Animal model
We studied wind-dependent wandering albatross Diomedea exulans using data from long-term tracking programmes in the Southern Indian Ocean
[9] where the foraging strategy of this species have been well characterised
[23–26]. When they make long-distance movements, during the incubation period, birds travel constantly and quickly to maximize their probability of encountering isolated prey or prey patches using the foraging-in-flight (FII) search strategy. In addition, birds are also attracted to oceanographic features such as shelf-breaks and seamounts where they spend more time searching for prey, using an area-restricted-search (ARS) behaviour. Even when sitting on the water, wandering albatrosses actively search and catch prey by showing a sit-and-wait (SAW) foraging strategy. During the brooding period, birds make shorter foraging trips and in this study we explicitly compared net energy gain to assess assumptions of optimal foraging theory during this stage.
Conceptual energetic framework
We built an instantaneous time-energy budget model along the track of individual albatrosses based on the simple assumption that net energy gain is the balance between energy gain and energy expenditure:
Energy gain was estimated based on (1) empirical prey capture data that provided instantaneous mass intake at high temporal resolution
[25] and (2) conversion factors considering the diet of wandering albatrosses (i.e., the energetic content and proportion of squid and fish in the diet)
[27]. Energy expenditure was estimated by developing an instantaneous energy expenditure model to obtain a continuous measure of heart rate values during a foraging trip, by (1) identifying activity patterns in detail, (2) estimating heart rate values of each activity, including a cost function for flying, and (3) using a non-linear relationship between heart rate and oxygen consumption to transform heart rate values to energy expenditure estimations (see Figure
1). Our energy expenditure predictions are equivalent to field metabolic rates and explicitly consider different non-flying (‘landing’, ‘30 min after landing’, ‘resting’; ‘30 min before take-off’ and ‘take-off’) and flying activities (‘flying’ 10, 30, 60, 120 and 720 min after take-off) that are known to have different energetic costs
[13], in addition to implicitly including other processes related to somatic maintenance such as thermoregulation. Estimates of energy expenditure of those processes are not currently available and this information could be included in the model when more detailed information on the ecological energetics of pelagic birds become available.
The energy-budget model predictions’ were validated against an independent empirical distribution of observed body mass change between the end and start of foraging trips. It was validated under the assumption that trip net energy gain (TNEG) converted to mass units should roughly correspond to albatross body mass (BM) change (i.e., difference between body mass at departure for the sea and at return on the nest), considering that 1 g of albatross fat is equivalent to 19.8 kJ (i.e., conversion factor)
[29]. This relationship is exemplified in the following equation:
Given the short duration of foraging trips during brooding (mean: 3 days, range: 0.2–12;
[30]), we assumed that body mass difference is an approximation to prey intake that will be provided to chicks and in turn we considered that there was no assimilation. Thus, we assumed that foraging energy expenditure was obtained almost exclusively from their energetic reserves and that birds did not likely obtain energy from ingested prey. This observation is realistic for the 30-day brooding period since this period is the only portion of the annual cycle when wandering albatrosses undergo a significant decrease in body mass, suggesting that they cannot meet their energy requirement
[27, 28, 31].
Empirical data
We developed and validated the energy budget model using GPS tracking data of 45 wandering albatrosses during the brooding period of 2002–2005
[25]. Birds were fitted simultaneously with a GPS (providing location coordinates within 5 m every 10 s; New Behaviour, Zurich), a stomach temperature transmitter and associated receiver-recorders (Wildlife Computer, Redmond, WA). Albatrosses were induced to swallow a 20-g pill which transmits stomach temperature every 15 s to a receiver/logger attached to the back of the bird. The changes in temperature allow estimation of the timing of prey ingestion and the mass of prey capture along the track (more details in
[25]). The total mass of the equipment was 90 g (0.7%–1.2% of body mass) which is well below the recommended 3% threshold
[32]. At departure and return to the nest albatrosses were weighted (without equipment) to the nearest 50 g using a Salter spring balance (Salter Weightronix Ltd, West Bromwich, UK).
