Philosophies for Character Ordering

```Most of us, indeed every theropod worker I've noted, treat characters as
ordered if they show any trend from one state to another.  So, for vertebral
or phalangeal number, we order the character ("sacral vertebrae - number -
five (0); six (1); seven (2); eight or more (3)").  This makes it easier for
a taxon with seven sacrals to evolve from an ancestor with six than it would
be for a taxon with eight sacrals to evolve from a taxon with six.  We
normally think this is logical in the sense the 8-sacraled taxon has to fuse
an extra vertebra compared to the 7-sacraled one.  Also, ordering makes it
so that all taxa with more than five sacrals are effectively grouped
together, as if "six or more sacrals" were it's own state.  The state "six
sacrals" won't group taxa in a clade separate from seven or eight sacraled
taxa merely because of their sacral number, instead they will be in a
poltomy with seven or eight sacraled taxa.  It's the same with
transformations in size.  Characters like "naris - size - small (0); medium
(1); large (2)".  Or position, like "naris - placement - tip of snout (0);
middle of snout (1); above orbits (2).
Characters that are unordered are those that show no obvious trends.  So
shape characters or nonlinear position characters are examples.  Such as
"orbit - shape - round (0); triangular (1); square (2)".  Any state can
change to any other with equal ease.
This is how most workers, from Holtz, to Sereno, to the Theropod Working
Group, code their states.

However, Wilson (2002) complicated things.  He agrees with linear position
being ordered, and shape being unordered.  But for serially ordered
elements, he recommends either an unordered (1999) or an unspecified (2002)
ordering strategy.  His rationale is-
Wilson, 1999- "Ordering these implies a developmental model in which
vertebrae and phalanges are added or lost incrementally.  Embryological data
from living organisms, however, do not support this transformational model.
The axial column and digits begin as condensations of a certain length that
are later divided into any number of segments (Burke et al., 1995).  Thus,
vertebrae or phalanges can change in number without requiring intermediate
stages.  A model of character evolution that allows one-step transformations
between character states (i.e., an unordered multistate character) best fits
available developmental information."
Wilson, 2002- "The first type of multistate character records variation in
the number of serially homologous elements, such as vertebrae, phalanges, or
teeth. Ordering this type of multistate character assumes incremental
increases and decreases in the number of segmental elements. That is, a
change from 12 to 17 cervical vertebrae requires passing through 13, 14, 15,
and 16- vertebrae stages, each costing a step. This multistate coding
assumption may be appropriate if vertebral and phalangeal elements are added
sequentially (i.e. if the 7th vertebra condenses prior to formation of the
8th). Assumption of unordered changes for this character type, in contrast,
means that transformations between any two states costs one step. This
coding
assumption seems appropriate if vertebral or phalangeal condensations can
change the number of resultant segmental units without requiring
intermediate stages. Vertebral segment identity may be controlled by a
single Hox gene. The cervicodorsal transition in many tetrapods, for
instance, appears to be defined by the expression boundary of the Hoxc-6
gene (Burke et al., 1995). Thus, development is not yet informative to the
coding strategy of serially homologous structures. As indicated in Table 4,
no particular coding is recommended for characters 37, 70, and 2 from Wilson
& Sereno (1998)."

I have a few problems with this.  First, leaving it unordered would make
intermediate states their own derived state.  So seven-sacraled
confuciusornithids and Protopteryx would be inclined to make a clade
separate from eight-sacraled ornithothoracines.  It doesn't make much sense
in my mind.  Even if vertebrae form from an undifferentated segment that is
later divided into any number of vertebrae, I can see this determining the
number of vertebrae, but not the vertebral identity.  I mean, when the first
sacral of ornithomimids' is clearly homologous to the last dorsal of
tyrannosaurids, surely the sacrum couldn't have developed by an amorphous
segment of "sacral condensation" that broke into six segments instead of
five.  It would make more sense as a way to explain the presence of new
vertebrae, such as in the neck of mamenchisaurs.  But if one can't tell
whether vertebrae are new or merely switched areas (dorsal to sacral, etc.),
what is one to do?  Another consequence of this is that grouping more than
one amount of vertebrae under one state would be inappropriate.  For
theropod tails, you couldn't have "more than 44 vertebrae (0); less than 45
vertebrae (1)" because it would be just as easy to evolve 50 vertebrae from
49 as it would be to do it from 20.  So you'd need a ton of states, which
would be impossible given PAUP's limit of 32 states for 32 bit machines.
Assigning uncertain polymorphisms to taxa would be untenable too, as NDE
only allows three states per polymorphism.

For changes in a structure's size, Wilson recommends a particular ordering
strategy called "easy loss".  He writes- "The second type of multistate
character records differences in the size of a structure, either in absolute
or relative terms. Partial ordering of this multistate type may be justified
on developmental evidence. A structure that increases in size during
development passes through intermediate stages or states. If this is
considered to be the means by which a structure becomes 'large' in a group's
evolutionary history, then ordering of size increases is justified. For size
reduction, however, ordering may not be justified. An evolutionary
transition from 'large' to 'small' may not require intervening stages. A
structure need not reach maximum size before it is reduced; its growth may
simply be arrested. Thus, size-related characters may be ordered on the way
'up' (gains accumulate), but left unordered on the way 'down' (losses can
occur in a single step). Maddison & Maddison (1992) call this an 'easy loss'
character, which can be coded in a step matrix (Table 5). Forey et al.
(1992: fig. 4.9) refer to this character type as one in which the Wagner
parsimony criterion is employed for accumulations and the Fitch parsimony
criterion for reversals."

This makes more sense, but I'm confused by an aspect of it.  Say the
character is "antorbital fenestra size".  Wilson would say, the pneumatic
diverticulum that occupies the fenestra could halt its growth during
development, so it should be treated as an easy loss character.  But
structures usually grow in concert with another structure shrinking.  When
the diverticulum enlarges, the surrounding bone shrinks.  So why not treat
the bone growth as easy loss instead of the diverticulum growth?  Instead,
the bone growth is effectively "easy gain", which no developmental
philosophy supports.

So, what do others think?

Mickey Mortimer

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