Physics-based simulations of aerial attacks by peregrine falcons reveal that stooping at high speed maximizes catch success against agile prey

Raptors avoid the confusion effect by targeting fixed points in dense aerial prey aggregations

Collective behaviours are widely assumed to confuse predators, but empirical support for a confusion effect is often lacking, and its importance must depend on the predator’s targeting mechanism. Here we show that Swainson’s Hawks Buteo swainsoni and other raptors attacking swarming Mexican Free-tailed Bats Tadarida brasiliensis steer by turning towards a fixed point in space within the swarm, rather than by using closed-loop pursuit of any one individual. Any prey with which the predator is on a collision course will appear to remain on a constant bearing, so target selection emerges naturally from the geometry of a collision. Our results show how predators can simplify the demands on their sensory system by decoupling steering from target acquisition when capturing prey from a dense swarm. We anticipate that the same tactic will be used against flocks and schools across a wide range of taxa, in which case a confusion effect is paradoxically more likely to occur in attacks on sparse groups, for which steering and target acquisition cannot be decoupled.

Flocking, schooling, and swarming prey are thought to benefit from a confusion effect. However, here the authors show that hawks attacking swarming bats avoid confusion by steering towards a fixed point in the swarm instead of targeting any one individual.

Optimization of avian perching manoeuvres

Perching at speed is among the most demanding flight behaviours that birds perform^1,2 and is beyond the capability of most autonomous vehicles. Smaller birds may touch down by hovering^3–8, but larger birds typically swoop up to perch^1,2—presumably because the adverse scaling of their power margin prohibits hovering⁹ and because swooping upwards transfers kinetic to potential energy before collision^1,2,10. Perching demands precise control of velocity and pose^11–14, particularly in larger birds for which scale effects make collisions especially hazardous^6,15. However, whereas cruising behaviours such as migration and commuting typically minimize the cost of transport or time of flight¹⁶, the optimization of such unsteady flight manoeuvres remains largely unexplored^7,17. Here we show that the swooping trajectories of perching Harris’ hawks (Parabuteo unicinctus) minimize neither time nor energy alone, but rather minimize the distance flown after stalling. By combining motion capture data from 1,576 flights with flight dynamics modelling, we find that the birds’ choice of where to transition from powered dive to unpowered climb minimizes the distance over which high lift coefficients are required. Time and energy are therefore invested to provide the control authority needed to glide safely to the perch, rather than being minimized directly as in technical implementations of autonomous perching under nonlinear feedback control¹² and deep reinforcement learning^18,19. Naive birds learn this behaviour on the fly, so our findings suggest a heuristic principle that could guide reinforcement learning of autonomous perching.

To perch safely, large birds minimize the distance flown after stalling when swooping up from a dive to a perch, but not the time or energy required.

Birds can transition between stable and unstable states via wing morphing

Birds morph their wing shape to accomplish extraordinary manoeuvres^1–4, which are governed by avian-specific equations of motion. Solving these equations requires information about a bird’s aerodynamic and inertial characteristics⁵. Avian flight research to date has focused on resolving aerodynamic features, whereas inertial properties including centre of gravity and moment of inertia are seldom addressed. Here we use an analytical method to determine the inertial characteristics of 22 species across the full range of elbow and wrist flexion and extension. We find that wing morphing allows birds to substantially change their roll and yaw inertia but has a minimal effect on the position of the centre of gravity. With the addition of inertial characteristics, we derived a novel metric of pitch agility and estimated the static pitch stability, revealing that the agility and static margin ranges are reduced as body mass increases. These results provide quantitative evidence that evolution selects for both stable and unstable flight, in contrast to the prevailing narrative that birds are evolving away from stability⁶. This comprehensive analysis of avian inertial characteristics provides the key features required to establish a theoretical model of avian manoeuvrability.

Analysis of inertial characteristics across 22 bird species shows that evolution has selected for avian manoeuvrability using both stable and unstable flight dynamics.

