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Cludistic~
(1992) 8:147-153
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James
1Department
of Entomology,
jVez> York,
Received for
in cladistics.
randomizations
M. Carpenter 1
American
New
Museum
York 10024,
of Natural
History,
1i.S.A.
publzcation 26 August 1991; accepted 28 October 1991
The paper by Faith and Cranston
phenomenon
CLADISTICS
(1991) is but the latest manifestation
ofa disturbing
In their paper, as well as in Archie ( 1989) and Faith ( I99 1) ~
of character
data are used to specify a decision
purpose here to argue that such applications
In Faith and Cranston
criterion.
It is my
are ill-conceived.
( 199 11 and Archie [ 1989), c h aracter states from a given data
matrix are reassigned to taxa under an equiprobable random model, the number and
frequency of states being maintained.
Cladistic analysis is then performed on the
contrived data set. The procedure is repeated a specified number of times (99 or 100,
respectively). The frequency of cladograms having a length at least as short as that tbr
the real data is treated
phylogenetically
as the critical
informative,
value for determining
that is, as the level ofsignificance
whether
the data arc
for a Type I error (in this
case, incorrect rejection of random congruence).
If the conclusion is no difference
between lengths for real and contrived data, the cladogram for the real data is regarded
as poorly supported.
Faith (199 1) extended the matrix permutation
approach
to specific
groups on the cladogram.
I will argue
statistics,
that these procedures
and add nothing
Probability
‘The weakness of the matrix
standard
particular
change
to no more than a misapplication
of
parsimony.
and Corroboration
permutation
approach
is precisely
the application
of
hypothesis-testing
techniques in a cladistic context. What justifies this
method of randomization chosen to specify probabilities? Why not randomly
entries
phylogenetic
departure
amount
to the use of cladistic
in
the
inference,
character
matrix
instead,
if one is really interested
from randomness
for example?
in doing significance
would seem more reasonable
For
purposes
of
tests, testing for
in the context
of alternative
theories, that is alternative phylogenies. Alternative phylogenies may well be viewed as
more likely to sprinkle state changes through the character matrix rather than leaving it
unchanged except for permutation. Matrix permutation amounts to a curious notion in
evolutionary
Huelsenbeck
terms, that the number and frequency ofcharacter states remain constant.
(1991) presents a different null model and significance test derived from
skewness in tree length distribution; this will not in general produce the same result as
matrix permutation.
However, Huelsenbeck
argues for the same interpretation
for
skewness, namely, as an indicator of “phylogenetic information content”. Still another
null model and significance test with the same interpretation could be derived from the
concept of “data decisiveness” (Goloboff, 1991a; that author explicitly does not, cf.
1991 b), and yet other possibilities can be imagined. Neither Faith and Cranston nor
IZrchie provide any discussion of why their significance tests should be regarded as
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Sorlcty
148
J. M. CARPENTER
correct,
or better
than
any
straightforward conclusions,
(see also Goloboff, 1991b).
other. These tests are presented as if they lead to
whereas in fact the conclusions rest upon arbitrary choices
Why should an arbitrary probability associated with a cladogram be treated as the
basis for a decision anyway? Why, to put it another way, is this probability equated with
degree ofcorroboration,
as explicitly attempted
misleading.
( 1968) ex pl ained, to state that a hypothesis
As Popper
by Faith and Cranston?
This equation is
is corroborated
means that it has been severely tested and has withstood the tests. He emphasized critical
tests, for he regarded corroboration
their number.
hypothesis
obtain.
as depending
The only possible corroboration
of randomness
is corroboration
That
degree of corroboration
resulting
from testing against
of the proposition
This result is plainly weak corroboration
Corroboration
on the severity of the tests rather than
and
in Popper’s
that randomness
a null
does not
sense.
Cladistics
is the support for cladistic hypotheses,
as for scientific
hypotheses in general, has been argued by many cladists (Wiley, 1975; Platnick and
Gaffney,
1977; Gaffney, 1979; Farris, 1983; and see also Hennig, 1966: 120-121).
