Ornithischia/Saurischia Ilium Mass Distribution Hypothesis

["Mike Milbocker" <mmilbocker@psdllc.com>]

Hypothetical: The mass distribution of Ornithischia Ilia appears to be
distributed more caudally with respect to the mass distribution of
Saurischian ilia.

This hypothesis is not equivalent to a comparison of the length of the
preacetabular process compared to the length of the postacetabular process,
which runs into problems with the Sauropoda.

A character based on the mass distribution hypothesis appears to eliminate
bird evolutionary convergence based on the position of the pubis with
respect to the ischium and ilium. Counter-examples are appreciated.

Formal Hypothesis: For any ilium of the Dinosauria, find the line L for
which the moment of inertia is a minimum; find the point H on the line L
which is the most cephalo for which a plane perpendicular to L and
containing H intersects a point on the ilium; find the point T on line L
which is the most caudal for which a plane perpendicular to L and containing
T intersects a point on the ilium. Now, find the point M equidistant from H
and T on L. A plane drawn through M and perpendicular to L divides the ilium
into 2 regions. If the mass of the cephalo region is greater than the mass
of the caudal region, the ilium is Saurischian, otherwise it is
Ornithischian.

Less Precise Restatement: If the Ilium looks forward heavy it's Saurischian,
otherwise its Ornithischian. This simple restatement runs into problems when
the ilium is substantially non-planar, the Formal Hypothesis does not.

A Practical But Imprecise Method: Take a plane view of a side of the ilium.
Draw the longest line segment between any two points on the periphery of the
ilium, i.e., find its axis. Find the center point on this line and draw a
perpendicular. The perpendicular divides the plane view of the ilium into 2
regions. If the area of the cephalo region is greater than the area of the
caudal region the ilium is Saurischian, otherwise, Ornithischian. [In most
cases this can be done by eye.]

Advantages: 1) Birds fall into the Saurischia unambiguously (at least for
the examples I have studied), 2) If used as a character Bird homoplasy is
removed, 3) Appears to work well for Heterodontosaurus, Lesothosaurus,
Herrerasaurus, Coelophysis, and Plateosaurus ( the last, when the ilium's 3D
structure is considered).

Disclaimer: My research resources are limited and I offer this hypothesis as
a topic for discussion only, and not as a hypothesis supported by the
preponderance of fossil evidence.

Regards, Mike Milbocker