Falcon Study

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2014. Published by The Company of Biologists Ltd | The Journal of Experimental Biology (2014) 217, 225-234 doi:10.1242/jeb.092403

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ABSTRACT

This study reports on experiments on falcons wearing miniature

videocameras mounted on their backs or heads while pursuing flying

prey. Videos of hunts by a gyrfalcon (Falco rusticolus), gyrfalcon (F.

rusticolus)/Saker falcon (F. cherrug) hybrids and peregrine falcons (F.

peregrinus) were analyzed to determine apparent prey positions on

their visual fields during pursuits. These video data were then

interpreted using computer simulations of pursuit steering laws

observed in insects and mammals. A comparison of the empirical and

modeling data indicates that falcons use cues due to the apparent

motion of prey on the falcons visual field to track and capture flying

prey via a form of motion camouflage. The falcons also were foundto maintain their preys image at visual angles consistent with using

their shallow fovea. These results should prove relevant for

understanding the co-evolution of pursuit and evasion, as well as the

development of computer models of predation and the integration of

sensory and locomotion systems in biomimetic robots.

KEY WORDS: Predation, Pursuit-evasion, Avian vision, Falcon,

Motion camouflage

INTRODUCTION

How predators track and capture their prey poses a fundamental

problem in animal behavior that combines sensory perception,

neural computation and locomotion. Empirical studies in

combination with computational modeling (Pais and Leonard, 2010;Reddy et al., 2006; Srinivasan and Davey, 1995) have identified

pursuit strategies used by insects (Olberg, 2012), bats (Ghose et al.,

2006), dogs (Shaffer et al., 2004), fish (Lanchester and Mark, 1975)

and humans (Fajen and Warren, 2004; McBeath et al., 1995).

However, no empirical studies have addressed how falcons and

other birds pursue flying prey, mostly due to the difficulty of

recording their 3D flight trajectories in the field. The pursuit

strategies used by birds have evolved in the context of their unique

flight capabilities, as well as their need to pursue rapid, erratically

moving prey in complex environments. Understanding their

methods for tracking and following rapidly moving objects should

provide inspiration for the design of unmanned aerial vehicles

(UAVs) and other biomimetic robots.

Stereoscopic video methods successfully used to study flocking(Ballerini et al., 2008a; Cavagna et al., 2010; Cavagna et al., 2008)

are challenging to apply to this problem because of the wide

geographic areas covered and the rapid, unpredictable motion of

both predator and prey. However, bird-mounted sensors offer new

opportunities for this field. While miniaturized, bird-mounted GPS

sensors have been used to study navigation, flocking energetics and

RESEARCH ARTICLE

Physics Department, Haverford College, Haverford, PA 19041, USA.

*Author for correspondence ([email protected])

Received 17 June 2013; Accepted 16 September 2013

decision making in bird flocks (Biro et al., 2006; Nagy et al., 2010;

Steiner et al., 2000; Usherwood et al., 2011), the 10 Hz data

collection rate and 0.3 m spatial resolution of the GPS are of limited

use in the present context. By contrast, miniaturized bird-mounted

cameras have proved effective in studying the aerodynamics of

avian flight (Carruthers et al., 2007; Gillies et al., 2011) and bird

behavior in other contexts (Bluff and Rutz, 2008; Moll et al., 2007;

Rutz and Bluff, 2008).

Here, we consider how animal-borne video data can distinguish

between different proposed pursuit strategies that use perceptual

cues from the environment. The simplest strategy is classical pursuit,

in which the pursuer (the predator) always flies directly toward theevading prey (Nahin, 2012) (Fig. 1A), so the evaders image is

centered on the pursuers visual field. Chases consistent with

classical pursuit have been observed for honeybees (Zhang et al.,

1990), flies (Land, 1973; Land, 1993; Trischler et al., 2010) and

tiger beetles (Gilbert, 1997).

In contrast, dogs (Shaffer et al., 2004), humans (Fajen and

Warren, 2004; McBeath et al., 1995), hoverflies (Collett and Land,

1975) and teleost fish (Lanchester and Mark, 1975) have been

observed to use constant bearing decreasing range (CBDR)

(Fig. 1B). To describe this strategy, it is useful to first define a

baseline vector oriented along the pursuer-to-evader line-of-sight

and with a length equal to the pursuerevader distance; in general,

either the magnitude or direction of the baseline vector can change

during a pursuit. In CBDR, the optimal bearing angle, o (definedas the angle between the pursuers velocity and the baseline vector)

is fixed at:

where vp and ve are the speeds of the pursuer and evader, and is

the angle between the evader velocity and baseline vector. This

strategy gives the minimum interception time for constant evader

and pursuer velocity if vpve sin, and this steering law can be

realized by the pursuers maneuvering to maintain the evader at a

constant angle in its visual field.

