Integrative and Comparative Biology
Integrative and Comparative Biology, volume 55, number 6, pp. 1142–1154
doi:10.1093/icb/icv103
Society for Integrative and Comparative Biology
SYMPOSIUM
Balancing Biomechanical Constraints: Optimal Escape
Speeds When There Is a Trade-off between Speed
and Maneuverability
C. J. Clemente1,* and R. S. Wilson†
*School of Science and Engineering, University of the Sunshine Coast, Sippy Downs, 4556, QLD, Australia; †School of
Biological Sciences, The University of Queensland, St Lucia, Brisbane, 4102, QLD, Australia
From the symposium ‘‘Towards a General Framework for Predicting Animal Movement Speeds in Nature’’ presented at
the annual meeting of the Society for Integrative and Comparative Biology, January 3–7, 2015 at West Palm Beach,
Florida.
1
E-mail: [email protected]
Synopsis The ability for prey to escape a pursuing predator is dependent both on the prey’s speed away from the threat
and on their ability to rapidly change directions, or maneuverability. Given that the biomechanical trade-off between
speed and maneuverability limits the simultaneous maximization of both performance traits, animals should not select
their fastest possible speeds when running away from a pursuing predator but rather a speed that maximizes the
probability of successful escape. We explored how variation in the relationship between speed and maneuverability—or
the shape of the trade-off—affects the optimal choice of speed for escaping predators. We used tablet-based games that
simulated interactions between predators and prey (human subjects acting as predators attempting to capture ‘‘prey’’
moving across a screen). By defining a specific relationship between speed and maneuverability, we could test the survival
of each of the possible behavioral choices available to this phenotype, i.e., the best combination of speed and
maneuverability for prey fitness, based on their ability to escape. We found that the shape of the trade-off function
affected the prey’s optimal speed for success in escaping, the prey’s maximum performance in escaping, and the breadth
of speeds over which the prey’s performance was high. The optimal speed for escape varied only when the trade-off
between speed and maneuverability was non-linear. Phenotypes possessing trade-off functions for which maneuverability
was only compromised at high speeds exhibited lower optimal speeds. Phenotypes that exhibited greater increases in
maneuverability for any decrease in speed were more likely to have broader ranges of performance, meaning that
individuals could attain their maximum performance across a broader range of speeds. We also found that there was
a differential response of the subject’s learning to these different components of locomotion. With increased experience
through repeated trials, subjects were able to successfully catch faster and faster dots. However, no improvement was
observed in the subject’s ability to capture more maneuverable prey. Our work highlights the costs of high-speed
movement on other traits, including maneuverability, which make the use of an animal’s fastest speeds unlikely, even
when attempting to escape predators. By investigating the shape of the trade-off functions between speed and
maneuverability and the way the environment and morphology mediates this trade-off, we can begin to understand
why animals choose to move at the speeds they do when they are running away from predators or attempting to capture
prey.
Introduction
Predation is one of the most powerful ecological
factors affecting the functioning of ecosystems
(Lima and Dill 1990). Both the direct and indirect
actions of predators can shape populations, communities, and ecosystems (Lima and Dill 1990; Schmitz
1998; Pavey et al. 2008; Wesner et al. 2012;
Miller et al. 2014). Because the threat of predation
is so important, animals must constantly decide how
best to use their time to balance the need to acquire
energy and nutrients for growth, maintenance, and
reproduction against the dangers of being eaten
Advanced Access publication September 2, 2015
ß The Author 2015. Published by Oxford University Press on behalf of the Society for Integrative and Comparative Biology. All rights reserved.
For permissions please email: [email protected].
Balancing biomechanical constraints
(Brown and Kotler 2007). Greater time spent foraging to gain resources makes it more likely that an
individual will encounter a predator (Brown and
Kotler 2007). Understanding how animals optimize
their foraging decisions to balance these trade-offs
between resources and predation has been a focus
within foraging ecology for decades (Ydenberg
et al. 2007). Although biomechanical trade-offs also
have the potential to shape the behavior of prey, we
know little about how animals balance these
competing functional demands (Wilson et al.
