It has been predicted that geometrically similar animals would swim at the same speed with stroke frequency scaling with mass 21/3 . In the present study, morphological and behavioural data obtained from free-ranging penguins (seven species) were compared. Morphological measurements support the geometrical similarity. However, cruising speeds of 1.8-2.3 m s 21 were significantly related to mass 0.08 and stroke frequencies were proportional to mass 20.29 . These scaling relationships do not agree with the previous predictions for geometrically similar animals. We propose a theoretical model, considering metabolic cost, work against mechanical forces (drag and buoyancy), pitch angle and dive depth. This new model predicts that: (i) the optimal swim speed, which minimizes the energy cost of transport, is proportional to (basal metabolic rate/drag) 1/3 independent of buoyancy, pitch angle and dive depth; (ii) the optimal speed is related to mass 0.05 ; and (iii) stroke frequency is proportional to mass 20.28 . The observed scaling relationships of penguins support these predictions, which suggest that breath-hold divers swam optimally to minimize the cost of transport, including mechanical and metabolic energy during dive.

SUMMARYEmperor penguins (Aptenodytes forsteri), both at sea and at an experimental dive hole, often have minimal surface periods even after performance of dives far beyond their measured 5.6min aerobic dive limit (ADL: dive duration associated with the onset of post-dive blood lactate accumulation). Accelerometer-based data loggers were attached to emperor penguins diving in these two different situations to further evaluate the capacity of these birds to perform such dives without any apparent prolonged recovery periods. Minimum surface intervals for dives as long as 10min were less than 1min at both sites. Stroke rates for dives at sea were significantly greater than those for dives at the isolated dive hole. Calculated diving air volumes at sea were variable, increased with maximum depth of dive to a depth of 250m, and decreased for deeper dives. It is hypothesized that lower air volumes for the deepest dives are the result of exhalation of air underwater. Mean maximal air volumes for deep dives at sea were approximately 83% greater than those during shallow (<50m) dives. We conclude that (a) dives beyond the 5.6min ADL do not always require prolongation of surface intervals in emperor penguins, (b) stroke rate at sea is greater than at the isolated dive hole and, therefore, a reduction in muscle stroke rate does not extend the duration of aerobic metabolism during dives at sea, and (c) a larger diving air volume facilitates performance of deep dives by increasing the total body O 2 store to 68ml O 2 kg -1 . Although increased O 2 storage and cardiovascular adjustments presumably optimize aerobic metabolism during dives, enhanced anaerobic capacity and hypoxemic tolerance are also essential for longer dives. This was exemplified by a 27.6min dive, after which the bird required 6min before it stood up from a prone position, another 20min before it began to walk, and 8.4h before it dived again.

The dead-reckoning technique is a useful method for obtaining 3-D movement data of aquatic animals. However, such positional data include an accumulative error. Understanding the source of the error is important for proper data interpretation. In order to determine whether ocean currents affect dive paths calculated by dead-reckoning, as has previously been hypothesized, we examined the directions of the estimated positions relative to the known real points (error direction) and the relationship between the error direction and the current direction. 3-D dive paths of emperor penguins Aptenodytes forsteri diving at isolated dive holes in eastern McMurdo Sound were reconstructed by dead-reckoning, and the net error and error direction were calculated. The net error correlated positively with the dive duration. The error directions were not distributed uniformly, and the mean error direction tended to be north of the starting point of dives. Because there was a southwardflowing current in eastern McMurdo Sound, the ocean current was likely to affect the calculated dive paths. Therefore, the method of error correction generally used, in which the net error divided by the dive duration is applied to each estimated position, is realistically appropriate, provided that the current does not change significantly during a dive.

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Tri-axis magnetism and acceleration data loggers have recently been used to obtain time-series headings and, consequently, the 3-dimensional dive paths of aquatic animals. However, problems may arise in the resulting calculation process with multiple parameters. In this study, the dive paths of loggerhead turtles and emperor penguins were reconstructed. For both species, apparently unrealistic movements were found. Time-series heading data of turtles showed small regular fluctuations synchronous with stroking. In the dive paths of penguins, infrequent abrupt changes in heading were observed during stroke cycles. These were unlikely to represent true behaviours according to observations of underwater behaviour and tri-axis magnetism and acceleration data. Based on the relationship between sampling frequency and frequency of body posture change, we suggest that (1) the changes in the animals' posture concurrent with strokes and (2) the mismatched treatment (i.e. filtering and non-filtering) of the acceleration and magnetism data caused the artefacts. These inferences are supported by the results of simulations. For data sets obtained at a given sampling frequency, the error pattern in calculated dive paths is likely to differ depending on the frequency and amplitude of body posture changes and in swim speed. In order to avoid misinterpretation, it is necessary to understand the assumptions and inherent problems of the calculation methods as well as the behavioural characteristics of the study animals.