In another strategy, termed motion camouflage (Justh and

Krishnaprasad, 2006), the pursuer maneuvers to reduce parallax-based cues on the evaders visual field (Reddy et al., 2006), a

behavior observed in dragonflies (Olberg, 2012), hoverflies

(Srinivasan and Davey, 1995), bats (Ghose et al., 2006) and humans

(Anderson and McOwan, 2003). The pursuer can achieve motion

camouflage by maneuvering to keep the evaders apparent position

on the pursuers visual field at a fixed angle (Fig. 1C); here, we

assume that the pursuers head is maintained at a constant angle with

respect to its velocity. For an evader that moves in approximately

linear trajectories with occasional changes in speed or direction, this

angle agrees with the value of o from Eqn 1 and CBDR for each

region of constant evader velocity. Eqn 1 sets the pursuers velocity

v

vsin

sin, (1)o

1 e

p

=

Falcons pursue prey using visual motion cues: new perspectives

from animal-borne camerasSuzanne Amador Kane* and Marjon Zamani


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perpendicular to the baseline equal to that of the evader, thus

ensuring that the baseline vector always points in the same direction,

as shown by the constant (absolute) value of , the constant target

angle. For this reason, this strategy is also called constant absolute

target direction (CATD). Consequently, the CATD version of motion

camouflage can be considered an extension of CBDR to the case of

maneuvering prey. CATD results in shorter times to capture than

classical pursuit for occasionally erratic prey motion.

The complexity of avian vision must be considered in

understanding pursuit strategies used by birds. So far, empirical

studies of how birds visually perceive their surroundings during flight

(Erichsen et al., 1989; Land, 1999; Martin, 2011) have not explored

how the apparent motion of prey on avian predators visual fields

influences pursuit strategies. However, research on the interactionbetween vision and flight in several avian species has provided

evidence that optical flow cues are used by budgerigars navigating

their environment (Bhagavatula et al., 2011), zebra finches avoiding

obstacles (Eckmeier et al., 2008), hummingbirds feeding (Delafield-

Butt et al., 2010; Lee et al., 1991) and Harris hawks and pigeons

landing on a perch (Davies and Green, 1990; Lee et al., 1993).

Raptors, in particular, have large, forward-facing eyes with such

a limited range of eye motion (25 deg) (Jones et al., 2007) that they

must move their heads to scan their field of view (ORourke et al.,

2010; Wallman and Pettigrew, 1985). Their effective visual fields

are complicated by the fact that each raptor eye has two foveae

(retinal regions with enhanced visual acuity) oriented at different

angles with respect to the head axis (Fig. 1D). The shallow, or

temporal, fovea has a line of sight oriented at 916 deg from theheads forward direction and is used primarily for visualizing objects

at close range (30 deg to the head axis (Frost et al.,

1990; Lord, 1956; Tucker, 2000; Wood, 1917).

As a result, a flying falcon cannot view distant prey at an optimal

angle for acute vision with its deep fovea and also face its head

forward; however, flying with its head turned to favor the deep

fovea significantly increases drag. Tucker and colleagues have

argued for a pursuit strategy in which falcons can view prey at the

optimal visual angle while keeping their heads facing forward by

flying along trajectories that resemble logarithmic spirals (Tucker et

al., 2000) (Fig. 1E). In this model, the falcon maintains a constant

angle, determined by the orientation of its deep foveal field, between

the line of sight to the prey and the falcon head axis. The falcon is

assumed to fly with its head oriented along its velocity, so its bearing

angle is fixed at f>30 deg. Using a telescopic tracking device,

Tucker and colleagues established that falcon pursuit trajectories are

indeed curved, although their results could not quantitativelydistinguish between the possible theoretical pursuit models (Tucker

et al., 2000). Walking flies have been shown to approach a stationary

blackwhite edge using a logarithmic spiral trajectory, consistent

with using a fixed bearing angle (Osorio et al., 1990).

In the optimal visual angle model, the value of fshould be fixed

at a constant value (e.g. ~30 deg or 916 deg for the deep or shallow

foveal fields, respectively), independent of predator and prey

velocities. By contrast, in CATD the value of o depends explicitly

on vp/ve and , while for classical pursuit, we always have =0 deg.

Thus, one can distinguish between these three strategies by

measuring the behavior of during pursuits: for optimal visual angle

and classical pursuit, the value of is held at the corresponding

constant values for all times, while for CATD the value of should

be constant (and equal to o) as long as the prey does not maneuver,but assumes a new constant value once the prey changes its velocity.

Even though each strategy considered here predicts the predator

maintains a constant bearing angle, it is important to note that

constant bearing angle does not necessarily correspond to a spiraling

predator trajectory. Because both CATD and CBDR result in both a

constant bearing angle and a constant baseline direction, the

predators trajectory is locally straight, not spiral.

Here, the question of which pursuit strategy is used by falcons

was addressed using the results of a study of three species of falcons

hunting avian prey in the field while wearing miniature

videocameras on their heads or backs. This approach overcomes the

naturally low pay-off ratio of filming predation in the field through

collaboration with several skilled falconers who routinely hunt with

falcons. The empirical findings were interpreted using computersimulations of a model predator pursuing flying prey using each of

the proposed pursuit strategies.

