to a
conclusion that is of maximum likelihood. Hence, ANY minimum-length tree
derived by "maximum parsimony" IS a maximum likelihood estimate. Thus, the
issue is not one of whether to use "maximum parsimony" or "maximum
likelihood;" the question is whether the causal theory employed is
inferentially acceptable. As I tried to show in my last message,
rate-dependent models are not amenable to the goal of cladistics.
It is also worthwhile noting that "statistical" probability is not
applicable to historical events. To observe a set of shared similarities,
as effects observed in the present that are due to causal events in the
past, one is attempting to infer what causal events best explain those
similarities. But, shared similarities are either due to common ancestry or
they are not. The "statistical" probabilities are either 0 or 1. Either
some causal event per some theory was the case or some other event
occurred. The only form of probability that applies here is logical
probability.
I pointed out in my last message the inherent difficulties with invoking a
rate-dependent model for the inference of cladograms. The standard
arguments for "maximum likelihood" outlined by Patrick do not address those
difficulties. Theories are never guaranteed to be fail safe, so the idea
that "maximum parsimony" can be "misleading" does not hold. One of the
greatest defects of the "maximum likelihood" argument has been the complete
misuse of the notion of "truth," as in assuming a "true" tree for showing
how "maximum parsimony" can "mislead." But more importantly, any
rate-dependent model is inconsistent with the relationship between
perceptions and causal explanations for those perceptions. The best that
can be said for "maximum likelihood" is that it provides the user an easy
means of obtaining the tree topology they think is "correct" based on ad
hoc conceptions of what the "truth" really is.
Kirk
"A man must be downright crazy to deny that science has made many true
discoveries. But every single item of scientific theory which stands
established today has been due to Abduction."
C.S. Peirce
------------------------------------------
Kirk Fitzhugh, Ph.D.
Associate Curator of Polychaetes
Research & Collections Branch
Los Angeles County Museum of Natural History
900 Exposition Blvd
Los Angeles CA 90007
Phone: 213-763-3233
FAX: 213-746-2999
e-mail: fitzhugh at bcf.usc.edu
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