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A question of ceratopsian horns

One wonders...now that ceratopsian phylogenies are
being stabilized, and sexual dimorphism being
recognized, one can pose a few questions. I have long
believed that the larger individuals are female, and
that horns/frills may not have been used solely for
predator defence strategies.
Unless, I am mistaken, the cores of their horns were
bony and highly vascularized, protected by keratin
shell. In warm environments, thus, large horns would
have radiated excess body heat, and in colder
environments inner thermoregulation would have been
operable. Based upon studies of bovid skull
thermoregulation, one can estimate that a ceratopsian
could have lost 20-30% of their resting metabolic
rates during colder periods.
It cannot be denied, of course, that sexual displays
(cf. the early work of V. Geist and J.T. Hogg on
mammalian horned taxa) played a likely role. However,
the thermoregulatory role of horns among ceratopsians
may have been analogous, a temperature higher than
cooler ambient environments being necessary to prevent
brain damage and horn tissue necrosis,  as animal fed
on plants with lower nutrient value than during warmer
months. Heat loss, hence, may account for the
variation in size and morphology of horns observable
on ceratopsian skulls. Horns with large surface areas
(I have seen stunningly large torosaurs)would be
effective heat unloaders. 
Moreover: in taxa living in cooler regions, it could
be their horns were smaller than others to reduce
energy costs. Among ceratopsians, heat flow in horns
had three routes (using bovids as templates): arterial
blood temperature determining thermal gradients of
heat unloading into the atmosphere; inner horn core
size determining size of capillary areas; keratin
thickness determining resistance to this flow of heat.
A smaller ceratopsian population in a cooler region
would have smaller body size, smaller frills and
horns, reducing heat loss. Animals with larger horns
and frills would have higher levels of "fitness"
costs, and among living mammalian bovids, larger horns
may result in costs approaching 30% of basal metabolic
The inner bone core of a horn was for support the
massive keratin protective sheath against shock
(head-butting, e.g., but also temperature shifts), and
smaller taxa would have smaller cores and sheaths. In
other words, it could well be that adaptations to
temperature zones among ceratopsians may have played a
greater role than "sexual selection". 
Larger taxa, as mentioned above, would have horns and
frills more for display vs. thermoregulation, head
unload by high arterial blood flow and vasodilation.
Smaller taxa in cooler regions would be adapted for
heat conservation: smaller horns = thicker sheaths. I
am willing to wager, so to speak, that
cross-sectioning of ceratopsian horns from various
regions would reveal that warm climate taxa would have
keratin sheaths and vasulcar beds extending almost the
entire length of the horns, amounting to ca. 98% of
probable heat flux. What is needed is a careful
analysis of all known ceratopsian skulls in museums to
measure core:sheath ratios, but I believe my thought
experiment might be substantiated. Some taxa might not
have been able to completely lower surface
temperatures of regions above the capillary beds,
resulting in higher heat loss.
It could very well be that distributions of
ceratopsians were analogous to those observable among
extant horned mammalians: a scimitar oryx has greater
heat loss from its horns due to forced convection than
for bighorn sheep. The former taxa have more
vertically oriented horns, above the low-velocity air
boundaries covering vegetation into areas where wind
is faster. During running, tropical horned taxa unload
more heat, living in regions with higher solar angles.
One asks if ceratopsians in more temperate
environments may have had ecomorphologies similar to
mammalian horned taxa: frills flatter on neck and
back, horns lowered and more curled, reducing
windspeed, increasing keratin thickness and inner horn
core temperature, convective loss reduced, the brain
better protected. In turn, this would be connected, as
mentioned above, to the fact that, during colder
months, food nutrients would be reduced, and the
energy costs of having enormous horns and frills may
have been to costly for survival.

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