RESULTS

Computer simulations

Computer simulations were performed to model classical pursuit,

optimal visual angle and CATD, but not CBDR because the falcons

avian prey maneuvers frequently during chases. The results were

displayed as a simulated video image of the prey as it would appear

on a camera mounted on the head of the pursuing predator (see

details in Materials and methods). Prey positions on the video are

displayed as a plot of the preys horizontal () and vertical () angles

with respect to the cameras optical axis, defined as (0 deg, 0 deg)

(Fig. 2A). Typical results are shown in Fig. 2B for all times duringsample chases for each strategy considered. Constant values of

ve=7.4 m s1, vp=10ms

1 were used, and initial distance between

falcon and prey (z) was fixed at 40 m; the direction of prey velocity

was initially 6.8 deg and 90 time steps between prey maneuvers

were chosen to conform with video data discussed below. For

classical pursuit, the preys simulated (, ) was maintained at

(0 deg, 0 deg) except at very low values ofz(not shown). There,

perspective effects shifted the apparent prey location to lower

values for all models, due to the cameras location above the body

and head axes. We did not model CBDR as a distinct case, as its

predicted predator motion via Eqn 1 is already incorporated into the

RESEARCH ARTICLE The Journal of Experimental Biology (2014) doi:10.1242/jeb.092403

List of symbols and abbreviationsCATD constant absolute target direction

CBDR constant bearing decreasing range

f focal length in pixels

I prey image size in pixels

n number of video frames analyzed

O prey actual size in m

t time

TR response timeve prey (evader) speed

vp predator (pursuer) speed

z distance between falcon and prey

constant target angle

angle between the evader velocity and the baseline

(pursuerevader distance) vector

t simulation time step

angle of the apparent prey position along the horizontal

direction

bearing angle

f optimal visual angle determined by high acuity fovea

orientation

o optimal bearing angle defined by Eqn 1

angle of the apparent prey position along the vertical direction


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algorithm used here for CATD for a maneuvering prey. For optimal

visual angle and CATD, the preys apparent location remained at

fixed angles (, ), although the non-zero response time resulted in

excursions from the optimal angles when the prey abruptly

maneuvered. Thus, for CATD, the simulations yielded a series of

apparent prey positions at values of (, ) that depended on prey and

predator velocity via Eqn 1, while for optimal visual angle at 45 deg

(Tucker et al., 2000), these values were independent of prey

maneuvering. For each choice of prey as it maneuvered, a differentaverage value (, ) was achieved after a small response time lag.

Using a realistic response time resulted in a small spread of angles

about the optimal values due to the time lag between the preys

maneuvers and the model predators response. (A more realistic

model for how the falcon accelerated during maneuvers would have

added to this variation.)

Pursuit analysis

The results of pursuit sequences recorded by bird-mounted cameras

were analyzed to measure the preys apparent motion on the video

image, its distance with respect to the falcon and the falcons roll

angle versus time. Here, a chase was defined as a sequence in which

the falcon initiated a pursuit and pursued the prey until losing it,

capturing it or attempting to capture it. The falcons studied here

[peregrine falcon (Falco peregrinus Tunstall) and gyrfalcon (Falco

rusticolus L.)/Saker falcon (Falco cherrugGray), hereafter termed

hybrid falcon] used the most common tactics observed in studies of

falcon attacks on individual birds (Dekker, 1980; Dekker and Lange,

2001) and flocks (Zoratto et al., 2010): the stoop, a steep, rapid dive

from above the prey; and the tail chase, in which the falcon usespowered level flight to pursue prey.

The head-mounted videos of the hybrid falcon recorded 15 chases

of carrion crows (Corvus corone) over fields in Belgium, while

those for the gyrfalcon recorded five chases of Houbara bustards

(Chlamydotis undulata) in the desert in Dubai. A total of 28 back-

mounted videos of peregrine falcons hunting crows and other birds

in a variety of terrains in the UK, Belgium and the USA were also

analyzed. The prey (, ) versus time data fell into three motifs: (1)

optical fixation with the preys image held at approximately constant

angles (, ) was present in 78% of the head-mounted and 54% of

back-mounted videos (Fig. 3); (2) constant angular rate of change

227


A D

B E

C

DS S

D

ve

=0 deg

vp

ve

ve(t3)

ve(t2)vp(t3)

vp(t2)

(t3)

(t2)

(t1)

vp

vp

ve(t1)

vp(t1)

Fig. 1. Trajectories resulting from alternative pursuit

strategies. (A) Classical pursuit; (B) constant bearing

decreasing range (CBDR); and (C) motion camouflage with

the baseline held at a constant absolute angle (after Ghose

et al., 2006). In B and C, the instantaneous baseline vector,

which points from the pursuer to the evader, is indicated by a

dashed line. (D) Orientation of the shallow (S) and deep (D)

visual fields and head axis (dashed line) in raptors (adapted

from Tucker, 2000). The effect of refraction by the cornea is

not shown. (E) Logarithmic spiral trajectory resulting fromkeeping the prey at optimal visual angle. , bearing angle;

, constant target angle; , angle between evader velocity

and baseline; ve, prey (evader) speed; vp, predator (pursuer)

speed; t, time. See List of symbols and abbreviations.


