University College London
CoMPLEX
Summer Project
The Scaling of Hunting Time in Mammalian
Carnivores
Supervisor:
Dr Chris Carbone
Dr Robin Freeman
Author:
Lucy van Dorp
August 22, 2013
Lucy van Dorp
Abstract
Mammalian carnivores are an ideal model species for understanding biological constraints on
animal energetics and movement, along with links between behaviour and population persistence.
Monitoring the energetic status of unrestrained organisms in their natural environment is important
for conservation efforts, particularly in mammalian carnivores, whose numbers are in decline. Here,
for the first time, data on the hunting times of carnivores over a range of masses is collated and
assessed. A pre-existing model of hunting times for a single species is expanded, in light of the
data, through introduction of a mass component. This allows assessment of how the proportion of
a day spent hunting scales with predator mass. It was found that there are statistically significant
differences in the scaling relationships of small carnivores (<10kg), such as weasels, foxes and martens,
compared to larger carnivores (>10kg), comprising the canidae and felidae. The model was able to
account for these differences but not accurately predict values of hunting times. A more appropriate
model is needed and this must be validated with more rigorous information on mammalian energetic
status. GPS, accelerometer and bio-logging devices offer potential for such advancements.
The Scaling of Hunting Time in Mammalian Carnivores
CoMPLEX MRes: Summer Project
1
CONTENTS
Lucy van Dorp
Contents
List of Figures
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List of Tables
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1 Introduction
1.1 Mammalian carnivores . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Hunting Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Hunting Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.1 The Least Weasel, Mustela nivalis - a search strategy . . . . . .
1.3.2 The Lion, Panthera leo - a stalking predator . . . . . . . . . . .
1.3.3 The African Wild Dog, Lycaon pictus - cursorial and cooperative
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hunting
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2 Energy Budgets
2.1 Measuring Energy Budgets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Doubly labelled water (DLW) and Heart Rate Techniques for Measuring Metabolic
Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Measuring Intake and Average Prey Mass - Scat, Stomach and Observational Analysis
2.1.3 Observational Studies for Recording Activity State . . . . . . . . . . . . . . . . . .
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3 Scaling Relationships
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3.1 Scaling of Metabolic Rate with Body Mass . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2 Scaling of Resting Metabolic Rate with Surface to Mass Ratio . . . . . . . . . . . . . . . . 13
3.3 Scaling of Active Metabolic Rate with Body Mass . . . . . . . . . . . . . . . . . . . . . . 13
4 Gorman Model
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5 Results
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5.1 Activity data from the literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
5.1.1 Resting Metabolic Rate from the Literature . . . . . . . . . . . . . . . . . . . . . . 19
5.1.2 Intake Rate from the Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
6 Determining Scaling Relationships and Incorporating them into the
6.1 Introducing a Mass Component - African wild dog values . . . . . . . .
6.2 Introducing a Mass Component - Literature values . . . . . . . . . . . .
6.2.1 Model predictions for all species . . . . . . . . . . . . . . . . . .
Gorman Model
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7 Discussion
7.1 Biological Context . . . . . . . . . . . . . . . . . . . .
7.1.1 Other Scaling Relationships . . . . . . . . . . .
7.1.2 Predator Prey Co-Evolution . . . . . . . . . . .
7.2 Problems with the Model . . . . . . . . . . . . . . . .
7.2.1 A two-state model is too simple . . . . . . . . .
7.2.2 Scaling relationships are generalised . . . . . .
7.2.3 Parameter Exploration . . . . . . . . . . . . . .
7.2.4 Possible Extensions - Effect of intake rate . . .
7.2.5 Possible Extensions - Effect of hunting success
7.3 Problems with the Data . . . . . . . . . . . . . . . . .
7.3.1 Observed activity . . . . . . . . . . . . . . . . .
7.3.2 Measures of metabolism . . . . . . . . . . . . .
7.3.3 Body weight . . . . . . . . . . . . . . . . . . .
7.4 Recommendations . . . . . . . . . . . . . . . . . . . .
7.4.1 Accelerometer Data . . . . . . . . . . . . . . .
7.4.2 Biologging . . . . . . . . . . . . . . . . . . . . .
7.4.3 Open Access to Tracking Studies . . . . . . . .
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The Scaling of Hunting Time in Mammalian Carnivores
CoMPLEX MRes: Summer Project
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2
CONTENTS
Lucy van Dorp
8 Conclusion
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9 Acknowledgements
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10 Bibliography
35
The Scaling of Hunting Time in Mammalian Carnivores
CoMPLEX MRes: Summer Project
3
LIST OF FIGURES
Lucy van Dorp
List of Figures
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Estimates of DEE against carnivore mass from Carbone 2007 . . . . . . . . . . . . . . . .
The elongate form of the Least Weasel Mustela nivalis . . . . . . . . . . . . . . . . . . . .
African lions Panthera leo feeding on a Grant’s zebra . . . . . . . . . . . . . . . . . . . . .
Lion dietary breadth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Image of African wild dogs Lycaon pictus hunting cooperatively . . . . . . . . . . . . . . .
Basal metabolic rate against mass exhibits a scaling of 3/4 power . . . . . . . . . . . . . .
Heusner argues a basal metabolic rate to mass relationship that scales to the power of 2/3
Metabolic rate when running scales to the power of 1 . . . . . . . . . . . . . . . . . . . . .
Scaling of Active and Resting Metabolic Rates . . . . . . . . . . . . . . . . . . . . . . . .
Replicate of Gorman (1998) Figure 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Percentage day active against body mass plotted on a linear and log-log scale . . . . . . .
Literature values against the expected relationship between hunting activity against predator mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Percentage of day active against body mass plotted on a log-log scale with fitted polynomial
Log Activity data mustelidae and canidae/felidae showing the marked difference in how
hunting time varies with mass amongst the species when grouped . . . . . . . . . . . . . .
Resting metabolic rate against mass for the Mustelidae and Canidae/Felidae . . . . . . .
Intake Rate (MJhr-1 ) against predator mass for the Mustelidae and Canidae/Felidae . . .
Average prey mass against predator mass for the Mustelidae and Canidae/Felidae . . . .
Plots of extrapolated relationships from Gorman’s African wild dog data. . . . . . . . . .
Intercepts used in extrapolation of the Gorman values for an African wild dog . . . . . . .
Mass incorporated into the model using data for African wild dogs . . . . . . . . . . . . .
The functional relationships for species groupings when mass is incorporated into the
Gorman model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Functional relationships for each species group plotted against the literature sourced values
Manipulation of constant values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The values of the constants for each scaling relationship are sensitive to perturbation . . .
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List of Tables
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Percentage of day active for 29 mammalian carnivores as obtained from the literature . .
T-test results showing there is a statistically significant difference between the Mustelidae
and Canidae and Felidae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Basal metabolic rate values from the literature . . . . . . . . . . . . . . . . . . . . . . . .
Average prey size, DEI and Intake rate values from the literature . . . . . . . . . . . . . .
Metabolic values and hunting times provided by Gorman (1998) for the African wild dog
Lycaon pictus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Values extrapolated for the African wild dog using assumed scaling relationships . . . . .
Constants and Exponents Determined from the Literature Values . . . . . . . . . . . . . .
Appendices of all the data sourced during the project . . . . . . . . . . . . . . . . . . . .
The Scaling of Hunting Time in Mammalian Carnivores
CoMPLEX MRes: Summer Project
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47
4
Lucy van Dorp
1
Introduction
The management and conservation of animal populations requires a scientific understanding of their
activity and behaviour [1]. The mammalian carnivores are one such grouping, and have been identified
as rare, threatened by such factors as climate change, biology and human-influence [2][3].
As top predators, the conservation and study of these carnivores is important. Predation is a major
influence on how populations interact [4], thus an understanding of predatory behaviour, at the top
trophic level, is important to the maintenance of biodiversity, stability and the integrity of ecological
communities [5][6]. One way of monitoring predation is to consider the time an animal spends hunting. A
measure of the proportion of a day a given species hunts is indicative of hunting strategy and can inform
values of the energy expended before, during and after a hunt. This is important in understanding how
prey population fluctuations affect predators.
A useful criteria for assessing carnivore behaviour is body mass, the range of which is unparalleled
to that in any other mammalian order. In mammalian carnivores, body mass spans more then 3 orders
of magnitude, ranging from the least weasel (100g) to the polar bear (up to 800kg) [7][8][9]. This range
in body masses lends itself to an approach whereby the scaling of hunting is considered in relation to
mammal size.
With these points in mind, an understanding of hunting times requires consideration of predator prey
dynamics, foraging strategies and mass. This project aims to explore these relationships through:
• Collation and evaluation of the available literature on activity states of species across a range of
masses.
• Incorporation of mass relationships into a pre-existing model of hunting time.
• Critical discussion on the success of such a model, including potential extensions and existing
limitations.
1.1
Mammalian carnivores
The mammalian order Carnivora is characterised by great morphological, ecological and behavioural
variation. In terms of habitat, carnivores are found to inhabit almost every vegetational zone, from
sparse woodland (the dwarf mongoose, Helogale parvula) and desert (the fennec fox, Vulpes zerda) to
short grassland (the meerkat, Suricata suricatta) and oceanic waters (the sea otter, Enhydra lutris)
[10][7]. Within these habitats they are found to occupy extremely wide range sizes, 2-3 fold that of
equivalent size herbivore species [2][11]. The African hunting dog, for example, has an extremely large
and non-defensible home range size of between 1500-2000km2 [12].
Behaviourally, a diversity of social structures exists within the order, ranging from solitary individuals
that only interact to mate (the ermine, Mustela erminae and cougar, Puma concolor ) to monogamous
pair bonding (golden jackal, Canis adustus) and those that live in extended social groups; dominated
by males (lions, Panthera leo) or females (spotted hyaenas, Crocuta crocuta) [10]. Reproductive rates
are also highly variable ranging from as little as one offspring every 5-7 years (in the black bear, Ursus
americanus) to as high as three litters of eight offspring a year in some populations of the dwarf mongoose
(Helogale parvula.
The carnivore-human relationships is fairly unique when compared to other mammalian orders. Carnivores need large amounts of space and this often leads to conflict with humans in terms of access to land
and preying on domestic livestock. The majority are thus threatened by some form of human activity,
be it from recreational hunting, poaching and/or habitat destruction [13]. Carnivores are also valued
for their commercial products, including the pelt from spotted cats, secretions from perineal glands of
African civets and the bile ducts of bears, along with the bones of tigers [14][13]. They are also important
for tourism, zoo visitor numbers and as figurehead species for conservation efforts.
The modern order comprises 271 extant species [10] [15] and under the most generally adopted scheme
of classification divides into 7 families :
• Canidae - The dog family. They comprise such species as wild dogs, wolves, jackals, foxes, maned
wolf, racoon dog and the bat-eared fox. They are all medium-sized carnivores adapted to running
on relatively open terrain [16]. They live mainly but not exclusively on meat.
The Scaling of Hunting Time in Mammalian Carnivores
CoMPLEX MRes: Summer Project
5
1.2
Hunting Strategies
Lucy van Dorp
• Ursidae - The bear family, these mammals are large and heavily built, adapted to moving in
mountainous terrain. The majority are omnivorous, primarily feeding on seeds, fruits and insects,
and rarely killing larger prey. They are adapted for a hunting strategy which relies on strength,
more then speed.
