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Am J Physiol Regul Integr Comp Physiol 292: R2028-R2038, 2007. First published January 11, 2007; doi:10.1152/ajpregu.00691.2006
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COMPARATIVE AND EVOLUTIONARY PHYSIOLOGY

Estimating the rate of oxygen consumption during submersion from the heart rate of diving animals

J. A. Green,1,2 L. G Halsey,2 P. J. Butler,2 and R. L. Holder3

1Department of Zoology, La Trobe University, Bundoora, Melbourne, Australia; and 2Centre for Ornithology, School of Biosciences and 3Department of Primary Care and General Practice, University of Birmingham, Edgbaston, Birmingham, United Kingdom

Submitted 2 October 2006 ; accepted in final form 3 January 2007


   ABSTRACT
TOP
 ABSTRACT
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX A
 APPENDIX B
 GRANTS
 REFERENCES
 
How animals manage their oxygen stores during diving and other breath-hold activities has been a topic of debate among physiologists for decades. Specifically, while the behavior of free-ranging diving animals suggests that metabolism during submersion must be primarily aerobic in nature, no studies have been able to determine their rate of oxygen consumption during submersion (VO2D) and hence prove that this is the case. In the present study, we combine two previously used techniques and develop a new model to estimate VO2D accurately and plausibly in a free-ranging animal and apply it to data for macaroni penguins (Eudyptes chrysolophus) as an example. For macaroni penguins at least, VO2D can be predicted by measuring heart rate during the dive cycle and the subsequent surface interval duration. Including maximum depth of the dive improves the accuracy of these predictions. This suggests that energetically demanding locomotion events within the dive combine with the differing buoyancy and locomotion costs associated with traveling to depth to influence its cost in terms of oxygen use. This will in turn effect the duration of the dive and the duration of the subsequent recovery period. In the present study, VO2D ranged from 4 to 28 ml·min–1·kg–1, indicating that, at least as far as aerobic metabolism was concerned, macaroni penguins were often hypometabolic, with rates of oxygen consumption usually below that for this species resting in water (25.6 ml·min–1·kg–1) and occasionally lower than that while resting in air (10.3 ml·min–1·kg–1).

penguin; model; oxygen stores; hypometabolism

FREE-RANGING, DIVING ANIMALS frequently engage in bouts of repeated and prolonged foraging dives. For decades, physiologists have attempted to understand how these animals manage their oxygen stores to achieve such behavior (for a review, see Ref. 10). Despite behavioral evidence indicating the contrary, the majority of these studies have tended to conclude that a large proportion of dives exceed the calculated aerobic dive limit (cADL) of the species in question (e.g., Ref. 30). cADL is defined as the volume of usable oxygen stores divided by the rate of oxygen consumption during submersion (VO2D). Under this definition, when a dive reaches the cADL, all usable oxygen has been depleted. However, the brain and central nervous system will always require some oxygen to maintain functionality; so if all oxygen is exhausted, then the animal will die. Therefore, to state that a dive may exceed the cADL merely indicates that the estimate of cADL is incorrect. This is not to say, however, that all natural diving utilizes only aerobic metabolism (11, 12). Kooyman et al. (38) demonstrated that diving animals will initiate the accumulation of lactate above resting levels well before all available oxygen has been consumed. The dive duration (tD) at which this accumulation of lactate occurs is the aerobic dive limit (37, 38), now often termed the diving lactate threshold (DLT; 10). In the case of the Weddell seal (Leptonychotes weddelli), the DLT was ~20–25 min and the maximum tDs recorded (probably close to cADL) were approximately two to three times this. However, only ~3% of observed dives had durations in excess of the DLT, and these were usually followed by extended periods at the surface, presumably to recycle accumulated lactate. Clearly cADL and DLT represent vastly different thresholds in the physiology of diving, and the two quantities should not be confused [see Butler (7) for a thorough discussion of this topic]. Furthermore, that the scope for energy expenditure is variable between dives, as a result of activities undertaken within the dive (e.g., Ref. 54), also indicates that to consider both cADL and DLT as single, one-dimensional, inflexible thresholds is an oversimplification of a complex system.

As indicated above, the majority of behavioral studies investigating the time budgets of diving animals suggest that surface interval (tS) durations are not long enough to allow for recovery from anaerobic metabolism i.e., that dives are generally almost completely aerobic (49) and thus do not exceed the DLT, let alone the cADL. This implies then that, when determining cADL, either the calculation of usable oxygen stores and/or the estimate of VO2D are incorrect. There is surely a limit to the inaccuracy in estimates of total body oxygen stores (35). Certainly, it seems unlikely that total body oxygen stores could be two or three times greater than current estimates, as would be necessary for all diving to be within the cADL (40). This indicates that most of the inaccuracy lies in the estimation of VO2D. As a result, a more accurate method to estimate VO2D is required, if we are to develop a solid working knowledge of the energetic costs of diving from which we can investigate physiological adaptations more robustly.