Corroboration
is measured by the parsimony criterion. Has hypothetico-deductivism
been discarded
by the proponents
of randomization
It seems that because the hypothetico-deductive
in cladistics?
interpretation
If so, why?
of cladistics has been
controversial, some cladists might deem it better to dispense with the concept altogether.
However, criticisms that have been offered of this interpretation are less than cogent. For
example,
Kitts (1977) argued that only strictly universal claims are falsifiable,
and that
the claims of systematics are numerically universal and therefore in principle verifiable.
His argument simply misinterprets Popper (Platnick and Gaffney, 1978); even singular
statements cannot be verified, because every description employs universal names. In
Popper’s well-known example, the statement “Here is a glass ofwater” connotes theories
on the nature of “glass” and “water”. Hull (1983) made an error similar to that of Kitts
(Platnick,
1986).
Cartmill
( 1981) asserted that the use of characters
as falsifiers can
imply that all phylogenetic hypotheses are false, which conflates a logical relation with
empirical proof (Farris, 1983). This accusation of naive falsification is surprisingly
common, even to the point ofcaricature
(Felsenstein,
1984, 1988; cf. Farris, 1985), but it
is baseless, as has been repeatedly pointed out (Platnick and Gaffney, 1977; Platnick,
1986). More recently, Bryant (1989) and Sober (1988) attempted to revive positivism in
their critiques of parsimony. Bryant argued that hypotheses of synapomorphy
are
falsifiable at the level of character delimitation [!I, and that cladograms are inductive
propositions, simply summarizing the information contained in characters. He appears
to believe that a conclusion on non-homology
can be reached only on the basis of
dissimilarity,
but contradicts
himself in observing
that an incongruent
new
synapomorphy
may be “reinterpreted
as an instance of homoplasy” (p. 219). Sober
argued that the link between character distributions and phylogenetic hypotheses is not
deductive,
because:
(1) symplesiomorphy
can reflect genealogy,
and (2) even
homologies can appear dissimilar if analysed in detail, so “true” homoplasies can exist.
His demonstration
of the first point (p. 118) consists of showing only that an
autapomorphy
can accord with a given system of phylogenetic
relationships.
His
argument for the second (p. 130) consists of conflating within- and between-group
variation. As Nelson (1989) observed, Sober misapprehends
the relative nature of
FORUM:
apomorphy,
RANDOM
149
CLADISTICS
and confounds homology with its explanation.
Finally,
Scott-Ram
(1990)
argued that Popper wrongly equates simplicity with support, hence cladistic parsimony
does not measure corroboration.
He arrived at this particular misinterpretation,
among
many others, by confusing testability with the results of testing, which of course is
something neither Popper not cladists have ever done.
Bryant, Sober and Scott-Ram
all failed to realize that the dismissal of conflicting
characters
on a geneaology
as homoplasies is ad hoc because they are synapomorphiesfor
1983). The relation between this point and Popper’s
(Farris,
alternative genealogies
requirement that degree of corroboration
depends on the severity of the tests is what
leads to cladistic parsimony. The weight of evidence for a phylogenetic hypothesis
decreases
directly
parsimonious
as characters
hypothesis,
are
dismissed
which requires
as homoplastic,
the least homoplasy,
hence
accords
the
most
best with the
available evidence. Where multiple equally parsimonious
cladograms
exist, the
evidence is ambiguous, but plainly a consensus tree has lower empirical content than
any of the most parsimonious
cladograms
(Mickevich
and Farris,
1981; Miyamoto,
1985; Carpenter,
1988). In the case of weighted characters, the strength of evidence
provided by each character differs, but a weighted parsimony is then calculated.’
The
most parsimonious
most highly
arbitrary
hypothesis is thus the one that has stood up best to testing, and so is
corroborated.
probabilities
Use of unjustified
to phylogenetic
methods
of randomization
to assign
hypotheses would seem to add nothing to degree
of corroboration;
certainly, this cannot lead to preference for an alternative hypothesis.
The contention that such probabilities provide an “absolute criterion” for judging the
worth of phylogenetic hypotheses (Faith and Cranston, 1991:3) is illusory.