• Procyonidae -Comprises the raccoons, coatis, potto, cacomistle and kinkajou. These are forest
dwelling and omnivorous species which tend to be adapted for an arboreal lifestyle.
• Mustelidae - Includes the weasels, martens, polecats, fisher, badgers, skunks and otters. They are
adapted for forest dwelling with long bodies and short legs. Their diet is fairly strictly carnivorous,
more so than the Canidae.
• Viverridae - Made up of the civets, genets, linsangs, mongooses. These are all small carnivores
which are primitive in their features.
• Hyaenidae - Comprises the spotted, striped and brown hyaenas and the aardwolf. These are large
mammals and highly adapted for flesh-eating and taking carion. They are capable of crushing
larger bones than any other carnivore [16].
• Felidae - The wild cats, made up of the ocelot, serval, caracal, lynx, puma, leopard, jaguar, lion,
tiger and cheetah. This family occurs in virtually every terrain and are strictly carnivorous with
vegetables playing little to no role in their diet.
Within the scope of this project the families under consideration will primarily be the Canidae,
Felidae, Hyaenidae and Mustelidae. These families were considered because they are the most strictly
carnivorous of the Carnivora. This permits uniform consideration across species in terms of prey selection
because those families which are predominantly omnivorous or piscivorous are excluded.
1.2
Hunting Strategies
The name “Carnivora” means “meat-eaters,” and indeed the majority of the order are meat-eating
predators and scavengers, adapted to their role as predators [16]. Most are easily recognized by their
highly specialised teeth, which include long sharp canines for killing and sharp scissor-like cheek teeth
for cutting (the carnassials) [13]. When it comes to the process of hunting, unlike herbivores, carnivores
experience a foraging problem in that their foods are differentially active, and thus differentially available
throughout a 24 hour period [17]. Predatory strategies are thus shaped and refined by natural selection
to maximize nutrient intake within the bounds of a wide range of ecological and geographical constraints
placed on both the predators themselves and their prey [18].
Alcock (2001) [19] points out that hunting behaviour can broadly categorised into 3 groups:
1. Searchers
2. Pursuers
3. Ambushers
Species vary in the relative importance of each hunting component:
• For predators primarily using a search strategy, the major energy expenditure is in finding prey,
and this takes a large proportion of their time [20]. To maintain this strategy, searchers focus on
prey that are both easy to catch and easy to handle. On the whole these tend to be small and/or defenceless animals of low mobility and frequently found in a clumped distribution. Such prey require
a small handling time and the capture and killing phases are often brief [20][21][11][22][23][24][25].
An example here is aardwolves, Proteles cristatus, which spend much of their time active, searching
for termite patches [26]. For predators using this strategy, a large intake is required to meet the
daily metabolic requirements.
• For predators employing a pursuit strategy, prey tend to be easy to find and subdue but are
typically difficult to capture. “Pursuit” predators consume fairly large prey because small prey are
not worth chasing, unless over short distances. The “pursuers” prey is generally large enough for
The Scaling of Hunting Time in Mammalian Carnivores
CoMPLEX MRes: Summer Project
6
1.3
Hunting Case Studies
Lucy van Dorp
one captured prey item to sustain the predator for several days [20]. Canidae, such as dogs and
wolves employ such a strategy. Spotted hyaenas (Crocuta crocuta), for example, can typically chase
prey for up to 5km [27][26]. Cursorial (running) strategies are often social, allowing predators to
take larger prey [7][28]. Subduing large prey, however, is difficult and has greater costs. There is a
greater chance of injury with increase in prey size and certainly amongst tigers, lions and cougars,
injury or even death during prey capture is not uncommon [4]. In this scenario, predator injury
could be considered an additional cost, with injured predators having a greatly reduced capture
success rate [27]. As a general rule pursuit predators are active diurnally.
• Ambush predators typically employ a sit and wait strategy, in which the predator minimises search
and pursuit costs by waiting for the prey to approach. A good example here is the red fox,
Vulpes vulpes, which when hunting mice stands motionless listens and watches intently before
leaping suddenly, bringing its forelegs straight down to pin the prey [13][29]. In some of the larger
mammalian carnivores, adaptation to an ambush strategy is often seen in the pelt, with many
species such as leopards (Panthera pardus), cheetahs (Acinonyx jubatus) and tigers (Panthera
tigris) exhibiting camoflague.
Ambush and pursuit predators are not exclusive. Lions, for example have been seen to employ both
stalk-run (pursuit) attacks, as well as ambush techniques (the lion lyes still watching the game move
past before running a short distance towards the prey) [30]. They are not exclusively a stalker or runner.
Furthermore there has been suggestion of a fourth grouping of hunting strategy. Dunstone [20] postulates
the existence of the “hunters”.
• This category comprises those predators which both actively search for prey and pursue it. These
hunters strike a balance between the time spent locating prey and the time spent pursuing it. This
is achieved by focusing on prey which is easy to capture. This strategy seems to well describe the
mustelids, which feed on a variety of easily captured small prey items such as small mammals,
birds and occasionally fish.
Differences in the killing and feeding behaviour of carnivores is reflected in their morphology [16][31][13].
Intuitively, the size of the predator is fundamental in determining what type of prey it can hunt
successfully[13], with smaller predators having lower absolute energy requirements than larger predators. The upper size limit of the prey species consumed is governed by how successfully large animals
can be captured and subdued, and comes with the advantage of providing food for a longer period of time
or for a larger number of individuals. The lower size limit of a predator depends upon how frequently
smaller prey species can be found and eaten [32] [33] and comes with the advantage of reducing risk of
injury during hunting, though does not sustain the predator for a very long time.
Ocelots (around 10kg) prey on mammals up to the size of a paca (6-10kg) and the Scottish wildcat (45kg) can tackle a rabbit (1.2-2kg). Larger sized mammals can catch larger prey, for example the caracal
(12kg) preys on the mountain reedbuck (25-30kg) and the lion (150-250kg) can successfully capture a
Cape buffalo (500kg)[4] [34][35][36]. Carbone (1999) [37] considered where this divide in large and small
carnivore dietary behaviour occurs. He found that among canids and felids, all species weighing over
21.5kg are vertebrate feeders [37]. At body masses less than 21.5kg, 53% of species are purely vertebrate
feeders, 29% are omnivorous, 2% are invertebrate feeders and in those species which feed on invertebrate
and vertebrate prey make up 16%. This implies that species less than 21.5kg are energetically constrained
to relying on small prey items. This explains the absence of medium to large carnivores feeding exclusively
on small prey items.
In later work, Carbone modelled how daily energy expenditure (DEE) varies with mass. The model
predicts a step increase in DEE of a factor 2.3, when a carnivore switches from hunting small to large
prey at the same mass [38], see Figure 1.
1.3
Hunting Case Studies
It is not possible to go into detail on the range of strategies used by all the mammalian carnivores
featured in this study. Instead, a brief case study will be made on three species which adopt different
hunting strategies; the least weasel (Mustela nivalis), the lion (Panthera leo) and the African wild dog
(Lycaon pictus).
The Scaling of Hunting Time in Mammalian Carnivores
CoMPLEX MRes: Summer Project
7
1.3
Hunting Case Studies
Lucy van Dorp
Figure 1: Estimates of DEE against carnivore mass from Carbone 2007 [38]. The model prediction of
DEE is shown in red, and the piecewise regression fit is shown in black. The model predicts a step
increase in DEE when carnivores switch to hunting large prey at the same mass. Triangles represent
estimates based on doubly label water, circles are based on behavioural observations, and squares are
based on captive studies of oxygen consumption. The vertical line represents the predicted threshold of
14.5kg where predators switch from small to large prey.
1.3.1
The Least Weasel, Mustela nivalis - a search strategy
The least weasel, Mustela nivalis, is the smallest of the carnivores, with a head to body length of only
114-260mm [13]. It feeds almost entirely on small rodents, such as mice, hamsters and gerbils, which are
relatively easy to kill but often hard to find because they hide in large areas or in complex cover.
Figure 2: The Least Weasel Mustela nivalis hunt with a search strategy and are specialised for hunting
through burrows because of their elongate bodies, narrow heads, long necks and short legs [39][40][41].
Image from Nowak (2005) [13].
The least weasel is specialised for the searching process, able to search through the burrows and
runway systems of rodents and lagomorphs. They can hunt at any time of day and under the majority of
conditions (including snow[42]), often taking over the burrows or nests of their most recent prey [43][7].
Foraging under cover has the added advantage of decreasing their own risk of predation by foxes and
birds of prey.
Being a predator small enough to enter a rodent runway, however, leaves the least weasel at risk of
being too small to effectively subdue and kill it’s prey. Weasels make up for this using their long bodies
which can be wrapped around a prey item as it struggles [44]. They also disproportionately strong, able
to run at speed carrying a carcass of up to half of its own weight.
Work by King (1980) found that for each male M. nivalis living in a British deciduous woodland,
search distances comprised between 7-15 hectares daily in order for the weasel to successfully capture
enough of the 21-39 rodents hidden per hectare to meet it’s energy demand [39]. In this way, weasels are
under a greater risk of failing to find a prey item than being injured by one during the hunting process
[7].
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1.3
Hunting Case Studies
1.3.2
Lucy van Dorp
The Lion, Panthera leo - a stalking predator
When it comes to large cats, felids tend to have a solitary existence, both hunting and feeding in isolation
[18][45]. Lions are the exception to this rule and regularly hunt cooperatively [34]. Lions, tend to use an
“ambush and pursuit” strategy, relying on vegetation cover and moonlight to capture prey, with activity
peaking between 17:00 and 08:00 [4]. The prey are typically large, preferentially between 190-550kg [46],
and thus the hunting costs are high, with long high-speed chases and energetically expensive capture and
killing phases [12][47][48][49]. Due to this, lions are selective about the prey they focus on, for example
there is a tendency when hunting gazelles to focus on males rather than females. Males tend to be less
vigilant, found in smaller groups and are concentrated on the periphery of groups[4].
Figure 3: Female African lions Panthera leo killing a Grant’s zebra Equus burchelli on the Serengeti.
When feeding lions force the contents of the intestines out by squeezing them in their mouths before
feeding [50][4]. Image from Nowak (2005) [13]
In an analysis of the stomach contents of Krugar lions between 1974-1978, Smuts found that the
dietary breadth is typically quite small with few significant prey types, see Figure 4.
Figure 4: Lion dietary breadth as recorded from the stomach contents of Krugar lions between 1974-1978
by Smuts 1979 [51]
1.3.3
The African Wild Dog, Lycaon pictus - cursorial and cooperative hunting
In contrast to lions, wild dogs do not stalk their prey but instead run towards them, in full view. They
appear to rely on stamina and speed rather than suprise for their success [26] and unlike lions do not use
cover to avoid detection [52]. 77% of the time they run straight at their selected prey, only approaching
slowly as a group in 23% of hunts [52].
African wild dogs are one of the most social canids and live in highly cohesive packs of a mean size of
4.8-8.9 individuals [54][55][52]. Like lions, they hunt in cooperative groups. Predators hunting in a group
are capable of subduing prey somewhat larger than that which could be killed by solitary predators of
The Scaling of Hunting Time in Mammalian Carnivores
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Lucy van Dorp
Figure 5: African wild dogs Lycaon pictus hunt both cooperatively and cursorially (running) relying
primarily on a “pursuer” strategy. Photo from Murdoch and Becker (2002) [53]
similar body size [26][4] [33]. In the case of African wild dogs, communal hunting has been shown to
increase both the range and size of prey available to predators, allowing them to make kills of size up to
a 200kg zebra Equus buchelli [7], despite weighting only between 18-22kg. Cooperative hunting improves
the success rate and also reduces the chase distance of a pursuit [52][56][57][54].