Progress with this work has been limited since it is not possible to measure VO2D directly (14). Several experimental techniques have been employed to estimate VO2D, but the results of these studies vary substantially. Respirometry has been used to calculate VO2, while animals are at the surface between dives from man-made holes in the ice of the Antarctic (13), and/or while they swim or rest in a static water channel or flume (e.g., Ref. 17). A recent new approach utilizes body movement as a calibrated proxy for VO2 (55). A first step in measuring VO2D has been made by measuring the decline in the partial pressure of oxygen (PO2) in the air sacs during dives of emperor penguins (Aptenodytes forsteri; 34). In free-ranging animals, isotopic techniques, including doubly labeled water, have often been used to estimate VO2 during complete foraging trips and to equate this (or a proportion of this) to VO2D (e.g., Ref. 15). Heart rate (fH) has been recorded during free-ranging diving in a variety of species, including elephant seals (Mirounga leonina; 31), Antarctic fur seals (Arctocephalus gazella; 5), and South-Georgian shags (Phalocrocorax georgianus; 2). If a relationship has been established between fH and VO2 for a given species, then it is possible to estimate the VO2 of a complete dive cycle [tD and the subsequent tS] from the mean fH of that dive cycle (e.g., Refs. 20 and 24). Unfortunately, however, fH measured while the animal is submerged or on the surface cannot be used to estimate VO2 directly, either while submerged or during the subsequent surface interval, as studies have shown that during diving the relationship between fH and VO2 is not consistent (4, 21).

Mathematical or modeling approaches have also been developed to ascertain VO2D. Recent work has included the effects of buoyancy and metabolic rate while resting (e.g., Ref. 30). Woakes and Butler (57) developed a model to calculate mean VO2D at the mean tD and tS of tufted ducks (Aythya fuligula) diving freely in a laboratory tank. The concept used was based on a technique first applied by Scholander (48), which obtained an estimate of VO2D by partitioning the oxygen uptake between dives into the amount of oxygen consumed during the surface interval and the amount consumed during the preceding dive. While instructive, this approach could only provide an estimate of VO2D for "average" dives. With a greater experimental data set and improved mathematical model, Halsey et al. (27) refined this approach. They controlled for the effects of tS by plotting changes in oxygen uptake after 10 s (sufficient time to replenish the oxygen stores of tufted ducks) against tD. Then, by assuming that VO2 while at the surface and while descending and ascending to the foraging site (a tray at constant depth) were fixed quantities regardless of tD, the slopes of these regressions represented VO2D during the foraging part of the dive (i.e., the part of the dive varying with tD). This represented the first direct and tangible estimate of VO2D during diving. Due to a relatively small sample size, Woakes and Butler (57) and even Halsey et al. (27) were obliged to assume that VO2 at the surface was independent of tS duration, thus regressing only tD against oxygen uptake at fixed durations of tS.

In contrast to these laboratory studies, recordings of heart rate during free-ranging diving are able to include a far greater number and variety of dives, allowing some of the limitations and assumptions of previous models to be eliminated. If fH over the dive cycle is used to estimate VO2, then it is possible to develop the models of Scholander (48), Woakes and Butler (57), and Halsey et al. (27) and not only quantify the rate of oxygen consumption during the dive cycle, but investigate how variability in different elements of the dive cycle (e.g., diving depth, tD, tS) might influence it. This development of the original model by Scholander (48) apportions total heart beats recorded over the diving cycle ({sum}HDC) to the time spent either submerged or on the surface. In the present study, we use an example data set of over 500,000 dives by macaroni penguins (Eudyptes chrysolophus) for which heart rate has been recorded, to illustrate how statistical modeling can take advantage of such a large number of dives, and demonstrate how VO2D can be predicted from factors as straightforward as the tS and dive depth. A key finding is that the duration of a surface interval often reflects the occurrence of energy-costly activities during the previous dive, not simply the duration of that dive.

We suggest that our estimates of VO2D in macaroni penguins are the most direct, plausible, and meaningful obtained to date for a free-ranging animal. This approach could have applications in other studies where it is of interest to look at rate of oxygen consumption at a fine scale, beyond that which can be achieved using respirometry or other methods that measure oxygen uptake, which is only equivalent to oxygen consumption when an animal is in steady state. Such applications could include studies of apnea (1, 39) or short periods of exercise (e.g., Ref. 33).


   MATERIALS AND METHODS
TOP
 ABSTRACT
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 APPENDIX A
 APPENDIX B
 GRANTS
 REFERENCES
 
Data Collection

The approach in the present study is based on the reanalysis of data collected on the diving behavior and energetics of macaroni penguins (22, 23). Briefly, the penguins were implanted with data loggers that recorded heart rate every 10 s and dive depth every 2 s. Data were analyzed from the winter migration of 18 penguins (9 male, 9 female) during 2002, since this period represented the most complete set of data for a single phase of the annual cycle (23). Data from both sexes were pooled, since, while the diving behavior and capacity varies between male and female macaroni penguins (23), there is no difference between the sexes in the relationship between fH and VO2 (26).

Several diving species intersperse foraging dives with shallow nonforaging dives, thought to have a role in the recovery from oxygen debt (e.g., Ref. 50). This behavior is not shown by macaroni penguins so, as in previous studies (23), only foraging dives (maximum depth > 10 m) were used in the analysis. Since fH was recorded less frequently than dive depth, dives with a tD or tS of <10 s (which would have included the majority of dives to < 10 m in any case) were ignored. Dives with a tS > 600 s were also ignored, as these were assumed to represent interbout periods rather than surface intervals for recovery from the previous dive and preparation for the next. In total, 514,106 dives were analyzed.