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along either or was observed in 22% of the remaining head-

mounted and 29% of the remaining back-mounted videos (Fig. 3B);

and (3) erratic motion of the prey on the image was observed in theremaining videos, which occurred at close distances when prey

accelerations resulted in large angular excursions. The video data

did not indicate that falcons kept the preys image fixed with respect

to distant objects.

The hybrid falcon made saccadic head motions during two chases;

head saccades were distinguishable from prey maneuvering or

acceleration by the falcon by the very rapid (0.1 s) motions of the

entire visual field and by its rapid return to the original position in

only 0.330.12 s (mean s.d.). For one chase video that recorded

six head saccades, it was possible to extrapolate (, ) for the prey

when it was off-camera by using the distant landscapes angular

movement (, ) added to the preys values of (, ) immediately

before and after the saccade (Fig. 4A). Most of the saccadic motion

was along , with a change in the vertical direction of only=0.211.8 deg (mean s.d.). The preys extrapolated values were

=363 deg (mean s.d.) during these events; values extrapolated

immediately before and after the falcon turned its head agreed

within experimental uncertainties.

The back-mounted video could sometimes image the falcons

head motion directly during foraging for prey and pursuits (Fig. 4B).

These videos showed that peregrine falcons usually oriented their

heads in the forward direction. However, they did regularly turn

their heads from side to side to scan the world during foraging

flights, looking downward to scan the ground with either their left

or right eyes with equal frequency.

In three chases recorded by a camera on a hybrid falcon, the video

recorded a second hybrid falcon intercepting prey birds in the air.

These videos showed that the second hybrid falcon approached thecrows with a velocity directed to an angle with that of their prey

(Fig. 4C). At the pursuits conclusion, the falcon needs to have its

final velocity vector oriented directly toward the prey so it can strike

the prey with its feet (Fox, 1995; Goslow, 1971). In our videos,

230 ms before impact, the falcon was observed to splay its tail and

spread its wings in anticipation of contact; the falcons feet went

from fully retracted to fully extended in 67 ms. In addition, we

obtained similar values for the times at which raptors spread their

wings and extend their feet before impact from our analysis of high

speed video of a red-tailed hawk and peregrine falcon attacking

falconry lures (Destin, 2012).

Lateralization of vision

The head-mounted video also allowed determination of the preys

position relative to the head axis angle during pursuits. To determinewhether falcons use a preferred eye while chasing prey, we

performed a statistical analysis of the distribution of and values

during pursuits. We verified that the small (25 deg) full range of


A B

50 40 30 20 10 0 5040302010

10

5

0

120

5

(deg)

(

deg)

23.0 deg, 11 deg

(+23.0 deg, +11 deg)

(x, y)

(0 deg, 0 deg)

Fig. 2. Computer-simulated bird-mounted video images of prey during pursuits. (A) Schematic and (B) simulated prey position on the image for classical

pursuit (red circles), motion camouflage (blue circles) and optimal visual angle (black squares). In B, black dashed circles enclose regions with different prey

velocities, while vertical lines at =23 deg indicate the edges of the video images. Shaded regions indicate the range of peak visual angles of the left deep

(red) and shallow (gray) foveae for other raptor species. , angle of the apparent prey position along the vertical direction; , angle of the apparent prey position

along the horizontal direction.

A

B

Time (s)

Visualangle(deg)

0 5 10 15 20

20

10

0

10

20

Fig. 3. Prey tracking data from bird-mounted videos. (A) Tracked prey

positions (red circles and lines) superimposed on a video image of a crow

(arrow) during pursuit by a hybrid gyrfalcon/Saker falcon. Black circles

indicate prey positions in regions of approximately constant bearing angle.

(B) Plots of camera angles (black squares and lines) and (red circles and

lines) versus time for the entire chase sequence for which an excerpt is

shown in A. The gray shaded region indicates the peak visual angles for the

left raptor shallow fovea for other raptor species.


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eye motion measured for other raptor species also applies to falconsby examining close-up videos of gyrfalcon and gyrfalcon/Saker

falcon hybrids posted online. As a result, we estimate that and

should agree with the predators actual bearing angles within

12.5 deg for the head-mounted video. Thus, by determining the

fraction of prey images recorded for negative or positive , we also

could determine whether the falcon favored its left or right eye for

viewing prey. We analyzed these data for head-mounted video from

the hybrid falcon and the gyrfalcon and from back-mounted videodata from the peregrine falcons.

Fig. 5 shows the resulting distributions of prey and for the

hybrid falcon and for the gyrfalcon. These results show the majority

of prey positions at negative , strongly suggesting that falcons prefer

to view prey using their left visual fields. The hybrid falcon data for

distant chases (defined here asz>8 m) had a mean =8.80.2 deg

(n=1277) with 94% of the prey images in the left visual field. For

distant chases, the gyrfalcon data had 79% of the prey images in the

left visual field, and an estimated mean of =7.60.3 deg (n=517,

where n=number of video frames analyzed), where the large error bars

are due to limitations from the limited camera calibration information

available.

