Integrative and Comparative Biology
Integrative and Comparative Biology, volume 55, number 6, pp. 1125–1141
doi:10.1093/icb/icv106
Society for Integrative and Comparative Biology
SYMPOSIUM
Predicting the Movement Speeds of Animals in Natural
Environments
Robbie S. Wilson,1,* Jerry F. Husak,† Lewis G. Halsey‡ and Christofer J. Clemente§
*School of Biological Sciences, The University of Queensland, St Lucia, QLD 4072, Australia; †Department of Biology,
University of St. Thomas, 2115 Summit Avenue, St Paul, MN 55105, USA; ‡Department of Life Sciences, University of
Roehampton, SW15 4JD, UK; §School of Biological and Health Sciences, University of the Sunshine Coast, Queensland
4556, 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 An animal’s movement speed affects all behaviors and underlies the intensity of an activity, the time it takes to
complete it, and the probability of successfully completing it, but which factors determine how fast or slow an animal
chooses to move? Despite the critical importance of an animal’s choice of speed (hereafter designated as ‘‘speed-choice’’),
we still lack a framework for understanding and predicting how fast animals should move in nature. In this article, we
develop a framework for predicting speed that is applicable to any animal—including humans—performing any behavior
where choice of speed occurs. To inspire new research in this area, we (1) detail the main factors likely to affect speedchoice, including organismal constraints (i.e., energetic, physiological, and biomechanical) and environmental constraints
(i.e., predation intensity and abiotic factors); (2) discuss the value of optimal foraging theory in developing models of
speed-choice; and (3) describe how optimality models might be integrated with the range of potential organismal and
environmental constraints to predict speed. We show that by utilizing optimality theory it is possible to provide quantitative predictions of optimal speeds across different ecological contexts. However, the usefulness of any predictive
models is still entirely dependent on being able to provide relevant mathematical functions to insert into such
models. We still lack basic knowledge about how an animal’s speed affects its motor control, maneuverability, observational skills, and vulnerability to predators. Studies exploring these gaps in knowledge will help facilitate the field of
optimal performance and allow us to adequately parameterize models predicting the speed-choice of animals, which
represents one of the most basic of all behavioral decisions.
Introduction
Movement is fundamental to animal behavior, governing the way animals use habitats, interact with
conspecifics, avoid predators, obtain food, and even
negotiate human-modified landscapes. A wide range
of factors drive movement, including an animal’s internal state (why move?), motion (how to move?),
and navigational decision-making (when and where
to move?). The rapidly expanding field of the ecology
of movement offers a unifying paradigm for the
causes, consequences, underlying mechanisms, and
patterns of movement-related phenomena (Nathan
et al. 2008), but what determines how fast an
animal chooses to move? This may seem like a
simple question, but it is a key one: speed underlies
the intensity of an activity, the time it takes to complete it, and the probability of successful completion.
Despite the universal importance of speed and its
central role in ecology, we still lack a framework
for understanding and predicting how fast or slow
animals should—or do—move through their environments. The goal of this article is to construct
such a framework, and thereby facilitate studies of
movement speed that integrate its biomechanical, energetic, and ecological foundations.
This kind of integration is not entirely new: the
functional traits of individuals—such as morphology,
physiology, and biochemistry—have long been linked
Advanced Access publication October 22, 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].
1126
5
Number of species
with reproductive success and survival via wholeanimal performance (Bartholomew 1966; Arnold
1983; Bennett and Huey 1990). Whole-animal performance is usually defined as the maximum speed
or effort an individual can attain in a task relevant to
their fitness. The integration of the function of
whole-animal performance into studies of the evolution of form and function was initially driven by the
realization that this level of function is more closely
related to fitness than to lower-level traits (Huey and
Stevenson 1979; Bennett 1980). However, the intuitive appeal of maximum performance as a critical
link between the phenotype and fitness has led to
an almost exclusive focus on maximal performances
when studying the determinants of success (Jayne
and Bennett 1990; Miles 2004; Irschick and Meyers
2007; Wilson et al. 2007a; Irschick et al. 2008). Some
studies have provided clear evidence supporting this
assumption. 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). Despite the obvious appeal that higher performers should have greater fitness, field observations
show that animals rarely move at their maximum
capabilities in nature (Jayne and Ellis 1998; Irschick
2002; Husak and Fox 2006) (Fig. 1).
A common interpretation of the rare use of maximal capacities is that animals should only use these
during rare fitness-defining activities like escaping
predators or capturing prey (Hertz et al. 1988;
Irschick et al. 2005). However, even during these
infrequent events, when success really matters, maximal speeds rarely are used (Irschick et al. 2005;
Wilson 2005; Husak and Fox 2006). For example,
collared lizards (Crotaphytus collaris) use only 30–
40% of their maximal capacity when trying to capture a simulated prey item and similar speeds when
attempting to capture real prey in the wild (Husak
and Fox 2006). Animals tend to use a greater proportion of their maximal capacity when running
away from predators (Irschick et al. 2005; Husak
and Fox 2006), but still it is often only 60–80% of
their maximal capacity (Husak 2006a). The use of
sub-maximal speeds when performing fitness-defining tasks is not just limited to lizards. Males of the
eastern mosquitofish (Gambusia holbrooki) only
obtain successful copulations using coercive swimming tactics in which they approach a female with
stealth, place their intromittent organ (gonopodium)
into the female’s gonadopore, and release their packages of sperm (Wilson 2005). Obviously, the ability
to obtain coercive matings is a critical determinant
of a male’s reproductive success for G. holbrooki, but
R. S. Wilson et al.
Escaping predator
4
Capturing prey
3
2
1
0
30
40
50
60
70
80
90
100
Percent maximal speed
Fig. 1 Distributions of speeds used by lizard species while capturing prey or escaping predators. Data compiled from Irschick
and Losos (1998), Jayne and Ellis (1998), Irschick and Jayne
(1999), Irschick et al. (2005), Husak and Fox (2006), and Muñiz
Pagan et al. (2012).
the approach speeds used by males to obtain copulations are only about 30% of their maximal speed of
swimming (Wilson 2005). Rather than being surprised by the low speeds of animals during critical
fitness-defining behaviors, we should ask ourselves
why animals rarely use their maximal capabilities
and how can we begin to predict the speeds they
choose in natural environments?
