Making overall dynamic body acceleration work: on the theory of acceleration as a proxy for energy expenditure


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1. The energetic costs of different behaviours are critical in modulating the behavioural ecology of free-living animals. Despite this, measurement of energy expenditure in the field has proved difficult.

2. A new method with broad application for field studies has been proposed for determining the rate at which animals expend energy, based on measurements of overall dynamic body acceleration (ODBA) through the attachment of miniature acceleration data-loggers. This technique is easy to implement and has the promise to be able to resolve energy expenditure with fine (sub-second) temporal resolution, making it the only method which promises to able to determine the cost of short-lived behaviours. Increasing evidence supports the validity of the approach although the rationale behind it is vague.

3. This study explores link between metabolic energy and acceleration by examining what is known about how muscular tissue converts metabolic energy to mechanical work via muscular contraction and how Newtonian physics facilitates a derivation of Power (the rate at which work is performed) from acceleration. The link between metabolic energy and acceleration appears to involve three discrete processes: (i) the ratio of mechanical work to metabolic work performed by a single muscle (mechano-chemical efficiency); (ii) the ratio of external and internal work performed (mechanical work of the limbs in relation to that of the centre of mass); and (iii) the ratio of inertial to de novo mechanical work. These processes may vary according to the animal’s mass, the medium in which it travels and its gait or behaviour.

4. Assessment of movement has limited application in defining non-movement energy expenditure such as that involved in specific dynamic action or non-shivering thermogenesis. However, this non-movement energy expenditure may often be modelled with reasonable confidence. The utility and appropriateness of the ODBA-energy expenditure method depends on a set of conditions, which we define and suggest should be assessed a priori.

5. This study explores the framework behind the ODBA-energy expenditure method to enable informed decisions to be made regarding the suitability for specific research questions addressed, as well as highlighting calibration needs.


The rate at which wild animals expend energy in relation to its acquisition (via feeding) determines how successful they are and, ultimately, whether they survive at all (Brown et al. 2004). Thus, quantification of energy expenditure is key to understanding issues such as life history (Hall, McConnell & Barker 2001), trophic flow (Lowe 2002), biogeography (McNab 2002) and behavioural strategies (Hinch & Rand 1998).

Initially, energy expenditure could only be approximated in the laboratory using direct and indirect calorimetry (respirometry) (e.g. Frappell, Blevin & Baudinette 1989), which often has little relevance to the field metabolic rate of wild animals (for example, see Tang et al. 2000). A commonly adopted method for determining the rate at which animals expend energy in the field uses doubly labelled water (DLW; Speakman & Racey 1988), which indicates how much total energy is expended over an integrated time period. Although there have been attempts to determine the costs of specific behaviours by examining time-energy budgets in DLW studies (Nagy, Siegfried & Wilson 1984; Costa & Prince 1987), such calculations suffer from biases (Wilson & Culik 1993) and are problematic to carry out due to difficulties in defining the conditions to which the wild animals were exposed to (Furness & Bryant 1996). In addition, the technique is not suitable for all taxa (Butler et al. 2004; Nagy & Costa 1980; but see Sparling et al. 2007). Heart rate (inline imageH), the other commonly used field method for determining energy expenditure assumes that heart rate increases as a function of increasing energy expenditure (Butler & Woakes 1984). inline imageH is commonly calibrated against inline imageO2 using gas respirometry and subsequently allows quantification of metabolic rate of animals fitted with heart rate loggers in the field. The major drawbacks of the inline imageH method are that fitting loggers is usually invasive (as loggers need to be implanted if they are to work under all conditions), and that other cardio-vascular processes may be associated with energy linked blood flow (Thorarensen, Gallaugher & Farrell 1996; Ward et al. 2002; Green et al. 2005).

A recent method for alluding to energy expenditure derives overall dynamic body acceleration (ODBA) as a proxy (Wilson et al. 2006) and appears less prone to the temporal limits inherent in the doubly labelled water or heart rate methods. The ODBA method proposes that, since the most (and in many cases the major) variable factor in modulating energy expenditure in many vertebrates is movement (e.g. Tatner & Bryant 1986; Boisclair & Siros 1989; Karasov 1992), measurement of body acceleration should correlate with energy expenditure (Meijer et al. 1989; Bouten et al. 1994; Wilson et al. 2006; Fahlman et al. 2008; Halsey et al. 2008, 2009b).