Wild dogs feed mainly on ungulates, primarily wildebeest (Connochaetes taurinus), impala (Aepyceros
melampus), kudu (Strepsiceros tragelaphus), gazelle (Gazella thosonii and G. grantii ) and warthogs
(Phacochoerus aethiopicus)[58] [52][56][57][55]. In general they target young, less mature animals which
are easier to catch than adults [4].
The greatest competitor of the African wild dog is the spotted hyaena, Crocuta crocuta. Hyaenas are
typically present for a large percentage of kills and often steal carcasses before dogs have finished feeding
from them [59][26][4][52].
2
Energy Budgets
All biological activities use time and depend on metabolic energy [60][61][62]. Energy is thus one of
the most important currencies in determining the fitness of an organism [61]. It is those organisms
that obtain and process energy most efficiently, and balance this against other costs impinging on their
reproductive success and survival, who will be most genetically fit [63].
Survival by large carnivorous mammals requires a continuous balance between energy expended in
daily living and energy acquired by hunting [64][65]. Energy is expended during tasks such as movement,
courtship, growth, foraging and body maintenance. It follows that species with high activity levels (active
for an extended period, utilise expensive forms of locomotion or engage in elaborate courtship rituals),
high costs of maintenance (endotherms), high rates of reproduction or engage in extended periods of
parental care, have the greatest energy expenditure [66]. Animals acquire energy by foraging or hunting
[67] with any body size requiring a sufficient rate of food supply to maintain it [68]. There are, however,
large costs associated with hunting and additionally the time spent hunting can be influenced by a
number of factors [17]. These include daily temperature fluctuations [69], interference from competitors
[70], risk of predation [40] and social behaviour [16][7].
In it’s simplest form, an energy budget is a number that indicates the amount of energy that is
expended over a given period of time [71]. It follows that if the energy budget is balanced (the energy
expended by an animal is equal to its energy gain), there is no net increased or decrease in internal
energy reserves [72].
Daily Energy Expenditure (DEE) - Daily Energy Intake (DEI) = 0
2.1
(1)
Measuring Energy Budgets
A wide variety of approaches have been used to get a comprehensive measure of the energetic status
of an animal [73][61]. These include the doubly labelled water technique and heart rate techniques for
measuring metabolism (Section2.1.1), scat and stomach content analysis for measuring intake (Section
2.1.2) and observational studies of activity state (Section 2.1.3).
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Lucy van Dorp
2.1.1
Doubly labelled water (DLW) and Heart Rate Techniques for Measuring Metabolic
Rates
The doubly labelled water method (DLW) for estimating CO2 consumption over time, is based on the
fact that the oxygen in respiratory carbon dioxide is in isotopic exchange equilibrium with the oxygen in
body water [74][75]. The technique uses stable isotopes of hydrogen and oxygen to trace the flow of water
and carbon dioxide through the body over time. This is done by administering a dose of doubly labeled
water, and then measuring the elimination rates of deuterium (an isotope of Hydrogen) and Oxygen 18
(18 O) in the subject over time. This is achieved through the regular sampling of heavy isotope concentrations in the body water (from saliva, urine, or blood). From the data it is possible to derive a single
estimate for the rate of oxygen consumption (V̇ O2 ) during the experiment [61]. Several studies have been
performed to evaluate the impact of the DLW method on animal behaviour (reviewed in Speakman 1997
[73]. In general they indicate that the animal is not compromised by the sampling method, so there is
no expected impact on estimates of daily energy metabolism [61].
The heart rate technique relies on the physiological relationship between heart rate and V̇ O2 [61], based
on Fick’s convection equation for the cardiovascular system:
V̇O2 = fH × Vs (Ca O2 − Cv̄ O2 ),
(2)
where Vs is cardiac stroke volume (the amount of blood pumped per heart beat), Ca O2 is the oxygen
content of arterial blood and Cv̄ O2 is the oxygen content of mixed venous blood [61]. The term Vs (Ca O2 −
Cv̄ O2 is known as the oxygen pulse, and gives the amount of oxygen consumed by the animal per
heartbeat [76]. Given there is a linear relationship between V̇O2 and the heart rate (fH ), the value of
oxygen consumption can be determined.
2.1.2
Measuring Intake and Average Prey Mass - Scat, Stomach and Observational Analysis
For terrestrial carnivores, scat analysis is the technique most commonly used to determine diet [77].
Results are expressed either as the frequency of occurrence of a particular species or as the percentage
volume or weight of the total amount of food. This is an indirect method and can be biased by many
variables such as laboratory procedure [78][79][80][81] and mis-identification of food items in the scat
[82]. Additionally, this method tends to underestimate the incidence of highly digestible morsels of food
[34].
An alternative method is to directly sift through the contents of predator stomachs though this does
not tend to be done as it requires sacrificing an animal, and additionally if the subject’s stomach is
empty, no data is provided[34].
Observational studies of predator ingestion are also possible but are notoriously difficult and unlikely
to produce an accurate analysis. In his study of serval (Leptailurus serval ) diet, for example, Geertsema
(1985) underestimated the proportion of frogs in the diet because it was not possible to follow the cats
into wetter areas of their range [23][34].
2.1.3
Observational Studies for Recording Activity State
Observational field studies of animal behaviour involve a researcher watching animals, typically in their
natural environment, and taking visual samples of behaviour [83]. To study wild animals in an unbiased
way is difficult. Generally animals will always behave differently in the presence of humans [84]. Additionally, it is challenging to constantly monitor wild animals, particularly when they live in habitats
where direct observation is difficult [85]. Even where constant observation is possible, behavioural state
is subjective to the observer and difficult to quantify .
3
Scaling Relationships
Scaling is the study of the structural and functional consequences of changes in proportions correlated
with changes in absolute magnitude amongst similar organisms [86][69]. It is a useful approach to
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3.1
Scaling of Metabolic Rate with Body Mass
Lucy van Dorp
understanding carnivore energetics as it provides a theoretical framework for drawing conclusions across
broad size ranges and hunting strategies.
The most common approach to scaling problems in ecology use allometric equations which are of the
form:
y = axb ,
(3)
where:
a = the proportionality coefficient (the intercept at unit y),
b = the exponent (the slope of the regression line).
When considering how relationships scale:
• b values greater than 1 (postitive allometry) imply a differential increase of y relative to x
• b values less than 1 (negative allometry) indicates that y/x ratios decrease with increasing absolute
magnitude of x
• b value of 1 (isometry) represents the maintenance of geometrical similarity with size increase.
Within ecology there are several established scaling relationships of metabolic rate related to mass.
3.1
Scaling of Metabolic Rate with Body Mass
One of the best established allometric relationships is that between metabolic rate and body mass. The
metabolic rate is, by convention, taken as the basal rate of metabolism (BMR) [87]. This is a repeatable
measure of the minimal rate of energy expenditure, under standard conditions, by endotherms. It is
defined as the rate, measured within the zone of thermo-neutrality, when an adult is post-absorptive,
inactive during the normal period of inactivity, and maintains its normal body temperature [88].
It is widely accepted that metabolic rate at rest (BMR) is proportional to body mass raised to the
three-quarter power (M0.75 ). This is known as Kleiber’s law after Kleiber’s now famouns 1932 article
“Body Size and Metabolism” [89][69]. The relationship described is seen in mammals ranging from mice
to elephants, comprising a 4000-fold difference in mass, see Figure 6. This Kleiber relationship is thought
to be a consequence of the physics and geometry of of mammalian circulatory systems [90].
Figure 6: Metabolic rates for mammals and birds plotted against body mass on a log scale. The
relationship forms a straight line of 3/4 power scaling. Adapted from Benedict (1938)[91] and extracted
from Schmidt-Nielsen (1984)[69]
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3.2
3.2
Scaling of Resting Metabolic Rate with Surface to Mass Ratio
Lucy van Dorp
Scaling of Resting Metabolic Rate with Surface to Mass Ratio
Some scepticism exists over the universality of Kleiber’s law [92]. Opponents argue that the true value
of metabolic scaling is not an exponent of 3/4 but instead an exponent of 2/3. This assertion is made
by assuming the principal determinant of metabolic scaling is not body mass, but the surface to mass
ratio of the organism [92].
Animals of different sizes have different structural requirements [93] and this is reflected in their
surface dimensions. Studying surface-to-mass scaling is significant in mamalian carnivores because,
being endotherms, they must metabolically produce enough body heat to equal the amount of heat lost
from their surface. Heat loss from a warm-blooded animal is roughly proportional to the free surface,
and given a small animal has a larger relative surface, it must also have a relatively higher rate of heat
production to balance this loss[69] . The exponent of 2/3 reflects the simple geometric scaling of body
surface area available for heat dissipation.
Heusner (1982) aruges that the true slope of the metabolic regression line is 0.67, in line with the
surface rule. Examining data from seven species of mammals ranging from 16g mice to 922kg cattle,
Heusner reported a mass exponent, b, of approximately 0.67 for any single mammalian species. He
suggests that the interspecies value of 0.75 is, in fact, a statistical artefact [92][94], see Figure 7.
Figure 7: It has been suggested by Heusner (1982) [94] that an overall regression line, with slope 3/4, is
obtained because it is a statistical artefact of species specific data which fall on the regression line with
a slope of 2/3. Extracted from Schmidt-Nielsen (1984)[69]
The general consensus amongst proponents of Kleiber’s law, however, is that the scaling of animals
geometrically is not equivalent across scales and thus mammals do not adhere to the surface rule. Isaac
and Carbone (2010) give a definitive view on this [95]. They state that scalings of metabolic rate are
highly heterogenous at fine taxonomic scales, but on an overall basis, a mass-exponent of [M]3/4 is
consistent with the data.
3.3
Scaling of Active Metabolic Rate with Body Mass
The amount of energy used by various mammals of different sizes, when running, was examined by Taylor
and colleagues (1970) [96][69]. Seven groups of mammals, ranging in mass from 21g - 18kg, were trained
to run on treadmills whilst their oxygen consumption was measured continuously. It was found that the
stead-state oxygen consumption of each animal increased nearly linearly with mass and that the faster
an animal runs the more energy they expend [97]. This is consistent with the notion that large-bodied
carnivores expend more energy hunting their prey.
When considering the resting and active metabolic rates according to the aforementioned scaling
relationships there is clearly a deficit (Figure 9). As the body mass of a mammal increases, this deficit
gets larger and is representative of the cost of hunting. The difference in scaling exponents implies that
as an animal gets larger, the costs it incurs foraging increases with a scaling of [M]0.25 . An animal can
thus hunt less for the same amount of time when compared to a mammal of smaller mass. With this
The Scaling of Hunting Time in Mammalian Carnivores
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Lucy van Dorp
Figure 8: Taylor found oxygen consumption increased linearly with animal mass, with the solid line
showing the line of direct proportionality. Here each point represents the mean of a single running speed.
From Taylor (1980) [98]
in mind, we hypothesize a scaling relationship of the time spent hunting as [M]-0.25 to allow for the
increasing energetic demands of hunting as mass increases.