The expectation that faster is always better is
overly simplistic. Maximum speeds are energetically
costly (Hoyt and Taylor 1981; Steudel-Numbers and
Wall-Scheffler 2009), constrain motor control and
maneuverability (Alexander 1982; Wynn et al.
2015), and may affect visibility and safety
(Bednekoff and Lima 1998; Treves 1998).
Therefore, the speed of movement, even during extreme situations like escaping predation, should be
based on a compromise between a range of factors.
Such constraints on speed also impact humans’ behavior during everyday activities—intuitively, we are
all aware of this. Humans rarely use their maximal
speeds for common daily tasks because high speeds
increase energetic costs (Steudel-Numbers and WallScheffler 2009) and can decrease the control and accuracy of a movement (Fitts 1954). Just consider
how one would approach typing out a text message
if one were already late to an important meeting. We
may not wish to be even later to the meeting—
especially given the social costs of delaying
colleagues—so getting the text message done without
delay may make rapid typing favorable. However,
typing requires accurate finger placement and a potential mistake, which is more likely at higher speeds,
could be very costly, both because of the social
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Predicting the speeds of animals
embarrassment of sending a message that is full of
mistakes and because it may be incomprehensible.
Typing at a slower, more measured speed is likely
to improve readability of the message and decrease
any chances of having to retype a message. In this
case, there may be an optimal speed for finger movement that is a compromise between speed, accuracy,
and social constraints. We expect similar constraints
to operate on the speeds of animals across natural
ecological contexts, with the ultimate selection of
speed based on a compromise between competing
demands.
In this article, we develop a framework for predicting speed that is applicable to any animal—
including humans—performing any behavior where
choice of speed occurs. Testing these ideas will require a trans-disciplinary approach, incorporating
expertise from the fields of metabolic physiology,
neurophysiology, biomechanics, mathematical modeling, behavior, evolution, and ecology; in fact, the
diverse expertise required to effectively study speedchoice is probably why the field has not progressed
further. To inspire new research in this area, we will
(1) detail the main factors likely to affect speedchoice, including organismal constraints (i.e.,
energetic, physiological, and biomechanical) and environmental constraints (i.e., predation intensity and
abiotic factors); (2) discuss the value of optimal foraging theory in developing a model of movement
speeds; and (3) describe how optimality models
might be integrated with the range of potential organismal and environmental constraints to predict
speed. We then consider how a framework for predicting speed-choice might be used in the fields of
animal behavior, evolution, conservation biology,
and sports science. Finally, we discuss the significance of predicting the movement speed of animals
in studies exploring the ecology and evolution of
organismal performance.
Building a universal framework for
predicting animal movement speeds:
what factors affect speed-choice?
Speed-choice is a complex trait, driven by an animal’s need for food and sociality but constrained
by energetic costs and the risk of injury or death.
In this section, we outline the factors that we
expect to affect speed and the parameters that will
form the basis of our predictive framework.
Although this is certainly not an exhaustive list, we
expect these to be the main drivers of speed-choice
across most ecological contexts (Fig. 2). We have
divided these factors into internal constraints,
which include the morphological, physiological, and
neurobiological features inherent to the individual
and external constraints, which include the biotic
and abiotic factors outside it.
Internal factors affecting the choice of speed
Increasing speed changes the biomechanics of movement and reduces an individual’s ability to observe
their environment. Consequently, we expect speedchoice to be influenced by (1) the energetic costs
of movement, (2) trade-offs between speed and maneuverability, (3) trade-offs between speed and motor
control, and (4) the costs associated with detection of
the environment (i.e., predators, prey, mates, or obstacles) during movement. The individual’s state—
including its body size, mass, sex, condition, and life
stage—should mediate these factors.
Energetics of movement
Locomotion is expensive, and the energetic costs of
movement are likely to be a major driver of an animal’s choice of speed in nature. As an animal moves
through a varied landscape, it expends energy differently, depending on how fast it is going and the
characteristics of the terrain it is traversing. For
many animals moving across level ground, the rate
at which energy is spent increases in direct proportion to the speed of the movement (Schmidt-Nielsen
1972; Taylor et al. 1982). This would seem to suggest
that individuals expend energy at the same rate when
moving themselves, regardless of speed, and that
there is no energetic advantage to moving slowly
versus quickly. However, movement bears fixed
costs not associated with speed: animals expend
energy for faculties not related to movement—even
as they move—and appear to pay an energetic price
simply for striking a posture for locomotion (Halsey
2013) (Fig. 3A). Because of this, lower speeds are
actually more costly per unit distance (net cost of
transport or NCOT), as fixed costs must be paid
over a greater period of time (Fig. 3A).
For some species, the NCOT varies in a complex
way with speed (Fig. 3B). Such species, which include humans, horses, ratites, salmon, and budgerigars, have also been observed to alter their speeds in
ways that minimize NCOT while moving (Tucker
1968; Hoyt and Taylor 1981; Farrell et al. 2003;
Steudel-Numbers and Wall-Scheffler 2009; Watson
et al. 2011; Halsey and White 2012), by altering
the length or frequency of strides (Zarrugh et al.