Overall dynamic body acceleration can be readily measured in animals by external attachment of a tri-axial acceleration logger. Importantly, laboratory work on a wide variety of mammals and birds of differing sizes exercising in respiration chambers show linear fits between inline imageO2 and ODBA with r2-values in excess of 0·85 (Halsey et al. 2008, 2009b) so ODBA does indeed appear to be a good proxy for metabolic rate. The application of ODBA as a measure of energy expenditure is so new, however, that, unlike the heart rate or doubly labelled water methods, its rationale and assumptions have not been explored in detail. This may be due to the difficulty in associating the physics of acceleration with the chemistry of energy expenditure based on adenosine triphosphate (ATP).

This study attempts to understand why ODBA correlates so well with oxygen consumption in laboratory trials. We explore the link between energy consumption and body acceleration, in order to highlight assumptions and variability in the relationship. Theoretical considerations are discussed in relation to some scenarios encountered during the field application of the method and suggestions are given as to how potential problems may be avoided with appropriate calibration against inline imageO2 and the incorporation of additional sensors into the recording unit.


Movement-related energy expenditure

In the physical sense, energy is the potential to do work. In the biological sense, energy is stored in the form of chemical bonds (e.g. Witter & Cuthill 1993), and is employed in, among other things, executing movement. To do this, animals convert chemical energy to mechanical work through muscular contraction (in all animals but the smallest) (Schmidt-Nielsen 1997). The rate at which this mechanical work is conducted (and therefore energy used) is the mechanical power (P). The ability of ODBA to act as a proxy for energy expenditure depends, in part, on the link between acceleration produced by muscular contraction and mechanical power.

Clearly, acceleration cannot be used to calculate the mechanical work of objects such as a car during steady level locomotion (and hence the rate at which its engine consumes energy, cf. Fig. 1a). Although net mechanical work is also zero during steady level animal locomotion, mechanical work is conducted within each single stride (Biewener 2006). Animals cannot power their movements in the same fashion as a car and rely on continual acceleration from their limbs which is manifest in the movement of the centre of mass (CoM) in relation to the environment (Fig. 1b).

Figure 1.

 Schematic figure showing major differences in acceleration patterns of a car (a), only displaying accelerations in the surging acceleration (broken black line) while the car is increasing in velocity, and not during steady velocity. A runner on the other hand experiences accelerations and decelerations throughout the gait cycle (b), resulting from the up and down movement of the centre of mass, which is manifested in the heaving acceleration (grey line), even during steady-state locomotion. The runner only experiences significant surging acceleration while increasing in velocity, similar to the car. In the case, not much motion is expected to be registered in the swaying dimension (broken grey line), but this may vary depending on animal type (see main text).

The continual loss of energy to the environment, e.g. ground deformation, movement of fluid (Alexander 2003) necessitates the continual replenishment of this lost energy with de novo mechanical work, in order to maintain a net mechanical work of zero (Fig. 2). This change in energy status is subsequently manifest in changes in acceleration, which can therefore be related to the power of the CoM (PCoM).

Figure 2.

 In order to maintain net mechanical work of zero, energy losses to the environment have to be balanced by the production of de novo mechanical work. The interchange between one energy state and the next is manifest in accelerations and decelerations, due to the constraints of the locomotory systems of animals.

The interdependence of acceleration and power

The relationship between ODBA and energy expenditure relies on the physical principles of Newtonian mechanics. Newton’s laws of motion explain how objects react in response to external force which, in our case, relate to the voluntary movement of the animal in relation to its environment. Acceleration (a) is the first derivative of velocity (V) with regard to time (t) and subsequently denotes change in velocity (ΔV) over time (Δt) according to:

image(eqn 1)

Accelerometers measure the instantaneous acceleration at any sampling point with regard to an inertial frame, i.e. they quantify an instantaneous change in velocity (French 1971).

Newton’s first law of motion states that the natural state of an object is at a constant velocity and any change in such requires an external force to change this motion. Hence, any change in acceleration is proportional to a force acting on the moving object. Such a change in motion, in an inertial system, is the Mechanical Work (W) performed by the object. Mechanical work is the amount of force (F) exerted over a given distance (d) so that:

image(eqn 2)

Force, in turn, can be derived using acceleration (a) and mass (m) via Newton’s second law of motion:

image(eqn 3)

Power (P) is the rate at which work is conducted and therefore the mechanical equivalent to energy expenditure.

image(eqn 4)

We can thus substitute work in Eqn 4 for Eqns 2 and 3 and simplify to,

image(eqn 5)

Since acceleration denotes a change in velocity over time (eqn 1) and velocity is distance over time, v can be derived from Eqn 1 through integration over time t:

image(eqn 6)

Thus, measurements of acceleration can determine the mechanical power performed via Eqns 4 and 5:

image(eqn 7)

Consequently, the magnitude and duration of any acceleration are proportional to the mechanical work performed, assuming that the object in question maintains a constant mass.