2014). For example, the ability for an animal to
escape a pursuing predator will rely not only upon
its speed of movement but also upon its ability to
make sharp, rapid turns away from the predator
(Howland 1974; Hedenstrom and Rosen 2001;
Wilson et al. 2013). However, the faster an animal
moves forward the poorer its ability to turn becomes
(Alexander 1982). Speed compromises turning ability
because animals require larger coefficients of friction
when turning at higher speeds or at sharper angles
(Alexander 1982). Northern quolls (Dasyurus hallucatus), for example, must decrease their speed to
about 35% of their maximum in order to
successfully navigate a 1358 turn, with speeds
higher than 50% of their maximum markedly
increasing their probability of crashing at this angle
(Wynn et al. 2015).
Given the biomechanical trade-off between speed
and maneuverability, and the importance of both
traits for escaping predators, how fast should an
animal run away from a pursuing predator?
Selection of the optimum combination of speed
and maneuverability should be based on the strategy
that results in the highest probability of survival.
Howland (1974) modeled the influence both of forward speed and of turning radius on whether prey
can escape a predator using sharp, rapid turns in a
turning game. Based on this model, he suggested that
a prey should escape when its normalized speed
(prey speed/predator speed) is greater than the
square root of its normalized turning radius (prey’s
turning radius/predator’s turning radius). One complication for exploring the importance of both speed
and maneuverability for escape behavior and
exploring the optimal locomotor behavior of prey
is that it is more difficult to quantify an individual’s
maneuverability than its straight-line speed.
Encouraging individuals to run and maneuver
around
obstacles
at
different
speeds
is
problematic—and it is not surprising that most studies of performance only quantify speed using straight
runways (Miles 2004; Irschick and Meyers 2007;
Irschick et al. 2008; Clemente et al. 2009).
1143
Recently, Clemente and Wilson (2015) used a
custom, tablet-based game that simulated encounters
between predator and prey as an alternative
approach for exploring the relative roles of speed
and maneuverability for success in escaping
predators. Human subjects were asked to ‘‘capture’’
simulated on-screen prey (dots on screen) by
touching them as they moved across the tablet’s
display; prey varied in size, speed, and
maneuverability. Clemente and Wilson (2015)
manipulated the prey’s maneuverability by altering
the angle that prey changed directions while keeping
the number of turns constant. The maneuverability
of their simulated prey was based on the evasive
tactics of fruit flies, which explore their habitat
using a series of straight flights interspersed with
rapid turns in random directions (Tammero and
Dickinson 2002). These routine erratic turns during
flight were found to be more successful in avoiding
predators than were active evasive maneuvers
(Combes et al. 2012). So is it better to be fast or
to perform erratic turns in order to escape
predation? Clemente and Wilson (2015) found that
success in escaping was determined both by speed
and by maneuverability—slow prey could still
escape predation when highly maneuverable, while
prey that were poorly maneuverable could only
escape when traveling rapidly. Importantly, because
small changes in speed translated into successful
escape in a different way than did changes in
maneuverability, the shape of the trade-off between
speed and maneuverability—or how an individual’s
ability to turn is affected by its speed—is likely to
have complex effects on the success of escape. Yet
would the same optimum behavior be found in a
wide variety of environments?
An animal’s environmental substrate is likely to
affect the way increases in speed affect its
maneuverability and the optimal combination of
both parameters for successful escape. For example,
surfaces with high friction should allow much greater
turning angles at high speeds than would surfaces
with low friction (Fig. 1) (Alexander 1982). Anyone
who has tried to change directions while running
along a slippery surface has experienced the dangers
of a low-friction surface for maneuvering. High
straight-line speeds may offer a much greater
probability of successfully escaping a predator on
low-friction surfaces (e.g., ice) than does using a maneuver that would only be possible at very low
speeds. In contrast, it may be possible to also use
highly maneuverable turns at a greater range of
speeds on high-friction surfaces, broadening the
potential fitness-landscape. In other words, the
1144
C. J. Clemente and R. S. Wilson
relationship between a prey’s speed and its
probability of escape. The logic behind our analyses
is that we sought to identify the speed of the prey
(which coincides with a specific maneuverability depending on the trade-off) that resulted in the highest
probability of successful escape. As each experiment
compared different trade-offs between speed and
maneuverability, we wanted to (i) compare the
optimum speed for successful escape among these
trade-off functions, (ii) detect the range of speeds
of potential prey that were associated with relatively
high success in escaping (performance breadth), and
(iii) identify the peak escape-performance that
occurred at their optimal speed.