1974) and shifting their center of mass (Gordon
et al. 2009). Although most animals select speeds
that minimize total cost when moving extended distances (Culik and Wilson 1991; Wickler et al. 2000;
1128
R. S. Wilson et al.
A
Maximum
performance
capabilities
Morphology
Physiology
B
Fitness
Ecological context
Performances
Foraging
Survival
Travelling
Maximum speed
Morphology
Physiology
Trade-offs
Energetics
Maneuverability
Motor control
Selected speed
Fitness
Biotic environment
Predation pressure
Resource availability
Observation skills
Fig. 2 (A) The hypothesized relationship between lower-level structural traits (morphology, physiology, and biochemistry) with fitness
via its effects on whole-animal performance (Arnold’s [1983] paradigm). This conceptual framework is based on the idea that organisms
will utilize their capabilities for maximum performance during important fitness-defining activities related to energy, safety, and reproduction. (B) An hypothesized relationship between lower-level structural traits (morphology, physiology, and biochemistry) with
fitness that places an emphasis on the importance of how animals choose the speed with which they perform important ecological
tasks. An animal’s underlying morphology, physiology, and biochemistry affects their maximum capabilities for speed and also other
critical traits that are compromised by high-speeds (energetics, maneuverability, motor control, and observation skills). Based on these
trade-offs, the ecological context of the activity being performed, and the biotic environment, an animal’s fitness will be dependent on
how fast they choose to move, which rarely will be at its maximum capability.
Minetti et al. 2003), they may move faster than their
energetically most efficient speed when they are chasing or being chased, or slower than their energetically
most efficient speed when actively scanning their environment (Wilson 2002).
Terrain also plays a major role in the energetic
costs of locomotion (Rees 2004; Shepard et al.
2013). More energy is required to walk on sand
than on grass (Pinnington and Dawson 2001), and
the costs of movement increase with depth of snow
(Pandolf et al. 1976; Fancy and White 1987; Crête
and Larivière 2003). Inclines increase NCOT (Snyder
and Carello 2008; Tullis and Andrus 2011; Lees et al.
2013), while declines require less energy for most
animals (e.g., Armstrong et al. 1983; Fancy and
White 1987), at least until the angle becomes steep
(Minetti et al. 2002). Animals may change their style
of locomotion and thereby take advantage of declines; for example, Adelie penguins use less energy
moving downslope via tobogganing, compared with
walking (Wilson et al. 1991).
Changing direction of travel also affects the energetics of movement (Wilson et al. 2013b; Amélineau
et al. 2014) unless the animal is able to use its environment to facilitate the change (as in soaring on
thermals; Shepard et al. 2013). A human walking in
a straight line at 1.67 m s 1 will increase his or her
expenditure of energy by 18% by turning 908 every
10 s and by nearly 30% if they turn 908 every 6 s
(Wilson et al. 2013b). Changing direction requires
a force to exact change, as well as forces to accelerate
and decelerate; animals on the move therefore do not
change direction or speed without good reason.
Maneuverability
Animals must maneuver around obstacles in complex habitats and often use tight turns in predator/
prey chases; yet few studies have directly modeled or
measured the costs of maneuverability in terrestrial
animals (but see Full et al. 2002). Early efforts in this
field focused on turning gambits between predators
versus prey in aerial animals. In a simulated turning
game, Howland (1974) examined how forward speed
and turning radius affected the ability to escape. His
model predicted that an individual prey should
escape when its normalized speed (prey’s speed/predator’s speed) is greater than the square root of its
normalized turning radius (prey’s turning radius/
predator’s turning radius). Although this simple
model has been useful in predicting the probabilities
of escape (Hedenstrom and Rosen 2001), it tells us
little about how turning and escape happen.
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Predicting the speeds of animals
Cost of transport p/km
A
Cost of transport p/km
B
Movement speed
Fig. 3 Hypothetical relationships between the expenditure of
energy per km and the speed of movement for different animals.
(A) For some animals the net cost of transport (NCOT) for a
given distance decreases with speed, whereas (B) for some
others (e.g., birds, kangaroos) the NCOT per unit distance varies
in a U-shaped function and the most energetically efficient means
of moving a fixed distance is at intermediate speeds.
Fundamentally, maneuverability is constrained by
the musculoskeletal system (Jindrich and Qiao 2009)
and basic physics (Alexander 1982). Turning when
running requires an animal to change the main
vector of motion and rotate its body to the new
orientation (Jindrich and Full 1999), meaning that
a turning animal must overcome its inertia and undergo angular motion (Zollikofer 1994). To do this,
it must produce greater stabilizing forces when turning than when running in a straight line. An animal
running at a particular speed (v) around a curve of
radius r can only continue forward motion as it
changes direction if the coefficient of friction of its
feet with the ground is at least v2/rg (Alexander
1982). This means that an animal needs a larger coefficient of friction to turn at higher speeds or sharper angles, and implies that speed should
compromise turning ability.
The risk of turning too quickly is skidding out, or
sliding, which can increase the likelihood of injury,
capture by predators, or loss of a prey item. Recently,
Wynn et al. (2015) used wild northern quolls
(Dasyurus hallucatus) to explore how the probability
they crashed when running around corners was
affected by their approach speed and turning angle.
Quolls that ran faster into the turn were more likely
to crash, and this probability was higher for tighter
turns. As a result, quolls modulated their speeds:
compared with straight-line running speeds (4.5 m/
s), quolls approached 458 corners 33% more slowly
and 1358 corners 45% more slowly. A similar result
was also shown for three different species of Anolis
lizards, which modulated their speeds when running
around corners of varying magnitude; lizards decreased their running speeds to about 48–79% of
their straight-line speeds when negotiating turns of
908 (Higham et al. 2001).
Maneuverability can also be important for escaping predators by reducing the predictability of the
trajectories of movement. Animals may choose to
maximize either speed or maneuverability under different conditions to take advantage of the unpredictability of movement. In a study of leaf-cutter ants
(Atta sexdens), Angilletta et al. (2008) found that
individuals ran away from threats using straighter,
more-predictable trajectories when they were faster
at high temperatures, but when they were slower at
lower temperatures they ran away using lesspredictable trajectories. Thus, when it is not possible
to move quickly, erratic maneuverable movements—
referred to as protean behavior—may reduce the
likelihood of predation (Humphries and Driver
1967; Driver and Humphries 1988).