Statistics
The alternative
interpretation
and Empiricism
of phylogenetic
inference
as a problem
in ordinary
statistics is a more recent theme, of Felsenstein, for example. That interpretation
has
simply not hitherto much influenced the development
of cIadistics. For standard
statistical methods to apply, it is necessary to specify an underlying probability
distribution for the universe being sampled, and there is clearly no empirical way to do
this for phylogeny.
Most of the work applying such methods has resorted to modeling
evolutionary process, allowing the model to determine a probability distribution. For
the sake oftractability,
the premises ofsuch models are typically unrealistic, ifnot known
to be false. If such claims about
inference
to proceed
evolutionary
under this approach,
process are required
that is clearly
for phylogenetic
a poor alternative
to the
hypothetico-deductive
interpretation,
which does not require such claims. As Farris
(1983) showed, cladistic parsimony is agnostic with respect to details of evolutionary
process, simply reflecting the empirical support for phylogenetic
hypotheses. The
substantial progress during 200 years of systematic effort, in the absence of evolutionary
modeling, is interpretable only within a cladistic framework. As elaborated by Nelson
and
Platnick
( 1981: 139),
Hennig’s
concepts
allow
“a deeper
and
more
critical
understanding of past taxonomic efforts, particularly why some succedded better, or
were more convincing, than others”. A pattern of congruent characters is the measure of
success in taxonomy, and is maximized by cladistic parsimony.
’ This point is apparently not as obvious as it seems (cf. Wilkinson,
rather obvious aspects of cladistic parsimony).
1991, who misapprehends
some other
150
J. M. CARPENTER
A different
resampling
attempt
schemes,
to apply
which
statistical
methods
need not require
to phylogenetic
a detailed
model
inference
is
of the evolutionary
process. Resampling as such may have a place in cladistics (e.g. Schuh and Farris, 198 I),
but of interest here is the application of resampling in assigning confidence limits to
phylogenetic
hypotheses.
The matrix
permutation
Felsenstein’s
(1985) use of bootstrapping
concocted by resampling the characters,
number
of characters
procedure
being preserved.
approach
is closely related to this.
is the best known example. Data sets are
with replacement, from a real data set, the
Phylogenetic
analysis is undertaken,
and the
repeated a specified number of times. The frequency with which a given clade
appears in these replicates
This interpretation
is taken as a confidence
interval on the group’s monophyly.
founders on the fact that the characters
in the original matrix do not
constitute a random sample of all characters (Farris, in Werdelin, 1989); indeed, such
sampling is neither attempted nor possible in actual systematic practice (Mickevich,
1980;
Farris,
1983).Characters
are simply
not drawn
from independent
distributed populations.
Incorrect premises aside, a question may be asked about this procedure,
equally
well to the matrix
permutation
approach.
Namely,
identically
that applies
what is learned
by the
exercise? Felsenstein (1985: 790) h’imself observed that, in the case ofperfect[v congruent
data, a group would not appear in the 95:/, confidence interval unless it was supported
by no fewer than three synapomorphies.
* He concluded
from this that: “I suspect that
the levels of uncertainty found in practice will be so great as to give pause to all but the
firmest exponents of nonstatistical
hypothetico-deductive
approaches
to inferring
phylogenies”
( 1985: 79 1). What this observation
use ofthe bootstrap;
a better way ofputting
really calls into question is simply the
it is that a hypothesis can be regarded as not
significantly supported when there is 110other hypothesis indicated b_ythe data. “Uncertainty”
in this situation can scarcely mean that there was no phylogeny, and it is not possible for
alternative
hypothesis
to be better supported.
Felsenstein‘s
a non-parsimonious
conclusion
is nothing
more than a departure
Permutation
Regarding
permuted
cladistics,
from empiricism.
and Corroboration
that the character
data deviate
or not from some
particular random model seems at best to test the accuracy of the random model chosen.
There is no reason whatever to suppose that such data really arose at random, and ifthey
arose in the course ofphylogeny, every reason to suppose that a random model is entirely
inappropriate.