Actively powered animal locomotion therefore features accelerations and decelerations, which may be used to estimate PCoM (given constant mass). Equation (7), however, requires knowledge of vt=0 (this value refers to the movement of the CoM, not the mean travelling speed) in order to calculate the velocity of the CoM accurately. Although the assumption of vt=0 = 0 has resulted in good estimates of PCoM for human walking (Meichtry et al. 2007) more ‘dynamic’ behaviour, such as gallop of a horse (Equus caballus) requires an estimate of vt=0 (Pfau, Witte & Wilson 2005). The proportion of mechanical work estimated by acceleration (and hence ODBA) therefore depends on vt=0 and its associated inertial energy. This ratio depends on the animal in question and its associated gait and is dealt with later in the study.

Derivation of ODBA

Overall dynamic body acceleration is a single, integrated measure of body motion in all three spatial dimensions and therefore requires that total acceleration be recorded in the three corresponding axes (see Fig. S1, Supporting Information, Halsey et al. 2009a). Body acceleration is measured by attaching an electronic data-logger with a tri-axial acceleration transducer to the trunk of an animal, so that acceleration is recorded close to the animal’s CoM, arising from the movement of the limbs (Shepard et al. 2010). The sampling frequency must be adequate to resolve the changes in velocity associated with individual behaviours. In studies to date, the minimum sampling frequency has typically been around 5 Hz (e.g. Wilson, Shepard & Liebsch 2008), though this should be a function of the rapidity of the study animal’s movements (cf. Goldbogen et al. 2006; Shepard et al. 2008), as larger animals generally have lower limb-stroke frequencies (Sato et al. 2007). However, for the sole purpose of calculating ODBA, even sampling frequencies as low as 1 Hz provide reasonable estimates, even in small animals (Halsey et al. 2009a).

The total acceleration recorded in each axis is the result of two components; a static acceleration component, which is the result of the earth’s gravitational pull and has a vectorial product of 1 g (9·81 m s−2) across axes, and a dynamic component, which results from animal movement and varies in magnitude according to the perceived motion (Shepard et al. 2010). ODBA uses the dynamic component, as only the dynamic acceleration is a function of the animal’s movement, the static component must be removed from the raw acceleration data (Fig. 3).

Figure 3.

 Graphical representation of the determination of ODBA from total acceleration. Data shown are of a Caribbean reef shark (Carcharinus perezi). (a) Gravitational acceleration is approximated by the smoothing of total acceleration using running-means (Shepard et al. 2008, 2010) or low-pass filters (Sato et al. 2003). (b) Dynamic acceleration (due to the oscillating signal due to tail-beat primarily in the swaying acceleration) is subsequently calculated by subtracting the gravitational acceleration from the total acceleration. The absolute acceleration values are then determined (black arrows) and added across all three spatial components to yield ODBA (grey arrows). The work performed is approximated by the mean ODBA (c) over a given time (cf. eqn 7).

The static acceleration can be approximated by applying a running mean (Wilson et al. 2006) or other smoothing function (cf. Sato et al. 2003) to the total acceleration recorded for each axis. The dynamic acceleration is then determined by subtracting the static component from the total acceleration (Wilson et al. 2006; Shepard et al. 2008). The ODBA is the sum of the absolute values of the dynamic accelerations from all three axes (Wilson et al. 2006). Although acceleration is a vectorial quantity, ODBA considers the three orthogonal planes (axes) independently, so that work is represented as three separate straight-line motions. Work can only be derived by acceleration if the motion path is linear and individual treatment of the three axes ensures this to be the case (French 1971). Indeed, most three-dimensional problems in Newtonian physics can be solved by separate treatment of the different components of a vector and the same principle applies to acceleration (French 1971). This, however, requires orientation of data-loggers to be consistent between individuals, as otherwise ODBA estimates will change according to orientation off-set between individuals. The same also applies to movement in varying dimensions, where perceived work increases. Thus, in cases where accelerometers cannot be accurately placed on the animal, or movements occur in a variable manner and along various planes, dynamic body acceleration calculated using the vectorial product (McGregor et al. 2009) may prove a more accurate predictor of activity, despite violating the assumption of linear motion outlined previously. No studies to date have compared VeDBA (vectorial dynamic body acceleration) and ODBA, despite this being an interesting and very important avenue for future investigations. As both the magnitude and the duration of accelerations are incorporated in calculations that derive ODBA (Fig. 3), measurements of acceleration are proportional to mechanical power, given the integration constant vt=0 can be approximated (cf. eqn 7).