Methods
Programming the tablet
Fig. 1 If the ability of the prey to make sharp, rapid turns (maneuverability) is affected by the friction of the substrate upon
which they are running (a), then the optimal seed of movement
that would maximize the probability of escape would differ
between substrates with low (dashed line) and high friction (solid
line) (b), assuming that the friction of the substrate only
influences the prey’s turning ability and not the predator’s.
optimum choice of speed for escape may be dependent on the environmental conditions that affect the
shape of the speed-maneuverability trade-off.
In this study, we explored how variation in the
relationship between speed and maneuverability—or
the shape of the trade-off—affects the optimal choice
of speed for escaping a predator. We built upon the
work of Clemente and Wilson (2015) by using the
custom, tablet-based game that simulated encounters
between predator and prey. By defining a specific
relationship between speed and maneuverability
(shape in trade-off), we could then test the survival
of each of the possible behavioral choices available to
this phenotype. Thereby, for each specific trade-off
between speed and maneuverability we could
determine the best combination for escaping a
predator. We used five independent experiments to
test how variation in the shape of the trade-off
between speed and maneuverability affects the
Our experiment was based on a simulated prey item
(dot) moving across the visual field of a predator
(human subject) and assessing the prey’s ability to
avoid capture. Each trial—or encounter with a
predator—involved a single dot (representing the
prey item) moving from left to right across the
screen of a 10-inch Android Tablet (Google Nexus
10—2560 1600 pixels, Running Android Ver 4.2).
The speed and maneuverability of the dot was varied,
based on a pre-populated list that was dependent on
the function of a trade-off between each parameter
of performance (Fig. 2—input). The ability of the
prey to escape was then assessed across the range
of combinations of speed and maneuverability that
were associated with each trade-off. Five functions
that described the trade-off between speed and
maneuverability were tested in each experiment.
Each function describing a trade-off was represented
by 20 individual prey that differed in speed and
maneuverability.
For each experiment, an individual human subject
was exposed twice to the 100 different combinations
of the speed and maneuverability of prey. That is,
each of the 100 phenotypes were taken from the five
trade-off functions, each represented by 20 individual
prey. The order of trials within each experiment was
randomly allocated using a random-sequence generator. In total, 152 subjects, half of which were males
and half of which were females, were recruited from
the University of Queensland and surrounding
suburbs. Each subject then attempted to catch the
prey item by tapping on the moving dot. Subjects
were given feedback on their success after each trial,
as either a hit (where error5radius) or a miss
(error4radius). Subjects were not required to
1145
Balancing biomechanical constraints
Comparison of prey’s escape-performance
between trade-off functions
Fig. 2 The typical shape of the curve for escape performance
with increasing speed, as well as the three variables used to
describe the shape. MaxErr—the maximum error score achieved.
SpEsc—the speed at MaxErr; BrScr is the breadth of the performance (error) score, calculated as the distance between the
maximum and minimum speeds when the error score was 80% of
MaxErr.
attempt to capture every prey dot, yet there was no
penalty for attempting to do so.
The program was written using the open-source
programming language Processing (Processing.org)
and then transferred to the tablet using the Androidsystem development kit (developer.android.com). The
code used during trials was similar to that used by
Clemente and Wilson (2015). In summary, the code
repeats a draw loop that moves an ellipse a given
distance for each loop. The draw loop functions at
60 Hz. At the beginning of each trial, speed and
maneuverability of the dot are read from the pre-populated list for each experiment. Speed was measured in
pixels per loop and determines the distance moved
from left to right per loop. Maneuverability defines a
potential arc of movement from 0 degrees (i.e., only
able to move left to right across the screen) to 180
degrees (able to move at any angle from the horizontal
of left to right). The direction is modified every 5th
loop by randomly selecting an angle that deviates from
horizontal, within the given arc. Thus, for each loop,
the dot will move a set distance in the direction defined by the angle from the horizontal.
Each prey continues across the screen until either
the screen is touched or the dot reaches the limit
of the screen’s width on the right-hand side of the
tablet. At the conclusion of each single event a line of
text is written that contains the trial number, the
distance and range moved, the position of the dot
when the screen is touched, and the center of the
point where the screen is touched. The error is
the straight-line distance between the center of the
dot and the center area of touch.
