An animal's maneuverability will determine the outcome of many of its most important interactions. A common approach to studying maneuverability is to force the animal to perform a specific maneuver or to try to elicit maximal performance. Recently, the availability of wider-field tracking technology has allowed for high-throughput measurements of voluntary behavior, an approach that produces large volumes of data. Here, we show how these data allow for measures of inter-individual variation that are necessary to evaluate how performance depends on other traits, both within and among species. We use simulated data to illustrate best practices when sampling a large number of voluntary maneuvers. Our results show how the sample average can be the best measure of inter-individual variation, whereas the sample maximum is neither repeatable nor a useful metric of the true variation among individuals. Our studies with flying hummingbirds reveal that their maneuvers fall into three major categories: simple translations, simple rotations and complex turns. Simple maneuvers are largely governed by distinct morphological and/or physiological traits. Complex turns involve both translations and rotations, and are more subject to inter-individual differences that are not explained by morphology. This three-part framework suggests that different wingbeat kinematics can be used to maximize specific aspects of maneuverability. Thus, a broad explanatory framework has emerged for interpreting hummingbird maneuverability. This framework is general enough to be applied to other types of locomotion, and informative enough to explain mechanisms of maneuverability that could be applied to both animals and bio-inspired robots.
An animal moving through its environment makes changes in course to maintain stability, avoid obstacles and hold direction towards a goal. These changes in speed and direction define complex locomotor behaviors, commonly called maneuvers (Dudley, 2002). Despite the universality of maneuverability in all mobile organisms, it has been difficult to develop and test hypotheses about complex locomotion. The central challenge to studying maneuverability is that the behavior is highly dynamic and variable. That is, an individual's expression of maneuverability can vary widely from one moment to the next, making maneuverability more difficult to quantify than other, more stable biological traits, such as body size. Dynamic traits such as maneuvering behaviors are also sensitive to perceived risks, rewards and social challenges from other organisms or stimuli. Although such effects can never be completely eliminated – indeed, they may be of interest – a standardized measurement environment is necessary to determine the sources of variation for maneuverability. Once these sources are identified, it is possible to investigate the physiological and biomechanical bases of maneuvering performance. Possible applications include the bioinspired engineering of robots and new treatments for locomotor impairment in humans. Knowledge of how an animal's morphology and physiology influence maneuverability is also required to determine how selection for some of the most critical behaviors – such as competition, mate displays, prey consumption and predator avoidance – have shaped ecology.
Burst muscle capacity
Maximal power output of a particular muscle or muscle group.
A repeatable combination of distinct simple maneuvers that can occur sequentially, or with overlap. A complex maneuver is defined by the temporal sequence of translation and rotation.
A change in a single component of translation or rotation.
Inter-individual differences in performance that result from motor learning and practice, whereby the level of performance of a given behavior increases with its repeated use and practice, leading to increased specialization.
Rapid and reversible changes to the size, area or shape of the wings during flight.
Rotation about the heading angle of a body.
Here, we focus on maneuvering in hummingbirds (Fig. 1, Movie 1). We have been studying hummingbird flight because their maneuvers are impressive and easy to observe, even within laboratory environments (Hedrick et al., 2009; Clark, 2011; Segre et al., 2015, 2016; Dakin et al., 2018). Considering how a hummingbird makes turns also illustrates the fundamental challenges to studying maneuverability: there are different mechanisms to accomplish the same or similar maneuvers. For example, a turn in place can be accomplished through yaw torque (see Glossary) or through rolling an upright body (Clark, 2011). Larger wings could be beneficial for a yaw turn if the animal can generate a strong difference in left–right force production (Dakin et al., 2018). However, larger wings could be detrimental for roll if the drag produced is too high, and the turn is slowed. Thus, the morphological features that facilitate one type of maneuver may hinder the performance of a different maneuver (Segre et al., 2015; Dakin et al., 2018). Further complicating matters, hummingbirds can make substantial but transient increases to their aerodynamic power output (Chai et al., 1997; Chai and Millard, 1997), which can, in principle, allow them to compensate for otherwise inefficient morphology with a burst effort.