ATP and mechanical work

For simplicity, we define muscle contraction as being geared either towards the production of work (efficiency) or the production of force (economy) (Goldspink 1977), though in fact this represents a continuum (see Alexander 2003). Biological systems, unlike physical systems, can use energy to generate force without any associated movement, for example when an organism bears a load. Clearly the ability of ODBA to predict energy expenditure is only linked to the production of movement (but see Green et al. 2009) so, in order to understand potential weaknesses in ODBA-derived energy expenditure, the interaction between movement and force generation needs examination.

Catalysed by the hydrolysis of ATP (Huxley & Simmons 1971), muscle filaments shorten, which produces movement. Under these conditions, there is a clear link between chemical and mechanical energy. However, during isometric contractions, muscle force is generated rather than movement (and therefore acceleration) (Goldspink 1977). The ratio between the mechanical power Pmech produced (the rate at which Wmech is performed) in relation to the energy expended (inline imageO2) is termed the mechano-chemical efficiency (η; cf. Alexander & Goldspink 1977).

image(eqn 8)

A key consideration in assessing the utility of ODBA in relation to any behavioural pattern is its associated mechano-chemical efficiency, as variation in η will result in a corresponding variation in the relationship between ODBA and energy expenditure. Where muscles are used primarily as force generators, such as a crab breaking open a mussel shell (cf. Dickinson et al. 2000), η will be almost zero, and ODBA is not able to estimate inline imageO2. Equation (6) assumes that the subject incurs no changes in mass between the initial calibration and field estimates. This assumption is clearly not valid in all cases; animals carrying loads (such as offspring or prey) may therefore expend more energy than is estimated by the acceleration method. This error should be proportional to the % change in body mass (cf. eqn 7, assuming all other factors remain constant) and its relevance will thus depend on the animal in question.

Since muscle has to supply mechanical power at varying rates, it is relevant how η is expected to change with increasing mechanical power output. In fact, rather than incurring changes in efficiency when increased power output is required, more muscle is recruited so that the strain remains constant for any given ATP cross-bridge thus not substantially changing the efficiency of the working stroke (Rome & Alexander 1970; Rome et al. 1988; Alexander 1991). However, in some systems, differences in the required speed of contraction may be fulfilled by animals employing different fibre types (i.e. slow-twitch to fast-twitch). This has been most widely documented in fish (Rome & Sosnicki 1990), where burst and cruising speeds are associated with white and red muscle fibres, respectively. Where there is a large difference in mechano-chemical efficiency (cf. eqn 8) between fibre types (Rome & Alexander 1970) it may be necessary to fit a two-part calibration regression between ODBA and energy expenditure.

Mechanical work: from single muscles to whole organisms

Measuring the body acceleration (being a measure of work performed by the CoM) is not directly equivalent to the work performed by the entire muscular system. Complex systems have many moving parts, and the overall mechanical work consists of the mechanical work conducted by these parts in relation to the CoM (Fedak, Heglund & Taylor 1982).

Any conservation of motion (as represented by vt=0) through steady locomotion will cause a change in the estimate of muscular work and subsequently energy expenditure. Steady level locomotion always has a net vt=0 > 0 (specifically greater than the travelling speed) which is only manifest in the surging acceleration (unless the animal travels sideways). The primary determinants of muscular work, however, are manifest in the other dimensions (see Fig. 3) where during the movement cycle vt=0 = 0 applies. For instance, the tail-beat of a shark is represented by oscillations in the swaying dimension, and at the point of maximum amplitude of the tail-beat, the segment of the shark’s tail to which the device is fixed will have a velocity of 0 (and hence a dynamic acceleration of a = 0, cf. Fig. 3). The same scenario applies to birds (during the wing-beat cycle) and terrestrial animals at the point of each stride where the CoM is at its lowest vertical position (just prior to push-off by the limb).

Indeed, whereas a single muscle contracts along a single plane, the movement of a limb is the resultant product of many muscles contracting in concert, many of which have a stabilizing function (Alexander 2003). This produces a resultant vector (responsible for the limb movement) but each muscle contracts along only one, specific dimension, and thus contributes its own force element to the overall resultant vector. The energy expenditure of each of the muscles is, therefore, proportional to its own vectorial component so that the sum of the energy expenditures of all muscles should be proportional to the sum of the vectorial components (the overall dynamic component) even though the resultant vector for the movement must be less. This indicates that the power requirements may be more adequately resolved when summed. However, this does not take the variability of orientation of the movement in relation to the alignment of the logger, which may vary. Thus, device orientation in relation to the primary direction of movement is important when considering potential errors in estimates of whole body work.