By contrast, for pursuits by the hybrid falcon where the prey was

8 m away, the distribution had a lower mean value of2.80.6 deg (n=231) and 72% of measured values were 0 deg.

For the gyrfalcon, average =1.10.8 deg for close-up chases

(n=201).

For the hybrid falcon data, the vertical angles were distributed

about the horizontal, with the mean of the distribution of for

chases >8 m away at 2.40.1 deg, and forz


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230

along the horizontal and vertical directions. Constant prey angle

with 0 deg could be consistent with classical pursuit if the

videocamera were oriented with its optical axis at a non-zero angle

to the falcons head axis. In case of such misalignment, for classical

pursuit the preys image would be stationary at a non-zero angle

because it would be at the focus of expansion on the optical flow

field, which would be offset on the cameras field of view. As

mentioned earlier, we ruled out this effect by measuring the optical

flow field to rule out such offsets in the cameras mounting angle.Thus, the apparent prey motion captured on video does not agree

with classical pursuit.

We now consider the extent to which the finding that falcons

maintain the prey at a constant bearing angle for long intervals of

time during pursuits is consistent with either CATD or optimal

visual angle. For distant chases, was peaked at values of

8.80.2 deg for the hybrid falcon and 7.60.3 deg for the

gyrfalcon. Although the shallow foveas optimal angle has not been

measured for these species, values for other raptors range from 9 to

15 deg. The measured range disagrees with the range of 3045 deg

found in other raptors for the deep foveas line of sight. Thus, the

range of observed is consistent with optimal visual angle strategy

using the shallow, but not the deep, fovea.

However, the measured constant values were also consistentwith those predicted by CATD for plausible values of predator and

prey velocity and prey maneuvering. The definitive test for CATD

is constancy of the baseline vectors orientation (Fig. 6C), but this

measurement was not feasible because of the difficulty of

performing 3D imaging of the wide-ranging birds. Instead, computer

simulations and animal-borne video were combined to provide an

alternative way to distinguish between these two strategies. As

previously noted, for optimal visual angle, the preys position should

remain at a fixed value of independent of predator and prey

velocity and set by the foveal optimal line of sight. By contrast, the

values of constant predicted by CATD vary when the prey

maneuvers, in agreement with what is seen in the video data. For

example, compare Fig. 2B and Fig. 3A: while the optimal visual

angle predictions always correspond to the same value, CATDresults in clusters of different constant values as the prey

maneuvers in the simulations, just as observed in the actual videos.

We might be able to reconcile the optimal visual angle strategy

with the video data if the falcons eyes could undergo saccades of

the angular magnitude observed, as this would create a mismatch

between the measured and the actual angle on the retinal field.

However, this discrepancy should be at most 12.5 deg, based on

observed raptor eye motions in other species and our own survey of

videos showing eye motion in gyrfalcons and gyrfalcon/Saker falcon

hybrids. Instead, we observed multiple cases where the change in (,

) values between apparent optical fixes was 10 deg. Thus, the

observed heterogeneity in the measured constant values supports

CATD over optimal visual angle, assuming that falcon eye motions

this large are unlikely.Overall, these data provide strong evidence that the falcons

studied use visual motion-based steering laws while pursuing flying

prey. The video data indicate that the falcon maneuvers so that the

preys constant (, ) values do not contribute to non-zero flow

vectors on the optical flow field. We suggest that the actual strategy

used may be a synthesis of both CATD and optimal visual angle.

Recall that the falcon can control the value of with which it

pursues the prey by varying its speed (Eqn 1). These birds can fly

fast enough to pursue their prey with values of not in agreement

with their shallow foveal fields. Instead, the falcons studied adjusted

their velocities during pursuits so as to utilize CATD while

maintaining the preys at values near-optimal for its shallow fovea.

This has an additional advantage, as the range of most observed

horizontal prey angles was consistent with the measured binocular

overlap region of 1018 deg measured in other raptor species

(Martin and Katzir, 1999; ORourke et al., 2010).

When not sustaining constant bearing angles, the falcons often

maintained the apparent prey motion at a constant angular rate of

change. For small falconprey distances, the falcon pursues its prey

at smaller average visual and bearing angles before interception andcapture. While data for the hybrid falcon and gyrfalcon showed a

strong preponderance of prey fixes in the left visual field, data for

the peregrine falcon from back-mounted video did not show any

evidence of lateralization. Other non-raptor bird species have been

found to favor the left or right eye for specific tasks, presumably due

to brain lateralization (Rogers, 2012). Further work will attempt to

discern the extent to which the observed lateralized prey positions

are found in other birds.