Conversions of fH to mass specific rate of oxygen consumption (sVO2; ml·min–1·kg–1) were made using equation 14 from Green et al. (26). Conversion to sVO2 is appropriate for this species, as they have a mass exponent of one (25). As with all studies of this type, using fH as a proxy for sVO2 assumes that the oxygen pulse (cardiac stroke volume multiplied by oxygen extraction by the tissues) varies with fH in a predictable way under all physiological circumstances (6). It is not possible to use the heart rate method to predict VO2 accurately for individual animals (6). Therefore, in the present study, all models were constructed and calculations computed using fH and {sum}HDC for each individual animal. Resulting mean values of fH and {sum}HDC for all animals were then converted to estimates of sVO2, as described above. The standard error of the estimate (SEE) for estimates of sVO2 was calculated following the procedures established by Green et al. (25).

Calculation

Structure of models. All calculations were based on the principle that the total volume of oxygen consumed during a dive cycle ({sum}O2DC) is a function of tD, tS, VO2D, and the rate of oxygen consumption during the subsequent surface interval (VO2s). This is summarized by Eq. 1.

Formula 1(1)

An important point to note is that Formula 1O2s represents the rate at which oxygen is consumed by the tissues during the surface interval. This is not equal to total oxygen uptake during the surface interval, which has to be sufficient to match oxygen used during both the previous dive and the subsequent surface interval and will, therefore, be equal to {sum}O2DC. As explained above, a calibration relationship between fH and Formula 1O2 can be used to estimate mean Formula 1O2 of a complete dive cycle from the mean fH of that dive cycle. Therefore, the same relationship can also be used to estimate the {sum}O2DCof a dive cycle from the {sum}HDC for that dive cycle. Thus, Eq. 1 can be converted to Eq. 2.

Formula 2(2)

Note that fHD and fHS from Eq. 2 are theoretical quantities that can be used to predict Formula 2O2D and Formula 2O2s, but are not equal to fH measured during submersion and the subsequent surface interval. As discussed earlier, within the dive cycle the fH/Formula 2O2 relationship is not constant, and fH during submersion cannot be used in any simple fashion to predict Formula 2O2D. It can be seen that for macaroni penguins (and indeed for many other diving animals) we can measure three of the components of Eq. 2 ({sum}HDC, tD, and tS) and that with a large enough data set it should be possible to use linear regression to determine fHD and fHS. The aim of the calculation procedure outlined in the present study is to determine fHD and fHS mathematically for each penguin, such that Formula 2O2D and Formula 2O2s can be calculated for the population. The calculation also allows fHD and fHS to vary with, for example, tD rather than be fixed quantities.

Four models were produced to estimate fHD and fHS, with each successive model including more details that may reasonably be expected to improve predictive validity. Because the statistical process is relatively involved, and possibly unfamiliar, we show the derivation of these models and how the models were used to calculate values for macaroni penguins. Model 1 is the simplest of the models, and the others add additional variables to this basic template. Each model described below incorporates between two and four constants, which are represented by Greek letters ({alpha}, beta, {varphi}, and {delta}).

Model 1

While the physiological state of a diving animal changes unpredictably during the course of a dive as they adjust their circulation and balance the demands of foraging, locomotion, and oxygen conservation (e.g., Ref. 3), it is reasonable to suppose that changes are much more predictable during the subsequent surface interval. If so, then at any given value of tS, we assume that within an individual animal, fHS is a constant. In other words, for all surface intervals of, for example, 30 s, fHS will always be similar. Therefore, at a given tS, fHS x tS will also be a constant ({alpha}). Similarly, if a surface interval is a period of recovery from the previous dive, then it seems reasonable to expect that during dives with a given surface interval the rate of energy expenditure (represented by fHD) during the previous dive will also be a constant (beta). While many studies show a close association between tD and tS, there will still be sufficient variability in tD within a given category of tS so that Eq. 2 can be rearranged to give Eq. 3.

Formula 3(3)

Model 2

Certain studies, both in the laboratory and in the field, indicate that mean fH of dive cycles is lower during longer dives (3, 24). It is possible that fHD also decreases as tD increases. If this is correct, then, rather than assume fHD is constant within a category of tS, it is replaced with a simple linear function of tD (Eq. 4). Incorporating this relationship into the model should improve the estimates of fHD and fHS. As before, at a given tS, fHS x tS is assumed to be a constant ({alpha}), therefore, substituting fHD in Eq. 2 with Eq. 4 gives us Eq. 5.

Formula 4(4)

Formula 5(5)

Model 3

For over 35 years the diving behavior of free-ranging aquatic species has been obtained by the attachment to study animals of data loggers that record changes in hydrostatic pressure over time (36). The diving parameters tD, tS, and hence dive cycle duration, are derived from the recorded depth data. Thus when data have been obtained on tD, they are usually also available for the maximum depths of those dives (depD). It is clear that depD is an important factor when diving animals prepare themselves to dive. Changes in buoyancy with increasing depth during dives affect the energetic cost of dives and the amount of air inhaled prior to submersion (46, 51, 56). These factors will conspire together to influence tD and fHD. For example, power costs of swimming may vary with depth (53). Alternatively, deeper dives may have a proportionately shorter bottom-feeding time that will affect the total energy requirement (32). Thus, the inclusion of depD may improve the predictive power of the model. Therefore, the potential effect of depD on fHD was added as a simple linear relationship between fHD, and depD (Eq. 6). As before, at a given tS, fHS x tS is assumed to be a constant ({alpha}), so substitution of Eq. 6 instead of fHD into Eq. 2 gives Eq. 7.