We used five independent experiments to test how
variation in the shape of a trade-off between speed
and maneuverability affects the relationship between
the speed of the prey and its probability of escape. In
Experiment 1, we examined how speed affected the
probability of escape for prey that possessed five different linear trade-offs between speed and
maneuverability (N ¼ 28 subjects). The point of intersection of all five trade-off models occurred at the
prey’s top speed in which their maneuverability was
lowest. Across all five trade-offs, speed varied from
0.1 to 60 pixels per loop. This upper limit of speed
was chosen because preliminary experiments found
this to be the approximate limit of most subjects’
ability to catch moving dots across the screen. Each
of the five trade-off functions differed in how
maneuverability increased with decreases in speed.
The shallowest trade-off was for the function in
which only small increases in maneuverability
resulted from larger decreases in speed. This
shallowest trade off was designed to replicate a
situation in which an animal is running along a
slippery substrate that constrains the animal’s ability
to change directions at higher speeds. Subsequent
models had steeper trade-offs between speed and
manoeuvrability, which are representative of running
and changing directions on increasingly higherfriction substrates. Experiment 2 was identical to
Experiment 1 except that the maximum absolute
speed was lower, and the range varied between 0.1
and 40 pixels per loop (N ¼ 30 subjects). We
expected that this lower range in maximum speed
would result in a lower probability of escape for
the prey that used only straight movements. This
accurately describes many predator–prey interactions
in nature in which it is the predator, rather than the
prey, that possesses the greater maximum speed.
In Experiments 3 and 4, we again explored how
speed of movement by the prey affected the
probability of escape when the magnitude of the
trade-off between speed and maneuverability varied.
However, in this case the points of intersection
between all the trade-off functions occurred at
mid-speeds. This meant that any increases in
maneuverability at lower speeds were associated
with equivalent decreases in maneuverability at
higher speeds. It was the slope of this function that
represented the magnitude of the trade-off. Thus, we
compared five different trade-off functions that
differed in magnitude, with the steepest trade-offs
possessing the highest maneuverabilities at low
1146
speeds and the lowest maneuverabilities at high
speeds. The lowest trade-off showed no change in
maneuverability with a change in speed. In
Experiment 3 the top speed was 60 pixels per loop
and in Experiment 4 the top speed was 40 pixels per
loop (N ¼ 30 subjects in each case).
Finally, in Experiment 5 we explored how speed of
the prey affected the probability of escape when the
shape of the trade-off between speed and
maneuverability varied in non-linear ways. The ability of some animals to change direction may not be
greatly affected until they are close to their top
speed. Alternatively, an animal’s ability to maneuver
may be compromised at low speeds. In Experiment 5
the top speed was 40 pixels per loop (N ¼ 30
subjects).
Varying predators’ ability
The above examples varied only the attributes of the
prey species, but it is also of interest to determine
the effect of variation in a predator’s performance as
it affects the prey’s optimal speed for escape. To do
this we allowed four subjects to complete Experiment
1 10 times in a row with the expectation that predators will become better at catching dots with more
experience. We then analyzed the effect of increased
skill of the predator on different types of trade-off.
Statistical analysis
The logic behind our analyses is that we sought to
identify the prey’s speed that resulted in the highest
probability of successful escape. For each trade-off
between speed and maneuverability, we wanted to
(i) compare the optimum speed to use for escape
among these trade-off functions, (ii) identify the
range of potential speeds of the prey that were
associated with high success in escape, and (iii)
ascertain the peak performance in escape that occurred at the prey’s best speed. Using performance
curves to evaluate function–value traits has a rich
history in thermal biology (Huey and Stevenson
1979; Huey and Kingsolver 1989; 1993; Angilletta
et al. 2002, 2010; Angilletta 2009) and we used the
methodologies for describing thermal performance
curves to compare the parameters of success for
each trade-off function between speed and
maneuverability. To quantitatively compare the
effects of the different trade-off functions within
each experimental group on the prey’s performance
in escape, we used the error distance (the distance
between the center of the dot and the center of
touch) as a continuous variable to produce a
performance curve for each trade-off model with
C. J. Clemente and R. S. Wilson
increasing speeds. The greater this distance, the
greater is the error by the predator, and the farther
is the prey from the predator’s strike. This distance
was logarithmically transformed to normalize it.
Based on analyses of thermal performance curves,
we then extracted three variables to compare
among the phenotypes with different trade-off
functions (Fig. 3). The maximum error of the score
(MaxErr) was the greatest mean distance between the
prey’s position and the central point of the
predator’s strike for each phenotype. The prey’s
speed at the maximum error was taken as a
phenotype’s optimal speed of escape (SpEsc). The
range of prey’s speeds over which a phenotype had
an error distance that was 80% of their maximum
error was taken as their breadth of performance
(BrScr).
