The search behavior of terrestrial mammals

Abstract

Animals moving through landscapes need to strike a balance between finding sufficient resources to grow and reproduce while minimizing encounters with predators. Because encounter rates are determined by the average distance over which directed motion persists, this trade-off should be apparent in individuals’ movement. Using GPS data from 1,396 individuals across 62 species of terrestrial mammals, we show how predators maintained directed motion ~7 times longer than for similarly-sized prey, revealing how prey species must trade off search efficiency against predator encounter rates. Individual search strategies were alsomodulated by resource abundance, with prey species forced to risk higher predator encounterrates when resources were scarce. These findings highlight the interplay between encounter rates and resource availability in shaping broad patterns mammalian movement strategies.

Full text

1
The search behavior of terrestrial mammals
Michael J. Noonan1, Ricardo Martinez-Garcia2,73, Christen H. Fleming3,4, Benjamin Garcia De
Figueiredo2, Abdullahi H. Ali6, Nina Attias7, Jerrold L. Belant8, Dean E. Beyer, Jr.8, Dominique
Berteaux9,10,11,12, Laura R. Bidner13,14, Randall Boone15,16, Stan Boutin17, Jorge Brito18, Michael
Brown4,19, Andrew Carter20,21, Armando Castellanos18,22, Francisco X. Castellanos18,22,23, Colter
Chitwood24, Siobhan Darlington1, J. Antonio de la Torre25, Jasja Dekker26, Chris DePerno27,
Amanda Droghini28, Mohammad Farhadinia29,30, Julian Fennessy19, Claudia Fichtel31, Adam
Ford1, Ryan Gill1, Jacob R. Goheen32, Luiz Gustavo R. Oliveira-Santos33, Mark Hebblewhite34,
Karen E. Hodges1, Lynne A. Isbell13,14, René Janssen35, Peter Kappeler31, Roland Kays36,37, Petra
Kaczensky38,39, Matthew Kauffman75,76, Scott LaPoint40,41, Marcus Alan Lashley42, Peter
Leimgruber4, Andrew Little43, David W. Macdonald29, Symon Masiaine44,45, Roy T McBride,
Jr.46, E. Patricia Medici47,48,49, Katherine Mertes4, Chris Moorman50, Ronaldo G. Morato51,
Guilherme Mourão52, Thomas Mueller53,54, Eric W. Neilson55, Jennifer Pastorini56,57, Bruce D.
Patterson58, Javier Pereira59, Tyler R. Petroelje60, Katie Piecora43, R. John Power61, Janet
Rachlow62, Dustin H. Ranglack63, David Roshier20,64, Kirk Safford65, Dawn M Scott66, Robert
Serrouya67, Melissa Songer4, Nucharin Songsasen4, Jared Stabach4, Jenna Stacy-Dawes45,
Morgan B. Swingen27,68, Jeffrey Thompson69, Marlee A. Tucker70, Marianella Velilla69,71,
Richard W. Yarnell66, Julie Young72, William F. Fagan3, and Justin M. Calabrese73,74,3
1Department of Biology, The University of British Columbia Okanagan, Kelowna, BC, Canada
2ICTP South American Institute for Fundamental Research & Instituto de Física Téorica, Universidade Estadual
Paulista - UNESP, São Paulo, SP, Brazil
3Department of Biology, University of Maryland, College Park, MD, United States of America
4Smithsonian Conservation Biology Institute, National Zoological Park, Front Royal, Virginia, United States of
America
6Hirola Conservation Programme, Garissa 1774-70100, Kenya
7Programa de Pós-Graduação em Biologia Animal, Universidade Federal do Mato Grosso do Sul, Cidade
Universitária, Campo Grande, Mato Grosso do Sul, Brazil
8Department of Fisheries and Wildlife, Michigan State University, East Lansing, Michigan, United States of
America
9Département de Biologie, Chimie et Géographie, Université du Québec à Rimouski, Rimouski,
Québec, Canada
10Canada Research Chair on Northern Biodiversity, Université du Québec à Rimouski, Rimouski, Québec, Canada
11Centre for Northern Studies, Université du Québec à Rimouski, Rimouski, Québec, Canada
12Quebec Centre for Biodiversity Science, Université du Québec à Rimouski, Rimouski, Québec, Canada