Formula 6(6)

Formula 7(7)

Model 4

Finally, to test all logical, yet simple, combinations, depD and tD were both considered as factors that might influence fHD. In this case, a multiple linear relationship between fHD, tD, and depD (Eq. 8) was tested. As before, at a given tS, fHS x tS is assumed to be a constant ({alpha}) and so substitution of Eq. 8 in place of fHD in Eq. 2 gives Eq. 9.

Formula 8(8)

Formula 9(9)

Calculations

Each dive for each animal was classified by tS bins of 4 s. Within each bin for each animal, {sum}HDC was regressed as a function of tD (and depD or tD2, as appropriate, depending on which model was being tested). Regressions were only performed if there were > 40 dive cycles with the appropriate tS within each bin (which left a total of 506,909 dives for development of all four models). Each regression generated values for between two and four constants (depending on the model). Values of weighted means (see APPENDIX A) were then calculated for these constants across all animals for each bin of tS. Further regression analysis investigated whether these constants varied as a function of tS or whether they were fixed quantities. Polynomial functions of tS (with 95% confidence intervals) were then developed as appropriate for these constants (termed "constant functions"). Substitution of the constants with the constant functions in Eqs. 3–9 allowed calculation of fHD and {sum}HDC using each of the four models. The 95% confidence limits and SEEs of fHD and {sum}HDC were generated by substituting the constant functions with the 95% confidence limits of the constant functions, in each of the four models.

Model Selection and Validation

First, the models were evaluated and compared with each other on the basis of the regression statistics within penguins and tS bins and subsequently by examination of how the model constants (fHS, beta, {varphi}, and {delta}) varied as a function of tS (constant functions). Models with better regression statistics were presumed to be more valid.

Any further validation of the model within the data set risks forming a circular argument. While a more robust test of the models would be to input data from other diving bouts, in this case, this would entail using data from another season. The seasonal variability in diving capacity shown by macaroni penguins (22, 23) means that a test of the models with data from another part of their annual cycle is not necessarily valid. Therefore, the models were tested on the data set used to derive them, in order at least to determine which model gave the most accurate estimates of {sum}HDC and, within that, fHD and fHS. To limit the circularity of the validation, the data were organized in a different fashion from that for the derivation of the models. For each animal, all dives were initially classified into bins by tD (4 s). Within each 4-s bin of tD, dives were then classified into 4-s bins of tS and then mean depD was calculated for each bin for each animal. A grand mean of depD for all animals was then calculated for each bin of tD and tS and this data set was used for the validation process. Initially, 1,625 combinations of tD and tS were generated. However, combinations that were only undertaken by one penguin were removed from the data set since, while these combinations were common (15.1% of all combinations), they represented only a small fraction of all dives recorded (0.6% of all dives) and so tended to skew subsequent analyses. The resulting validation data set contained 506,607 dives in 1,381 combinations.

The final step of the validation process made an assumption that the underlying premise of the exercise was correct and that the process would derive a value (or range of values) for Formula 9O2D, which indicate that all dives would be within the cADL. As discussed in our other work on this topic, cADL should not be considered a fixed value for a particular species (22, 24). If we accept that Formula 9O2D can vary, then by definition, cADL will also vary. In previous studies, we have used mean rate of oxygen consumption for the dive cycle (Formula 9O2DC) as a proxy for Formula 9O2D, determined the cADL for dives of different duration, and found that up to 70% of dives had a tD in excess of the cADL. We concluded that Formula 9O2D must be less than Formula 9O2DC. Therefore, we have adopted a similar approach in the present study and used each model to estimate Formula 9O2D and, therefore, cADL for each combination of tD and tS. For comparison, the same approach was also applied to Formula 9O2DC estimated from measured {sum}HDC. For each model (and measured {sum}HDC), the proportion of dives in excess of cADL was calculated. Confidence intervals (95%) for these estimates were calculated by repeating the procedure using Formula 9O2D calculated from the lower 95% confidence limit of fHD – SEE and Formula 9O2D calculated from the upper 95% confidence limit of fHD + SEE (22). As in our previous work (22), macaroni penguins are assumed to have usable body oxygen stores of 58 ml/kg, although, in this case, we allowed uncertainty in this estimate of ±10%, which was incorporated into the calculation of the confidence intervals.


   RESULTS
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 APPENDIX A
 APPENDIX B
 GRANTS
 REFERENCES
 
Table 1 shows the summary statistics for the regressions of each model within bins of tS, within each penguin. Mean r2 was significantly different between all four models (ANOVA with Tukey's post hoc testing, P < 0.001 in each case). Both the intercept and slope were significant in nearly every case in model 1. However, the mean r2 of model 1 regressions was the lowest of the four. All three multiple regressions fitted the data very well, although the coefficients of the slopes were statistically significant, most frequently, and had higher partial correlation coefficients for model 3. Furthermore, model 3 had the highest mean r2. Certainly, adding all of the variables into one model (model 4) did not appear to produce the most descriptive model.