Due to several logistic constraints (i.e., electronic problems, premature loss of logger), prey capture data were available only for 18 foraging trips. Because not all foraging trips recorded simultaneously geographic position and prey capture data, we obtained 5 completely tracked foraging trips, 5 near-complete (tracks stopped recording when birds were heading to the colony), and 8 incomplete. Available tracking data corresponded to a 4-year period and we did not find inter-annual differences in foraging trip characteristics such as mean flying speed (F
3,14
= 0.38, P = 0.766), maximum flying speed (F
3,14
= 1.15, P = 0.364) and distance travelled per day (F
3,14
= 0.46, P = 0.715). Thus, all years were pooled to develop the instantaneous time-energy budget model. Before any data processing, locations obtained from GPS with an associated speed between successive positions above 90 km h-1 were discarded
[33].
Estimation of energy expenditure was based on mean and SD values of heart rate obtained empirically when wandering albatrosses were equipped with miniaturized external heart-rate recorders (PE4000, Polar, Elektro Oy, Kempele, Finland), satellite transmitters (Microwave Telemetry, Columbia, MD, USA) and activity recorders (Francis Instrument, Cambridge, UK)
[13] (Figure
1). GPS foraging trips were resampled to obtain one position every 1 min in order to match the temporal unit of heart rate values (beats min-1)
[13]. For each position, we estimated the distance from the previous location and to the colony, travel speed, flight direction (angle with respect to north), the azimuth and elevation of the sun (for estimating the day/night periods), as well as wind direction α, wind speed w and the angle between albatross flight direction and wind direction θ. More information on wind data can be found in the Additional file
1. For the diel cycle, we defined ‘night’ as the period in which the sun was six degrees or more below the horizon and ‘day’ otherwise using the ‘tripEstimation’ package
[34]. We estimated flight direction (i.e., angle with respect to north) using the ‘circular’ package
[35].
Estimation of net energy gain
Instantaneous net energy gain was estimated at our basic temporal unit (i.e., 1 min) as the difference between energy gain and energy expenditure based on Eq. 1. Similarly, total trip net energy gain was estimated by cumulative summing instantaneous net energy gain along the foraging trip.
Regarding the estimation of instantaneous energy gain, we first estimated instantaneous mass intake (kg min-1) based on prey capture data. Then instantaneous mass intake was transformed into energy gain by assuming that the 75% and 25% of prey capture data corresponded to squid and fish (prey identification was not possible), with an energetic content of 5.61 kJ g-1 and 4.64 kJ g-1, respectively
[29, 36].
Regarding estimation of instantaneous energy expenditure (R-based script will be made available on request to the corresponding author), we first identified albatross activities at the instantaneous level along the foraging trip (see workflow in Figure
1). The two main activities (i.e., flying and sitting on the water) were identified based on the travel speed by using the threshold of 10 km h-1. Those locations with a travel speed above and below 10 km h-1 corresponded to flying and resting activities, respectively
[37]. Detailed tracking data showed that landing and take-off were characterised by elevated heart rate values, as well as those periods (i.e., 30 min) preceding and following landing and take-off
[13]. Therefore, we considered five non-flying activities (A: ‘landing’, B:’30 min after landing’, C: ‘resting’; D: ‘30 min before take-off’ and E: ‘take-off’) and five flying activities (‘flying’ 10, 30, 60, 120 and 720 min after take-off, corresponding to F, G, H, I and J activities) as described in
[13] (see an example in Additional file
2).
While energy expenditure during flight is usually considered when analysing optimal flying pathways of pelagic seabirds in relation to wind conditions, energetic cost of resting (i.e., sitting on the water), take-off and landing have been seldom considered (e.g.,
[14, 38]). However, we included the energetic cost of resting in our energy balance because albatrosses can spend on average 46.7% of their time on water (range: 24.6–68.3%, present study) whereas this percentage was higher during the night (average: 63.5%, range: 37.1-95.1%) compared to the day (average: 28.5%, range: 10.2–61.8%) and because the energetic expenditure of resting is nearly as costly as flying with favourable wind conditions
[13]. One limitation of our approach was that we were not able to provide different heart rate values for resting and sitting on the water while trying to locate, secure and swallow prey, provided that the latter provide higher heart rate values.