In this Commentary, we argue that rigorous tests of inter-individual variation are needed to understand maneuverability and other highly dynamic traits. We show how studies of voluntary behavior can leverage large sample sizes to provide potential insight into maximal performance, even when maximal performance has not been measured. We next explain why it is useful to distinguish between simple maneuvers (see Glossary) that are governed largely by physical constraints, and complex maneuvers (see Glossary) that involve behavioral choices and skill (see Glossary). An outcome from our work on this topic is that simple maneuvers can be further classed as either translational or rotational movements, whereas complex maneuvers often combine translation and rotation. Complex maneuvers can combine these features in parallel or in series, and we provide detailed description of two specific types of complex turns exhibited by hummingbirds. We then reinterpret previous work on body and wingbeat kinematics in terms of this geometric framework. We conclude with a discussion of how the grouping of maneuvers into these three categories (simple rotations, simple translations and complex turns) can be applied to other animal groups and other types of locomotion.
Big data and individual variation
The first step in the study of any dynamic behavior is to determine whether the measurements are repeatable in the statistical and biological sense. That is, can some of the measured variation in maneuverability be attributed to differences among study subjects? In this context, repeatability is defined as the proportion of total variation in a performance metric that is attributable to differences among individuals (Nakagawa and Schielzeth, 2010). The repeatability of a phenotype is important for two reasons. The first is that repeatability among individuals is often an upper bound on heritability. In the absence of genetic information, a phenotypic measurement that is highly repeatable is more likely to capture the heritable differences among individuals that contribute to functional performance. This was demonstrated in a recent meta-analysis showing a strong positive correlation between repeatability and heritability, when both could be estimated for the same phenotype (Dochtermann et al., 2015). It is important to note that repeatability is not a guarantee of heritability; for example, in the meta-analysis, only 52% of the repeatable variation in behavioral studies was attributed to additive genetic variation (Dochtermann et al., 2015). A second reason why repeatability is important is that it is a prerequisite for understanding the relationship between performance and traits that are considered to be fixed within individuals, such as body length or wing size. By definition, any trait that is only measured once from each subject, or that is not measured as varying from one moment to the next, cannot explain moment-to-moment variation in an individual's maneuvering behavior. Therefore, if we wish to understand how a trait such as body length may affect maneuverability, it is a prerequisite that the maneuverability metrics be repeatable, at least to some extent. Note that although repeatability is most often considered at the among-individual level, this logic also applies to other levels of analysis, such as comparisons among populations or species.
So how can we achieve repeatable measures of a voluntary behavior that is highly dynamic? One solution is to integrate over a large number of repeated measures (Rushton et al., 1983). A good analogy can be found in methods used to quantify students' academic performance (such as classroom tests), or an individual's gait. Any single quiz question, or single step, would not provide an accurate characterization of individual differences. And yet, when we analyse performance over many questions, or many steps, we are able to measure repeatable and potentially heritable differences among human subjects (Rushton et al., 1983; Devlin et al., 1997; Adams et al., 2016).
Here, we use a simulation to illustrate how this logic applies to the performance of voluntary behaviors such as acceleration maneuvers (Fig. 2A). Consider that each individual animal has a true (unobserved) distribution of peak acceleration values, and that these distributions vary among individuals (repeatability). We use ‘true’ here to refer to the complete underlying distribution of performance values that a given individual is capable of (Fig. 2B), whereas ‘sample’ refers to a series of repeated, voluntary behaviors observed from a given individual within a study (Fig. 2C). Thus, individuals differ in their intrinsic average and maximal capacities, yet at any given moment, their acceleration performance can fluctuate widely (Fig. 2A,C), as is common for many voluntary behaviors. The simulation therefore assumes that true maximal performance is exceedingly rare during voluntary performance, consistent with our recent data on hummingbirds showing that each individual's performance follows a Gaussian distribution (e.g. Segre et al., 2015). In our simulation, a single peak acceleration value is calculated from each maneuver in the sample (Fig. 2A). After collecting a large sample size of 1000 observations per animal (Fig. 2C), we see that the sample means provide the correct ranking and relative magnitude of the intrinsic differences among individuals, even though neither animal achieved its true maximum from Fig. 2B during the sample period.