These results indicate that the falcons only occasionally view

distant prey using their deep fovea during pursuits. By instead

viewing the prey using its shallow fovea, the falcon can take

advantage of higher acuity vision, (possibly) binocular vision and a

shorter interception path while reducing drag by keeping its head

oriented forward. The hybrid falcon was observed to perform headsaccades consistent with imaging the prey using its deep fovea in

one chase. The falcons also occasionally tilted their heads while

foraging, presumably to scan the ground for prey. These results

agree with findings of an earlier study of head motions used by

flying gull-billed terns (Gelochelidon nilotica, another bifoveate

species) foraging for and capturing prey (Land, 1999). The resulting

eye orientation was consistent with their using the deep fovea for

this purpose, without any evident lateral preference. Given these

results, it would be worth examining results for helical raptor

soaring trajectories for evidence of a preferred handedness (Akos et

al., 2008). Finally, the preference for viewing prey with an average


A B

C

or

Videocamera

Prey imagez f

O

h

v

Prey

I

Fig. 6. Bird-mounted camera mounting geometries. (A) Schematic

diagram showing the relative orientation of the camera optical axis and body

axis in flight on the back-mounted videocameras. (B) Head-mountedvideocamera on gyrfalcon/Saker falcon hybrid. (C) Pinhole optics geometry

for measuring angles (, ) of the prey from its image, and z, the distance

from the falcon to its prey (not to scale). O, prey actual size (m); f, focal

length (pixels); I, prey image size (pixels); h, distance above the eyes.


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0 deg agrees well with the fact that raptors have a high acuity

horizontal retinal streak (Inzunza et al., 1991; Jones et al., 2007).

In the one instance of prey capture recorded on video, we found

that the falcons began to spread their wings and brake for impact

with the prey at 230 ms and that their feet went from fully retracted

to fully extended in 67 ms, consistent with our analysis of high

speed videos of raptor strikes (results not shown) (Destin, 2012) and

with published values of 210 ms [the time at which Harris hawks

were found to begin preparing to land on a perch (Davies and Green,1990)] and 60100 ms (the time for foot extension for peregrine

falcons attacking birds on the wing (Goslow, 1971)].

These results have implications for the co-evolution of pursuit-

evasion mechanisms. Most prior research on optimal evasive

responses by birds has focused on locomotion rather than sensory

inputs (Hedenstrom and Rosen, 2001; Howland, 1974; Van den

Hout et al., 2010; Weihs and Webb, 1984). A recent review of prey

escape strategies has commented on the tendency of prey to double

back and move toward the pursuing predator (Domenici et al.,

2011), a strategy found to result in lower capture rates for owls

(Shifferman and Eilam, 2004). Such prey maneuvers may be

attempts to move out of the predators high acuity visual field. One

study allowed pursuer and evader visual systems to evolve

computationally in response to the outcomes of simulated pursuitsand captures; this work found that the angle for optimal vision for

pursuers agreed with the observed orientation of the shallow or the

deep fovea (Cliff and Miller, 1996). In the absence of empirical data,

computational models of predation on flocks (Ballerini et al., 2008a;

Ballerini et al., 2008b; Lee, 2006; Lee et al., 2006; Mecholsky et al.,

2010) have assumed classical pursuit. These results should be

revisited to model how likely pursuit strategies used by falcons on

single birds influence their attacks on flocks.

The emerging evidence indicates that a wide variety of animals

utilize visual motion-based cues and CATD/motion camouflage-based

strategies for the pursuit and capture of individual prey. It also

reinforces the importance of using a sensory ecology approach

(Martin, 2012) in understanding problems such as bird collisions with

man-made objects (Martin and Shaw, 2010) and antipredatorsurveillance (Fernndez-Juricic, 2012). The complexity and extreme

speed of the falcons attack and its avian preys evasive response raise

important, unresolved questions. Raptor pursuit strategies have

evolved under the constraints of avian flight aerodynamics, prey

behavior and environment. How optimal are the actual pursuit

strategies used by falcons? How do their hunts adapt to different

hunting tactics? What import do these results hold for the study of

attacks on flocks? How do prey evasive strategies relate to the falcons

hunting methods? Our ongoing experimental and modeling efforts

will explore these issues by extending pursuit-evasion models into

three dimensions and adding in realistic predator-maneuvering

capabilities, as well as exploring different ways to model the fitness

of pursuit strategies.

MATERIALS AND METHODS

Animals

This study used six peregrine falcons (F. peregrinus) and two gyrfalcon (F.

rusticolus)/Saker falcon (F. cherrug) hybrids (hybrid falcons) flown and

housed by participating falconers who were provided with videocameras,

mounts, data storage media and instructions for using the equipment and

conducting and documenting the field studies. The experiments explored

predation by free-flying falcons in the field in all cases. All prey were wild,

free-living birds encountered by the raptors during hunting flights. Most

videos analyzed here were recorded in collaboration with four falconers who

hunted with six different peregrine falcons and two hybrid falcons, in the

USA (Pennsylvania, Arizona and Wyoming) and in the UK, The

Netherlands and Belgium. Filming occurred during autumn and winter

20092013. All falconers were licensed and had all necessary permits; all

personnel involved followed the relevant regulations and laws of each

country in question, as well as those of Haverford Colleges Committee on

Animal Care and the ARRIVE guidelines (NC3Rs, 2010). All back-mounted

videos were filmed with peregrine falcons. The head-mounted camera was

used only with a hybrid falcon because of that species greater mass. The

male hybrid falcons hunted in a pair while one of the birds wore a video

camera. Only one of the hybrid falcons was habituated to wearing the head-

mounted camera, so the video data presented here are from one individual.In two chases, the hybrid falcon wearing the camera recorded the other

hybrid falcon pursuing and capturing a prey bird. In the remaining chases,

the falcon wearing the camera recorded the prey bird during a solo pursuit.