Emergence of splits and collective turns in pigeon flocks under predation

Complex patterns of collective behaviour may emerge through self-organization, from local interactions among individuals in a group. To understand what behavioural rules underlie these patterns, computational models are often necessary. These rules have not yet been systematically studied for bird flocks under predation. Here, we study airborne flocks of homing pigeons attacked by a robotic falcon, combining empirical data with a species-specific computational model of collective escape. By analysing GPS trajectories of flocking individuals, we identify two new patterns of collective escape: early splits and collective turns, occurring even at large distances from the predator. To examine their formation, we extend an agent-based model of pigeons with a 'discrete' escape manoeuvre by a single initiator, namely a sudden turn interrupting the continuous coordinated motion of the group. Both splits and collective turns emerge from this rule. Their relative frequency depends on the angular velocity and position of the initiator in the flock: sharp turns by individuals at the periphery lead to more splits than collective turns. We confirm this association in the empirical data. Our study highlights the importance of discrete and uncoordinated manoeuvres in the collective escape of bird flocks and advocates the systematic study of their patterns across species.

Self-organization of collective escape in pigeon flocks

Bird flocks under predation demonstrate complex patterns of collective escape. These patterns may emerge by self-organization from local interactions among group-members. Computational models have been shown to be valuable for identifying what behavioral rules may govern such interactions among individuals during collective motion. However, our knowledge of such rules for collective escape is limited by the lack of quantitative data on bird flocks under predation in the field. In the present study, we analyze the first GPS trajectories of pigeons in airborne flocks attacked by a robotic falcon in order to build a species-specific model of collective escape. We use our model to examine a recently identified distance-dependent pattern of collective behavior: the closer the prey is to the predator, the higher the frequency with which flock members turn away from it. We first extract from the empirical data of pigeon flocks the characteristics of their shape and internal structure (bearing angle and distance to nearest neighbors). Combining these with information on their coordination from the literature, we build an agent-based model adjusted to pigeons' collective escape. We show that the pattern of turning away from the predator with increased frequency when the predator is closer arises without prey prioritizing escape when the predator is near. Instead, it emerges through self-organization from a behavioral rule to avoid the predator independently of their distance to it. During this self-organization process, we show how flock members increase their consensus over which direction to escape and turn collectively as the predator gets closer. Our results suggest that coordination among flock members, combined with simple escape rules, reduces the cognitive costs of tracking the predator while flocking. Such escape rules that are independent of the distance to the predator can now be investigated in other species. Our study showcases the important role of computational models in the interpretation of empirical findings of collective behavior.

Quantifying avian inertial properties using calibrated computed tomography

Estimating centre of mass and mass moments of inertia is an important aspect of many studies in biomechanics. Characterising these parameters accurately in three dimensions is challenging with traditional methods requiring dissection or suspension of cadavers. Here, we present a method to quantify the three-dimensional centre of mass and inertia tensor of birds of prey using calibrated computed tomography (CT) scans. The technique was validated using several independent methods, providing body segment mass estimates within approximately 1% of physical dissection measurements and moment of inertia measurements with a 0.993 R2 correlation with conventional trifilar pendulum measurements. Calibrated CT offers a relatively straightforward, non-destructive approach that yields highly detailed mass distribution data that can be used for three-dimensional dynamics modelling in biomechanics. Although demonstrated here with birds, this approach should work equally well with any animal or appendage capable of being CT scanned.

Bird-inspired dynamic grasping and perching in arboreal environments

Birds take off and land on a wide range of complex surfaces. In contrast, current robots are limited in their ability to dynamically grasp irregular objects. Leveraging recent findings on how birds take off, land, and grasp, we developed a biomimetic robot that can dynamically perch on complex surfaces and grasp irregular objects. To accommodate high-speed collisions, the robot’s two legs passively transform impact energy into grasp force, while the underactuated grasping mechanism wraps around irregularly shaped objects in less than 50 milliseconds. To determine the range of hardware design, kinematic, behavior, and perch parameters that are sufficient for perching success, we launched the robot at tree branches. The results corroborate our mathematical model, which shows that larger isometrically scaled animals and robots must accommodate disproportionately larger angular momenta, relative to their mass, to achieve similar landing performance. We find that closed-loop balance control serves an important role in maximizing the range of parameters sufficient for perching. The performance of the robot’s biomimetic features attests to the functionality of their avian counterparts, and the robot enables us to study aspects of bird legs in ways that are infeasible in vivo. Our data show that pronounced differences in modern avian toe arrangements do not yield large changes in perching performance, suggesting that arboreal perching does not represent a strong selection pressure among common bird toe topographies. These findings advance our understanding of the avian perching apparatus and highlight design concepts that enable robots to perch on natural surfaces for environmental monitoring.