Data were analyzed in the statistical computing
language R (R Development Core Team 2014). We
used the glm.R function from the base package in R
to perform the binomial generalized linear model fit,
to confirm that both speed and maneuverability had
a significant effect on the probability of the dot being
hit. For each of the three variables that were extracted from the performance curves, we used a
one-way within-subjects ANOVA using the aov.R
function from the base package in R. Tukey posthoc tests were performed using the TukeyHSD.R
function also from the base package. To
determine the effect of learning we used the error
distance
in a
three way-factorial
design
implemented using the aov.R function in R,
including speed, maneuverability, and trial number.
Similarly for performance-curve variables, we used a
two-way within-subjects ANOVA using the aov.R
function.
Results
Both speed and maneuverability independently
affected the probability of escape (Experiment 1:
Speed z ¼ 32, P50.001; Maneuverability z ¼ 11,
P50.001). The relationship between a prey’s speed
and its success in escaping was described by a logistic
function (Fig. 4a) while there was a positive linear
relationship between maneuverability and escape
(Fig. 4b).
For Experiment 1, the peak performance and the
optimal speed of escape did not significantly vary
among the phenotypes that differed in trade-offs
between speed and maneuverability (MaxErr
F ¼ 0.84, P ¼ 0.499; SpEsc F ¼ 1.8, P ¼ 0.133).
However, the range of speeds over which escape
performance was 80% of maximum significantly
Balancing biomechanical constraints
1147
Fig. 3 The input (left) and results (right) for five different experiments modeling trade-offs between speed and maneuverability. For
each experiment five different model trade-offs were tested, representing low friction surfaces (lighter shades) to higher friction
surfaces (darker shades). (This figure is available in black and white in print and in color at Integrative and Comparative Biology online.)
1148
C. J. Clemente and R. S. Wilson
Fig. 4 Effects of speed and maneuverability showing the effect of speed for all points in Experiment 1, model 1 where maneuverability
is nearly constant (a) and the effect of maneuverability, when speed is held constant at 21 pixels/loop (b). The line in each panel
represents the curve predicted from the logistic regression model for each performance measure with the probability of being hit. (This
figure is available in black and white in print and in color at Integrative and Comparative Biology online.)
varied among phenotypes with different trade-offs
(BrScr F ¼ 7.1, P50.001; Fig. 5). A Tukey post-hoc
test suggested that phenotypes with the shallowest
trade-offs (phenotypes 1 and 2) were significantly
different from phenotype 5. In Experiment 2, peak
escape performance and the optimal speed of escape
also did not significantly vary among the phenotypes
(MaxErr F ¼ 0.35, P ¼ 0.854; SpEsc F ¼ 0.34,
P ¼ 0.849). However, the breadth of speeds over
which escape performance was 80% of maximum
significantly varied among the phenotypes (BrScr
F ¼ 4.7, P ¼ 0.001; Fig. 5), with a significant
difference between the two most extreme phenotypes
(phenotypes 1 and 5) (Tukey post-hoc test).
For Experiment 3, peak performance significantly
varied among the phenotypes that differed in tradeoff functions (MaxErr F ¼ 4.59, P ¼ 0.002; Fig 5),
with a Tukey’s post-hoc test revealing phenotype 1
(no trade-off) as having the highest peak performance and phenotypes 4 and 5 (steepest trade-offs)
the lowest. However, the optimal speed of escape did
not vary significantly among the phenotypes that differed in trade-off functions (SpEsc F ¼ 0.67,
P ¼ 0.611), with the mean optimal speed across all
phenotypes at approximately 90% of maximum
speed. As for previous experiments, the range of
speeds over which performance was 80% of maximum significantly differed among phenotypes
(BrScr F ¼ 4.2, P ¼ 0.003; Fig. 5). Phenotypes with
the steepest trade-offs (phenotypes 4 and 5) had
the broadest range in performance (Tukey post-hoc
test). For Experiment 4, the peak performance and
the optimal speed of escape did not vary significantly
among the phenotypes that differed in trade-off
functions (MaxErr F ¼ 0.88, P ¼ 0.479; SpEsc
F ¼ 1.5, P ¼ 0.198), but breadth did vary significantly
(BrScr F ¼ 2.62, P ¼ 0.039; Fig. 5) and was broadest
for those phenotypes with the steeper trade-offs
(phenotypes 3 and 5).