Metabolic Rate
Scaling of Active
Metabolic Rate
@MD1
@MD0.75
Scaling of Resting
Metabolic Rate
@MD0.25
Hypothesized Scaling
of Hunting Cost
Body Mass
Figure 9: Scaling of active and resting metabolic rates. The deficit in the scaling relationships is hypothesized as the cost of hunting and given an exponent value of [M]0.25 .
4
Gorman Model
Gorman (1998) considered the energetics of hunting in the African wild dog Lycaon pictus with a view
to understanding how their population dynamics change in response to populations of spotted hyaena,
Crocuta crocuta [12]. Gorman was interested in how klepto-parasitism by spotted hyaena affected the
time an African wild dog had to spend hunting to achieve energy balance.
The model, set out in equation 4 follows a simple cost-gain principle to compute the hours an animal
spends hunting:
The Scaling of Hunting Time in Mammalian Carnivores
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Lucy van Dorp
Th =
24 × Er
,
(I + Er − Eh )
(4)
• where Th is the number of hours of hunting needed per day to achieve a daily energy balance,
• where I is the rate of capture of prey in kJ per hour,
• where Er is the rate of energy expenditure when resting, in kJ per hour,
• where Eh is the rate of energy expenditure when hunting, in kJ per hour.
Gorman’s equation is not derived in the paper but can be reconstructed through consideration of a
linear combination of the metabolic rate of resting (Er ) and the metabolic rate while hunting (Eh ) for a
specific time period, given energy intake and expenditure must balance:
(Tr × Er ) + (Th × Eh ) =
Energy
.
Intake
(5)
If energy gain per hour hunting is given as I, and you can only gain energy when you hunt, then the
energy intake per day is given as Th × I:
(Tr × Er ) + (Th × Eh ) = Th × I.
(6)
Tr + Th = 24
(7a)
Tr = 24 − Th .
(7b)
(24 − Th )Er + (Th × Eh ) = Th × I,
(8)
Th (Eh − Er − I) = −24 × Er.
(9)
Given there are 24 hours in a day:
From equations (6) and (7) it follows that:
which can be written as:
These can be rearranged to give the Gorman equation:
Th =
24 × Er
.
(I + Er − Eh )
(10)
The first step in understanding the model is to replicate the results obtained by Gorman in Figure
1 of the paper [12]. In this figure, Gorman utilises the expression given in equation 4 to predict the
numbers of hours that dogs would need to hunt if they were losing various percentages of their food to
hyaenas. This is achieved through incorporation of a parameter δ which represents the energy lost:
energy lost
,
100
and incorporating this expression into the model (Figure 10).
δ =1−
Th =
5
24 × Er
.
δI + Er − Hh
(11)
(12)
Results
In line with the projects aims, the results presented include sourced literature values and the development
and critique of the Gorman model of activity times [12].
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Lucy van Dorp
Hours hunting to balance the energy budget
25
20
15
10
5
0
5
10
15
20
25
30
% energy lost to hyaenas
Figure 10: Replicate of Figure 1 from Gorman et al [12] describing the time for which a wild dog needs
to hunt each day as a function of the amount of food they lose as a result of klepto-parasitism, primarily
by hyaenas. The plot shows that a small loss of food to hyaenas has a relatively large effect on the time a
wild dog spends hunting. For example, if an African wild dog loses 25% of it’s prey to hyaenas it would,
given the model, need to hunt for over 12 hours a day to achieve energetic balance.
Species Name
Mustela nivalis
Mustela frenata
Martes americana
Mustela erminae
Mustela putorius
Vulpes cana
Mustela vison
Martes martes
Vulpes velox
Martes pennanti
Vulpes vulpes
Proteles cristatus
Canis adustus
Meles meles
Felis canadensis
Leptailurus serval
Felis caracal
Felis pardalis
Canis latrans
Lycaon pictus
Canis lupus
Panthera pardus
Acinonyx jubatus
Puma concolor
Crocuta crocuta
Panthera onca
Panthera leo
Panthera tigris
Ursus maritimus
Common Name
Least Weasel
Long-tailed weasel
American marten
Stoat
Polecat
Blandford’s fox
American mink
Pine marten
Swift fox
Fisher
Red Fox
Aardwolf
Side-striped Jackal
Badger
Canadian lynx
Serval
Caracal
Ocelot
Coyote
African wild dog
Timber wolf
Leopard
Cheetah
Puma
Spotted hyaena
Jaguar
Lion
Tiger
Polar bear
Mass(kg)
0.14
0.23
0.96
0.95
1.03
0.956
0.79
1.2
2.14
3.75
4.6
8.35
11.2
13
10
11.7
12
11.7
11.5
22
46
46.5
58.6
51.9
58.6
76.9
120
227
257
% Resting
79.45
90.8
62.25
77.78
69
62
70.07
63.45
49.6
73
71.39
73.29
65.4
65.84
58.5
69.9
64.3
56.4
53.3
85.42
54.8
47.8
83.33
62.2
78.44
47.5
91
77
84.72
% Active
20.55
9.2
37.75
22.22
31
38
29.93
36.46
50.4
27
28.61
26.71
34.6
34.16
41.5
30.1
35.7
43.6
46.7
14.58
45.2
52.2
16.67
36.36
21.56
52.5
9
23
15.28
References
[17][99][100][101]
[17][102]
[17][103]
[7][104][105][106][107][108]
[109][110][111]
[112][113]
[114][115][20]
[116][117]
[38][118]
[38][119][120]
[38][121]
[118][122]
[38][123]
[124][119]
[121][125]
[38][7]
[38][7][126]
[22][127][35]
[123][128]
[7][129][54]
[130][131]
[38][7][132]
[105][133][134][135][136]
[38][134][137]
[38][105][133][134][26]
[38][50]
[2][38][7][130][4]
[38][138]
[38][7][139]
Table 1: Percentage of day active for 29 mammalian carnivores. The majority of the literature is from
studies on an individual species, for example; Olson’s study of the canadian lynx [125] using GPS collars,
Avenant and Nel’s study of radio-tracked caracals [126], Schaller’s observational study of Serengeti lions
[4] and Weller and Bennett’s study of the behaviour of captive ocelots [127]. Collated data included that
on weasels by Zielinski et al. (2000) [17] along with information on some of the larger carnivore species,
as presented by Gittleman (1985) [7].
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5.1
5.1
Activity data from the literature
Lucy van Dorp
Activity data from the literature
An extensive literature review was undertaken comprising a number of ecological papers, textbooks and
online resources.
Information on mammalian mass was primarily obtained from the Pantheria database [140] which
assembles multi-species trait data from a range of literature sources. By accounting for many literature
sources, the database allows for individual differences in mammalian mass as a result of gender, age and
health, through presentation of an average value.
The remaining data was taken from an independent literature survey and is available in it’s entirety
in the appendices, Table 8, but will be presented here in sections for ease of discussion. Literature values
were obtained for DEI and DEE, average prey mass, basal metabolic rate, time resting and time active,
along with their supporting literature references. Where possible an average value was always taken from
multiple literature sources.
The proportion of the day spent active is a useful measure of metabolic activity, giving an indication
of the costs of hunting and how intake rate effects an animal’s behaviour. Until now, no paper has
collated data on the time spent active over a broad species range. Data was collated for 29 mammalian
carnivore species, Table 1.
A plot of the time active against carnivore body mass reveals no clear relationship when plotted
on a linear or log-log scale, see Figure 11. Additionally, there are marked inconsistencies between the
literature values collected and the predicted scaling relationship of [M]-0.25 , see Figure 12.
60 50 % of Day Ac:ve 40 y = -­‐0.0577x + 33.528 R² = 0.08883 30 20 10 0 0 50 100 150 200 250 300 Body Mass (kg) (a) Linear Plot of Activity Data
100 Log % of Day Ac9ve y = 28.981x-­‐0.006 R² = 0.00072 10 1 0.1 1 10 100 1000 Log Body Mass (kg) (b) Log Plot of Activity Data
Figure 11: Percentage day active against body mass plotted on a linear and log-log scale. When plotted
on a log-log scale, the hypothesized scaling relationship of [M]-0.25 is not obvious.
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5.1
Activity data from the literature
Lucy van Dorp
60
50
40
30
20
10
0
50
100
150
200
250
Hypothesized Scaling of Exponent -0.25
Literature Data
Figure 12: Literature values against the expected relationship of hunting activity against predator mass
2 1.8 Log % Day Ac;ve 1.6 1.4 1.2 1 0.8 y = -­‐0.1552x2 + 0.2426x + 1.4732 R² = 0.31488 0.6 0.4 0.2 0 -­‐1.5 -­‐1 -­‐0.5 0 0.5 1 1.5 2 2.5 3 Log Body Mass (kg) Figure 13: Log Activity data from the literature with fitted polynomial
One way to better represent the literature data is to fit a polynomial (Figure 13). Interestingly, Figure
13 exhibits a trend whereby mammals of a small mass, increase the time they spend active as body size
increases. Larger mammals (>10kg) instead exhibit a negative relationship, decreasing the time they
spend hunting as their mass increases. For large mammals, the downward trend in activity is expected,
and in line with the hypothesized increase in the cost of hunting with mass (see Section 3.3, Figure ??).
For smaller mammals, however, the trend in activity times seen in the literature is unexpected. This
relationship implies that up to a certain body mass, the smallest carnivores (weasels, foxes and martens)
experience a decreasing hunting cost as the species size increases.
One way of explaining this is relating the cost of hunting to foraging strategy. The smallest mammalian carnivores exhibit a “searcher” strategy. Most of the costs of hunting are associated with the
process of searching for prey. That said, when a mammal is very small (<1kg), and hunting rodent prey,
the disparity in the mass of predator and prey is likely to be small. One would expect this to cause
the animal to incur large capture and subduing costs as it handles prey close in size to itself. Small
carnivores of a greater mass (4-10kg) have an average mass to prey mass ratio which is smaller. The
costs associated with the “search” element of the hunt are still the same, but the costs associated with
capture and killing are likely to be markedly smaller. This is one possible explanation for the positive
scaling relationship seen in species under 10kg.
The polynomial plot presented in Figure 13, indicates that the scaling of activity cannot be considered
consistent across all the species studied. There is a marked difference in how very small species of carnivores divide their activity levels compared to those greater than 10kg. To de-construct the relationships,
the activity data collated in Table 1 was considered according to the species type. Plots were made of
mammals under 10kg, primarily the mustelidae group, along with the equivalent plots for the canidae
and felidae, see Figure 14.
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5.1
Activity data from the literature
Lucy van Dorp
100 y = 67.376x-­‐0.227 R² = 0.1784 Log % Time Ac<ve y = 27.881x0.2503 R² = 0.33724 10 1 0.1 1 10 100 1000 Log Body Mass (kg) Felidae and Canidae Mustelidae and Others Figure 14: Log Activity data mustelidae and canidae/felidae showing the marked difference in how
hunting time varies with mass amongst the small and large carnivores. This difference is apparent
visually but also in the scaling constants and exponents of the linear regression lines.
To consider if this is a legitimate assumption to make statistically, a t-test was applied to each of the
scaling relationships considered during the study, see Table 2. A P-value of 0.0034 was reported when
looking for evidence of a significant difference between the body masses of the small (mustelidae and
others) versus large carnivores (canidae and felidae). This confirms it is statisticaly valid to consider
these species in the groupings suggested by the literature values. A significant difference is also seen
when average prey mass (p-value of 0.0007) and resting metabolic rate (p-value of 0.0041) are considered.
