title: The scaling of diving time budgets: insights from an optimality approach.
abstract: Simple scaling arguments suggest that, among air-breathing divers, dive duration should scale approximately with mass to the one-third power. Recent phylogenetic analyses appear to confirm this. The same analyses showed that duration of time spent at the surface between dives has scaling very similar to that of dive duration, with the result that the ratio of dive duration to surface pause duration is approximately mass invariant. This finding runs counter to other arguments found in the diving literature that suggest that surface pause duration should scale more positively with mass, leading to a negative scaling of the dive-pause ratio. We use a published model of optimal time allocation in the dive cycle to show that optimal decisions can predict approximate mass invariance in the dive-pause ratio, especially if metabolism scales approximately with mass to the two-thirds power (as indicated by some recent analyses) and oxygen uptake is assumed to have evolved to supply the body tissues at the required rate. However, emergent scaling rules are sensitive to input parameters, especially to the relationship between the scaling of metabolism and oxygen uptake rate at the surface. Our results illustrate the utility of an optimality approach for developing predictions and identifying key areas for empirical research on the allometry of diving behavior.
authors.affiliation: Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom. philip.stephens@durham.ac.uk
authors.forename: Philip A
authors.initials: PA
authors.lastname: Stephens
authors.forename: Chris
authors.initials: C
authors.lastname: Carbone
authors.forename: Ian L
authors.initials: IL
authors.lastname: Boyd
authors.forename: John M
authors.initials: JM
authors.lastname: McNamara
authors.forename: Karin C
authors.initials: KC
authors.lastname: Harding
authors.forename: Alasdair I
authors.initials: AI
authors.lastname: Houston
mesh_terms: D000818:Animals; D001717:Birds / Q000502:physiology; D001835:Body Weight / Q000502:physiology; D004242:Diving / Q000502:physiology*; D008322:Mammals / Q000502:physiology; D008954:Models, Biological; D010101:Oxygen Consumption / Q000502:physiology*; D013997:Time Factors