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  		Table 1. Results of four different linear regression models to predict total dive cycle heart beats ({Sigma}HDC) from time spent submerged and dive depth in 18 macaroni penguins

 
As a test of the four models, each was used to predict {sum}HDC for all combinations of tD and tS (4-s bins) from the validation data set. Figure 1 shows predicted {sum}HDC as a function of measured {sum}HDC for all four models. A weighted regression (APPENDIX A) was used to assess predicted {sum}HDC as a function of measured {sum}HDC. All four regressions were significantly different from the line of equality (t-tests, P < 0.001, Table 2) but with such large sample sizes (n = 1,381 in each case) this is not surprising. To provide further comparisons of the validity of each model, the mean percentage error of predictions made using the four models was also calculated (Table 2). Mean percentage error gives a measure of the accuracy of predictions compared with a measured standard. Mean percentage error was lowest for model 3, although all four models were accurate (< 5% in each case). The standard error of the mean percentage error was greatest for model 3, implying that this model was less precise than the others. However, in each case the standard error of the mean was rather low and the resulting confidence intervals of mean percentage error would also have been relatively small. As a result, the conclusion is that the precision for all models was relatively high.


Figure 1
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  		Fig. 1. Plot of predicted total heart beats during a dive cycle ({sum}HDC) as a function of measured {sum}HDC. Each point represents a unique combination of dive duration (tD) and surface interval duration (tS). Predictions were made for 4 different models (models 1–4). See text for details of models. Shades denote the number of dives observed at each combination of tS and tD in which black = 1,001–10,000, dark grey = 101–1,000, midgrey = 11–100 and light grey = 1–10. Also shown is the line of equality (solid line) and the weighted regression line between the 2 variables (dashed line).

 

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  		Table 2. Regression relationships and mean percentage error between measured and predicted total {Sigma}HDC

 
Figure 1 and Table 2 both suggests that all four different models can be used to predict {sum}HDC with a relatively high degree of accuracy. However, the aim of the modeling procedure was to derive a technique for the reliable estimation of Formula 9O2D. Each model was used to predict Formula 9O2D for each combination of tD and tS in the validation data set. cADL was then determined for each combination by dividing usable oxygen stores for macaroni penguins (58 ml/kg ± 10%) by this value of Formula 9O2D. This procedure was also repeated for Formula 9O2DC calculated from measured {sum}HDC (Table 3). Only under models 1 and 3 were the vast majority of dives within the cADL. Formula 9O2D predicted using models 2 and 4 barely increased the proportion above estimates made using {sum}HDC.


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  		Table 3. Percentage of dives that would have a duration shorter than the calculated aerobic dive limit (cADL) when the rate of oxygen consumption during diving (Formula 3O2D) was calculated using 4 different models

 
In conclusion, models 1 and 3 appear to be superior in predicting both fHD and {sum}HDC. The addition of an effect of tD on fHD in models 2 and 4 barely increased the accuracy of prediction (Tables 1 and 2) and produced improbable results in terms of the proportion of dives within the cADL (Table 3). When comparing models 1 and 3 with each other, there is little to choose between them. However, while the accuracies in terms of individual regressions and calculation of cADL are very similar, model 3 adds an extra easily measured variable (depD), which increases the accuracy of prediction of {sum}HDC (Tables 1 and 2) and reduces the variability in the percentage of dives within the cADL (Table 3). We suggest that other studies explore all possible models when applying this technique in future, but in the present study we have selected model 3 as the best way to predict both fHD (Eq. 10) and {sum}HDC (Eq. 11) in macaroni penguins.

Figure 2 shows how the different constants associated with model 3 varied as a function of tS (constant functions). In all models, fHS was equal to {alpha} divided by tS. Weighted polynomial regressions (APPENDIX A) showed that fHS (3rd order), beta (4th order), and {varphi} (4th order) varied significantly as a function of tS (Fig. 3). Substitution of these constant functions into Eqs. 6 and 7 generated the predictive equations for fHD (Eq. 10) and {sum}HDC (Eq. 11).

Formula 10(10)

Formula 11(11)

Formula 11O2D varies considerably as tS and depD vary. APPENDIX B contains similar derivations for the other three models. Figure 3 shows a frequency distribution of all the values of Formula 11O2D calculated for the validation data set using Eq. 10 (model 3) and converted to rate of oxygen consumption. During the winter, Formula 11O2D varied from 4 to 28 ml·min–1·kg–1 with a median value of 11.25 ml·min–1·kg–1. The 95% confidence intervals of these predictions, incorporating both the uncertainty in the model development and the error in conversion of fH to Formula 11O2 ranged from 1 to 40 ml·min–1·kg–1 but were clustered tightly around the predictions (Fig. 3).


Figure 2
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  		Fig. 2. A: variation in mean (open symbols) heart rate during a surface interval between two dives (fHS) as a function of the duration of that surface interval (tS). B and C: variation in the mean (open symbols) of 2 constants (beta and {varphi}; dimensionless) relating to the response of heart rate during the previous dive as a function of tS. See text for details of derivation of these constants. Also shown are fitted, weighted, polynomial regression curves with 95% confidence intervals (dashed lines) and their equations. All three relationships were significant (P < 0.001, r2 = 94.8, 97.5, 89.1, respectively). Data are taken from 18 male and female free-ranging macaroni penguins diving during their winter migration.

 

Figure 3
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  		Fig. 3. Frequency distribution (black bars) of rate of oxygen consumption during submersion (Formula 3O2D) estimated from tD, tS, and maximum dive depth (depD) using model 3. Also shown are the minimum (grey shadow) and maximum (white shadow) 95% confidence intervals of this distribution.