An Algorithmic Approach to Natural Behavior

Uncovering the mechanisms and implications of natural behavior is a goal that unites many fields of biology. Yet, the diversity, flexibility, and multi-scale nature of these behaviors often make understanding elusive. Here, we review studies of animal pursuit and evasion - two special classes of behavior where theory-driven experiments and new modeling techniques are beginning to uncover the general control principles underlying natural behavior. A key finding of these studies is that intricate sequences of pursuit and evasion behavior can often be constructed through simple, repeatable rules that link sensory input to motor output: we refer to these rules as behavioral algorithms. Identifying and mathematically characterizing these algorithms has led to important insights, including the discovery of guidance rules that attacking predators use to intercept mobile prey, and coordinated neural and biomechanical mechanisms that animals use to avoid impending collisions. Here, we argue that algorithms provide a good starting point for studies of natural behavior more generally. Rather than beginning at the neural or ecological levels of organization, we advocate starting in the middle, where the algorithms that link sensory input to behavioral output can provide a solid foundation from which to explore both the implementation and the ecological outcomes of behavior. We review insights that have been gained through such an algorithmic approach to pursuit and evasion behaviors. From these, we synthesize theoretical principles and lay out key modeling tools needed to apply an algorithmic approach to the study of other complex natural behaviors.

Aerial attack strategies of hawks hunting bats, and the adaptive benefits of swarming

Aggregation can reduce an individual’s predation risk, by decreasing predator hunting efficiency or displacing predation onto others. Here, we explore how the behaviors of predator and prey influence catch success and predation risk in Swainson’s hawks Buteo swainsoni attacking swarming Brazilian free-tailed bats Tadarida brasiliensis on emergence. Lone bats including stragglers have a high relative risk of predation, representing ~5% of the catch but ~0.2% of the population. Attacks on the column were no less successful than attacks on lone bats, so hunting efficiency is not decreased by group vigilance or confusion. Instead, lone bats were attacked disproportionately often, representing ~10% of all attacks. Swarming therefore displaces the burden of predation onto bats outside the column—whether as isolated wanderers not benefitting from dilution through attack abatement, or as peripheral stragglers suffering marginal predation and possible selfish herd effects. In contrast, the hawks’ catch success depended only on the attack maneuvers that they employed, with the odds of success being more than trebled in attacks involving a high-speed stoop or rolling grab. Most attacks involved one of these two maneuvers, which therefore represent alternative rather than complementary tactics. Hence, whereas a bat’s survival depends on maintaining column formation, a hawk’s success does not depend on attacking lone bats—even though their tendency to do so is sufficient to explain the adaptive benefits of their prey’s aggregation behavior. A hawk’s success instead depends on the flight maneuvers it deploys, including the high-speed stoop that is characteristic of many raptors.

Swarming bats emerging from a massive desert roost reduce their predation risk by maintaining tight column formation, because the hawks that predate them attack peripheral stragglers and isolated wanderers disproportionately. Whereas a bat’s predation risk depends on maintaining its position within the column, the catch success of a hawk depends on how it maneuvers itself to attack, and is maximized by executing a high-speed dive or rolling grab maneuver.

Attack behaviour in naive gyrfalcons is modelled by the same guidance law as in peregrine falcons, but at a lower guidance gain

The aerial hunting behaviours of birds are strongly influenced by flight morphology and ecology, but little is known of how this relates to the behavioural algorithms guiding flight. Here, we used GPS loggers to record the attack trajectories of captive-bred gyrfalcons (Falco rusticolus) during their maiden flights against robotic aerial targets, which we compared with existing flight data from peregrine falcons (Falco peregrinus). The attack trajectories of both species were well modelled by a proportional navigation (PN) guidance law, which commands turning in proportion to the angular rate of the line-of-sight to target, at a guidance gain N However, naive gyrfalcons operate at significantly lower values of N than peregrine falcons, producing slower turning and a longer path to intercept. Gyrfalcons are less manoeuvrable than peregrine falcons, but physical constraint is insufficient to explain the lower values of N we found, which may reflect either the inexperience of the individual birds or ecological adaptation at the species level. For example, low values of N promote the tail-chasing behaviour that is typical of wild gyrfalcons and which apparently serves to tire their prey in a prolonged high-speed pursuit. Likewise, during close pursuit of typical fast evasive prey, PN will be less prone to being thrown off by erratic target manoeuvres at low guidance gain. The fact that low-gain PN successfully models the maiden attack flights of gyrfalcons suggests that this behavioural algorithm is embedded in a guidance pathway ancestral to the clade containing gyrfalcons and peregrine falcons, though perhaps with much deeper evolutionary origins.