Motor control
Movement—particularly that which requires precision
and control—occurs via a complex interplay between
the central nervous system and the musculoskeletal
system, known as motor control. Motor control is
constrained by biomechanical trade-offs that reduce
the accuracy of limb placement at high speeds and
is especially important as animals move across
uneven substrates, over rocks, through trees or anywhere that falling presents a serious risk. Work todate has focused mainly on its physiological and
neural pathways (Daley and Biewener 2006;
Kohlsdorf and Biewener 2006; Toro et al. 2006),
and more recent studies have explored the evolutionary consequences of motor skill (Byers and Kroodsma
2009; Byers et al. 2010; Barske et al. 2011). Previous
studies have not attempted to quantify how the speed
of movement affects the motor control of animals in
natural environments. However, a recent re-analysis of
data from Husak and Fox (2006) revealed that the
Probability of success
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R. S. Wilson et al.
1
Detection of food and danger
0.5
0
0.5
1
1.5
2
Foraging speed (m/s)
Fig. 4 The function describing the effect of approach speed on
the probability of an accurate strike toward a simulated prey item
by collared lizards (Crotaphytus collaris). Videos used by Husak
and Fox (2006) were re-analyzed to determine which lizards
successfully caught the prey item relative to the speed of approach. A logistic regression was used to model the probability of
success for each lizard. If the trials had involved a real prey item,
then the left side of the curve would likely be different, with the
probability of success decreasing at low speeds. Real prey would
have been able to escape the lizards that used low speeds,
whereas in the trials they could not.
faster that collared lizards (C. collaris) ran, the more
likely they were to inaccurately strike at a prey item
and miss it, demonstrating how speed can constrain
motor control in an ecologically important task.
Interestingly, the function of this relationship between
speed and accuracy was logistic whereby there was a
rapid decrease in accuracy above a critical running
speed (Fig. 4).
Early studies of the speed-accuracy trade-off were
based on Fitt’s law (1954), which posits that the time
it takes to move accurately to a target depends on
the size of the target and the distance between the
individual and the target. Accurate movement takes
longer when the target is smaller or father away.
Taken one step further, we can see that hitting the
target becomes less likely when the individual moves
quickly or is particularly uncoordinated (Fig. 5A).
For example, consider a hunter attempting to spear
a fish: the harder the individual throws the spear, the
faster the spear moves between the hunter and the
fish and the more likely he or she is to hit the fish
before it swims away. Although faster throws should
be less accurate they do not necessarily miss the
target (fish) completely—the likelihood of doing so
is simply lower. The spear either misses the fish or it
doesn’t, and by how much it misses is almost irrelevant. This emphasizes the point that we need to
calculate how speed affects the probability of accuracy, rather than the average miss-distance (Fig. 5B).
Speed is also likely to affect an animal’s ability to
observe its surroundings and detect the presence of
predators, mates, and food. Intuitively, we know that
moving slowly increases sensory resolution—imagine
a driver slowing down to look for house numbers—
yet we find no studies exploring this relationship in
animals. Foraging animals routinely pause to scan
their environment for danger (Bednekoff and Lima
1998; Treves 1998), but what about when they are
moving? The shape of the function between speed
and ability to observe could dramatically affect an
animal’s behavior and movement. For example, if
small increases in speed (even at low speeds) decrease the ability to observe, then animals in risky
environments might favor short, rapid movements
interspersed with quick scans (Fig. 6). An extreme
example is found in tiger beetles. These beetles are
capable of running so fast that their vision cannot
cope with the detection of light at these high speeds.
To deal with the blurred vision at high speeds, they
run in a staccato fashion of stops and starts to allow
their vision to become clear (Gilbert 1997). Tiger
beetles also incorporate mechanosensory input
while running, rigidly holding their antennae forward
and slightly downward to detect obstacles (Zurek
and Gilbert 2014).
If an animal’s ability to observe begins to decline
only at moderate speeds, then animals might favor low
to moderate speeds of movement, even when predators are common or food is inconspicuous. The relationship between speed and the ability to observe
could be measured by manipulating the density or
conspicuousness of food in the wild, in semi-natural
arenas, or along a treadmill in the laboratory. In these
cases, the proportion of food detected and the rate of
detection over time can be compared with the animal’s
selected speeds in the wild. This is a key area requiring
more research on behavior and performance.
External factors affecting speed-choice
Abiotic factors such as slope and type of substrate
and habitat are likely to affect movement speeds via
their influence on the internal factors governing the
choice of speed (i.e., energetics of locomotion, maneuverability, motor control, and ability to observe).
For example, animals may be more likely to make
mistakes when running over uneven or low-friction
surfaces, and they may modulate their speeds to account for these risks.
The threat of predation is one of the most powerful selective forces acting on animal behavior, yet
we know little about how speed changes the risk of
1131
Predicting the speeds of animals
A
X
Average error
X
X
X
Un-coordinated
X
X
X
X
X X
X X X
X
X X XX
XX
X X XX X
X
Coordinated
Movement speed
Frequency of event
B
X
X X XX
XX
X X XX X
X
Low movement
speed
High movement
speed
X
X
X X
X
X
X
X
X
X
X X X
0 Miss to the right
Distance from target
Miss to the left
Fig. 5 (A) The faster an individual performs a movement the lower the accuracy of the movement, which will be manifest in a greater
average distance away from the target. In addition, the average accuracy of un-coordinated individuals when performing an action
toward a target will be more affected by increases in speed than for coordinated individuals. When performing a task like throwing a
spear at a fish, then, we would expect a more coordinated individual to have a higher probability of hitting the target than an
uncoordinated individual. (B) The faster an individual performs a task the greater is the increase in the variance in the accuracy. This
change in the variance in accuracy with increasing speed of movement needs to be quantified in order to model an individual’s optimal
speed for a task that is affected by the trade-off between speed and accuracy. When throwing a spear at the fish then we would expect
slower throws to have a higher probability of hitting the target than faster throws, assuming the fish does not swim away.