To formally compare the approach of using the sample means versus sample maxima, we expanded the simulation to create 20 individuals that differed in performance, and we simulated a series of experiments with sample size n ranging from 10 to 5000 peak accelerations per individual. Each experiment was repeated twice to determine the repeatability of the sample maximum and mean (Fig. 2D). Furthermore, to determine the best measure of the true variation in maximal performance, we examined the Pearson's correlations between the true maxima and either the sample maxima or the sample means, respectively (Fig. 2E). The results shown in Fig. 2D,E demonstrate how the sample mean for moderate-to-large sample sizes is highly repeatable, and the sample mean is also highly correlated with an individual's true maximal performance (even if true maximal performance is never reached in the study sample!). This is because the law of large numbers (LLN) guarantees that if we sample repeatedly from each individual, the sample average will converge on each animal's true mean performance. In contrast, the sample max is not repeatable, even when n=5000 events per individual are recorded. This is because the LLN does not apply to the sample maximum. Moreover, the sample maximum is not correlated with the individual's true maximal ability, even for large sample sizes. This is an important point that bears repeating: taking the maximum of a voluntary sample of behaviors is not useful for comparing individuals, because it provides no information about the underlying between-individual differences in performance. Instead, when performance is voluntary, the sample mean is the best measure of individual variation, and for moderate-to-large sample sizes, we expect it to be correlated with an individual's true maximum. This general principle can also explain why studies that rely on voluntary maxima are not repeatable (Careau and Wilson, 2017).
Using big data to study maneuverability in hummingbirds
Based on the principles described above (LLN and the repeatability of voluntary averages), we developed a novel computational approach to define maneuvers from high-throughput data streams (Fig. 3A), that can be used for correlative, experimental (manipulative) and field-based studies. Applied to hummingbird flight, this approach has allowed us to quantify among-individual variation on a suite of flight maneuvers (Fig. 3B), including accelerations, decelerations, rotations and several types of aerial turns (Segre et al., 2015). We first validated the method by establishing that the performance metrics were indeed repeatable when the same individual was tested a second time (Segre et al., 2015), as expected (Fig. 3C). Next, we showed that within a single species, the Anna's hummingbird (Calypte anna), this repeatable variation in performance is predominantly explained by differences in burst muscle capacity (see Glossary; Segre et al., 2015). Specifically, individuals with greater flight muscle capacity exhibit faster accelerations and decelerations, faster rotations and more demanding complex turns as compared with their conspecifics. This result suggests that burst muscle capacity is a major determinant of variation in maneuvering performance within this species. In a subsequent study, we further tested this hypothesis by measuring maneuvering flight in the same individual hummingbirds tested across elevations (Segre et al., 2016), which represents a natural manipulation of burst muscle capacity (Altshuler et al., 2004). As predicted, maneuvering performance declines for most metrics at high elevation as compared with low elevation. To determine whether the challenge to burst muscle capacity derives more from limitations of metabolic input (oxygen availability) or mechanical power output (specifically air density), we next measured hummingbird maneuverability in physically variable gas mixtures. These manipulations confirmed that the effects of burst muscle capacity on maneuvering performance are primarily mediated by mechanical power output.