At the least, if nature is hierarchical,
characters
cannot be independent
from phylogeny. The rejoinder that the question is whether characters are random with
respect to a particular phylogenetic hypothesis merely raises the question as to just how
“random” is defined (see also Goloboff, 1991b). If it is meant that the characters are
uninformative about the truth of the hypothesis, that is a conclusion inferred from the
analysis, and randomization is then otiose. Ifit is meant that the characters conform to a
particular random model, the choice of that model needs to be defended. Any defense
will encounter a situation analogous to that with the bootstrap: a well-corroborated
from a matrix
hypothesis
may nevertheless
appear similar to a set generated
permutation.
This scarcely
?“Perfectly
congruent”
matrix,
groups disappear
means that the randomized
rrfers only to informative
under the bootstrap.
characters.
distribution
‘4s autapomorphies
is true (see also
are added
to a data
FORUM:
Farris,
1981: 81; Cracraft,
structure”.
charactrrs
RANDOM
1983: 461)-or
CLADISTICS
that the data do not in
have “cladistic
CddCt
For example, with perfectb; congruent data for three taxa, a minimum off&r
is required to produce a significant value for Faith and Cranston’s
“permutation
tail probabilit! “, but again, it is not possible for a non-parsimonious
alternative hypothesis to he better supported. As Farris ( 1991: 91) put it, “Congrurncr
is
not qilite all there is to phylogenetic
Farris ( !977) made some pertinent
assumption of character randomnrss
noted that ifthis assumption
were justified for all characters.
attempting phylogenetic inference.
suc~h random
effects-if
they occur
\-ariation show-n by the data.
parallelism
evidence”.
points in a different context. Arguing against the
made by the merhods of Le O_uesnc I 19741. he
there would be no point to
As he observed ,p. 801, “it is much more likely that
at allaccount
for only some fraction of the total
Earn
a character
showing
is unlikely- to be totally randomly- distributed
relationships.
and the assumptions
ofrandomncss
on? or more instances
of
with respect to phylogrnctic
are unlikely to apply with equal fi)rre
to all characters”.
He also pointed out that it was reasonable to interpret an example
data set “as haling only a small or non-existent random component. inasmuc,h as it
appears to display a system of perfectly congruent s>napomorphies”.
This is quite like
tl-1~points made above. Justification
of any particular random model is likely to provr
elusil-e.
Corroboration
Proponents
corroboration
inference:
and Choice
ofrandomization
have thrown away corroboration for nothing. Degree of
offers something too important to be simply discarded. In cladistic
parsimony
corresponds
to degree of corroboration
in phylogenetic
analysis
and measures evidential support. Choosing the best corroborated hypothesis is based on
confi>rmity to evidence. ‘1Yell-corroborated
hypotheses require the fewest (in hoc
dismissals of evidence and maximize explanatory power (Farris, 1983). Conformit)
evidence has a long history in science, for it is vital to scientific advance. Conformit,
evidence
is precisely
what matrix
dependent
approaches
substituted
for conformity
permutations
to the study
to evidence.
decisions,
do not offer. Just
of phylogeny,
unrralistic
to
to
as with model-
presuppositions
are
Lack of realism seems unlikely to improve the
accuracy
of-scientific
cladistics
is due in large part COavoiding presupposition.
and is unnecessary
to cladistics.
Indeed,
the success of
In conclusion, I would observe that the reconstruction ofthe unique events ofsingular
histories does not lend itselfreadily to inferenre based on modeling evolutionary process:
general models might not apply in specific casrs: while specific models cannot be general.
‘I’his applies all the more to random models. Interpretation
of the significance \:alues
provided by such approaches is at best suspect. Life is short and the labor of scirncr is
long. Cladists would be better off not expending their timr on randomized cladistics.
Acknowledgments
I thank K&e Bremer, Jon Coddington, Joel Cracraft. Tim Crowe, Dan Faith, Steve
Farris,
Pablo Goloboff,
Chris Humphries,
Arnold Kluge, Jim Liebherr.
Dave
.\laddison, Diary Mickevich,
Gary Nelson, Laurence Packer, Rod Page, Norman
PIatnick, Dave Wagner, John N’enzel, Quentin Wheeler and Ward Wheeler for
suggestions. This work was supported by NSF grants BSR-8817608
and BSR-9006102.
152
J. M. CARPENTER
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