We are not the first to suggest that a long neck might be beneficial for low browsing [1
]. However, here we interpret this in an energetics context appropriate for foraging, and use a very simple calculation to evaluate the potential energetic consequences of neck elongation. We predict that initial small elongations would have offered significant energetic benefits, thus aiding the initial evolution of neck extension. Greater and greater extension offers smaller and smaller additional benefits. Thus, we would not expect run-away selection for ever-longer necks, but rather a length would be reached where other factors (perhaps mechanical aspects of the support and control of a long structure—or breathing considerations) prevent evolution of further neck extension.
Our calculations involve many simplifying assumptions. However, we expect the qualitative conclusions drawn from our calculations to hold quite broadly. For example, although sauropods varied considerably in mass, the mass exponents of basal metabolism and cost of transport assumed in our calculations are very similar, so we would expect our conclusions to hold across all sizes of sauropods. The Brachiosaurus
was unusual in that its front legs were substantially bigger than its hind legs, whereas normally the reverse was true [1
]. This means that the height of the neck attachment is unusually high on Brachiosaurus
, increasing the value of H
. For most other sauropods, we would expect H
to be proportionately smaller; and this will have the effect of accentuating our predicted benefit from neck elongation. We were similarly conservative in assuming that the low-growing forage was at ground level. However, forage up to 3 m off the ground might still reasonably be considered as providing low-growing forage to a Brachiosaurus
. Such forage raised a little off the ground would decrease the effective value of H
and thus accentuate the benefits of a longer neck. Our model assumed considerable lateral neck flexibility, with the ability to twist the neck so as to orient the mouth at right angles to the main body axis. It seems that sauropods may have varied in their neck flexibilities, and in at least some, the neutral pose would have allowed low foraging without muscular exertion [5
]; however, our broad conclusions hold for more restricted movements provided that there is some ability to flex the neck laterally. The addition of extra cervical vertebrae associated with long necks is suggestive of considerable flexibility [7
]. We assume that the neck is held straight except for pivoting at the neck joint to simplify our calculations, but again our general conclusions are robust to relaxation of this to allow for greater neck flexibility. Finally, average speed of movement v
will decline with increasing neck length L
because of the finite time taken to sweep the head through its foraging arc. However, since v
cancels out of our final equation, this biological complication should not affect our model predictions.
If we argue that long necks are selected (at least in part) to reduce transport costs during foraging, then we must address why this selection pressure was important for sauropods more than for other herbivorous vertebrates. The dominant feature of sauropods was their massive size. This size is intrinsically linked to their small, light head and long neck [2
]. From the elementary theory of levers [8
], the cost of supporting the head increases with neck length, and thus a small, light head is a necessary consequence of a long neck. This light head means that sauropods lacked the massive dental batteries of elephants for example, and thus could do little processing of forage prior to ingestion. This in turn requires a massive body in order to achieve long digestion times and good digestive efficiency. However, the key to our argument is that the cost of moving the head and neck of such an animal would have been much less than that of moving the whole animal; thus, if this neck movement (because of the long neck) allowed a greater envelope of feeding from a stationary position, then considerable energetic saving could be had. Our model implicitly assumes that forage is available as a uniform carpet through which the animal moves. However, our argument also holds if the animal experiences a mosaic of different quality forages within which it must select the choicest patches, provided the variation in forage quality occurs on scales smaller than the length of the animal. Here, the saving comes because the animal can save costs of moving its whole body by small increments as it moves from one small micropatch to the next, by instead swinging its neck.
It is reasonable to ask why sauropod-style long necks have not evolved in the large mammalian herbivores that arose after the K-T extinction of the dinosaurs. First, it should be noted that none of these mammals have ever reached the huge size of the largest dinosaurs: perhaps because a mammalian high metabolism combined with a mammalian respiratory system (that is less efficient than an avian one—which sauropods might have shared [9
]) would have made overheating difficult to avoid for such giants [10
]. However, again analogy with domestic vacuum cleaners may be instructive. Cylinder vacuum cleaners were largely replaced by upright ones, only because improvements in materials and technology allowed reduction in size and weight: allowing the user to easily manoeuvre the whole machine. One of the defining features of the mammals is their more complex dentition than previous groups; it may have been the preprocessing of forage by the dental batteries characteristic of large herbivorous mammals that allowed more efficient processing of forage and thus removed the need for exceptionally large body size.
We believe that we have made a strong case here for low browsing causing a substantial positive selection pressure for sauropods to evolve long necks. However, we do not see this as an argument against the potential benefits that a long-necked individual could obtain from high browsing. It is entirely plausible that a given sauropod experienced both these selection pressures, and that these two pressures would then have interacted. It seems very probable that there is no one answer to the question of why sauropods had long necks. Different species would probably have experienced these two different selection pressures to varying degrees (along with other functions, such as potentially reaching otherwise inaccessible aquatic plants). For some species, high browsing may have been very important; however, an important inference from our work is that long necks might have been selected even in groups that devoted themselves entirely to low browsing.