problem, Motani (2002A,B) introduced a different model
that does not require energetic assumptions. He established
a correlation between a set of kinematic variables
and Reynolds number in axial swimmers (sensu Massare,
1988). Using this equation, it is possible to calculate the
optimal swimming speed of extant axial swimmers from
some body dimensions. This is possible because large axial
swimmers are under stringent physical constraints that
probably allow only a limited range of body shapes to be
efficient at a given body size. Calculations for ten specimens
of Stenopterygius, with preserved approximate body
outlines, suggest that their optimal cruising speeds were
slightly lower than in cetaceans of the same body length,
but were comparable to those of similar-sized tunas.
One interesting ramification from the kinematic-based
model of M otani (2002A) is that it can be combined with
the energetics-based model (Motani, 2002B) to infer likely
metabolic rates. In Stenopterygius, the kinematics-based
model gave a speed-size distribution that is almost identical
to the one given by the energetic-based model when
assuming that the genus had similar basal metabolic rates
as in extant tunas. It is therefore likely that the metabolic
level of Stenopterygius was similar to that of tunas (i.e.,
raised ectothermic level, which is slightly lower than truly
endothermic level but much higher than the average ectothermic
level). Extant thunniform swimmers are known to
have metabolic rates at least as high as raised ectothermic
level, and, therefore, this result for Stenopterygius is unsurprising.
Raised metabolic rates had already been suggested
for Stenopterygius in the past, largely based on the inferred
presence of a thick fat layer for insulation (Wiman,
1946).
Vision and Bio-optics
It has been known that ichthyosaurs had large orbits filled
with scleral rings, and hence large eyeballs (see above).
However, it was not until recently that the dimensions of
their eyes were compar parvipelvian ichthyosaurs had
unusually large eyeballs for their body size. Given the
allometric trend (i.e., larger animals tend to have relatively
small eyes for the body), it can be said that Ophthalmosau-
rus had the largest allometric constant for relative eye size
(or, in allometric terms, the largest eyeballs). Furthermore,
Temnodontosaurus platyodon had eyeballs exceeding 250 mm,
the largest absolute size that have ever been recorded for
any animal. After the publication of the 1999 paper, RM
had the opportunity to examine a specimen at the National
Museum of Wales, Cardiff, whose eyeball was at least
260 mm across - the largest measurement RM has obtained
to date.
In comparative ophthalmology, absolute eyeball size is
considered to reflect approximate visual capacity, because
photoreceptive cells cannot be smaller than certain sizes;
therefore, larger eyeballs can contain more photoreceptive
cells on average, and a high number of cells, in turn, can be
used to increase either the visual acuity or sensitivity
(Walls, 1942; Prince, 1956; Hughes, 1977; A u & Klyne,
1985). Because of the large size of eyeballs, enhanced visual
capacity has long been suspected for ichthyosaurs (see
Introduction). This inference corresponds to the intuitive
functional morphology (Level 1 inference). The allometric
comparison made by Motani et al. (1999) represents a
basic quantitative functional morphology of eyeballs (Level
2 inference), which suggests that ichthyosaurs indeed
had enhanced vision compared to the other vertebrates of
similar body size.
Motani et al. (1999) also developed a method to ^estimate
the minimum f-number of eyes in ichthyosaurs.
F-number is a basic variable in optics that reflects the
relative brightness of the optical system. Using the estimated
f-numbers, Motani et al. (1999) inferred that Ophthalmo-
saurus, with its very low f-numbers comparable to those of
extant nocturnal vertebrates, was probably capable of seeing
in very dim light. This inference, rooted in optical
principle, can be considered a Level 3 inference.
Body Mass ~
Body mass can never be calculated exactly for extinct animals.
Nevertheless, it is a fundamental variable in biology,
and forms the basis of many paleobiological inferences.
Therefore, it is unsurprising that efforts have been made to
improve the accuracy of body mass estimations.
There are two different approaches to estimate body
mass: one is to use osteological correlates, and the other is
to use reconstructed body shapes. Osteological correlates
have only been used for terrestrial amniotes, whose limb
bone dimensions, especially propodial circumferences, are
highly correlated with body mass (e.g., Anderson, 1985;
Alexander, 1989). It would be interesting to determine if a
similar correlate exists for marine amniotes. Body shape
reconstructions have been used for both terrestrial and
marine vertebrates. The shape may be reconstructed mathematically
in a virtual space (e.g., computer program), or
actually in the form of artistic models (e.g., clay model). In
the former case, the volumes of the mathematical models
are calculated mathematically (Hurlburt, 1999; Henderson,
1999; Seebacher, 2001; Motani, 2001). In the latter
case, the volume of the model can be measured directly
(Colbert, 1962; A lexander, 1985,1989), and then converted
to mass by assuming a density (usually 1 g/cm3 for
terrestrial vertebrates, or 1.024 g/cm3 for marine vertebrates).
Some mathematical models involve unnecessary
graphical and mathematical transformations (e.g., Seebacher,
2001) and are not very plausible. Also, many of the
mathematical models assume elliptical body cross-sections
(Henderson, 1999; H urlbert, 1999), but this has been
challenged by the observed cross-sectional shapes (Motani,
2001). Motani (2001) instead recommended using a set
of superellipses to bracket the actual cross-sectional area.
For marine reptiles, whose body axis is almost straight,
estimates from the PaleoMass computer program (Motani,
2001) are probably the most reliable at present, although
there is room for improvements. Using the specimens of
Stenopterygius with preserved approximate body outlines,
Motani (2001) found that the body mass of the genus was
slightly lower than those of average delphinids with similar
body lengths (but was well within the range known for
cetaceans). For example, a typical small individual (body
length about 1 m) probably weighed about 11 kg, while a
large adult (body length about 2.5 m) was about 165 kg.
Note that a 2.5 fold difference in length implies 2.53=15.6
fold difference in body mass, when using a simple cubic
relationship, so the seemingly large difference between the
two is actually reasonable. Motani et al. (1999) estimated
a 4-m-long Ophthalmosaurus to be about 950 kg, using a less
sophisticated method than Motani (2001).