“Mustelidae and Others” versus “Canidae and Felidae”
Body Mass (kg)
Average Prey Mass (kg)
BMR (ml O2 per hour)
P-value
0.0034
0.0007
0.0041
Table 2: T-test results of each scaling relationship as considered for the Mustelidae and other small
carnivores, compared to the canidae and felidae. The p-values presented suggest that it is legitimate to
consider these species as separate groups.
5.1.1
Resting Metabolic Rate from the Literature
Data for the resting metabolic rate of the study mammals was primarily obtained from the Pantheria database [140], although some data was also available from review papers by White (2003) [105]
and McNab(1989) [66]. The majority of the data was obtained using the doubly-labelled water technique (see Section 2.1) and was thus presented in mlO2 hr-1 . The Gorman model (Equation 4), requires
metabolic data in the form of MJhr-1 and thus a conversion was applied as detailed by Ainsworth
(2000,2003)[141][142].
The conversion assumes that:
kJ
mlO2
= 4.184
,
(13)
3.5
kg.min
kg.hour
which is multiplied by Kg to give
mlO2
kJ
= 4.184
.
(14)
min
hour
The metabolic data used in this project is in units of ml of O2 per hour so to change from minutes to
hours:
mlO2
4.18
1
=
(15)
hour
3.5 × 60
3.5
The Scaling of Hunting Time in Mammalian Carnivores
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5.1
Activity data from the literature
Lucy van Dorp
mlO2
0.01992 M J
MJ
=
= 1.99 × 10−5
.
hour
1000 hour
hour
Thus to convert the metabolic data in to rates of change of energy:
1
1
mlO2
MJ
≈ 2 × 10−5
.
hour
hour
(16)
(17)
With this conversion applied, literature sourced data for the resting metabolic rate was tabulated (Table
3) in order to compare the relationship of BMR to mass in the context of the expected 3/4 power
relationship.
Species Name
Mustela frenata
Martes americana
Mustela vison
Martes martes
Vulpes vulpes
Canis latrans
Felis pardalis
Acinonyx jubatus
Puma concolor
Panthera onca
Panthera leo
Common Name
Long-tailed weasel
American marten
American mink
Pine marten
Red fox
Coyote
Ocelot
Cheetah
Puma
Jaguar
Lion
Mass (kg)
0.23
0.96
0.79
1.2
4.6
11.5
11.7
58.6
51.9
76.9
120
BMR (ml.O2 hr-1 )
241
595
488
717
2442
2687
3126
8982
8842
11189
16954
BMR (MJhr-1 )
0.00482
0.0119
0.00976
0.01434
0.04884
0.05374
0.06252
0.17964
0.17684
0.22378
0.33908
References
[143][144]
[105][145]
[105][146]
[105][145]
[105][147]
[105]
[105][66]
[105]
[105]
[105][66]
[105][66]
Table 3: Basal metabolic rate values from the literature
A plot of resting metabolic rate against mass for the Mustelidae and Canidae/Felidae was made, Figure 15, to give a scaling relationship of 0.0064[M ]1.0643 for carnivores less than 10kg, and 0.0099[M ]0.7231
for the canidae and felidae grouped together.
1 Log Res6ng Metabolic Rate (MJ/hr) 0.1 1 10 100 1000 0.1 y = 0.0099x0.7231 R² = 0.995 0.01 0.001 0.0001 y = 0.0064x1.0643 R² = 0.33349 Canidae and Felidae Mustelidae and Others Log Body Mass (kg) Figure 15: Log resting metabolic rate converted to units of MJhr-1 against mammal body mass. A
species-grouped linear regression gives power relationships of 0.0064[M ]1.0643 for carnivores less than
10kg, and 0.0099[M ]0.7231 for the canidae and felidae grouped together.
The Scaling of Hunting Time in Mammalian Carnivores
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5.1
Activity data from the literature
Lucy van Dorp
The scaling of metabolic rate for the canidae and felidae (>10kg) is close to what is expected under
Kleiber’s law, with an exponent value of 0.7231. In carnivores under 10kg in body mass, however, the
exponent value is much greater (1.0643), which is close to the linear relationship we would be expecting
for the scaling of active metabolic rate with mass. One explanation for this is that the literature sourced
data of mammals under 10kg is dominated by the smallest mustelids (<1kg), which are more capable
of metabolic adjustment compared to the larger mustelid species [148]. In these small mustelids, the
BMR can be two to six times higher than that of non-elongate mammals of the equivalent weight [143]
[148][149]. This may explain the steeper scaling extracted from the literature values and provides further
support for treating the smaller carnivores as a distinct group when considering scaling relationships
across a breadth of masses.
5.1.2
Intake Rate from the Literature
Data on species specific energy intake was obtained from DEI values sourced from the listed references.
These values were divided by the literature values of the number of hours spent hunting to determine a
rate of energy intake in MJhr-1 . Values for average prey mass come primarily from those presented by
Carbone (2007) [38], see Table 4.
Species Name
Common Name
Mass(kg)
Ave. Prey Mass(kg)
DEI(MJ)
Intake Rate(MJ/hr)
References
Mustela nivalis
Mustela frenata
Mustela erminae
Mustela putorius
Mustela vison
Martes martes
Vulpes vulpes
Felis canadensis
Canis adustus
Canis latrans
Lycaon pictus
Canis lupus
Crocuta crocuta
Felis caracal
Felis pardalis
Panthera pardus
Acinonyx jubatus
Puma concolor
Panthera onca
Panthera leo
Least Weasel
Long-tailed Weasel
Stoat
Polecat
American Mink
Pine Marten
Red Fox
Canadian Lynx
Side-striped Jackal
Coyote
African wild dog
Timber Wolf
Spotted hyaena
Caracal
Ocelot
Leopard
Cheetah
Puma
Jaguar
Lion
0.14
0.23
0.95
1.03
0.79
1.2
4.6
10
11.2
11.5
22
46
58.6
12
11.7
46.5
58.6
51.9
76.9
120
0.02
0.04
0.05
0.1
0.1
0.05
0.48
1.4
0.78
41.06
33.75
81.33
107.33
16.5
11.82
33
33.75
76
40.7
137.25
0.21
0.69
0.35
1.20
1.52
1.30
1.77
6.31
10.29
5.14
25.12
45.72
35.28
6.86
4.79
37.94
53.57
37.19
34.17
77.89
0.04
0.31
0.07
0.16
0.21
0.15
0.26
0.63
1.24
0.46
7.18
4.21
6.82
0.80
0.46
3.03
13.39
4.26
2.71
36.06
[11][150]
[4]
[11][4]
[11]
[7][151]
[11]
[11][152]
[22]
[151]
[153]
[7][138]
[11][154][155]
[12][37][156]
[157]
[24]
[31]
[138][158]
[159][160][161]
[159][162]
[138]
Table 4: Average prey size, DEI and Intake rate values from the literature
A plot of the intake rate per hour of hunting for the Mustelidae and Canidae/Felidae was made,
Figure 16. The resulting scaling relationships were 0.1526[M ]0.2616 for carnivores less than 10kg, and
0.5478[M ]1.0629 for the canidae and felidae grouped together. The scaling relationships show pronounced
differences, particularly in the value of the exponent which scales over 6 times more steeply in the large
carnivores (canidae and felidae).
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5.1
Activity data from the literature
Lucy van Dorp
Log Intake Rate pr =me hun=ng (MJ/hr) 100.00 y = 0.5478x1.0629 R² = 0.89309 10.00 Mustelidae and Others 1.00 0.1 1 10 100 1000 Canidae and Felidae y = 0.1526x0.2616 R² = 0.17004 0.10 0.01 Log Body Mass (kg) Figure 16: Intake Rate (MJhr-1 ) against predator mass for the Mustelidae and Canidae/Felidae. For
carnivores less than 10kg the scaling relationship is 0.1526[M ]0.2616 and for the canidae and felidae the
scaling relationship is given as: 0.5478[M ]1.0629
1000 y = 0.2743x1.3261 R² = 0.55511 Log Average Mass Prey (kg) 100 10 Mustelidae and Others Canidae and felidae 1 0.1 1 10 100 1000 0.1 y = 0.0893x0.78 R² = 0.79063 0.01 Log Body Mass (kg) Figure 17: Average prey mass against predator mass for the Mustelidae and Canidae/Felidae.
The differences observed in the scaling relationships are likely to be, in part, due to the stark contrast
in the types of prey eaten by the small and large carnivore groupings. That said, when looking at the
average prey mass consumed by each species (Figure 17), the differences in the scaling relationships
between the small and large carnivores are not as marked (0.0893[M]0.78 versus 0.2743[M]1.3261 ). This
suggests that the time an animal is active is having a large effect on the data for intake rate.
Considering Figure 17 the Canadian Lynx (Felis canadensis) and side-striped jackal (Canis adustus)
are seen to look quite different to other members of the canidae and felidae. This is likely to be because
they are two carnivores at the threshold mass of around 10kg (10kg and 11.2kg respectively), which seem
to consume smaller prey than other members of their grouping. This may suggest these species use a
mixture of strategies, sometimes behaving more like a small carnivore and sometimes more like a large
carnivore.
This seems to be consistent with the literature. The Canadian lynx, Felis canadensis, predominantly
preys on the snowshoe hare, Lepus americanus, which weight in the region of 0.9-1.8kg [163]. That said in
summer, when the populations of L. americanus are low, they tend to eat smaller prey including rodents
and birds. A similar tendency is seen in the side-striped jackal, which is one of the least carnivorous
of the jackals. Their dietary preferences are highly variable with season, and they tend to focus on
The Scaling of Hunting Time in Mammalian Carnivores
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22
Lucy van Dorp
invertebrates during the wet season and small mammals such as the spring-hare in the drier months
[55][164]. Additionally fruit can make up to 30% of their dietary intake[34].
Amongst the other large mammal species, the leopard (Panthera pardus), cheetah (Acinonyx jubatus)
and jaguar (Panthera onca) hunt prey of average mass lower than themselves, whilst the coyote (Canis
latrans), African wild dog (Lycaon pictus), timber wolf (Canis lupus), spotted hyaena (Crocuta crocuta),
caracal (Felis caracal ), ocelot (Felis pardalis), puma (Puma concolor and lion (Panthera leo) hunt prey
that are, on average, heavier than themselves.
Amongst the smaller carnivores, the most pronounced difference in predator to prey mass is seen in
the red fox, Vulpes vulpes (4.6kg), who typically hunt prey of average mass 0.48kg. This reflects the
literature which identifies them as one of the most omnivorous of mammals studied in this project. As
well as rodents and lagomorphs, the red fox’s diet includes insects, fruit and small invertebrates [13].
Interestingly, none of the small carnivores presented here, eat prey larger than themselves.
6
Determining Scaling Relationships and Incorporating them
into the Gorman Model
One possible approach for understanding the way in which mammals, of increasing mass, balance their
energy budgets is to incorporate a mass component into an existing energetic model.
6.1
Introducing a Mass Component - African wild dog values
The first steps in incorporating a mass component into the Gorman model involve using known values
for the African wild dog (available in Table 5). This is because the model was originally designed for
this species so incorporating mass should be theoretically possible [12]. Initially, the scaling relationships
discussed in Section 3 were used to extrapolate across mass values.