More recently, we have used our high-throughput approach in a comparative study to determine how evolutionary changes in body size, wing morphology and muscle capacity have shaped distinct components of complex locomotion in the evolution of hummingbirds (Dakin et al., 2018). The dataset for this comparative analysis included extensive recordings from over 200 individuals from 25 different species, and thus it encompassed both within- and among-species variation. The advantage of studying comparative, among-species variation is that evolution explores a larger phenotypic space than is available in a single species, making it possible to determine the contributions of multiple biomechanical traits to maneuverability. Our analysis revealed how different flight maneuvers can be grouped into three major clusters: (1) simple translational maneuvers, for which variation is driven mainly by changes in muscle capacity; (2) simple rotational maneuvers, for which variation is driven mainly by changes in relative wing size; and (3) complex turns, for which variation is driven mainly by changes in wing shape (aspect ratio; Dakin et al., 2018). We also showed that in the hummingbird family (Trochilidae), the larger species have evolved greater aerial maneuverability than many of the smaller species, because the larger species have evolved disproportionately greater wing size and muscle capacity (Dakin et al., 2018). This enables larger hummingbirds to outmaneuver many smaller species that would otherwise be expected to have an advantage in this context. Finally, we discovered that there is substantial (and repeatable) variation in the choice of which maneuvers to use. This indicates that individuals, and even species, have preferences for particular types of maneuvers (Segre et al., 2015; Dakin et al., 2018). These preferences for a particular maneuver often correspond with having a higher level of performance on that same maneuver, leading us to propose that skill is an important driver of performance diversity. Here, we use ‘skill’ to refer to process of motor learning and specialization, wherein individuals that use a particular maneuver more often are able to improve their level of performance on that particular maneuver.
Are the three categories of hummingbird maneuverability (simple translations, simple rotations and complex turns) and their morphological associations general features of maneuverability shared by most or all mobile animals? Answering this question will necessarily require investigating voluntary maneuvers in diverse animal taxa. To guide this new work, we suggest that our previous results are consistent with four broader hypotheses for maneuverability. The first is that all animal maneuvers can be described as being either a simple translation, a simple rotation or a complex turn, defined as a stereotyped combination of either two or more simple rotations, or of rotations and translations (hypothesis 1). A fourth possible category, which we have not described for hummingbirds, is a stereotyped combination of simple translations such as an acceleration followed by a drop (decrease in altitude). Some of the behaviors described in swifts and swallows by Warrick (1998) may fit this category.
The associations we found between biomechanical traits and maneuvers suggest two further hypotheses. (2) Most translational maneuvers are associated with the capacity to modulate symmetrical mechanical force. For flying animals, we can use the lift (or thrust) equation to predict that the ability to modulate symmetrical changes in wing velocity will be the most important trait, followed by the ability to modulate symmetrical changes in wing area. An obvious exception would be a sideways (sideslip) maneuver, which is translational, but would require a left–right asymmetry in force. (3) Rotational maneuvers are associated with the ability to generate force asymmetries, which for most bats, birds and insects will depend on the ability to generate asymmetries in wing motion and wing angle of attack. In the case of bats and birds, which are capable of wing morphing (see Glossary), asymmetries in wing area may also be important.
The complex turns exhibited by hummingbirds during voluntary flight fall into two categories, arcing turns and pitch–roll turns (Fig. 4). These turns and the search parameters we used to extract the maneuvers from tracking data are described in detail in Segre et al. (2015). Briefly, arcing turns involve changes in both heading (>90 s−1) and translational (>0.5 m s−1) velocities with substantial distance traveled in the horizontal (>25 cm) but not vertical (<10 cm) direction. Pitch–roll turns involve a characteristic sequence of deceleration followed first by an increase in pitch to near vertical, then by rolling of the body, and ending with acceleration in a new direction. Although arcing turns have been observed in almost every animal that flies, pitch–roll turns may only be available to animals that are capable of hovering or slow flight such as small bats, insects and hummingbirds. This is because the animal is essentially hovering at the apex of a pitch–roll turn.
We found that different features of complex turns are associated with different traits in hummingbirds, and we also observed that individuals and species differ in the use of the two major types of complex turns described above (Segre et al., 2015; Dakin et al., 2018). Given this level of variation, and given that other species vary extensively in body mass and flight style, we do not expect there to be universal relationships between types of wingbeat kinematics and the performance of complex maneuvers. Instead, we expect that across other animal taxa, metrics of complex turns should be repeatable within individuals and shared among species. These observations lead to our fourth general hypothesis: (4) animals exhibit preferences for the types of complex turns that they are best designed to perform relative to their limb and/or body morphology and their muscle capacity (Warrick, 1998).