B
C
D
Prob. of detecting
a predator p/time
A
Movement speed
Fig. 6 The function describing the relationship between an animal’s speed and their probability of detecting a predator per unit time
(p/time) will have implications for optimal speeds when animals are foraging and traveling between patches. The possible functions
could show: (A) Individuals will have a high probability of spotting danger unless they are traveling at high speeds, (B) there is a
threshold speed after which animals are unlikely to detect a threat, (C) a linear decrease in the probability of detecting a predator, and
(D) a rapid decrease in the probability of detecting a threat, even at low speeds of movement.
predation. Movement can make animals more conspicuous to predators, depending on the size and
coloration of the moving animals, their style of
movement, and even the noise they make as they
move, and different habitats offer predators or prey
better places to hide or to blend with their surroundings (Brown and Kotler 2007). Quantifying the relationship between speed, pattern of movement, and
1132
conspicuousness is an important area for future research as the threat of predation should affect the
speeds of most animals across ecological contexts.
Optimality theory as a framework for
predicting animals’ speeds
Optimality theory is an ideal framework for new
models exploring the speed choices of animals. For
40 years, optimality theory has distilled the decisionmaking processes of animals into their competing
demands: energy, time, safety, and social interaction
(Krebs and Kacelnik 2007). At the heart of this approach is the assumption that evolution selects for
approximating efficiency in behavior (i.e., maximizing net gains). Models approach problems by considering an animal’s (1) objective or goal, (2)
available choices, and (3) constraints on these
choices (e.g., physiological limitations on behavior).
Ultimately, we can predict behavior by showing how
constraints affect decision-making; for selection of
speed, these are likely to include energy, safety, biomechanics, and social interactions. Although many
have criticized the assumptions underlying optimality
in studies of animal behavior, it is clear that our
understanding of the factors governing the decisions
of animals and the constraints acting upon behavior
have been enlightened using optimality theory
(Stephens et al. 2007).
To illustrate the utility of optimality for understanding the behavioral choices of animals, let us
consider one of the most basic concepts in optimality
theory, the marginal value theorem (MVT). The
MVT is an optimality model that describes the decision that maximizes the gain of resources per unit
time in systems in which resources—and thus, the
rate of returns—decrease with time (Charnov 1976).
For example, in areas where food is located in defined patches across the landscape, animals must
consider food intake, travel time, and foraging time
as they decide where to go and how long to spend
there; the MVT can then be used to predict when an
animal should give up foraging where they are and
move to another patch, given these factors.
The value of these models is that they can be applied to any situation with diminishing returns.
Consider, for example, copulation by yellow dungflies (Scathophaga stercoraria): in this species, male
flies gather on cow droppings and wait for females
to arrive in smaller groups to lay their eggs. The
longer a male copulates with a female, the more of
her eggs he can fertilize—but by doing so, he misses
out on copulations with other females. How long
should a male spend with each female? MVT predicts
R. S. Wilson et al.
that a male should copulate with a female just long
enough to fertilize about 80% of her eggs (41 min),
because after that point he will fertilize more eggs
per unit time by copulating with a new female rather
than staying with the initial one (Parker 1970); there
are diminishing returns to mating with the same
female. In fact, male flies copulate on average for
very close to the predicted time—about 36 min
(Fig. 7) (Parker 1970).
An optimality approach has already been used to
predict speed by flying animals and by those chosen
by drivers of automobiles, although neither case is
easily generalizable. According to aerodynamic
theory, the total mechanical power needed to
propel a bird through the air is characterized by a
U-shaped curve (e.g., Pennycuick 1969, 1975; Rayner
et al. 2001), in which there are high energetic costs at
high and low speeds. This means that the energetic
costs of flight can be minimized in two ways: either
by selecting the speed that minimizes the power required to fly a given time (Vmp), which reduces
expenditure of power, or the speed that minimizes
the expenditure of energy per distance traveled
(Vmr) (Pennycuick 1975; Rayner et al. 2001). Small
migrating birds seem to fly at their predicted Vmp
when they perform song flights and are ‘‘flying nowhere’’ (Hedenström and Alerstam 1995), while
higher speeds at about Vmr are used when migrating
(Hedenström and Alerstam 1995).
Like studies of flight, research has examined the
factors that influence selection of speed by the drivers of automobiles, although in this case the goal is
manipulating speed to enhance public safety (Graves
et al. 1989; Rodriguez 1990; Andersson and Nilsson
1997). Drivers seem to choose speed based on their
perceptions of safety on a road and the designated
speed limit, and manipulations of speed-choice usually are attempted by increasing the costs of speed via
enforcement (Graves et al. 1989; Rodriguez 1990;
Andersson and Nilsson 1997; Kockelman 2006;
Archer et al. 2008). Drivers do respond to enforcement by reducing their speed—but only when they
perceive the speed limit as appropriate (see e.g.,
Shinar and McKnight 1985)—and the effect of enforcement seems confined to the particular site and
nearby locations and times (Graves et al. 1989;
Rodriguez 1990; Andersson and Nilsson 1997;
Kockelman 2006; Archer et al. 2008). Research is
now being directed toward changing drivers’ perceived speed of travel, for example by using patterned road surfaces that make it appear that they
are driving faster than they are.
From these studies, we know that chosen speed
reflects the balance between energy consumed and
1133
157 min
Number of eggs fertilized
Predicting the speeds of animals
Time to find mate
(mins)
Observed
36 mins
Predicted
41 mins
Copulation time
(mins)
Fig. 7 Parker (1970) empirically measured the effects of copulation time on the number of eggs fertilized by males of the
yellow dung-fly and the average time taken to locate a female
(157 min). Based on the marginal value theorem, Parker (1970)
predicted that males of the yellow dung-fly should copulate with
females for 41 min, which was close to the empirically measured
copulation time of 36 min.
distance moved (in flight) or between travel time and
safety (in driving), but these examples have little relevance for understanding how terrestrial animals
move in nature. They focus primarily on directional
travel between two distant points, when most movements by animals (e.g., foraging, escaping predators,
interactions with conspecifics) vary over short scales
of time and distance. To predict these moment-tomoment choices, we must extend models to incorporate threats of predation, abilities to detect food or
mates, motor control, and maneuverability.