Model Parameter
Time Hunting (Hd )
Metabolic Rate of Resting (Er )
Metabolic Rate of Hunting (Eh )
Intake Rate (I)
Value for a 25kg Dog
3.45 hr
0.2175MJhr-1
3.14MJhr-1
4.43MJhr-1
Table 5: Values given for a wild dog [12]
Given the values, for a 25kg African wild dog, the constant intercept values of the scaling relationships
were determined through extension of a linear regression line. A resting metabolic rate exponent of [M]0.75
was used, and a active metabolic rate exponent of [M]1 1 was used. A time hunting exponent of [M]-0.25
was used, in line with our hypothesis. The resulting values are supplied for a mammal of mass 0.1-1000kg,
6.
Mass (kg)
0.1
1
10
25
100
1000
Er (MJhr-1 )
0.003
0.019
0.109
0.217
0.615
3.459
Eh (MJhr-1 )
0.013
0.126
1.256
3.140
12.560
125.600
Tr (hr)
9.774
16.000
19.501
20.422
21.470
22.577
Th (hr)
14.226
8.000
4.499
3.578
2.530
1.423
Total Intake (MJ)
0.212
1.316
7.783
15.675
44.980
256.771
Intake Rate (MJhr-1 )
0.015
0.165
1.730
4.381
17.780
180.491
Table 6: Values extrapolated from the wild dog values using estimated exponents of the scaling relationships to determine the value of the intercepts.
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6.1
Introducing a Mass Component - African wild dog values
Lucy van Dorp
Under the assumed scaling relationships, the African wild dog values give the power equations and
plots (Figure 18) as follows:
• Resting Metabolic Rate 0.0195[M]3/4
• Active Metabolic Rate 0.1256[M]1
• Intake Rate per hour of hunting 0.1616[M]1.0201
Th =
24 × Er(0.0195M 0.75 )
I(0.1616M 1.0201 ) + Er (0.0195M 0.75 ) − Eh (0.1256M )
1000.000 Log Res2ng Metabolic Rate (MJhr-­‐1) y = 0.0195x0.75 R² = 1 1.000 1.000 10.000 100.000 1000.000 0.100 Log Ac2ve Metabolic Rate (MJhr-­‐1) 10.000 0.100 (18)
0.100 y = 0.1256x R² = 1 100.000 10.000 1.000 1.000 10.000 100.000 1000.000 0.010 0.100 0.001 0.010 Log Body Mass (kg) (a) Scaling of Resting Metabolic Rate
Log Body Mass (kg) (b) Scaling of Active Metabolic Rate
Log Intake Rate per 9me Hun9ng (Mjhr-­‐1) 1000.000 0.100 y = 0.1616x1.0201 R² = 0.99995 100.000 10.000 1.000 1.000 10.000 100.000 1000.000 0.100 0.010 Log Body Mass (kg) (c) Scaling of Intake Rate
Figure 18: Plots of extrapolated relationships from Gorman’s African wild dog data.
In the allometric relationships considered here:
y = axb ,
(19)
the constant values, a are made up of the scaling relationships of resting (ar ) and the active metabolic
rate (ah ). In order to consider the sensitivity of the relationship between constants, ar was plotted
against ah (Figure 19).
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6.2
Introducing a Mass Component - Literature values
Lucy van Dorp
Figure 19 shows that there are in fact an infinite number of constant combinations capable of producing the relationships described by Figure 18. There are, however, biological limits under which these
are valid. When a constant value falls below zero, for example, it is implied that an animal is producing
energy. This is not biologically realistic.
ah
0.15
0.10
0.05
0.02
0.04
0.06
0.08
0.10
ar
-0.05
Figure 19: Intercepts used in extrapolation of the Gorman values for an African wild dog. Constants are
marked on the plot where ar = 0.0195 and ah = 0.125.
Given the constants marked in Figure 19, the scaling of mass to the considered relationships can be
used to test the Gorman model (Figure 20). The model predicts that a carnivore of 25kg will hunt an
estimated 3.08 hours of the day. The value cited by Gorman gives 3.45 hours of hunting a day which is
very close to the modelled value.
4
Hours Active
3
2
1
0
0
50
100
Body Mass HkgL
150
200
Figure 20: Mass incorporated into the model using data for African wild dogs.
6.2
Introducing a Mass Component - Literature values
Given the scaling relationships determined from the literature-sourced activity data (see Sections 5.1,5.1.1
and 5.1.2), it should be possible to incorporate these relationships into the Gorman model. A summary
of the relationships extracted from the literature review are available in Table 7 and can be incorporated
into the model as follows:
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6.2
Introducing a Mass Component - Literature values
(
Th (M ) =
T small (M )
T large (M )
Lucy van Dorp
if m < 10kg,
if m ≥ 10kg,
(20)
where
24 × Er(0.0064M 1.0643 )
,
+ Er (0.0064M 1.0643 ) − Eh (0.0523M )
24 × Er(0.0107M 0.7118 )
T large (M ) =
.
1.0629
I(0.5478M
) + Er (0.0107M 0.7118 ) − Eh (0.1256M )
T small (M ) =
I(0.1526M 0.2616 )
(21)
(22)
The scaling relationships presented in Table 7 are, on the whole, highly dependent on the literature
sourced data (Appendices Table 8). There is, however, limited information on active metabolic rates
available in the literature for the species under consideration in this study. Thus, for canidae and felidae
species, the scaling of active metabolic rate derived from the values of African wild dogs was used (see
Table 6). For the smaller mammals, however a literature value was sourced for the least weasel. Chappell
and collegues (2013) [165] considered the scaling of metabolic rate in least weasels under forced running.
They recorded a value of 23.7ml.O2 min-1 , which equates to 7.053 x 10-3 [165]. The scaling relationship
for the Mustelidae and others given in Table 7 is found by extrapolating from this data assuming the
relationship is [M]1 , as set out by Taylor (1970) [96].
Scaling Relationship Considered
% Day Active
Basal Metabolic Rate (ml.O2hr-1 )
Basal Metabolic Rate (MJ-1 )
Average Prey Mass (kg)
Daily Energy Intake (MJ)
Daily Energy Expenditure (MJ)
Intake Rate (MJhr-1 )
Metabolic Rate Active (MJhr-1 )
Constants and Exponents for Species Groupings
Mustelidae and Others
Felidae and Canidae
27.881[M]0.2503
67.376[M]-0.227
0.7898
528.1[M]
493.52[M]0.7231
1.0643
0.0064[M]
0.0107[M]0.7118
0.78
0.0893[M]
0.2743[M]1.3261
0.4825
0.795[M]
0.5478[M]1.0629
0.5958
0.7227[M]
0.1424[M]1.2244
0.1526[M]0.2616
0.5478[M]1.0629
1
0.0523[M]
0.1256[M]1
Table 7: Constant and exponent values from the scaling relationships when the literature sourced values
are plotted. Species are grouped according to those less than 10kg (mainly the mustelids) and those
greater than 10kg(the canidae and felidae).
6.2.1
Model predictions for all species
For small and large mammals (<10kg and >10kg), the activity times computed when scaling relationships
are incorporated into the Gorman model are given in Figure 21. For Mustelids, the model accurately
predicts a positive correlation, such as that seen in the data but is unable to produce the values expected
from the literature. For the canidae and felidae, the model is inappropriate, suggesting that a carnivore
less than 70kg has to spend an infinite amount of time hunting. For mammals greater than 70kg, the
time spent active decreases with an increase in mass. This is the expected trend given the increasing
cost of hunting.
When all the data is presented with the functional relationships derived, Figure 22, one can observed
the marked inconsistencies in the data compared to the model predictions. Those predictions closest to
the data supplied in literature are found in the small carnivores between masses of 1.2kg - 5kg, which
comprises the Pine marten (Marte martes), the Swift fox (Vulpes velox ), the Fisher (Martes pennanti )
and the Red fox (Vulpes vulpes). The most accurate prediction is of the jaguar, Panthera onca, with a
disparity in the modelled hunting times to the literature of a factor 1.8.
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6.2
Introducing a Mass Component - Literature values
Lucy van Dorp
Proportion of day hunting H%L
50
40
30
20
10
0
0
10
20
30
Body Mass HkgL
40
50
(a) Mustelids and others
Proportion of day hunting H%L
100
80
60
40
20
0
0
100
200
Body Mass HkgL
300
400
.
(b) Canidae and felidae
Figure 21: The functional relationships for species groupings when mass is incorporated into the Gorman
model.
Percentage of Day Active
100
80
Activity Function for Canidae and Felidae
60
Literature Data of Mustelidae and Others
40
Activity Function for Mustelidae and Others
20
Literature Data for Canidae and Felidae
0
0
50
100
150
200
250
Mass HkgL
Figure 22: When the functional relationships of activity with mass are plotted against the literature
values for each species grouping, large disparities between the values predicted by the model and the
values determined from the literature are seen.
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Lucy van Dorp
7
Discussion
The Gorman model was unable to accurately predict activity patterns when a mass component was
introduced. The trends seen in the literature for an increase in activity time with mass in mammals
under 10kg and a decrease in activity with mass in larger mammals was seen (Figure 21). That said, we
were not able to predict species activity time with any accuracy and we do not see the [M]-0.25 scaling of
hunting time we were expecting. This is due to simplifications in the model and marked inconsistencies
in the values provided in the literature.
7.1
Biological Context
One of the key findings is that activity data compiled from the literature, despite inconsistencies in
the method of attainment, is able to identify statistically significant groupings of species in line with a
small/large mammalian carnivore divide. In this work, the smallest carnivores are identified as those
less than 10kg in mass, whilst the larger carnivores are those greater than 10kg. Previous work, by
Carbone 2007, identified the point of divide as 21.5kg [38]. When considering the data obtained here, a
10kg divide seems statistically appropriate. The discrepancy from Carbone’s work may be in the species
studied, as this study was limited to those species where data was available.
It would be interested to see if grouping species in different ways substantially alters the scaling
relationships derived. In this study, members of the order Carnivora were grouped in mass-related groups
defined by order (the “mustelidae and others” and the “canidae and felidae”). Alternative approaches
would be to group species by activity patterns (diurnal/nocturnal), shared prey or hunting strategy.
Grouping by prey type/mass may be an interesting approach given when Figure 17 is viewed, it can
be seen that there are 2 evident transitionary species; the Canadian lynx (Felis canadensis) and the
side-striped jackal (Canis adustus). Here the regression line for the small mass carnivores could easily
be extended to fit these two species. This suggests that these intermediate species, are having a large
effect on the regression of the large mammal data. The scaling relationship with these species removed
would produce a larger constant value, which is likely to be more biologically appropriate.
7.1.1
Other Scaling Relationships
Another approach to the problem would be to consider what other relevant factors scale with body mass.
Both day range size [11, 166] and bite strength [167][168] exhibit scaling relationships [11, 166, 169]. For
bite strength, bone and skull dimensions scale linearly with mass. Mammals with strong, larger jaws,
such as Crocuta crocuta and Hyaena hyeana engage in bone crushing carnivory, which is energetically
expensive but yields high intake rates. Amongst the felidae, skulls are shorter, and this is thought to
aid predators in withstanding the forces produced by struggling prey [167]. Given these measurements
are taken non-invasively, an approach considering skull dimensions, to infer hunting strategy, may be
useful. Similarly, home range scales linearly with mass and increases with metabolic demands on a
species [170, 169].