For Experiment 5, the peak performance and the
optimal speed of escape significantly varied among
phenotypes that differed in trade-off functions
(MaxErr
F ¼ 7.1,
P50.001;
SpEsc F ¼ 4.3,
P ¼ 0.003), but the breadth of the curve did not
change
among
phenotypes
(BrScr
F ¼ 1.0,
P ¼ 0.384). The peak performance was greatest for
those phenotypes in which increases in the speed
of the prey decreased maneuverability only at the
higher speeds (phenotypes 4 and 5). Optimal
speeds of escape were also lowest for those phenotypes in which increases in the prey’s speed decreased
maneuverability only at the higher speeds, which was
approximately 70% of peak speed (Tukey’s post-hoc
test).
Effect of learning on prey’s survival
When our human subjects conducted more trials
their ability to capture the simulated ‘‘prey’’
moving across the tablet’s screen improved. Success
in capturing prey increased and the mean error
distance decreased as participants performed more
trials (Fig. 6). However, the effect of learning on
success in capturing prey was dependent on the
prey’s speed but not on its maneuverability,
suggesting that any improvement in the subjects
increased their ability to capture fast, but not
maneuverable, prey (Table 1).
We also compared how improvement in the
subject’s ability affected parameters that described a
prey’s performance among the different phenotypes
with varied trade-off functions (Fig. 7). Maximum
performance by the prey was affected by its
phenotype and trial number. Further, the ability of
the subject to improve depended upon the prey’s
phenotype, with steeper trade-offs associated with a
lower learning response (Table 2). However, optimal
escape speed was not affected by the prey’s
phenotype or by the trial number (Table 2).
1149
Balancing biomechanical constraints
Fig. 5 Effects of different models (group) on the curve for escape performance shown in Fig. 3. Max error is the maximum error-score
achieved. Speed at max error is the speed at which the maximum error-score was achieved, and the breadth of the performance
(error) score, is the calculated distance between the maximum and minimum speeds when the error score was 80% of the maximum
error. Only plots with significant results are shown (N.S. indicates non-significant results, where P40.05). Boxes represent the median
with hinges representing the first and third quartiles. Whiskers represent the 95% CI, and dots represent outliers. (This figure is
available in black and white in print and in color at Integrative and Comparative Biology online.)
Finally, the range of speeds over which performance
was 80% of maximum was significantly affected by
the prey’s phenotype (as shown above in Experiment
1) but not by its trial number (Table 2). These results indicate that only the maximum performance of
the prey was affected by learning, and the magnitude
of this change was dependent upon the prey’s
phenotype.
Discussion
Animals rarely use their fastest running speeds in
nature, even when they are fleeing from predators
(Irschick and Losos 1998; Wynn et al. 2015). The
biomechanical trade-off between speed and
maneuverability—both of which are important for
escaping predators, make the use of top speeds
when running away from predators unlikely. In this
1150
C. J. Clemente and R. S. Wilson
Fig. 6 The influence of learning on the successful capture of ‘‘prey’’ (dots), measured as total error between the dot and the center of
touch in pixels (a) and the number of hits; a hit is deemed to have occurred if the error5radius of the dot (b). The line represents the
least-squares regression for the linear model comparing trial number with the total error (or total hits). See Table 1 for the results of a
three-way model comparing speed, maneuverability, trial number, and their interactions. (This figure is available in black and white in
print and in color at Integrative and Comparative Biology online.)
Table 1 The effect of learning on success in escaping when
co-varied with speed and maneuverability based on a three-way
factorial design implemented using the aov.R function in R of the
form fit5- aov(Error Speed * Maneuverability * Trial)
F-value
Speed
Maneuverability
Trial
Speed : Maneuverability
2678
444.3
11.03
213.3
P-value
50.001
50.001
50.001
50.001
Speed : Trial
8.617
0.003
Maneuverability : Trial
0.769
0.380
Speed : Maneuverability : Trial
1.062
0.302
study, we explored the influence of different trade-off
functions between speed and maneuverability on the
way an animal’s selected speed affects its success in
escaping predators. We used tablet-based games that
simulated the interactions between predators
and prey—human subjects acted as predators by
attempting to capture ‘‘prey’’ (dots) moving across
the screen. Our metric of success in escaping was the
distance between the prey (position of the dot on the
screen) and the human ‘‘subjects’’ point of contact
on the tablet’s screen. The assumption was that the
greater the distance between the subject’s contact
with the screen and the prey’s position, the lower
would be the probability of capture. Although results
varied among experiments, we found the shape of
the trade-off function between speed and
maneuverability affected the prey’s optimal speed
for success in escaping, and the breadth of speeds
over which the prey’s performance was high relative
to its maximum performance.