Predicting the speeds of animals when
traveling between patches, foraging, and
during risks to survival
We have now highlighted a range of factors likely to
affect speed and have shown how optimality theory
can use these constraints to predict animals’ decision-making. Below, we discuss how this knowledge
can now be applied to the study of animals’ movement across three important ecological contexts: (1)
traveling between foraging patches, (2) during foraging, and (3) during survival situations like escaping
predators and capturing prey.
Speed when traveling between foraging patches
As shown in studies of avian migration (Hedenström
and Alerstam 1996; Nilsson et al. 2013, 2014), travel
between foraging patches is likely to be driven by the
energetic efficiency of movement—minimizing the
expenditure of energy per unit time or per unit distance. However, two other constraints must be considered: the way that speed affects the likelihood of
spotting, or being spotted by, a predator and the loss
of foraging time during travel. Thus, we would
expect the selection of speeds by animals moving
between feeding patches to be affected by: (1) the
energetic costs of movement per unit time and/or
per unit distance, (2) the probability of detecting
predators, (3) the probability that predators detect
them, and (4) the energetic costs of lost feeding opportunities when traveling.
One of the main issues with multi-factor models is
that each parameter must be incorporated into
models in the same units. In the case of optimal
foraging theory, both the benefits of energy consumption and the costs of predation are translated
into a life-history framework—as energy and predation both impact survival and reproductive success,
or fitness (Ydenberg et al. 2007). We must be able to
translate the costs and benefits of speed in a similar
way.
Urban koalas are ideal for studies of speeds between foraging patches, and information on their
decision rules would also aid conservation efforts.
Koalas are common in southeastern Queensland,
where they spend most of their time foraging in particular types of Eucalyptus trees—preferentially selecting larger foraging trees and leaves of low
toxicity, high digestibility, and high nutritive value
(Hindell and Lee 1987; Lawler et al. 2000; Moore
and Foley 2005; Moore et al. 2010; Ellis et al.
2013). The most dangerous time of a koala’s life is
when it is on the ground moving between trees; between 1997 and 2011, more than 5200 koalas were
killed by dogs or cars in southeastern Queensland
alone, and nearly 6000 additional koalas died from
a combination of cars, dogs, and/or disease during
this time.
Given that koalas are relatively safe in trees but
vulnerable on the ground, how fast should they
move between their foraging patches? A model of
koalas’ transit speeds would need to incorporate
(1) the energetic costs of movement over distance
and time, (2) the link between speed and detection
of, and detectability by, dogs and drivers, and (3) the
energetic costs of lost foraging time, estimated via
the nutritive value of local Eucalyptus trees. Each of
these factors can be empirically determined, allowing
us to develop a model of optimal movement speeds
for koalas that can be tested against observations in
the wild. Ultimately, this work could facilitate habitat
1134
management that minimizes the koalas’ movements—particularly through dangerous areas—and
encourage safer driving during times when koalas
are most likely to be on the ground.
Speeds during foraging
Foraging animals must obtain enough energy for
growth and reproduction while minimizing the
risks of encountering predators, so we expect the
selection of speed to reflect (1) the energetic costs
of movement per unit time, (2) the rate of encountering food, (3) the probability of detecting food
when it is encountered, (4) the probability of being
detected by predators, and (5) the ability to spot
predators while foraging. Again, we must translate
the costs and benefits of speeds into units of fitness,
using a life-history framework.
Consider an actively searching forager, like a monitor lizard—the faster it moves through its environment, the greater number of food items it is likely to
encounter per unit time, but a fast-moving lizard
may also detect fewer food items, so the speed that
maximizes net energy intake is likely to be intermediate (Fig. 8). To the best of our knowledge, no
studies have explored these competing demands on
the foraging speeds of animals, although they could
be easily conducted by manipulating the openness of
the habitat. We expect that animals should move
more quickly in open habitats or where food items
are large—that is, where food is easier to spot—than
in cluttered habitats or where food items are small or
camouflaged (Fig. 8). Because high speeds are also
energetically costly, they should rarely be used by actively foraging animals, although in some cases safety
may play a prominent role in the choice of speed.
Speeds during risky situations
How fast should animals move during situations affecting survival, that is, when attempting to escape
predators or to capture prey? Failure has a high cost,
particularly for those animals attempting to escape
predators, so we do not expect energetic costs to
drive speed-choice in these circumstances; prey will
go as fast as they need to in order to escape. The
stakes for predators are lower than for prey, but
predators’ speeds should still be determined by biomechanical trade-offs between speed, maneuverability, and motor control, and largely ignore the
energetic costs. Thus, in order to predict speeds
during the capture of prey or escape from a predator
we need to quantify: (1) how speed affects success in
the task when free of mistakes, (2) the nature of
trade-offs between speed, maneuverability, and
R. S. Wilson et al.
motor control, (3) how maneuverability and motor
control each affect the task’s success, and (4) the
costs of mistakes. Obviously, the importance and relevance of each factor will be associated with the species and the task that the animal is performing. For
example, the rapid strike of a sit-and-wait snake
toward a mouse is likely to depend more on speed
and accuracy than on maneuverability, and the capture of a gazelle by a cheetah should depend more on
speed and maneuverability than on motor control,
because of the fast speeds and rapid turns in these
chases (Wilson et al. 2013a). Unlike models predicting the movement speed of animals traveling between patches or when foraging, the competing
costs and benefits during situations risking survival
should be modeled using probabilities of the task’s
success.