Inertia vs. mechanical power

The last link in the chain between chemical energy and ODBA is the proportion of kinetic energy conserved through inertia during the movement cycle (represented by the integration constant vt=0 in eqn 7). These effects vary according to circumstances discussed in the following sections. Thus, the slope of the ODBA/inline imageO2 relationship represents the mechanical power performed by the CoM that is attributed to changes in acceleration (PAccCOM) in relation to energy expended (the ‘apparent efficiency’ξ; Figs 4 and S2, Supporting Information):

image(eqn 9)

The link between energy in the form of ATP can therefore be traced to ODBA in three discrete steps, each with their own theory and associated assumptions (see Fig. S2, Supporting Information). These can subsequently be used to evaluate the requirements for ground-truthing, or alternatively help allude to potential errors, where respirometry is not feasible.


Locomotion constitutes a highly variable part of the time budgets of animals (Garland 1983), from continuous (e.g. pelagic fish) to intermittent (e.g. passerine birds). Despite the often minor contribution of locomotion to time budgets, the large cost of moving the whole body mass amounts to a significant contribution to animal energy budgets (e.g. Bryant 1986; Birt-Friesen et al. 1989) and therefore requires specific attention here.

Thus far, only Halsey et al. (2008) have investigated the relationship of ODBA and inline imageO2 in a range of species. They concluded that the relationship of ODBA and inline imageO2 is different for different types of animals (ranging from bipeds to quadrupeds, waddlers and inverted-pendulum walkers) and that the relationship is affected by the mass of the animal. This is expected as both resting metabolic rate (RMR) changes according to body mass (Peters 1983) and mass determines the amount of work performed in relation to measured acceleration (cf. eqn 7). However, beyond this, Halsey et al. (2008) report differences in the ODBA/inline imageO2 relationship for the diverse group of animals they studied and their various locomotory modes. Although differing locomotory modes do not differ at the muscular molecular level, as common rules apply regarding force/movement generation (Hill 1938), the biomechanics differ substantially between different media (terrestrial vs volant and aquatic) and animal groups (e.g. hopping vs. walking, caudal propulsion vs. pectoral propulsion). Thus, the ODBA vs. inline imageO2 relationship is expected to vary according to whether the propulsive system depends on fluid forces (flying, swimming) or gravitational forces (walking, hopping) although the ODBA/inline imageO2 relationship may be similar for animals with similar body plans and utilizing the same propulsive modes (after correction for mass effects). As muscular contraction and limb movement occurs over a predictable path (i.e. lateral movement of the tail of a fish or dorso-ventral movement of a bird’s wings), loggers should be aligned with the major plane over which these contract, to reduce orientation error (see Derivation of ODBA).

Terrestrial locomotion

Terrestrial locomotory cycles are generally dominated by two phases, negative work (motion of body being slowed during limb making contact with the ground) and positive work (the push-off). This is represented by both acceleration and deceleration phases in the heaving dimension and is manifest as such by the tri-axial accelerometers (cf. Fig. 3, Halsey et al. 2008). Here, the use of absolute acceleration values in the mathematical derivation of ODBA ensures that both phases are indeed represented as energy expenditure, even if the two processes are characterized by different mechano-chemical efficiencies.

Pendula and springs

There are a number of modes of terrestrial locomotion, which can be characterized by how energy is interchanged to create motion. Most mammals rely on some form of inverted-pendulum effect in the heaving dimension (Cavagna & Kaneko 1963), whereas many species of bird rely on a swaying motion (waddling) to transfer momentum (Pinshow, Fedak & Schmidt-Nielsen 1977). In both cases, the principal of a moving pendulum transfers energy from one step to the next involving the interchange of kinetic and potential energy (Cavagna & Kaneko 1963; Heglund, Cavagna & Taylor 1982). This is potentially problematic in relating ODBA to inline imageO2 because the energy transfer during the pendulum effect (which does not equate with energy loss) will be accompanied by substantial changes in acceleration over the cycle. This is unimportant if the energy re-use during the pendulum process always equates to a specific percent of the total energy used because calibration of ODBA against inline imageO2 will define this. Part of the pendulum effect will also incorporate energy recovered from the elasticity of tendons (acting as springs), which varies substantially according to animal type (cf. Alexander & Bennet-Clark 1977). The ODBA/inline imageO2 relationship appears primarily linear for terrestrial locomotion (Wilson et al. 2006; Halsey et al. 2008, 2009b), which is expected due to the generally linear increase of mechanical work with velocity and inline imageO2 (Heglund, Cavagna & Taylor 1982; Taylor, Heglund & Maloiy 1982) although we expect that it may be modulated by the gait issue (see above) so that the slope of ODBA against inline imageO2 (ξ) may get better fits using e.g. two- or even three-part calibration equations (Halsey et al. 2008).