7.1.2
Predator Prey Co-Evolution
The relationships seen in the data, may not be solely down to an animal’s energetic status. Certainly
where it comes to intake rates and average prey size, co-evolution is likely to be occuring between
predators and their most frequent prey items [171]. Co-evolution occurs when two species adopt reciprocal
evolutionary adaptations. These occur when a change in one species acts selectively on another species,
that in turn acts on the first species [172]. Prey are an integral part of the predator’s environment.
Without a sufficiently high intake rate, a predator will die. To minimise this risk, evolution works so as
to improve those factors which aid predation; be it speed, camouflage, sense of small, size etc. Likewise,
prey will die if eaten by a predator, so evolve strategies to minimise the predation risk. These may
include speed, camouflage and defense mechanisms such as poison or thorns.
A classic example here is the lion (Panthera leo) and the zebra (Equus burchelli ). Both lions and
zebras have evolved to become faster. An increase in running speed in the lion will select for traits which
increase the running speed in the zebra. The metabolic rate of running in the lion, will thus not only
be a reflection of it’s own physical ability and physiological limits, but a by-product of an underlying
evolutionary strategy.
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7.2
Problems with the Model
Lucy van Dorp
With this in mind, a full understanding of hunting times, requires more extensive consideration of
prey items and how predators and prey interact.
7.2
Problems with the Model
For the data sourced on activity times, the Gorman model, with mass incorporated, is unable to make
useful predictions. This is largely due to the Gorman model being too simplisitic and relying on a number
of assumptions.
7.2.1
A two-state model is too simple
One of the greatest assumptions of the Gorman model is that the basic time budget, for a 24 hour
period, is split into only two components; resting and hunting; and these states are ill defined. In reality,
an animal does much more. Aldama (1991) [173] in his model of the energetics of the Canadian Lynx
(Felis canadensis) split the activities an animal engages in into resting, locomotion, hunting and feeding,
as well as acknowledging the metabolic costs of thermoregulation. This approach is only possible with
extensive data on the proportion of time spent in each activity to validate the model. In general, this
kind of data is not available over a range of species masses, as would be required to adopt this approach
for the questions addressed here. The model also, and somewhat necessarily, ignores additional factors
which may effect hunting such as animal’s age, gender and reproductive status, along with such elements
as diurnal or nocturnal activity patterns, and the presence of energy-conserving mechanisms such as fat
reserves and hibernation.
7.2.2
Scaling relationships are generalised
Scaling relationships are complex and sensitive to many secondary factors [87] so it is unrealistic to
expect a regression line (or equation) to describe precisely what the specific metabolic rate will be for
an animal of any given body mass. What can instead be determined is the expected mean value for
a typical mammal of a given size and biologically an animal will always deviate more or less from this
idealized norm [69]. This is particularly the case when considering the use of the Taylor relationship for
the scaling of active metabolic rate [96][98][160]. The relationship observed experimentally by Taylor
and colleagues, was of various mammalian species running. When incorporating mass into the Gorman
equation, the metabolic rate of running is used as a proxy for the metabolic rate of hunting (Eh ). During
the extent of any foraging activity, an animal is unlikely to be experiencing the same metabolic demands
as it would running. This is particularly the case for those predators who employ a “searcher” strategy,
stalking or seeking prey for extended periods of time. That said, even for the cursorial predators, such
as the majority of the canidae, running makes up only one component of the hunting process. The
use of an “active” metabolic scaling, as opposed to a true ”hunting” metabolic scaling is an invalid
assumption when introducing mass relationships into the model. That said, limitations in the process of
data collection and it’s availability in the literature, mean that use of the Taylor scaling is, for the main,
a suitable approach.
7.2.3
Parameter Exploration
These things considered, it is worth noting that the model is capable of predicting the functional form
we expect having obtained activity data from the literature, for example the polynomial curve fitted in
Figure 13, Section 5.1.
Where the intercept values (a) for the scaling relationships of resting metabolic rate (ar ), active
metabolic rate (ah ) and intake rate (ai ) are manipulated relative to each other, it is possible to construct
a curve whereby the time spent hunting mirrors the relationships we would expect for carnivores less
than and greater than 10kg.
The model is very sensitive to perturbations in the values of the constants considered in Figure 23,
and these constant values themselves are inherently uncertain, being obtained from inconsistent data
(see Section 7.3). Given a more extended study, a sensitivity analysis would be performed, but the
susceptibility of parameters can be assessed manually by plotting the functional relationships for time
hunting over a range of constant values, Figure 24.
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7.2
Problems with the Model
Lucy van Dorp
Figure 23: Manipulation of constant values to construct a scaling of activity time in line with what we
would predict. The intercept value for the scaling relationships used was manipulated, where ar is the
constant for the scaling of resting metabolic rate, ah is the constant for the scaling of active metabolic
rate, and ai is the constant for the scaling of intake rate.
Percentage of Day Active H%L
Figure 24 shows that the constant for the scaling of resting metabolic rate (ar ), increases the percentage of of time active logarithmically. The greater the value of the constant, the less influence it has
to the model output, changing the activity time progressively less. The active metabolic rate constant
increases exponentially with an increase in constant value. This is the case up to a constant value of
0.094 at which point an increase in the value of the constant will have no effect on the time spent hunting.
For the scaling of intake rate, the opposite relationship is seen. In this case, at a constant value of 0.065
hunting time is infinite before decreasing exponentially with increasing constant value. In every case, an
change in the constant value has quite a marked effect on the model output.
15
ah
10
ar
5
ai
0
0.00
0.02
0.04
0.06
0.08
0.10
Range of Constant Values
Figure 24: The values of the constants for each scaling relationship are very sensitive to perturbation.
Here ar denotes the constant in the scaling of resting metabolic rate, ah denotes the constant in the
scaling of active metabolic rate and ai denotes the constant in the scaling of intake rate.
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7.3
Problems with the Data
7.2.4
Lucy van Dorp
Possible Extensions - Effect of intake rate
One way of critically assessing the Gorman model is to consider how other factors which impinge on the
time an animal spends hunting could theoretically be incorporated into the model. An obvious extension
is to consider how the intake rate effects an animals foraging behaviour.
A high intake rate implies that the animal is in an environment where prey abundance is high. There
are no constraints on the availability of food. In this situation, one would expect the costs of hunting to
be dominated by the capturing, subduing and killing phases of the hunt, rather than those involved in
searching for prey. Biologically it would also seem logical that an animal will reach satiation once it’s
energetic requirements are met [67]. Sated animals are unlikely to actively seek food [174][17]. Satiation
seems to be a particular influential in small carnivores. The least weasel, for example, when allowed to
feed freely after a 16 hour deprivation could only consume no more than an average of 3.1g of food in an
hour and 11.4g in 8 hours [175]. They are physiologically constrained. In this way, intake rate is likely
to effect a species motivation to forage.
Conversely, a low intake rate implies prey populations are low. There is little food to go around,
perhaps as a result of environmental factors such as poaching, drought or disease. In this scenario
mammals are struggling for food and the intake rate is likely to be low. Even extended periods of
hunting may not result in a kill. In this situation a decision must be made as to whether the energetic
costs of hunting justify looking for prey or if it is best to conserve energy and risk an energetic deficit.
7.2.5
Possible Extensions - Effect of hunting success
The success of hunting is also likely to be important as animals very rarely obtain prey items every time
they hunt. For example, nearly 80% of all wild dog hunts end in a kill; but in comparison, the success
rate of lions, often viewed as ultimate predators, is only 30% [4].
Definitions of capture success in ecology vary greatly [176], but typically it is thought of as a function
of prey size [27].
To introduce a hunting success component into the model, one would deconstruct the intake rate into
two parameters: the kill rate per hour and the energy gained per potential prey item, Equation 23.
Intake Rate (I) = Successful kill rate (per hour) × Energy of potential prey (MJ)
(23)
This equation could be incorporated into the Gorman model to allow assessment of how these factos
influence activity times.
7.3
Problems with the Data
The scaling relationships used to incorporate mass into the Gorman model are determined from literature
sourced values. A large part of the difficulties associated with a modelling approach to hunting energetics
is that this data is highly inconsistent and for all intensive purposes can not be used to inform a model.
These are large inconsistencies in the species covered in the literature, how the data is sourced and how
well the values match a real-life biological situation.
7.3.1
Observed activity
Much of the activity data cited is the result of prolonged observational studies of animal movement
and behaviour patterns. This data is inconsistent. Different observers may classify different behaviour
differently, and furthermore, the very presence of an observer has the potential to alter an animal’s
behaviour. It is also difficult to monitor an animal over the extent of it’s range, particularly in the largest
carnivores. To get around this problem, some studies have been conducted in captive environments. Data
collected in this way also has it’s problems. Captive animals have predetermined diets and are often fed
at specific times of day. Any activity witnessed is thus unlikely to be a direct result of them needing
to balance their energy budgets. Captive animals also frequently exhibit pacing behaviour. Although
there have been some studies to indicate that this rhythmic locomotion is related to the light-dark cycle,
[177] [108][102] [178], it’s occurrence is generally not seen as natural behaviour. Observations of pacing
behaviour are thus likely to distort the observers measurements of the time spent active during a day.
When an animal is observed is also likely to be of significance. Bashaw and colleagues (2007), for
example, noted that the activity budgets of large felids is hugely variable and dependent on the time of
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7.4
Recommendations
Lucy van Dorp
day [179]. Seasonal differences n activity also exist. The serval, Leptailurus serval, for example, is active
for a greater proportion of the day when the weather is cooler and more overcast [25][180]. Contrastingly,
most mustelids, are less active during winter than in summer [181][182][183][108][184][103]. A reduction
in activity in winter is fairly common, also seen in ursids and procyonids. It offers a possible adaptation
to cold stress [16][17].
Ecological pressures are also of importance. In his study of hyaenas in the Kalahari, Mills notes that
ecological pressures also have an effect on activity budgets [185]. In the highly productive Ngorongoro
Crater spotted hyaenas (Crocuta crocuta) were less active than in other areas, and in the intermediately
productive Kruger National Park they were active for longer than in Ngorongoro but for less time than
in the Kalahari. In a food-rich situation along the Namid Desert coast individual brown hyaenas were
considerably less active than their Kalahari counterparts. In the Serengeti, the striped hyaena (Hyaena
hyaena), which is ecologically similar to the brown hyaena, was found to be active at night for less time
than were Kalahari brown hyaenas (Hyaena brunnea). A similar phenomenon was observed by Schaller
in his study of the Serengeti lions [4]. Schaller, observed that prides living in woodland habitats with
plenty of cover hunt in daylight more often than those living on open plains.
7.3.2
Measures of metabolism
Questions exist over the most appropriate measure of metabolism. Here the basal rate of metabolism
is used but a similar analysis could be performed using field metabolic rates of energy expenditure.
Likewise when it comes to measuring metabolic data, multiple methods are available, see Section 2.1. In
this study, metabolic data measured using all of these different techniques has been collated and average
values taken. There is little evidence to suggest whether it is valid to gather and group metabolic rates
measured by different techniques in this way [61]. The conversion factors used to move between units
of oxygen consumption to energy (Section 5.1.1) are also unlikely to be perfect. Furthermore, the point
in time when metabolic measurements are taken, regardless of method, are very subjective to external
conditions such as the environment and seasonal variability in animal behaviour. These external factors
make it difficult to make comparisons across species[87].