As an example, let us consider a mouse running
away from a cat (Fig. 9). First, we must describe the
relationship between the mouse’s straight-line running speed (assuming no errors) and its probability
of escape (Fig. 9A). Is the likelihood of escape best
described as a linear function, or as a logistic function—where there is little improvement in escape
probability above a critical speed? Although no studies have quantified the shape of the function between
speed and the escape from predators under natural
conditions, Clemente and Wilson (2015) did so
using a tablet-based game in which human subjects
were asked to ‘‘capture’’ moving prey items (dots on
screen) by touching them as they passed over the
screen. They found a logistic relationship between
speed of the prey and its probability of escape: at
low speeds of the prey, most prey were captured
but the probability of escape rapidly increased over
intermediate speeds to a high speed at which probability of escape was high (Clemente and Wilson
2015) (Fig. 9A). The shape of this function has profound implications for understanding the running
speed selected by escaping prey.
We must then quantify the relationship between
the mouse’s maneuverability and its probability of
escape. In other words, how does the magnitude
of the turn a mouse can make affect its probability
of getting away from the cat? Clemente and Wilson
(2015) found a linear relationship between the sharpness of the turn and the probability of escape—this
can be used as a starting point for predicting escapespeeds in our mouse example (Fig. 9B). Next, we
need to incorporate biomechanical constraints between speed and maneuverability into our model;
in other words, how does speed change the magnitude of turns the mouse can produce and its likelihood of slipping during a turn? It is important to
1135
Predicting the speeds of animals
C
Open habitat
Food
Tree
Food encounter rate
A
Open + cluttered
habitat
B
Cluttered habitat
Food detection rate
D
Open habitat
Cluttered habitat
Energy gained p/time
E
Open habitat
Cluttered habitat
Movement speed
Fig. 8 Exploring the speed of an actively foraging animal when searching for food in a habitat that is open (food easier to find) (A) and
a habitat that is more cluttered (food harder to find) (B). We hypothesize that the speed of the foraging animal will depend on the way
the speed of the search affects the rate of encountering food (C) and the rate of food detection (D). Based on these relationships, we
hypothesize that the effects of speed on the gain of energy per unit time will be different for animals foraging in the open and those in
cluttered habitats. In addition, the optimal speeds for energy gain per unit time will differ for animals foraging in the open compared
with those foraging in cluttered habitats (E).
note that the magnitude of this trade-off will be affected by the substrate on which the animals are
running; a grippy surface will allow much sharper
turns to be made at higher speeds than a slippery
surface (Fig. 9C). By incorporating the costs of any
mistakes (slips or falls)—in this case, how mistakes
would affect the probability of capture—then it is
possible to construct an optimality model of escape
probability based on speed, maneuverability, tradeoffs between speed and maneuverability, the probability of mistakes, and the cost of mistakes. This
model allows us to quantitatively predict how fast
the mouse should run away from a predator.
Manipulations of substrate should change the optimal speed for escape by modifying the trade-off
between speed and maneuverability.
As part of this symposium, Wheatley et al. (2015)
developed a simple mathematical model that
predicted the optimal speed for an animal running
away from a predator along a straight beam. The
straight beam was used as a proxy for straight-line
running that required accurate placement of the feet
in order to avoid mistakes. Although faster speeds
without mistakes were assumed to increase the probability of escape, higher speeds were also more likely
to result in inaccurate placement of the feet, thereby
leading to higher frequencies of mistakes. Their
model predicted that animals should run slower
when the beam was narrower—with greater costs
for missteps—or when an animal’s coordination is
worse. This simple model, consistent with empirical
studies of arboreal lizards on different-sized substrates (Losos and Sinervo 1989; Irschick and Losos
1998, 1999; Spezzano and Jayne 2004; Mattingly and
Jayne 2005; Jones and Jayne 2012), emphasizes the
point that speeds of escape are unlikely to be
1136
R. S. Wilson et al.
maximum speeds across all contexts and that it is
possible to develop quantitative predictions for optimal speeds for escape.
One could similarly apply this framework to tasks
that are associated with social contexts such as sexual
displays or fighting, though the costs and benefits
would be different. For example, males may take
more risks for mating success benefits (Snell et al.
1988; Magnhagen 1991; Andersson 1994). The cost
of rivals usurping mates may also result in higher
movement speeds in order to oust intruding rivals
(Husak et al. 2006, 2008). The same constraints
associated with making mistakes would apply if the
goal is simply to chase away a rival, but the probability of making a costly motor mistake may be
much lower.
Discussion
Movement speed affects all behaviors and can determine the fate of individuals across all ecological contexts. In this article, we set the foundations for
understanding the speed-choices of animals, but
more importantly, we outlined a framework for predicting animals’ speed-choices. By utilizing optimality theory, we show it is possible to provide
quantitative predictions of optimal speeds across different ecological contexts. However, the usefulness of
any predictive model is still entirely dependent on it
being able to provide relevant mathematical functions to insert into the model. We still lack basic
knowledge about how an animal’s speed affects its
motor control, maneuverability, observational skills,
or vulnerability to predators. Studies exploring these
gaps in knowledge will help facilitate the field of
optimal performance and allow us to adequately parameterize models for predicting speeds.
One important factor that complicates our ability
to predict the speeds of animals in nature is determining whether an animal’s speed is because they
choose that particular speed or because they are
forced to use that speed because of some external
environmental constraint. For example, the incline,
compliance, and rugosity (the amount of unevenness) of the substrate on which animals run can dramatically affect the maximum speeds attainable. For
terrestrial organisms, moving on soil, sand, or rocks
presents challenges and potential constraints to
Fig. 9 The hypothesized relationship between the speed (without
mistakes) (A) and maneuverability (B), of a prey species and their
probability of escape from a predator based on the work of
Clemente and Wilson (2015). 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 (C), then the optimal
Fig. 9 Continued
speed for successful escape would differ between low-friction and
high-friction substrates (D). Assuming that the friction of the
substrate only influences the prey’s turning ability and not that of
the predator.
Predicting the speeds of animals
locomotion (Jayne and Irschick 2000; Goodman
et al. 2008; Goodman 2009; Collins et al. 2013).
For example, Sathe and Husak (2015) found a
three-fold decrease in speed when green anole lizards
(Anolis carolinensis) ran on a racetrack with pegs (a
cluttered environment) compared with the same
racetrack without pegs (an open environment).