Effects of terrain

Beyond this, we would expect, in the wild, that substrate would affect the recovery of energy by tendons because substrate type can increase or decrease the economy of travel, often without any changes in the movement by the subject (Kerdok et al. 2002). Although this effect, under normal circumstances, is expected to be minor, extreme cases, where animals travel on sand or snow might have a significant impact on estimates of energy expenditure using acceleration. Finally, the relationship between ODBA and mechanical power may vary if the animal moves up or down an incline (Halsey et al. 2008). Moving up an incline, muscles are required to perform more expensive positive work, due to the effects of gravity. Whereas, moving down an incline, animals perform more negative work (Gottschall & Kram 2005). As both these processes are characterized by differing η, differing regressions are expected for varying slopes. Remotely sensing the slope an animal is travelling on, is possible by incorporating a barometer into the acceleration-recording unit (e.g. Wilson, Shepard & Liebsch 2008) and otherwise, accelerometer-derived pitch angles (Sato et al. 2003) may help define this.


The cost of locomotion in swimming animals is determined by the loss of energy to their fluid environment and the cost of maintaining dynamic equilibrium by resisting buoyant forces. The forces resisting motion of aquatic organisms therefore are different to those of terrestrial animals and are thus subject to different assumptions and problems.

Drag and power

Few data are currently available for aquatic animals, and the exact shape of the relationship between ODBA and energy expenditure is unclear (Fahlman et al. 2008; Gleiss et al. 2010). Fahlman et al. (2008) obtained linear relationships for Stellar Sea Lion (Eumetopias jubatus), whereas Gleiss et al. (2010) suggested drag and associated thrust scale (and therefore work performed) with the cube of the speed (Boisclair & Tang 1993), thus yielding a power function for the relationship between ODBA and inline imageO2. However, if ODBA scales linearly with mechanical work, the resultant relationship should be linear, given that mechanical work equals metabolic work (above RMR). Swim-tunnel data from sockeye salmon (Oncorynchus nerka) suggest the relationship to be linear (Clark et al. 2010); however, acceleration data were not presented as dynamic body acceleration. Some aquatic animals may also travel using various gaits (depending on speed travelled) although these gaits equate with using different propulsive systems (e.g. parrot-fish travel by pectoral as well as caudal fin propulsion) rather than a change in the organization of a single propulsive system such as occurs during terrestrial locomotion. Such changes in locomotory modes will probably produce differing ODBA/inline imageO2 relationships and hence require separate calibration.


Beyond swim speed, aquatic animals with air-filled spaces (lungs, swim-bladders, etc.) may have to invest substantial amounts of energy to counteract buoyancy, which changes with depth (e.g. Lovvorn, Jones & Blake 1991). Given that this involves active swimming via modulation of stroke frequency and amplitude (Tanaka, Takagi & Naito 2001; Watanuki et al. 2003), ODBA is predicted to vary with depth. Indeed, Wilson et al. (2006) showed that ODBA calculated for imperial cormorants descending to various depths to be directly proportional to upthrust experienced by the birds.


It is not immediately clear what form the relationship between ODBA and inline imageO2 will take for flying animals and how the slope of any such relationship will compare to that of terrestrial or aquatic locomotion. Given that continuous flapping flight costs are often constant over a range of speeds (Engel, Biebach & Visser 2006), the ‘relationship’ might essentially consist of a single point for flight and another corresponding to non-flight RMR. Many animals modulate flight effort by gliding between bursts of flapping (Rayner et al. 2001) and may indeed reduce flapping flight to virtually nothing (Pennycuick & Scholey 1984). This scenario is markedly different from flapping flight, not only because gliding flight is dominated by isometric contraction, but also because it uses much less power (Weimerskirch et al. 2000). ODBA is poorly equipped to determine metabolic rate from isometric contraction and is likely to be affected by air turbulence rather than animal-initiated ODBA. The extent of the error on both these counts may be apparent after considering the relationship between cumulative ODBA and energy expenditure using doubly labelled water on e.g. procellariiform foraging trips (cf. Furness & Bryant 1996).