We found that the optimal speed for escape
only varied when the trade-off between speed
and maneuverability was non-linear. Phenotypes
possessing
trade-off
functions
in
which
maneuverability was only compromised at high
speeds exhibited lower optimal speeds of escape.
Because speeds at 80% of a phenotype’s maximum
also exhibited relatively high maneuverabilities, then
these speeds offered the highest probabilities of
successful escape. In contrast, phenotypes possessing
trade-offs in which substantial increases in
maneuverability were only possible at very low
speeds possessed higher optimal speeds for success
in escaping. Thus, our results, based on our
simulated predator–prey games, show that optimal
speeds of escape can be dependent on the nature
of the trade-off between speed and maneuverability.
Testing this idea using real-world predator–prey
interactions is an important next step and could be
undertaken by examining the speeds and trajectories
of animals running on different substrates. First,
one could quantify the effect of substrate friction
(e.g., compacted substrate versus slippery rock) on
the straight-line running speed and turning ability
of an animal. Next, one could observe the actual
selected running speeds of the study animal when
escaping along the different substrates, thereby
testing how they modify their locomotor behavior
in response to the kind of substrate. Intuitively, we
know that humans do this when running or driving
along different substrates (e.g., dry bitumen versus
ice), so we should also expect animals to be capable
of selecting the most appropriate locomotor behavior
for specific circumstances.
Phenotypes that exhibited greater increases in
maneuverability for any decrease in speed were
more likely to have broader ranges of performance,
Balancing biomechanical constraints
1151
Fig. 7 The interaction between learning (trial) with different trade-off models based on three characteristics of the performance curve:
(a) the maximum error over a range of speeds—MaxErr, (b) the speed at the maximum error—SpEsc, and (c) the breadth score of the
performance curve when the error is greater than 80% of maximal error—BrScr. Boxes represent the median with hinges representing
the first and third quartiles. Whiskers represent the 95% CI, and dots represent outliers. (This figure is available in black and white in
print and in color at Integrative and Comparative Biology online.)
meaning that individuals could attain at least 80% of
their maximum performance across a broader range
of escape speeds. Greater potential speeds with similar successes in escape offer prey a broader range of
strategies, making the tactics of prey more difficult to
predict. In other words, the advantage of this strategy
would be increased behavioral flexibility, allowing an
organism to be able to negotiate a range of
1152
C. J. Clemente and R. S. Wilson
Table 2 The effect of learning on the shape of the escapeperformance curve shown in Fig. 3
F-value
P-value
MaxErr
Model
Trial
Model : Trial
3.81
20.1
0.005
50.001
2.86
0.025
Model
1.92
0.109
Trial
0.31
0.581
Model : Trial
0.31
0.872
SpEsc
BrScr
Model
6.79
50.001
Trial
3.14
0.078
Model : Trial
0.73
0.569
Notes: MaxErr is the maximum error over a range of speeds. SpEsc is
the speed at the maximum error, and BrScr is the breadth score of
the performance curve when the error is greater than 80% of the
maximal error. For each performance variable a two-way factorial
analysis design was used implemented via the aov.R function in R.
environments without a drastic reduction in fitness.
Erratic and unpredictable movements can reduce the
likelihood of predation (Humphries and Driver 1967;
Driver and Humphries 1988; Combes et al. 2012). In
addition, a wider range of strategies can allow prey
to potentially tailor their escape behavior to specific
predators and thereby exploit the predator’s
weaknesses. Some predators may be very successful
at capturing rapid, straight-running prey but struggle
when attempting to capture prey that use more
maneuverable strategies. Several examples exist in
which prey species tailor their escape strategy to
the identity and the perceived threat of a predator
(Bonenfant and Kramer 1996; Cooper 1997, 2011;
Blumstein and Daniel 2005; Cooper and Frederick
2007). If prey species can select among multiple
strategies with similar successes, then they should
select the strategy that is going to be more difficult
for the specific predator.