The effect of wind speed w on energy expenditure cannot be neglected since wind speed can have important implications for the energy budget during flying activities
[14, 38]. To account for the impact of w and the angle between flight and wind direction θ on energy expenditure, we adapted the flying cost function developed by
[14] to wandering albatrosses using field data from
[13]. The flying cost function was applied to flying activities (F to J in Figure
1a) in order to obtain energy expenditure values (i.e., heart rate; more details of flying cost development is provided in Additional file
3) (Figure
1b). Our flying cost function was valid since the relationship between the angle between flight and wind direction and energy expenditure patterns during flight were similar in both studies, even though they were based in different energy expenditure approaches (Additional file
3)
[13, 14]. Thus, the flying cost model was able to provide energy expenditure estimates based on two variables: wind speed w (ranging from 0 to 30 m s-1) and the angle between flight and wind direction θ (ranging from 0° to 180°, indicating that birds were flying with tail and head winds, respectively). The energy expenditure while flying was intermediate in two situations: in the absence of wind and when birds were flying with cross winds (light blue values in Figure
1b). From this intermediate reference level, energy expenditure decreased when birds were flying from cross winds to tail winds at increasing wind speed. On the contrary, energy expenditure increased when birds were flying from cross winds to head winds at increasing wind speed (Figure
1b).
Instantaneous heart rate values at 1-min resolution were converted to energy expenditure values based on the relationship between heart rate and oxygen consumption. This relationship was linear for incubating (resting) wandering albatrosses
[39], but could follow a power-curve when birds are engaged in locomotory activities (i.e., larger oxygen pulse conditions)
[40]. In fact, when other flying birds (e.g., wild geese) were active in a wind tunnel the relationship between heart rate and oxygen consumption was significantly different between walking and flying (i.e., power-curve relationship
[41]). This was also true for black-browed albatrosses Thalassarche melanophrys walking on a treadmill
[4, 42]. In the present study, we followed the power-curve relationship of black-browed albatrosses and included both basal
[39] and maximum values of heart rate for wandering albatrosses
[13] to obtain a mass specific power-curve relationship for the species:
where Oxygen consumption is in mLmin-1 kg-1.Then, oxygen consumption values were converted to energy units by assuming that 1 mL of oxygen is equivalent of 20.112 J
[4]. A mass specific relationship was used since heart rate basal values increase with body mass in wandering albatrosses
[39]. We acknowledge that further research would be needed to directly measure heart rate and oxygen consumption on flying wandering albatrosses to improve this relationship (c.f.
[41]), although this would be logistically and biologically difficult with present technologies.
Energy-budget model validation
We validated our energy-budget model (i.e., the assessment of the accuracy of predictions) by calculating the agreement between observed and predicted values. In the present study, we predicted the body mass change of wandering albatrosses by transforming trip net energy gain to mass units applying Eq. 2. The limitation of the present validation approach is that we needed complete foraging trips since body mass change is a reflection of the whole trip net energy gain. In order to robustly validate our modelling approach, we additionally used instantaneous energy expenditure estimates measured with the Doubly Labelled Water method (see below). Thus, we validated our energy budget model at two different temporal scales: at the foraging trip and instantaneous levels.
At the trip level, we used the mass gain measured by the birds equipped with stomach temperature pills and assumed that the trip net energy gain is a measure of albatross’ body mass difference between arrival and departure for the foraging trip, Eq. 2. Predictions of body mass change were also contrasted against an empirical distribution from the long-term tracking database of wandering albatross
[9, 43] for 97 independent individual (more details in Additional file
4).