 

   DISCUSSION
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
APPENDIX A
 APPENDIX B
 GRANTS
 REFERENCES
 
For over 100 years, physiologists have been striving to discover how animals are able to perform extraordinary feats of diving [see Butler and Jones (9, 10) for reviews of the history of diving physiology studies]. Many of these studies have focused on attempting to estimate Formula 11O2D, despite the obvious challenges of such an objective (14). In the present study, using macaroni penguins as an example, we have developed a model that allows the prediction of Formula 11O2D from fH based on temporal and physical characteristics of the dive (tS and depD). The iterative process of model construction and generation allowed the inclusion of various factors that might feasibly have influenced Formula 11O2D and facilitated the unbiased selection of the most appropriate model. In the example calculation with macaroni penguins, there were still a few dives (1.3% with confidence intervals of 0.3–6.6%) that appeared to exceed the cADL. This can be attributed to variability in the factors within the model and suggests that inclusion of more predictive factors or information about the dives could further improve the accuracy of this technique.

Factors Influencing Dive Behavior and Energetic Costs

Perhaps the most interesting aspect of the present study is the factors that proved to be significant and aided in the selection of a model and those which did not. Model 3 gave the best predictions. However, despite being the simplest of all of the models, including only the effects of tS on fHD, model 1 also gave excellent predictions of both fHD and {sum}HDC. While model 3 improved upon this by adding an effect of depth, the most important factor in defining the metabolic cost of a dive appears to be the subsequent tS. To some extent this is a question of cause and effect, as it is unlikely that the rate of metabolism during a particular dive is set by the subsequent tS. Physiologically speaking, Eq. 10 should really be rearranged such that tS is dependent on fHD. In other words, the rate at which oxygen is consumed while submerged will have a profound effect on the subsequent tS. Furthermore, the shape of the curve of cumulative oxygen uptake suggests that this relationship is not simply linear (28). That tS and fHD are linked is perhaps not surprising, although it is gratifying that the process of model development should reveal this link.

It is also not surprising that depD is an important predictor of Formula 11O2D. Much recent work on diving physiology (with penguins in particular) has revealed that animals often appear to match aspects of their physiology to the intended depth of a dive. King penguins (Aptenodytes patagonicus), Adélie penguins (Pygoscelies adeliae), and magellanic penguins (Spheniscus magellanicus) modulate their inhaled air volume prior to submersion such that when their intended depth is reached they are neutrally buoyant (46, 56). Magellanic penguins also appear able to predict the rate of oxygen consumption in a forthcoming dive based on its duration and likelihood of prey capture (51). Macaroni penguins actively stroke their flippers during descent but during ascent are able to glide for at least half of the time (45). Mean stroke frequency during descent is independent of dive depth, but during ascent it decreases with increasing dive depth. As a result, in mechanical terms at least, Formula 11O2D will be influenced by depD (30, 53). These data show that penguins make decisions based on complex environmental parameters, suggesting a remarkably efficient use of time during foraging (51). In the case of macaroni penguins, Formula 11O2D and depD interact to define the tS.

While our models are unable to include the likelihood of occurrence of prey capture events, our findings may suggest that these events are critical in determining Formula 11O2D and tD. In other species of free-ranging penguins feeding on euphausids, prey capture events are associated with rapid acceleration and deceleration (44). Rapid acceleration and deceleration during horizontal swimming is energetically expensive and is therefore likely to limit tD and distance swum (18). Furthermore, prey pursuit by penguins may involve swimming at speeds higher than the optimal cost of transport, and the power costs of swimming increase with the cube of swim speed (54). As a further complication, the required prey capture speed may vary between prey patches or between different target prey species, all of which will introduce further variability (54). Respirometry studies of Weddell seals suggest that Formula 11O2D is greater during foraging dives than during exploratory dives (40). If prey capture events are unpredictable and energetically expensive, then they are likely to have an important effect in shortening or lengthening dives, and, as a result, the duration of a dive is not necessarily a guide to its energetic cost. In other words, a dive of 1 min duration could vary substantially in Formula 11O2D, depending on the type or prey and whether or not energetically expensive prey capture events occur. The duration of the bottom phase of dives and subsequent behavior during ascent (whether an immediate return to the surface or prey searching) vary substantially in macaroni penguins and are dependent on each other (45), suggesting that prey capture rates also vary substantially between individual dives.

While the rejection of models 2 and 4 shows that fHD is not dependent on tD at all, tD is of course critical in determining the total energy expenditure of the dive (Eq. 1). There is little reason to assume that the duration of any given event should affect the rate at which energy is expended; in fact, the reverse is more likely. In a resource-limited environment, the rate at which energy is required for a given activity (which, in the case of Formula 11O2D, appears to be highly variable and dependent on extrinsic factors) is more likely to limit its duration than vice versa. Hence there is a lack of dependence of fHD on tD. Figure 4 illustrates the complex nature of the interactions between tD, tS, and depD. Figure 4 shows the tremendous variation in combinations of tD and tS or depD. While the majority of dives have a tD-to-tS ratio of ~5, this ratio varies from 0.25 to 18. Clearly, tS is influenced by factors other than tD alone. This variability in tS (i.e., recovery and preparation duration in terms of oxygen restocking, CO2 elimination, and possibly lactate conversion) for a given tD presumably represents variability in the level of total oxygen stores before and after a dive (due to the shape of the curve of cumulative oxygen uptake) or energetic costs during the preceding dive, due either to differences in depD or prey capture events (see above) or other energetically costly activities. Similarly, the wide variation in tD at a given depD suggests that differing costs within a dive to a given depth may lead to different levels of Formula 11O2D, which will in turn affect its duration (tD).