Hummingbird wingbeat kinematics during flight maneuvers
There have been several studies examining the detailed wingbeat kinematics of maneuvering hummingbirds, which allow us to ask whether these results are consistent with our hypotheses. The kinematics of hummingbirds during translational flight have been investigated across different horizontal flight speeds in wind tunnels (Greenewalt, 1960; Tobalske et al., 2007) and during voluntary vertical ascents in a narrow chamber (Ortega-Jiménez and Dudley, 2018). As horizontal flight speed increases, the hummingbird wing stroke moves from nearly horizontal during hovering flight to nearly vertical at maximum forward speed (Greenewalt, 1960). Because the orientation between the wing stroke and the body remains nearly constant, the body moves from a near vertical to a near horizontal position across the same range (Tobalske et al., 2007). Wingbeat frequency remains relatively constant across flight speeds, but wing stroke amplitude is maximal at both hovering (0 m s−1) and the fastest forward speed recorded (12 m s−1). Similarly, during voluntary vertical ascents, the most obvious changes in kinematics are a reorientation of the body in the direction of travel and an increase in wing velocity. However, in this case, the change in wing velocity derives from massive increases in both wingbeat frequency and stroke amplitude. These changes were predicted based on several prior load-lifting studies (Chai and Dudley, 1995; Chai and Millard, 1997; Altshuler and Dudley, 2003), which also demonstrate that there is an increase in both wingbeat frequency and stroke amplitude when birds need to generate high vertical force. Collectively, these studies indicate that, in hummingbirds, body orientation is used for the direction component of velocity, whereas increases in wing stroke amplitude and in some cases also wingbeat frequency are associated with translational acceleration. These observations are consistent with hypothesis 2.
Simple rotational maneuvers obviously require asymmetrical forces relative to one of the body axes, but are there traits that are consistently associated with this ability? In our comparative study of hummingbird maneuverability (Dakin et al., 2018), the velocity of pitching upward was influenced by muscle capacity, whereas the velocity of pitching downward and yaw were influenced by variation in wing area. We are not aware of kinematic studies that have focused on specific pitch-up or pitch-down maneuvers, but previous work from our group measured the kinematics employed by hummingbirds docked at moving feeders to elicit pure yaw turns (Altshuler et al., 2012) and arcing turns at different velocities and turn radii (Read et al., 2016). During yaw turns, the most significant changes were an increase in the stroke amplitude of the outer wing during the downstroke, and inner–outer changes in the angle, elevation and deviation of the stroke planes. We observed generally similar changes during arcing turns. Specifically, differences between the inner and outer wings of the stroke plane angle, the elevation angles and the angle of attack were associated with changes to the arcing turn radius. Conversely, changes to the arcing turn velocity were associated with changes in body orientation and more symmetrical changes in wing orientation. These two studies are broadly consistent with hypothesis 3 because the rotational components of the maneuvers were strongly associated with left–right differences in wingbeat kinematics. However, both of these results should be interpreted with caution, given our more recent findings that hummingbirds can also use the motion of a feeder to drive their position through space (Goller et al., 2017).
Conclusions and future research on the biomechanics of maneuvering in flying animals
In this Commentary, we have discussed the importance of repeatability and best practices for leveraging high-throughput data on animal performance. We have shown how these principles can be used to understand the causes of performance variation. From our observations of hummingbird flight, we propose four general hypotheses for maneuverability in flight. Support for these hypotheses for different animals would derive from data that are consistent with four predictions. (1) All maneuvers can be grouped into two classes of simple motions, translations and rotations, and a third category of complex turns that is defined by the combination of multiple simple maneuvers. (2) The ability to perform translations is determined by motor capacity to control velocity. (3) The ability to perform rotations is determined by the ability to manipulate limb motion to produce asymmetry in force. (4) Individuals choose complex turns that play to their morphological and physiological strengths, with the effect that complex turning performance is determined by skill.