7.3.3
Body weight
Some inconsistencies are also likely to exist in the measures of mammal weight which form the x-axis
for the bulk of the scaling relationships considered. Data on body mass was primarily taken from the
Pantheria database [140] which aims to account for differences in body mass related to age, gender and
sub-type. That said, it is unlikely that every one of these variables is taken into account. The body
mass of different genders, for example, can be quite markedly different. In the Caracal (Felis caracal )
for instance, Botswana series males are typically 14kg (12-18kg) and females weight 10kg (8-13kg) [25].
7.4
Recommendations
The Gorman model is not an appropriate approach to the biological problem addressed here, in the
main because of the lack of consistent and readily available data across sepcies. There is no uniform
method for recording mammalian activity (see Section 2.1) and it is difficult to differentiate different
behaviour states even if the researcher is in a position to observe the animal. In order to produce a
realistic predictive bio-energetic model, detailed information is required on the movement and activity
patterns of a mammal and this data must be comparable across a range of species [186].
Remote measurement of the behaviour and energetic activities of free-living animals is becoming
increasingly possible and effective [187][188]. Use of remote devices allows data to be collected in realtime from undisturbed, free-ranging species [85][187][189]. There are several approaches to collecting the
sort of data required to validate a successful model of activity times with tools ranging from transmitters
that send their signals to receivers a few kilometres away to those that send data to orbiting satellites
and more frequently to devices that log data.
7.4.1
Accelerometer Data
Accelerometers can be attached to individual animals and used to monitor behaviour. They give a
indication of both static acceleration (the animals posture with respect to the gravitational field), and
The Scaling of Hunting Time in Mammalian Carnivores
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Lucy van Dorp
dynamic acceleration, which is derived from animal movements [84]. A major focus is the use of triaxial acceleration data which provides measurements in three axes aligned to the dorso-ventral, anterior
posterior and lateral axes of the subject animal [84]. These axes are analogous to the X, Y and Z axes
of cartisan co-ordinates[84]. Typically these devices also record environmental factors such as pressure,
temperature magnetic field and light level[186]. This data can be used in conjunction with movement
data to re-construct a picture of how the animal is behaving.
7.4.2
Biologging
Biologging is defined as ”the use of miniaturized animal-attached tags for logging and/or relaying data
about an animal’s movements, behaviour physiology, and/or environment”[85][188]. It has been used in
several studies recording the behaviour and physiology of free-ranging animals [190][191][192][193][194][195]
[196][197][198][189]. In biologging, data is relayed to receivers which are either ground-operated or satellites. Data is stored on these devices for future transmission or on data-loggers for downloading[85].
Research efforts are expanding with the development of smaller, more sophisticated devices, with better
battery life and memory capacity [85]. Holland and colleagues (2009) [199], for example used inter-species
bio-logging of Galapagos sharks fitted with acoustic ”business-card” tags. When tagged sharks came into
contact, mobile ”peer-to-peer” transmission occurred allowing animals movements to be recorded and
considered on an ecosystem level[188].
A good example of a device which combines these approaches is Mataki (http://mataki.org/), an
open, reconfigurable, flexible, low-cost tracking technology that comes with a set of software tools to
help analyse the data gathered. Unlike other low-cost tracking devices, Mataki is wirelessly enabled
and readily reprogrammable. This means data can be retrieved without having to recover devices and
researchers can explore novel tracking approaches through the development of their own firmware.
7.4.3
Open Access to Tracking Studies
Several organisations are involved in tracking wildlife but predominantly the data obtained from tracked
species is inaccessible and/or not publicly available. The open science debate has focused on the publishing of observations and results of scientific activities so that they are available for anyone to analyse
and reuse. In the context of this study, an open attitude to the presentation of the data from tracking
studies, would be highly beneficial to advancement in the fields of ecological and behavioural studies. A
good example is Movebank (https://www.movebank.org/), a free online database of animal tracking
data. Via this website, researchers can choose to make part or all of their study information and animal
tracks visible to other registered users, or to the public. For progress in the questions addressed in this
project, collaboration with such a web-based organisation, would be a sensible next step.
8
Conclusion
This project is the first of its kind to collates data on mammalian carnivore hunting times acros a range
of masses. In line with previous work, our results reaffirm that large carnivores (>10kg) must be thought
of as an ecologically and physiologically distinct group; and not merely a scaled-up version of a small
carnivore (<10kg).As it stands small carnivores increase the time they spend active with mass, whilst
the largest carnivores decrease their foraging activity as their size increases. The Gorman model of
hunting energetics is too simplistic to be truly informative about these kinds of biological problems.
This, together with the lack of consistently sourced field data makes it difficult to extend or validate.
A better model of time hunting would include factors such as the effect of intake rate, and the way
in which capture success influences behavioural dynamics. A bio-energetic model of this kind would
rely on consistent, multi-state data across a range of species. This may be possible with the advent of
increasingly sophisticated tracking and bio-logging devices and more open sharing of ecological data.
The Scaling of Hunting Time in Mammalian Carnivores
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Lucy van Dorp
9
Acknowledgements
Thanks go to the project supervisors Dr Chris Carbone and Dr Robin Freeman for their support and
advice throughout the duration of the project. Support on mathematical elements of the project was
provided by Jaspal Puri.
The Scaling of Hunting Time in Mammalian Carnivores
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Lucy van Dorp
10
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The Scaling of Hunting Time in Mammalian Carnivores
CoMPLEX MRes: Summer Project
45
Lucy van Dorp
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The Scaling of Hunting Time in Mammalian Carnivores
CoMPLEX MRes: Summer Project
46
The Scaling of Hunting Time in Mammalian Carnivores
CoMPLEX MRes: Summer Project
% Resting
79.45
90.8
62.25
77.78
69
62
70.07
63.54
49.6
73
71.39
65.4
53.3
85.42
54.8
78.44
58.5
64.3
56.4
47.8
83.33
62.2
47.5
91
77
DEI(MJ)
0.21
0.69
NA
0.35
1.2
0.28
1.52
1.3
NA
NA
1.77
10.29
5.14
25.12
45.72
35.28
6.31
6.86
4.79
37.94
53.57
37.19
34.17
77.89
NA
Table 8: Appendices of all the data collected
[213] [107] [106] [214]
[213] [215] [216] [111]
[38]
[114] [115] [177]
[41] [117] [181]
[38]
[124, 217, 184]
[38]
[38]
[38]
[30, 218]
[41] [219] [201]
[38]
[38]
[38]
[38]
[30]
[4, 220, 30]
[38]
[38]
[4] [27] [221] [30] [33]
[222]
References
[201]
NA
NA
NA
NA
[31]
NA
NA
[31]
[203]
NA
NA
[204]
[205]
NA
NA
[173]
NA
NA
NA
NA
NA
NA
[138]
NA
References
NA
[143, 144]
[105, 145]
NA
NA
NA
[146, 105]
[105, 145]
NA
NA
[147, 105]
NA
[105]
NA
NA
NA
NA
NA
[66, 105]
NA
[105]
[105]
[66, 105]
[66, 105]
NA
DEE(MJ)
0.22
NA
NA
NA
NA
0.64
NA
NA
1.78
1.16
NA
NA
4.51
15.29
NA
NA
0.84
NA
NA
NA
NA
NA
NA
36.72
NA
BMR (MJ/hr)
NA
0.005
0.012
NA
NA
NA
0.01
0.014
NA
NA
0.049
NA
0.054
NA
NA
NA
NA
NA
0.063
NA
0.180
0.177
0.224
0.339
NA
References
[200, 11]
[4]
NA
[11, 4]
[11]
[11]
[151, 7]
[11]
NA
NA
[11, 152]
[151]
[153]
[138, 7]
[204, 155, 154]
[37, 12, 156]
[22]
[157]
[24]
[207]
[11, 158]
[159, 160, 161]
[162, 208, 159]
[138]
NA
Referenes
[209] [210] [211] [178] [212]
[102]
References
[100, 101, 99, 17]
[102, 17]
[103, 17]
[107, 106, 7, 104, 108, 105]
[109, 111, 202, 110]
[113, 112]
[20, 114, 115]
[117, 116]
[38, 118]
[38, 119, 120]
[38, 121]
[38, 123]
[38, 128, 123]
[54, 7, 129]
[130, 131]
[38, 134, 133, 105]
[121, 125]
[206, 38, 7]
[35, 127, 64]
[132, 38, 7]
[134, 135, 133, 136, 105]
[38, 134, 137]
[38, 50]
[38, 2, 7, 130, 4]
[138, 38]
Average Prey Mass (kg)
0.02
0.04
NA
0.05
0.1
0.03
0.1
0.05
1.35
0.78
0.48
0.78
41.06
33.75
81.33
107.33
1.4
16.5
11.82
33
33.75
76
40.7
137.25
78.6
% Active
20.55
9.2
37.75
22.22
31
38
29.93
36.46
50.4
27
28.61
34.6
46.7
14.58
45.2
21.56
41.5
35.7
43.6
52.2
16.67
36.36
52.5
9
23
Intake Rate (MJ/hr)
0.043
0.311
NA
0.065
0.161
0.031
0.211
0.149
NA
NA
0.258
1.240
0.459
7.180
4.215
6.817
0.634
0.801
0.457
3.028
13.389
4.261
2.712
36.059
NA
Mass (kg)
0.14
0.23
0.96
0.95
1.03
0.956
0.79
1.2
2.14
3.75
4.6
11.2
11.5
22
46
58.6
10
12
11.7
46.5
58.6
51.9
76.9
120
227
Common Name
Least Weasel
Long-tailed weasel
American marten
Stoat
Polecat
Blanford’s fox
American mink
Pine marten
Swift fox
Fisher
Red fox
Side-striped jackal
Coyote
African wild dog
Timber wolf
Spotted hyaena
Canadian lynx
Caracal
Ocelot
Leopard
Cheetah
Puma
Jaguar
Lion
Tiger
Common Name
Least Weasel
Long-tailed weasel
American marten
Stoat
Polecat
Blanford’s fox
American mink
Pine marten
Swift fox
Fisher
Red fox
Side-striped jackal
Coyote
African wild dog
Timber wolf
Spotted hyaena
Canadian lynx
Caracal
Ocelot
Leopard
Cheetah
Puma
Jaguar
Lion
Tiger
Species Name
Mustela nivalis
Mustela frenata
Martes americana
Mustela erminae
Mustela putorius
Vulpes cana
Mustela vison
Martes martes
Vulpes velox
Martes pennanti
Vulpes vulpes
Canis adustus
Canis latrans
Lycaon pictus
Canis lupus
Crocuta crocuta
Felis canadensis
Felis caracal
Felis pardalis
Panthera pardus
Acinonyx jubatus
Puma concolor
Panthera onca
Panthera leo
Panthera tigris
Species Name
Mustela nivalis
Mustela frenata
Martes americana
Mustela erminae
Mustela putorius
Vulpes cana
Mustela vison
Martes martes
Vulpes velox
Martes pennanti
Vulpes vulpes
Canis adustus
Canis latrans
Lycaon pictus
Canis lupus
Crocuta crocuta
Felis canadensis
Felis caracal
Felis pardalis
Panthera pardus
Acinonyx jubatus
Puma concolor
Panthera onca
Panthera leo
Panthera tigris
Lucy van Dorp
47