As with terrestrial animals climbing slopes or carrying load, ODBA may vary according to powered climb rate, load and, additionally, altitude. Experimental work using e.g. doubly labelled water and multiple parameter regressions on wild birds will clarify the extent to which the ODBA/inline imageO2 relationship is altered by such parameters.

Differing behaviours

Although a large fraction of an animal’s energy budget can be accounted for by locomotion, simple small movements may also make up a substantial proportion of an animal’s energy budget (Karasov 1992) that may be accessed by ODBA and may be subject to varying conditions.

Based on the chemical requirements of mechanical work, it is reasonable to assume that ODBA can provide a proxy for the energy requirements of movements, including those that characterize behaviours other than locomotion. However, since calibrations of ODBA against energy expenditure have mostly been conducted using animals exercising on a treadmill in a respirometry chamber (Wilson et al. 2006; Green et al. 2009; Halsey et al. 2009b), ODBA/MR relationships will depend on ξ for those particular conditions. Activities not related to locomotion, such as preening, scratching or displaying may be characterized by a significantly different value of ξ. Despite this, Green et al. (2009) demonstrated that in bantam chickens (Gallus gallus), metabolic power engaging in a range of behaviours could be determined with relatively high predictive power using the acceleration method (in their case bi-axial), especially by using two-part regressions which separate small motor activity from major motor activity. The behaviour of the chickens (unlike that of a galloping horse) are probably associated with minimal inertia (and hence low vt=0) as there is little conservation of motion, even during steady locomotion. Thus, the potential variance of vt=0 between different behaviours is expected to be low and the acceleration method is not subject to large variance. Yet as behaviours other than locomotion occur over less predictable orientation planes, which presumably may be quite variable in comparison to locomotion, it is possible that errors associated with device orientation in relation to the plane of muscular contraction may result in variable and thus greater error compared to steady locomotion. Thus, in such cases VeDBA may prove more appropriate.

More work of this nature is critical to assess the robustness of the ODBA method beyond animal locomotion although respirometric problems in achieving steady-state conditions for such transient behaviours are appreciable. Unfortunately, these limitations for ground-truthing energy expenditures are unlikely to be resolved soon so that the value of ODBA for transient behaviours cannot be put to the test. In general though, if differing behaviours and even differing locomotory types (such as a cormorant walking or diving or flying), give rise to different ODBA/inline imageO2 relationships, special software could identify behaviour from the acceleration signals (Grundy et al. 2009; Sakamoto et al. 2009) before applying the appropriate conversion to inline imageO2 for any period of time. The amount of work to derive the different relationships is, however, extensive, so it is to be hoped that different behaviours, at least, do not have markedly different ODBA/inline imageO2 relationships from each other (cf. Halsey et al. 2008; Green et al. 2009).

Movement and energy expenditure: how and when is it important?

The total metabolic rate of an animal can be attributed to a number of components, not all of which are related to mechanical work. Activity can constitute the predominant component of energy expended, accounting, for instance, of 67% and 56% of the daily energy expenditure (DEE) of non-reproducing mammals and lizards, respectively (Karasov 1992; Christian, Baudinette & Pamula 1997). The percentage contribution of activity is obviously greater during active (awake) periods of animals because terrestrial mammals, for example, expend energy due to movement at an approximate rate of 4·1 × standard metabolic rate (Karasov 1992). Ultimately, the percentage contribution of movement-associated metabolic rate to the total metabolic rate is highly variable and depends on the ecology of the animal in question (Garland 1983; Karasov & Anderson 1984; Aubin-Horth, Gingras & Boisclair 1999). Accurate energy budget construction based on ODBA necessitates that we predict all parameters contributing to DEE.

Metabolic rate at inactivity

Standard metabolic rate can be derived from extensive data in the literature.(see, e.g. Aschoff & Pohl 1970; Clarke & Johnston 1999) and this constitutes the point of intercept of ODBA/MR regressions (although in terrestrial animals this includes postural costs, as well as fluctuations of internal muscular work, such as peristalsis during digestion; see inactive metabolic rate (IMR) in Fig. 4, cf. Halsey et al. 2008). It has to be noted, however, that simple allometric prediction may have substantial error as intraspecific differences may be substantial due to varying physiological state (e.g. Portugal, Green & Butler 2007). Thermoregulation can also be a significant component of DEE (e.g. 40–60% of a small bird’s DEE; Wolf, Wooden, & Walsberg 2000) but estimates of this could be obtained using known relationships between metabolic rate and temperature and incorporating temperature transducers with the accelerometer loggers (cf. Wilson, Shepard & Liebsch 2008), however, it might be necessary to measure the temperature below the layer of insulation, which can be dramatically different to the exterior temperature.