We expect that key evidence will come from large data sets of voluntary locomotion, which are currently rare. Prediction 1 is met, to the best of our knowledge, from all available observations of maneuvering in animals, and others might argue that this prediction is tautological. Our hope is that this prediction serves as a useful framework to organize future analysis and a benchmark against which search parameters for other maneuvers can be explored. There are a suite of well-studied maneuvers performed by diverse taxa, including sprinting in lizards (Huey and Hertz, 1982), escape responses of fishes (Webb, 1976) and lunge feeding of whales (Goldbogen et al., 2006), which could be compared with their other voluntary maneuvers for biomechanical tests of the predictions about translational and rotational maneuvers.
It is not our intention to provide a comprehensive review of this literature here, but we do note that studies from lizards, insects and other bird species are consistent with the expectations of predictions 2, 3 and 4. For example, there is evolutionary evidence for both morphological and physiological adaptions to increase translational acceleration (prediction 2). Across a clade of lacertid lizards, faster sprinting is correlated with longer hind limbs relative to body mass and higher optimum temperatures for muscle activity during sprinting (Bauwens et al., 1995). Further support for the association between motor capacity and translational performances comes from bird populations that have colonized small islands, and that exhibit reduced translational performance and smaller flight muscles (Wright et al., 2016). Evidence for associations between rotational maneuvers and the ability to generate limb asymmetries (prediction 3) comes from studies of free flight, development and bioengineering. In vivo force measurements from pigeons (Columba livia) revealed that left and right wings generate measurably different force while navigating through a slalom obstacle course (Warrick and Dial, 1998). Both birds (cockatoos Eolophus roseicapillus; Hedrick and Biewener, 2007) and fruit flies (Drosophila melanogaster; Fry et al., 2003) use left–right differences in wing motion to generate turns. It is reasonable to expect that asymmetries in wing motion would lead to stronger force asymmetries for larger wings, all else being equal. Evidence to support this comes from the work of Ray et al. (2016), who, taking advantage of the molecular tools available in D. melanogaster, used RNAi to genetically lengthen the wings. This produced flies that were able to make faster and tighter turns. Evidence for the ability of wing morphing to control turns comes from a recent study by Chang et al. (2020), who developed a biohybrid aerial robot that had a wing design based on the planform of pigeons and included pigeon feathers. During flight tests, asymmetries in wing morphing that were actuated by as little as a single distal joint (the robotic equivalent of a finger) were sufficient to control steady-state turns with a strong yaw component. To the best of our knowledge, the relationship between the types of complex turns that an animal uses and its skill at performing those types of turns (prediction 4) has not yet been investigated in other animals. However, at least one large data set for turns in fruit flies indicates that turning characteristics are repeatable and that routine turning performance is important for escaping predators (Combes et al., 2012).
Overall, the complex locomotor behaviors known as maneuvers have until recently been largely unmeasurable especially in unconstrained and natural environments. Many previous descriptions of distinct maneuvers have been intriguing but difficult to generalize. With increasing availability of portable high-speed cameras, automated tracking and statistical methods for coping with large data sets, the causes and consequences of maneuverability are now within reach. We hope that our efforts to employ these tools to generate large data sets on hummingbird maneuverability has provided motivation, specifically in the form of four testable hypotheses, to guide this future research.
We thank Sylvia Heredia for the illustrations in Fig. 4, and Andrew Straw, Michael Dickinson and Victor Zordan for early conversations on the biomechanics of maneuvering flight. We thank Maria Mahar and Thomas Strich for use of their photography.
R.D. and D.L.A. wrote the manuscript. All authors developed the ideas and edited the manuscript.
Our research on hummingbird maneuverability was funded by grants from the US National Science Foundation (IOS 0923849) and the Natural Sciences and Engineering Research Council of Canada (402667 and RGPIN-2016-05381).
The authors declare no competing or financial interests.