In a few cases, videos were drawn from publically available archives on the

internet where they had been posted by falconers, including five chases with

a gyrfalcon wearing a head-mounted camera hunting Houbara bustards

(Chlamydotis undulata) in the desert in Dubai (Abu Dhabi Sports Council,

2011), and two pursuits of ring-necked doves (Streptopelia capicola) by a

peregrine falcon wearing a back-mounted camera in Arizona (Gonzales,

2010).

Video methods

The back-mounted cameras and battery packs for the head-mounted cameras

were mounted on unanesthetized birds using Marshall Radio Telemetry

(North Salt Lake, UT, USA) Trackpack backpacks designed to secure radiotelemetry transmitters on falcons and hawks (Fig. 6A). These mounts use

in Teflon ribbons to hold the cameras stably between the falcons wings,

just above and to the rear of the birds head. In a few cases, we were able to

obtain video recorded from videocameras mounted in specially made

falconry hoods (Fig. 6B). Falconers experienced in hood-making prepared

hoods customized for each falcon and acclimated the birds to wearing them

before their actual use in hunting.

We used commercially available miniature (mass 14 g) model 808

camcorders (Toplanter, Huizhou, China). Including mounting hardware, the

total mass was 20 g,


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vertical axis was oriented along the birds ventraldorsal axis (Fig. 6A). As

a consequence, objects in the environment rotated on the back-mounted

video when the falcons body rolled from side to side. By separately

measuring roll using the orientation of a distant, level horizon, we were able

to correct for this by rotating the resulting images to compensate.

Because the videocameras used have pinhole optics, we can estimate

distances,z, to objects of known size, O, using the relationship:

z= Of/I , (2)

wherefis the camera focal length in pixels andIis the image size in pixels(Fig. 6C) for objects not foreshortened due to linear perspective. The angle

of the apparent prey image located at a distance (x,y) in pixels from the

image center is at angles and with respect to the camera defined by

(Fig. 2A):

If the falcons eyes are oriented forward in their primary position of gaze [as

is typical for raptors (Wallman and Pettigrew, 1985) and as we have found

to be true by examining videos of different falcon species], then (, )

constitute the horizontal and vertical components of . The resulting preypositions on the video are shown plotted as angles (, ) on the cameras

visual plane, with 0 deg corresponding to both the image center and the

falcons forward head axis (for head-mounted video) or forward velocity

direction (for back-mounted video) at large distances,z(Fig. 2A). Positive

values of are on the birds right visual field, negative angles on its left

visual field; positive (negative) values of indicate that the prey was located

above (below) the forward axis. The prey images were displaced downward

before interception and capture at very low zdue to the mounting of the

camera above the head and body axis. Video frames show the cameras total

field of view in the coronal plane of the falcons head or body within the

cameras field of view: 2323 deg and 10.5510.55 deg. Although

these cameras cannot image all objects visible to the falcon, because its deep

foveal retinal field extends to higher angles, by tracking background objects

visible immediately before and after the prey moved off-camera, we were

able to infer its position at higher angles. Finally, we checked that thevideocamera was not oriented at an angle to the head forward axis by

computing optical flow fields during prey pursuits for approximately linear

falcon velocity; this established that the focus of expansion was indeed along

the center of the cameras field of view.

Image processing and data analysis

We performed calibrations of the bird-mounted videocameras focal length,

distortion parameters and other optical parameters (Bradski and Kaehler,

2012; Cyganek and Siebert, 2009) using OpenCV version 2.3.1 programs

written in Python 2.7 (http://www.python.org). The results indicated that the

pinhole optics resulted in only small barrel distortions with a standard

deviation of 0.8 pixels and a maximum range of deviation of 1.5 pixels

over the entire 1280720 pixel image. The resulting focal lengths also were

measured to 0.5%, using filming of objects of known length as an

additional check. For the head-mounted video of a gyrfalcon from anothersource, wide-angle lens distortions limited our ability to perform analyses

of the angles (, ) (Abu Dhabi Sports Council, 2011) beyond approximate

values near the preys average apparent position.

To analyze the tracks of birds and other objects on video, we used the

image analysis program ImageJ (National Institutes of Health, Bethesda,

MD, USA). Videos were first converted into image stacks using VirtualDub

(http://www.virtualdub.org), checking that no frames were dropped or added.

Separate checks were performed by filming a fast clock to make sure that

the videocameras did not skip or add frames. The image stacks were then

converted to grayscale, the background subtracted when possible, and an

image intensity threshold was applied to obtain a binary image of only

moving prey birds. Tracking was performed using one of two ImageJ

plugins: MTrack2 (for automatic tracking) or MTrackJ (for manual

x

f

y

f

tan ,

tan . (3)

1

1

=

=

tracking). [Particle image velocimetry methods were attempted, but did not

yield useful results because of the falcons erratic motion and the resulting

unstable rotating and moving high-contrast background.] Fitting, statistical

analysis, Fourier transforms, correlation functions, and other data analysis

was carried out in Origin 8.6 (OriginLab, Northampton, MA, USA). All

error bars reported here are s.e. unless noted otherwise. The estimated error

in tracked prey angles was 0.2 deg.