Figure 4
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  		Fig. 4. Frequency plot of combinations of tD and subsequent tS (A) and tD and maximum dive depth (B) recorded from 18 male and female free-ranging macaroni penguins during their winter migration. Shades denote the number of dives observed at each combination in which black = 1,001–10,000, dark grey = 101–1,000, midgrey = 11–100, and light grey = 1–10.

 
Variability in Rate of Oxygen Consumption During Submergence

In the absence of detailed measurements or predictions, many studies have assumed that Formula 11O2D is constant across all dives and independent of other factors associated with the dive (e.g., Ref. 15). However, in the present study, we show that Formula 11O2D can have a wide range of values (Fig. 3). Some other studies have also shown this to be the case; for example, postdive respirometry of Weddell seals suggests that Formula 11O2D is subject to considerable variability (40), which is further supported by theoretical calculations (30). Further evidence in support of this comes from the only two studies that have measured DLT. Both emperor penguins (41), and to a lesser extent Weddell seals (37), show variation in their lactate response at a given tD. Figure 2 from Ponganis et al. (41) shows clearly how in one of four penguins (only 22 dives were analyzed) lactate production is substantial during a dive of ~5.75 min, but in another dive of ~6.25 min, postdive lactate levels were barely elevated above resting levels. This illustrates that even within an individual animal performing a small number of dives from a fixed location, either oxygen stores or Formula 11O2D must be subject to substantial variation, and DLT represents rather more than a fixed time threshold beyond which lactate accumulation always occurs, as many authors use it (e.g., Ref. 15).

As the limit of oxygen stores is approached, dives are likely to have a high component of anaerobic metabolism, as in Weddell seals and emperor penguins (Fig. 5). Unfortunately, the present study gives no insight as to what tD and activity might correspond to the DLT for macaroni penguins. It should be noted again that in Weddell seals < 3% of dives exceeded the DLT; so for macaroni penguins, the proportion of dives where Formula 11O2D does not account for all of the metabolism during a dive is also likely to be very low and correspond only to the longest and/or most energetically demanding dives. The ratio of tD/tS (Fig. 4) indicates that only a small percentage of dives by macaroni penguins are likely to exceed their DLT.


Figure 5
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  		Fig. 5. Schematic diagram of the relative contributions of aerobic (solid line) and anaerobic (dashed line) metabolism toward ATP production during diving. ATP production/consumption is assumed to remain constant throughout the dive. Note that before the diving lactate threshold (DLT; grey zone in this example) is reached the majority of metabolism is aerobic in nature, leading to a linear decrease in oxygen stores (solid diamonds). The point at which aerobic metabolism reaches zero is when all the usable stores of oxygen have been exhausted and is the calculated aerobic dive limit (cADL). In dives beyond the DLT, with an increasing proportion of anaerobic metabolism, using heart rate will predict only the aerobic component of metabolism and hence will underestimate total ATP production.

 
Rate of Oxygen Consumption During Submergence

In the absence of measurements, several authors have speculated on what Formula 11O2D might be. Some authors have noted that for all dives to be within the cADL, Formula 11O2D must be lower than that while animals rest in water, i.e., they exhibit (aerobic) hypometabolism. (8). Other studies have used Formula 11O2 while animals rest on land as a proxy for Formula 11O2D (30), which also suggests hypometabolism, since in most species studied to date, Formula 11O2 while resting on water is approximately twice that while resting on land. Other studies have used the metabolic cost of swimming in a static water canal but admit that there are limitations with this analysis, which are likely to lead to an overestimation of Formula 11O2D (16, 18). As mentioned above, in the current study, we have found that Formula 11O2D is not a fixed value but rather that it varies in association with depth and possibly with the performance of energetically costly activities. Predicted values of Formula 11O2D ranged from 4 to 28 ml·min–1·kg–1 (Fig. 4), although 93% of dives were in the range of 6 to 20 ml·min–1·kg–1, and the median was 11.25 ml·min–1·kg–1. By way of comparison, mean Formula 11O2 was 10.3 ml·min–1·kg–1 while macaroni penguins rested on land and 25.6 ml·min–1·kg–1 while they rested in water (26). To illustrate the effect of using different proxies for Formula 11O2D, we have recalculated cADL and the proportion of dives within this limit by using a variety of methods (Table 4). This exercise illustrates that for macaroni penguins at least, the present approach is the most plausible estimate of mean Formula 11O2D to date, but in the absence of similar data, resting Formula 11O2 in air is the most reasonable substitute.


