Nested Hierarchies and more

From: Pim van Meurs <>
Date: Sat Aug 06 2005 - 02:04:03 EDT

Some additional information to help resolve some of the confusion. When
I mention that manufactured processes do not recover a nested hierarchy,
I am not arguing that such hierarchy cannot be created but rather that
such a hierarchy is not objective and the the hierarchy is not unique
and consistent when applied to other measures.

CH sent me an offlist response and I responded off list but I will
include my response which are stripped from references to CH's offlist

Hope this clarifies the confusion

 From Douglas Theobalt

Although it is trivial to classify anything subjectively in a
hierarchical manner, only certain things can be classified /objectively/
in a consistent, unique nested hierarchy. The difference drawn here
between "subjective" and "objective" is crucial and requires some
elaboration, and it is best illustrated by example. Different models of
cars certainly could be classified hierarchically—perhaps one could
classify cars first by color, then within each color by number of
wheels, then within each wheel number by manufacturer, etc. However,
another individual may classify the same cars first by manufacturer,
then by size, then by year, then by color, etc. The particular
classification scheme chosen for the cars is subjective. In contrast,
human languages, which have common ancestors and are derived by descent
with modification, generally can be classified in objective nested
hierarchies (Pei 1949
<>; Ringe
1999 <>).
Nobody would reasonably argue that Spanish should be categorized with
German instead of with Portugese.

The difference between classifying cars and classifying languages lies
in the fact that, with cars, certain characters (for example, color or
manufacturer) must be considered more important than other characters in
order for the classification to work. Which types of car characters are
more important depends upon the personal preference of the individual
who is performing the classification. In other words, certain types of
characters must be weighted subjectively in order to classify cars in
nested hierarchies; cars do not fall into natural, unique, objective
nested hierarchies.

Because of these facts, a cladistic analysis of cars will not produce a
unique, consistent, well-supported tree that displays nested
hierarchies. A cladistic analysis of cars (or, alternatively, a
cladistic analysis of imaginary organisms with randomly assigned
characters) will of course result in a phylogeny, but there will be a
very large number of other phylogenies, many of them with very different
topologies, that are as well-supported by the same data. In contrast, a
cladistic analysis of organisms or languages will generally result in a
well-supported nested hierarchy, without arbitrarily weighting certain
characters (Ringe 1999
Cladistic analysis of a true genealogical process produces one or
relatively few phylogenetic trees that are much more well-supported by
the data than the other possible trees.

The degree to which a given phylogeny displays a unique, well-supported,
objective nested hierarchy can be rigorously quantified. Several
different statistical tests have been developed for determining whether
a phylogeny has a subjective or objective nested hierarchy, or whether a
given nested hierarchy could have been generated by a chance process
instead of a genealogical process (Swofford 1996
p. 504). These tests measure the degree of "cladistic hierarchical
structure" (also known as the "phylogenetic signal") in a phylogeny, and
phylogenies based upon true genealogical processes give high values of
hierarchical structure, whereas subjective phylogenies that have only
apparent hierarchical structure (like a phylogeny of cars, for example)
give low values (Archie 1989
Faith and Cranston 1991
Farris 1989
Felsenstein 1985
Hillis 1991
Hillis and Huelsenbeck 1992
Huelsenbeck /et al/. 2001
Klassen /et al/. 1991


So lets imagine a constructed goods example and create a nested hierarchy.
Do we recover a consistent hierarchy or not when applying to other

Now combine two different sources aka twin nested hierarchy
One let's say based on morphology, the other one let's assume is based
on genetic data
and they match...

In both cases biology finds extremely consistent results not found in
constructed objects, other than perhaps java classes but they use a
concept of inheritance :-)

Douglas again

[quote]The stunning degree of match between even the most incongruent
phylogenetic trees found in the biological literature is widely
unappreciated, mainly because most people (including many biologists)
are unaware of the mathematics involved (Bryant /et al/. 2002
Penny /et al/. 1982
Penny and Hendy 1986
Penny and Hendy have performed a series of detailed statistical analyses
of the significance of incongruent phylogenetic trees, and here is their

"Biologists seem to seek the 'The One Tree' and appear not to be
satisfied by a range of options. However, there is no logical difficulty
in having a range of trees. There are 34,459,425 possible [unrooted]
trees for 11 taxa (Penny /et al/. 1982
and to reduce this to the order of 10-50 trees is analogous to an
accuracy of measurement of approximately one part in 10^6 ." (Penny and
Hendy 1986
p. 414

In other words, repeated independent methods find the same phylogeny,
something which is analogous to an accuracy of measurement better than
we have for G, the gravitational constant.

Hunter stated in

Penny^[ ^8 <>] obtained his
trees by culling those that were most parsimonious—that is, he selected
the trees that showed the least amount of evolutionary change to
represent the history of life. The first problem is that Penny’s method
works perfectly fine on things we know did not come about via Darwinian
evolution. For example, Penny’s method would also claim that
automobiles evolved from one another. Consider a group of vehicles,
beginning with a small economy car and increasing in size to larger cars
and to minivans and large-sized vans. One could quantify several
aspects of the vehicle designs, such as tire size, steering mechanism,
engine size, number of seats and so forth. Presupposing the
evolutionary paradigm and searching for parsimonious relationships, we
would find that most of the design measures suggest the same
relationship. The smaller vehicles have smaller tires, manual steering,
smaller engines, and fewer seats. The larger vehicles have larger
tires, power steering, larger engines, and more seats. In other words,
the groupings suggested by the different design measures (tire size,
steering mechanism, engine size, etc.) tend to be similar. But of
course, the family of automobiles did not evolve from one another via
random mutations. The groupings of the design measures are a natural
result of engineering and have nothing to do with Darwinian evolution.
How then can Penny’s results provide “strong support” for evolution?
(Hunter, 40.)

There are some problems here as they remain unsupported such as "Penny’s
method works perfectly fine on things we know did not come about via
Darwinian evolution"

As Theobald observes

[quote]As pointed out above, Hunter is incorrect. Hunter makes the bold
claim that "Penny's method would also claim that automobiles evolved
from one another" in the absence of any evidence to support that claim.
Automobiles might give a most parsimonious tree (though this is not
assured), but even if they do, the resulting tree will be bunk. It will
not satisfy the mathematical requirements for nested hierarchies, and
the reasons are explained in Prediction 2
<>. If Camp
and Hunter think otherwise, they should determine a phylogenetic tree of
cars, using standard phylogenetic programs, that has statistically
significant high values of cladistic hierarchical structure. To really
drive the point home, they could derive two trees independently, and
then show that they match with statistical significance. If they are
correct, they could easily prove their point—but in reality they will be
unable to do so.[/quote]
Received on Sat Aug 6 02:06:23 2005

This archive was generated by hypermail 2.1.8 : Sat Aug 06 2005 - 02:06:23 EDT