Figure 4.

 Relationship of ODBA and inline imageO2 for five great cormorants (Phalacrocorax carbo) reported by Wilson et al. (2006). Overlaid are the two components of the regression: namely apparent efficiency ξ = ΔODBA/Δinline imageO2 and inactive metabolic rate (IMR). Any scaling of ODBA will subsequently have to manipulate these coefficients. Indication as to the trends in relation to major variables (such as mass, temperature and behaviour) are given in the main text.

Metabolic rate and temperature

How ODBA relates to environmental temperature is not straightforward because animal metabolic rate increases with temperature in ectotherms and increases outside the thermo-neutral zone in endotherms (Clarke & Johnston 1999; Gillooly et al. 2001), which presumably results in a change in the intercept of the ODBA/MR relationship (the point of IMR –Fig. 4). Estimates of the extent of this change can be derived from temperature scaling coefficients which are available for most taxa (e.g. Clarke & Johnston 1999; but see Green et al. 2009). Changes in the slope of the ODBA/MR relationship are more difficult to predict because activity is thermogenic and so may mitigate against non-movement thermogenesis at temperatures below the thermo-neutral zone (Wilson & Grémillet 1996; Chai, Chang & Dudley 1998; Lovvorn 1999). The degree to which activity will substitute thermogenesis is variable, ranging from undetectable to significant substitution (Lovvorn 2007). The opposite can be the case at temperatures above the thermo-neutral zone where animals incur higher energetic costs at the point of IMR and any activity beyond this produces an additive heat dissipation problem. These effects are also expected to vary significantly depending on body size due to surface area/volume ratio changes and the resultant higher thermal inertia of larger animals (Peters 1983). Endotherms generally have stenothermic muscular temperatures but ectotherms may experience changes of over 10 °C over short temporal scales which affect mechano-chemical efficiency (Smith, Barclay & Loiselle 2005) and thus how ODBA scales with temperature. Other temperature-dependent physiological processes complicate the issue (Dickinson et al. 2000), so that how ODBA relates to temperature in ectotherms is currently best examined in a proper experimental context.

How well does ODBA work?

Overall dynamic body acceleration as a proxy for metabolic rate is expected to have its limitations, for the reasons outlined above, yet it allows us to quantify the part of the energy budget that has been, to date, the most difficult to quantify; that of movement. Overall, the studies relating inline imageO2 to ODBA to date (Wilson et al. 2006; Fahlman et al. 2008; Halsey et al. 2008, 2009b; Green et al. 2009) make it seem extremely promising as a method that is uncomplicated to implement and calculate and, above all, one that has the potential to remove the temporal limits for the determination of energy expenditure so that even fleeting or rapidly changing behaviour may be taken into account. Indeed, the full potential of the temporal resolution of accelerometers can only be conclusively proven when physiologists are able to measure metabolism at relevant temporal scales. In the meantime, we see no reason why every stride, whose costs will be a calculable fraction of the total number of strides in a steady-state respirometric calibration, should not pertain to that fraction of the metabolic energy used by muscles for the relevant period. Transient behaviours, for example the acquisition of food and the avoidance of predation, may play substantial roles in animal fitness, so an ability to approximate their costs may prove pivotal in understanding limitations vs. gains. Indeed, ODBA works best when animals are active, incurring increasing error as motor activity decreases (Green et al. 2009).

In this work, we have highlighted a number of sources of potential variability, although the degree to which these will affect the accuracy of the method and under what circumstances still needs further work. The issue of data processing in particular now requires direct comparison of summed and vectorial acceleration data under various circumstances to test on a case-by-case basis which approach is superior. Our discussion could be used to inform and guide future calibration procedures to build a thorough understanding of the limitations of the method. Since the ODBA approach is grounded in physics, future work should focus on attempting to scale the relationships between individuals and species based on the many principles presented in this study (see Fig. S2, Supporting Information). We would hope that such work might uncover universal rules for the scaling of the ODBA/metabolic rate relationship (Halsey et al. 2009b) and thus greatly simplify the ease with which this technique may be implemented.


We would like to thank two anonymous referees whose comments have greatly improved this manuscript. A.C.G. is supported by a Swansea University Research Fees Scholarship and a Wingate Foundation Scholarship. E.L.C.S. is funded by an NERC studentship (award number NER/S/A/2005/13416A). Device development was supported by a Rolex Award for Enterprise, awarded to R.P.W. Reef Shark data were collected in Collaboration with the Wildlife Conservation Society and Rachel Graham.