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  		Table 4. Rate of VO2D and the resulting percentage of naturally occurring dives that would be within the cADL

 
When compared with resting data, the ranges of Formula 11O2D determined using the present approach suggest that macaroni penguins reduced their metabolic rate below the resting level in water to extend tD (see Ref. 8). This may be possible in part since heat generated by the pectoral muscles during locomotion can be used to substitute for thermoregulatory costs (52). In the present study, we were unable to explore hypometabolism in detail and ascertain whether it might also be associated with observed decreases in abdominal temperature during diving (24). Debate continues on the role of regional heterothermy in energy saving during diving (29, 42, 43, 47). By contrast, recent work on king penguins suggests that such low values of Formula 11O2 while resting on water do not represent a hypometabolic state. Unlike fasted birds (as most animals in respirometry studies tend to be), well-fed king penguins had a resting Formula 11O2 in water that was not significantly different from that while on land (19). This finding matches data from macaroni penguins which suggest that by the middle of winter, Formula 11O2 while inactive at sea (at night, not while foraging) is closer to resting Formula 11O2 on land than it is to resting Formula 11O2 on water (22).

In conclusion, we have combined two established techniques (multiple regression calculation of Formula 11O2D in the laboratory and prediction of Formula 11O2 from fH in free-ranging animals) to show how the rate of oxygen consumption during submersion (or indeed any other breath-hold activity) can be estimated from heart rate and time-budget information. Using macaroni penguins as an example, we present the most plausible estimates to date of Formula 11O2D in a free-ranging diving animal. Many studies have reported that an unlikely proportion of dives by animals appear to exceed cADL (30). However, few studies have been prepared to examine further whether they have been overestimating Formula 11O2D, and/or underestimating total body oxygen stores. As mentioned above, it seems likely that the uncertainty lies in estimates of Formula 11O2D. Our estimates are lower than previously used values, suggesting that these animals rely on (aerobic) hypometabolism to some extent. More importantly, in contrast to many other proxies used for Formula 11O2D, our findings are consistent with the behavioral observations that suggest the majority of dives performed by macaroni penguins are essentially aerobic in nature.


   APPENDIX A
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX A
APPENDIX B
 GRANTS
 REFERENCES
 
Calculation of Weighted Means

Weighted means of regression coefficients were calculated for each bin of tS since the strengths of the regressions varied between individual penguins. Each regression parameter estimate (E; the intercept and one or more slopes) for each penguin has a standard error (S). The weight (W) of each estimate is calculated as

Formula 11

The mean estimate (E) is calculated as

Formula 11

The standard error (Formula 11) of this weighted mean is calculated as

Formula 11


   APPENDIX B
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX A
 APPENDIX B
GRANTS
 REFERENCES
 
Model 1

Total {sum}HDC was regressed as a function of tD within each 4-s bin of tS for each penguin. Both {alpha} (equivalent to fHS x tS) and beta (equivalent to fHD) were significant in most of the regressions (Table 1). A weighted mean ± SE (APPENDIX B) of fHD and fHS was calculated for each 4-s bin of tS using the coefficient and its mean ± SE for each penguin represented in that bin. The weighting accounted for differences between individual penguins in the variance of the mean value of the dependent variable in each tS bin. Mean fHS and fHD were then plotted as a function of tS and a weighted polynomial regression (maximum 4th order) was used to ascertain whether there were relationships between tS and fHS or fHD. Both fHS (3rd order) and fHD (4th order) varied significantly as polynomial functions of tS (Fig. 1). Substitution of these relationships into Eq. 2 generated our first predictive equation of {sum}HDC (Eq. 10).

Formula 1(B1)

Model 2

In a similar fashion to model 1, {sum}HDC was regressed as a function of tD and tD2. Therefore, as well as fHS, coefficients beta and {varphi}, respectively, were generated for each penguin in each bin of tS, most of which were statistically significant (Table 1). As before, a weighted mean of fHS, beta, and {varphi} was calculated for each bin of tS and plotted against tS (Fig. 2). Weighted polynomial regressions showed that fHS (3rd order), beta (4th order), and {varphi} (4th order) varied significantly as a function of tS. Substitution of these relationships into Eq. 5 generated our second predictive equation of {sum}HDC (Eq. 11).

Formula 2(B2)

Model 4

As with models 1–3, {sum}HDC was regressed as a function of tD, tD2, and depD. Therefore, as well as fHS, coefficients beta, {varphi}, and {delta} were generated for each penguin in each bin of tS, many of which were statistically significant (Table 1). As before, a weighted mean of fHS, beta, {varphi}, and {delta} was calculated for each bin of tS and plotted against tS (Fig. 4). Weighted polynomial regressions showed that fHS did not vary significantly as a function of tS (Fig. 4). However, the three constants beta (2nd order), {varphi} (2nd order), and {delta} (4th order) all did vary significantly as a function of tS. Substitution of these relationships into Eq. 7 generated our fourth and final predictive equation of {sum}HDC (Eq. B2).

Formula 3(B3)


   GRANTS
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX A
 APPENDIX B
 GRANTS
REFERENCES
 
This work was originally funded by Natural Environment Research Council (NERC) under their Antarctic Funding Initiative with logistical support provided by the British Antarctic Survey. The authors also thank NERC and La Trobe University for financial support during the writing of this article.


   ACKNOWLEDGMENTS
 
The authors thank the editor and anonymous referees for their considerable assistance in improving this manuscript.


   FOOTNOTES
 

Address for reprint requests and other correspondence: J. A. Green, Dept. of Zoology, La Trobe Univ., Bundoora, Melbourne, Victoria, 3086, Australia (e-mail: jon.green{at}latrobe.edu.au)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.


   REFERENCES
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX A
 APPENDIX B
 GRANTS
 REFERENCES
 

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