Scaling of swim speed in sharks: a reply to Morrison (2016)

Morrison [1] raises concerns about the parametrization of our scaling model and its wider relevance to swim speeds among this group of marine predators. We welcome the opportunity to discuss these issues further and feel that this conversation highlights several interesting points for debate.

Our original approach includes a focus on frontal area that we believe is a critical factor determining water flow to the gills in ram-ventilating sharks and this typically scales to two-thirds of body mass. In support of this, a study on shark body form found that the scaling of frontal length measured in terms of ventral, lateral and dorsal spans all scaled isometrically with total body length [2], which in turn scales to the one-third of body mass. Notably, with these assumptions, our predictions are consistent with the empirical data we gathered across 26 species of shark. Morrison noted that gill surface area scales more steeply than two-thirds, and therefore, sharks need not increase speeds with increasing size to maintain respiratory balance. We believe that oxygenated water flow over the gills will be regulated by frontal area and swim speed as oxygen levels will be at their highest as they enter the animal, then becoming increasingly more depleted with increasing contact with the gills themselves. As such, we would argue that there is a complex relationship between gill area, water flow and oxygen exchange.

We would argue that the weak scaling of swim speed with mass predicted by our model is consistent with that observed among sharks and other fish ranging between 0.08 and 0.2 [3–5]. While we concede that alternative theoretical models such as Weihs [6] may produce similar scaling estimates, the fact that alternative models have similar predictions is not unusual across scientific disciplines. Indeed, it is interesting that the two approaches, Weihs based on fluid mechanics and ours based on oxygen uptake, have convergent predictions. In addition, our model differs from Weihs' [6] in that it makes a mechanistic link between swim speed and oxygen uptake and therefore could be adapted to explore respiratory adjustments, during different states of behaviour among fish, where oxygen uptake potentially matches the costs of movement, such as during high-speed hunting bouts or higher cruising speeds in low oxygen environments [7].

We acknowledge that we made an unfortunate error in our calculation of megalodon swim speed and thank Morrison for drawing our attention to this. A correction, including a revised prediction of 1.34 m s⁻¹, has now been published.

Competing interests

We declare we have no competing interests.

Funding

All authors were supported by core funding from the Zoological Society of London.