Regarding validation at the instantaneous level, we contrasted our predictions of energy expenditure (based on heart rate values) against an empirical distribution of energy expenditure of wandering albatrosses measured by a different method (Doubly Labelled Water, DLW)
[44–46]. DLW provides energy expenditure estimates averaged over the measurement period which is normally restricted to a few days
[46]. In contrast, heart rate provides continuous measurement that can be used to estimate energy expenditure of specific activities
[13]. In order to pool DLW-based available data, we ensured (by means of ANOVA) that there were no differences between years (season 1982/1983 vs. 1998 for brooding: F
1,18
= 0.885, P = 0.359 and breeding stages (for 1998: F
1,17
= 0.021, P = 0.886). We expect that our heart rate (HR)-based estimates of energy expenditure for free-ranging albatrosses might be lower than DLW-based estimates
[47]. One of the best approaches to accurately validate predictions using heart rate methods is to simultaneously measure energy expenditure with HR and DLW in the same individual while foraging at sea. However, this has not yet been done in the field
[40, 48] showed that energy expenditure measurements of incubating wanderers did not significantly differ when using DLW or HR methods, even if the latter provided lower estimates. However, when marine predators are engaged in energetically more costly activities at sea DLW-based energy expenditure values could be overestimated due to technique assumptions
[47], providing higher values of energy expenditure than HR methods. These authors also suggest the possibility that HR methods could underestimate energy expenditure values
[47].
Finally, we compared the modelling output including ten detailed (fine-scale) activities (sensu[13]) with estimations under the common practice of using only the two wide-scale activities: resting and flying (e.g.
[49]). For that, we regrouped fine-scale activities from A to E as resting and from F to J as flying.
Coupling instantaneous energy-budget models and behavioural mode analysis
By coupling instantaneous energy-budget models with behavioural mode analysis, we were able to provide an energetic perspective to the characterisation of foraging strategies. We applied a new algorithm called Expectation Maximization Binary Clustering (EMBC) to obtain behavioural modes from direct analysis of movement trajectories. The EMBC algorithm fills a gap in movement trajectory segmentation procedures by reaching a good compromise between meaningful and easily interpretable behavioural segmentation and sound (and robust) statistical performance
[18]. As an unsupervised and non-intensive computing method, the EMBC algorithm is particularly suited for big data and large scale analyses where comparisons across species, sampling schemes, tracking technologies, and ecological contexts are looked for
[18].
The EMBC algorithm models behavioural modes as a multivariate Gaussian mixture
[18]. Here we considered the simplest behavioural space possible defined by two movement variables: speed and turning angle. The EMBC algorithm determines the maximum likelihood partition into four regions characterized by high and low values of each variable, in this case, for speed/turn values. This partitioned space can be then associated to stereotypic behaviours such as relocation (e.g., high speeds and low turns), extensive search (e.g., high speeds and high turns), intensive search (e.g., low speeds and high turns) and as resting (e.g., low speeds and low turn)
[18]. Intensive search mode is referred to negligible horizontal displacement (e.g., low speed) with active (e.g., high turning angle) searching behaviour. Thus, the EMBC algorithm classified each position with an instantaneous behavioural mode at 1-min resolution. Then, individual foraging strategies were defined by the percentages of these four stereotypic modes within the foraging trip and help identifying the main foraging strategy used by each bird, as well as secondary alternative strategies. According to previously described foraging strategies, those individuals showing high percentages of relocation, extensive search, intensive search and resting would be using foraging-in-flight (FII), area-restricted search (ARS), sit-and-wait (SAW) and resting (RES) strategies, respectively.
In order to group individual foraging strategies, we performed a hierarchical clustering analysis based on the relative duration (%) of each behavioural mode within a foraging trip using the Pvclust package, specifying the Euclidean distance and Ward agglomeration method
[50]. Pvclust calculates P-values for hierarchical clustering via multiscale bootstrap resampling and significant clusters with probability P ≥ 0.95 were extracted. After individual grouping, clusters were characterised by means of movement and energetic parameters. Movement parameters included both mean and maximum speed (m s-1), maximum range (i.e., maximum distance attained from the colony; km) and trip duration (h). Energetic parameters included daily energy expenditure (kJ d-1), daily energy gain (kJ d-1), daily net energy gain (kJ d-1), prey mean weight (g), prey weight variability (i.e., SD in g), number of prey per day, foraging efficiency and mass at departure (kg). Then, an ANOVA analysis (when normally distributed) or a non-parametric Kruskal-Wallis test was applied for selecting the most significant parameters characterising clusters. Significance was set at P < 0.1 and marginal significance at P < 0.2. Finally, we classified low, intermediate and high mean values of behavioural modes, movement and energetic parameters per foraging strategy to better illustrate clustering output.