Flexible tailored strategies have also been observed
in response to specific environmental conditions in
leaf-cutter ants, Atta sexdens (Angilletta et al. 2008).
Leaf-cutter ants used straighter, more-predictable
trajectories at higher temperatures (when ants are
faster) and curved, less-predictable trajectories at
lower temperatures (when ants are slower). In a similar way, specialization of Anolis lizards to different
diameters of perches can have consequences for their
behavioral flexibility. Anolis with short limbs tend to
occupy habitats with narrow perches, while longerlimbed species occupy broad, flat surfaces (Williams
1983). The long-limbed species are faster than
shorter-limbed species on broad, flat surfaces, but
their speeds dramatically decline on the narrow
perches, along with an increase in the number of
slippages (Losos and Sinervo 1989). In contrast, the
shorter-limbed species experience little decline in
speed on narrow perches (Irschick and Losos 1998,
1999; Spezzano and Jayne 2004), and have the flexibility to choose escape paths on narrow and broad
surfaces with little decrease in the capacity for
performance.
Another potential advantage for a maneuverable
strategy is that it could be more difficult for a
predator to learn to adapt to unpredictable turns
than to the more predictable, but faster, straight-line
movement. We tested this idea by examining the
ability for our human subjects to learn to capture
high-speed prey and highly maneuverable prey. We
found there was a differential response to learning
these different locomotor components. With
increased experience through repeated trials, subjects
were able to successfully catch faster and faster dots.
However, no improvement was observed in the
subject’s ability to capture more maneuverable
prey. This reflects previous results using this tabletgame; human subjects waited for longer periods
before attempting to catch faster prey, but the time
it took to capture the dot was insensitive to changes
in the prey’s maneuverability (Clemente and Wilson
2015). Together, these data suggest that when
predators have the potential to improve with
experience, there may be a survival advantage for
those prey favoring maneuverability at the expense
of speed, which decreases the optimum speed for
successful escape.
Previous studies exploring the underlying
determinants of success in escaping predators have
primarily focused on the role of maximum running
speeds. There is certainly an intuitive appeal to the
idea that individuals with the fastest straight-line
running are those that are most likely to escape
predation. Indeed, some studies reveal that faster
individuals are more likely to escape predators than
are slower individuals, but many studies also show a
limited influence of the maximum speed of prey on
the probability of escape. For example, faster
juveniles and adults of the lizard Urosaurus ornatus
were more likely to survive until the next sampling
period than were slower individuals (Miles 2004;
Irschick and Meyers 2007); yet sprint speed did not
affect survival for hatchlings of the lizard Sceloporus
occidentalis (Bennett and Huey 1990). However, both
speed and maneuverability are likely to determine
the probability of escape from a pursuing predator,
Balancing biomechanical constraints
and because these two traits are negatively associated
we should also expect that the highest probability of
escape would result from a compromised strategy
between the relative importance of speed and
maneuverability. We found that the shape of
the trade-off function between speed and
maneuverability affects the optimal speed for escape
and the flexibility of the behavioral options available
to the prey. Our work highlights the need to recognize that the costs for high-speed movement on
other traits, including maneuverability, make the
use of an animal’s fastest speed unlikely, even when
attempting to escape predators.
By investigating the shape of the trade-off
functions between speed and maneuverability and
the way the environment mediates this trade-off,
we can begin to understand the choices of speed
by animals running away from predators or attempting to capture prey. We also hope that tablet-based
games inspire further studies investigating the
evolution of predator-avoidance tactics. The current
program has the potential to directly compare the
strength of selection on different performance
variables, by including multiple generations of dots
that are subjected to predation events. Selection of
traits over successive generations may highlight competing strategies associated with phenotypic tradeoffs and behaviors, and lead to a better understanding of this process, in a way that is almost impossible
when studying natural populations.
Funding
C.J.C. was supported by an ARC DECRA Fellowship
(DE120101503) and R.S.W. was supported by an
ARC Discovery Grant (DP150100198). We thank
the Company of Biologists for a travel award that
helped support attendance at the SICB conference.
We also thank members of the Wilson Performance
Lab for assistance with running the experiments
and critiquing earlier versions of the program. We
particularly thank Nora Allen for help in finding
volunteers to help catch dots. The University of
Queensland Ethics Committee for Human
Experimentation approved all experiments. We
thank both anonymous reviewers for their comments
and suggestions that substantially improved the
manuscript. The authors declare no conflict of
interest.
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