To measure roll angle from the bird camera video, we used the

orientation of the distant level horizon when visible. The horizons

orientation was automatically detected using an Opencv 3.2 programwritten in Python 2.7. Each image frame was individually converted to

grayscale and smoothed using a Gaussian filter, then subjected to an

adaptive threshold to compensate for non-uniform illumination and five

rounds of dilation/erosion filters to remove speckle noise while preserving

large features. Finally, a Canny filter and probabilistic Hough Line

transform were used to find the orientation of the horizon lines, which

were inspected by hand to confirm only distant horizon lines were

analyzed (Bradski and Kaehler, 2012).

Computer simulations

Computer simulations of birdcamera videos generated by each pursuit

model considered were written in Python 2.7. All simulations assumed the

chase was confined to a horizontal plane because this sufficed to model

the behavior of interest here. Simulation parameters were drawn whenever

possible from empirical data for flight speeds and aerodynamicparameters. Maximum flight speeds were unavailable for carrion crows,

but values from 7.4 to 15.6 m s1 have been reported for other species of

crows (Broun and Goodwin, 1943; Schnell and Hellack, 1978; Verbeek

and Caffrey, 2002). For peregrine falcons, empirical data for maximum

speeds in level flapping flight ranged from 10 to 31 m s1 (Alerstam, 1987;

Cochran and Applegate, 1986; Pennycuick, 1997; Pennycuick et al.,

1994). Measured flight speeds for diving and stooping falcons range from

3 0 m s1 for diving peregrine falcons (Alerstam, 1987) to 58 m s1 for

stooping gyrfalcons (Tucker et al., 1998). Roll angles were computed

using the balanced turning approximation (Pennycuik, 2008) and

aerodynamic parameter estimates for falcon lift coefficient=0.53 to 1.65

at Reynolds number=105 and wing area=0.132 m2 (Tucker, 1998). The

simulations assumed no limitations on turning radius or other maneuvers

required to implement each strategy, because birds can separately move

and shape each wing (and their tails) to achieve low radius turns, abruptrolls and other maneuvers not permitted by fixed wing aerodynamics

(Carruthers et al., 2007; Pennycuik, 2008; Warrick et al., 2002).

Birds, including raptors, can process visual information at rates 90Hz

(Fox, 1995; Jones et al., 2007). Consequently, the simulation time step was

fixed at t=1/(329.97 Hz)=11.1 ms1/90 Hz to agree with this limit; this

value was also close to an integral multiple of the video frame capture rate.

Simulated video images were generated every three time steps. The

projective geometry for simulating images corresponded to that for the

empirical videocamera mounting geometry. The timing and direction of prey

accelerations were drawn from approximate values observed on video. In

the simulations, capture was defined as a falconprey distance of 0.25 m,

and events during the actual capture were not simulated.

The model pursuer moved at a constant speed, so only its bearing and roll

angles changed in response to perceived evader motion. To account for

predator response time, TR, to prey maneuvers, the program computed themotion of the pursuer at time tusing the preys position and velocity at tTR.

The time lag between perceived prey motion and predator response was set

at TR=6t, assuming the falcon requires at least three flicker fusion periods

to detect prey acceleration and a 38 ms reaction time once the stimulus is

received (Pomeroy and Heppner, 1977; Potts, 1984); this value for TRis also

consistent with the 6724 ms for birds in a flock to respond to the initiation

of turning (Potts, 1984).

AcknowledgementsWe wish to thank the falconers who participated in this study: Eddy de Mol and

Francois Lorrain, Dennis Decaluw, Troy Morrs and Stephen Lea, and other

falconers who contributed valuable advice: Robert Giroux, Jack Hubley and Patrick

Miller. Robert Musters fabricated the hoods used to hold the videocameras, and



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Bruce Boyes helped to design and adapt the backpack mounts. Emily

Cunningham played a key role in the early conception of this project. We would

like to acknowledge helpful conversations with Peter J. Love (Haverford College),

Charlotte Hemelrijk and Hanno Hildebrandt (University of Groningen). We wish to

express our appreciation for the helpful comments and suggestions by two

anonymous reviewers.

Competing interestsThe authors declare no competing financial interests.

Author contributionsS.A.K. and M.Z. jointly digitized, analysed and interpreted the video data received

from cooperating falconers. S.A.K. conceived of the experimental and

computational study design, provided video equipment and instructions to the

falconers, performed the computer modelling, and wrote the paper with input from

M.Z. during the initial drafting and revisions.

FundingThis research was supported in part by a grant to Haverford College from the

Howard Hughes Medical Institute and by a Special Projects Award from the Marion

E. Koshland Integrated Natural Sciences Center of Haverford College.

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Falcon Study