Predator-informed looming stimulus experiments reveal how large filter feeding whales capture highly maneuverable forage fish

The unique engulfment filtration strategy of microphagous rorqual whales has evolved relatively recently (<5 Ma) and exploits extreme predator/prey size ratios to overcome the maneuverability advantages of swarms of small prey, such as krill. Forage fish, in contrast, have been engaged in evolutionary arms races with their predators for more than 100 million years and have performance capabilities that suggest they should easily evade whale-sized predators, yet they are regularly hunted by some species of rorqual whales. To explore this phenomenon, we determined, in a laboratory setting, when individual anchovies initiated escape from virtually approaching whales, then used these results along with in situ humpback whale attack data to model how predator speed and engulfment timing affected capture rates. Anchovies were found to respond to approaching visual looming stimuli at expansion rates that give ample chance to escape from a sea lion-sized predator, but humpback whales could capture as much as 30-60% of a school at once because the increase in their apparent (visual) size does not cross their prey's response threshold until after rapid jaw expansion. Humpback whales are, thus, incentivized to delay engulfment until they are very close to a prey school, even if this results in higher hydrodynamic drag. This potential exaptation of a microphagous filter feeding strategy for fish foraging enables humpback whales to achieve 7× the energetic efficiency (per lunge) of krill foraging, allowing for flexible foraging strategies that may underlie their ecological success in fluctuating oceanic conditions.

Hawks steer attacks using a guidance system tuned for close pursuit of erratically manoeuvring targets

Aerial predators adopt a variety of different hunting styles, with divergent flight morphologies typically adapted either to high-speed interception or manoeuvring through clutter, but how are their sensorimotor systems tuned in relation to habitat structure and prey behavior? Falcons intercept prey at high-speed using the same proportional navigation guidance law as homing missiles. This classical guidance law works well in the open, but performs sub-optimally against highly-manoeuvrable targets, and may not produce a feasible path through the cluttered environments frequented by hawks and other raptors. Here we identify the guidance law of n = 5 Harris’ Hawks Parabuteo unicinctus chasing erratically manoeuvring artificial targets. Harris’ Hawks use a mixed guidance law, coupling low-gain proportional navigation with a low-gain proportional pursuit element. This guidance law promotes tail-chasing and is not thrown off by erratic manoeuvres, making it well suited to the hawks’ natural hunting style, involving close pursuit of agile prey through clutter.

Hunting styles and flight morphologies of aerial predators are adapted to their habitat structure and prey behaviour. Here, the authors reconstruct flight trajectories of Harris’ Hawks Parabuteo unicinctus and find that these follow a mixed guidance law that is not thrown off by erratic manoeuvres of prey.

Sexual size dimorphism, prey morphology and catch success in relation to flight mechanics in the peregrine falcon: a simulation study

In common with many other raptors, female peregrine falcons Falco peregrinus are about 50% heavier than males. Their sexual dimorphism is thought to allow breeding pairs to exploit a wider range of prey through a division of labor: the male being able to catch more maneuverable prey species; the female capable of carrying larger ones. Given the difficulty of assessing the catch success and load carrying capacity of both sexes of falcon in the field, we here adopt a novel approach to test the division-of-labor theory by using a detailed physics-based flight simulator of birds. We study attacks by male and female peregrines on prey species ranging from small passerines to large ducks, testing how catch success relates to the flight performance of predator and prey. Males prove to be better than females at catching highly maneuverable prey in level flight, but the catch success of both sexes improves and becomes more similar when diving, because of the higher aerodynamic forces that are available to both sexes for maneuvering in high-speed flight. The higher maximum roll acceleration of the male peregrine explains its edge over the female in catching maneuverable prey in level flight. Overall, catch success is more strongly influenced by the differences in maneuverability that exist between different species of prey than between the different sexes of falcon. On the other hand, the female can carry up to 50% greater loads than the male. More generally, our detailed simulation approach highlights the importance of several previously overlooked features of attack and escape. In particular, we find that it is not the prey's instantaneous maximum centripetal acceleration but the prey's ability to sustain a high centripetal acceleration for an extended period of time that is the primary driver of the variation in catch success across species.