When determining the extent to which abiotic factors limit speed, one must first determine an animal’s maximum capabilities under the relevant
conditions. For example, when wishing to predict
an animal’s selected speed when running along a
beam of a certain width, one must determine an
animal’s maximum capabilities when running along
this beam while subjected to encouragement by the
experimenter when running freely and without any
mistakes. By then measuring how speed along the
beam affects the animal’s energetic costs of movement, probability of mistakes, ability to observe
their surroundings, and vulnerability to predators
we can then parameterize any model predicting optimal success.
Increased probabilities of mistakes represent one
of the most important costs for high-speed movement. Mistakes can be manifest as slippages when
trying to turn too quickly, tripping when approaching an obstacle too fast, or an inability to accurately
control placement of the limbs at high speeds.
Mistakes make success in any task less likely, but
despite the importance of mistakes, biologists rarely
quantify such mistakes. In order to advance our ability to predict the speeds of animals, we need to begin
to study their mistakes. Because mistakes can also
vary in their costs—or probability of leading to failure of the task—we need to understand the relationship between the types and magnitudes of mistakes
and how they affect success. For example, errors in
the placement of limbs may have very different consequences for quadrupedal animals if they involve
the hind limb rather than the forelimb. In addition,
the costs of crashing could substantially differ between small and large prey running away from a
predator. A loss of footing and a crash for a larger
animal may have much greater costs if it takes longer
to recover and a greater chance of severe injury, and
these costs may be enhanced in arboreal species.
Smaller animals can have spectacular crashes but recover almost immediately and with little chance of
injury.
Our framework for predicting optimal speeds also
has the potential to add to the fields of sports science, conservation biology, and human health.
Improving the performance of athletes in tasks that
require both power and accuracy for success offers
1137
an obvious extension for studies of optimal performance (Lailvaux et al. 2014; Wilson et al. 2014).
Whether it is kicking a football, serving in tennis,
or throwing a ball, success requires both speed and
accuracy. Our framework for studying optimal performance could be used to identify the optimal efforts supporting an individual’s peak success in
performing a task and provide pathways for better
protocols of training (Wilson et al. 2014). In addition, by understanding an animal’s ‘‘decision rules’’
for selecting speeds in nature we could begin to provide a mechanistic understanding of how an animal
uses its home range. Management strategies for most
threatened species focus on when and where animals
move, and the types of habitats they select, but this
ignores how an animal moves through a landscape
and why it chooses to move the way it does. Our
work could enhance conservation efforts by providing a mechanistic understanding of an animal’s use
of its home range and how this use varies as a result
of
environmental—and
anthropogenic—
modifications.
In the context of predator–prey contests it is important to acknowledge that the best strategy for the
predator is going to depend on the strategy used by
the prey. This means a game-theoretic approach
would be best under these circumstances, but
simple models that just consider the behavior of
either the predator or the prey, independent of the
other, will still undoubtedly enhance our understanding of the speed-choices of animals. In addition,
we should acknowledge that there is unlikely to be
just a single optimum value for success in any task.
There may be a variety of speeds for which success is
identical (multiple optima) or a range of speeds over
which success varies little (performance range). For
example, an individual hunter attempting to spear
a fish may be extremely accurate at low throwing
speeds but lose accuracy rapidly at intermediate
speeds before his accuracy plateaus again at
high speeds (logistic relationship). This may mean
that the hunter’s ability to hit the fish may have
equally high probabilities at specific low speeds and
specific high speeds, thus providing multiple optima.
In contrast, another hunter may lose accuracy at a
rate that is proportional to increases in throwing
speed, which effectively results in a very consistent
rate of success (probability of hitting a fish) across all
speeds of throwing (wide performance range). By
quantifying the shape of any function that describes
the relationship between speed and success at a task
should reveal how variance in selected speeds can
affect overall success (Huey and Stevenson 1979;
Bennett 1980).
1138
How does the expectation that animals will rarely
use their maximal capabilities, even during escape from
predators or capture of prey, affect our interpretation
of Arnold’s (1983) eco-morphological paradigm? It is
clear that there are many cases in which variation in
survival and reproductive success are associated with
maximum whole-animal performance (Miles 2004;
Husak 2006b; Irschick and Meyers 2007; Wilson
et al. 2007b; Irschick et al. 2008), suggesting maximum
performance is still important in some circumstances.
We should also still expect maximum performance to
be closely linked with success for any activity for which
maximum performance is positively associated with
optimum performance. However, when one considers
tasks performed by humans and for which success is
dependent both on power and accuracy (e.g., tennis
serve), it is clear that the fastest or strongest individuals
are not necessarily going to be the best performers.
There is no reason to expect this will be any different
for non-human animals. The connection between variation in form and fitness is going to be a lot more
complicated than just via the impacts of form on maximum capacity for performance—and this may be an
important reason why variation in individual maximum capabilities often explains limited variance in
success. Our understanding of how animals select
their speeds of movement in nature is clearly in its
infancy, but studies exploring their speed-choice offer
exciting opportunities for learning more about a basic
decision made by all animals across almost all behavioral contexts. To move this research program forward,
we need further empirical and theoretical studies exploring the relationship between variation in an animal’s maximal capabilities with the magnitude of their
optimum performance and ability to accurately select
their optimum. We believe that now is an exciting
time for studies exploring the relationship between
form, performance, and fitness.
Acknowledgments
The authors thank the Society for Integrative and
Comparative Biology (SICB) for supporting
and hosting our Symposium. They also thank SICB
and the Company of Biologists for financial support
for running and attendance at the symposium. They
also thank Amanda Niehaus for numerous helpful
comments and edits, and we also thank Ray Huey,
Simon Lailvaux, and an anonymous reviewer for
their numerous insightful comments.
Funding
This work was financially supported by the Australian
Research Council Grant [DP150100198 to R.S.W.].
R. S. Wilson et al.
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