13Department of Anthropology, University of California, Davis, Davis, California, United States of America
14Mpala Research Centre, Nanyuki, Kenya
15Natural Resource Ecology Laboratory, Colorado State University, Fort Collins, Colorado, United States of
America
16Department of Ecosystem Science and Sustainability, Colorado State University, Fort Collins,
Colorado, United States of America
17Department of Biological Sciences, University of Alberta, Edmonton, Alberta, Canada
18Instituto Nacional de Biodiversidad (INABIO), Quito, Ecuador
19Giraffe Conservation Foundation, Windhoek, Namibia.
20Australian Wildlife Conservancy, Subiaco East, Western Australia, Australia
21Gulbali Institute of Agriculture, Water and Environment, Charles Sturt University, Albury, New South Wales,
Australia
22Andean Bear Foundation, Quito, Ecuador
23The Ray Laboratory, Department of Biological Sciences, Texas Tech University, Lubbock, Texas, United States of
America
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24Department of Natural Resource Ecology and Management, Oklahoma State University, Stillwater, Oklahoma,
United States of America
25Instituto de Ecología, Universidad Nacional Autónoma de México and CONACyT, Ciudad Universitaria, México,
México
26Jasja Dekker Dierecologie, Arnhem, The Netherlands
27Fisheries, Wildlife, and Conservation Biology Program, North Carolina State University, Raleigh, North Carolina,
United States of America
28Alaska Center for Conservation Science, University of Alaska Anchorage, Alaska, United States of America
29Wildlife Conservation Research Unit, Department of Zoology, University of Oxford, Tubney House, Oxfordshire,
Oxford, United Kingdom
30Future4Leopards Foundation, Tehran, Iran
31German Primate Center, Behavioral Ecology & Sociobiology Unit, Göttingen, Germany
32Department of Zoology and Physiology, University of Wyoming, Laramie, Wyoming, United States of America
33Department of Ecology, Federal University of Mato Grosso do Sul, Campo Grande, Brazil
34Department of Ecosystem and Conservation Sciences W.A. Franke College of Forestry and
Conservation, University of Montana, Montana, United States of America
35Bionet Natuuronderzoek, Stein, The Netherlands
36North Carolina Museum of Natural Sciences, Biodiversity Lab, Raleigh, North Carolina, United States of America
37Fisheries, Wildlife, and Conservation Biology Program, North Carolina State University, Raleigh, North Carolina,
United States of America
38Department of Forestry and Wildlife Management, Inland Norway University of Applied Sciences, Evenstad, Stor-
Elvdal, Norway
39Research Institute of Wildlife Ecology - FIWI, University of Veterinary Medicine Vienna, Vienna, Austria
40Black Rock Forest, Cornwall, New York, United States of America
41Lamont-Doherty Earth Observatory, Columbia University, Palisades, New York, United States of America
42Department of Wildlife Ecology and Conservation, University of Florida, Florida, United States of America
43University of Nebraska-Lincoln, School of Natural Resources, Lincoln, Nebraska, United States of America
44Twiga Walinzi Initiative, Laikipia and Samburu Counties, Nanyuki, Kenya
45San Diego Zoo Institute of Conservation Research, Escondido, California, United States of America
46Faro Moro Eco Research, Departamento de Boquerón, Paraguay
47Lowland Tapir Conservation Initiative (LTCI), Instituto de Pesquisas Ecológicas (IPÊ), São Paulo, Brazil
48IUCN SSC Tapir Specialist Group (TSG), Campo Grande, Brazil
49Escola Superior de Conservação Ambiental E Sustentabilidade (ESCAS/IPÊ), São Paulo, Brazil
50Department of Forestry & Environmental Resources, North Carolina State University, Raleigh, North Carolina,
United States of America
51National Research Center for Carnivores Conservation, Chico Mendes Institute for the Conservation of
Biodiversity. Estrada Municipal Hisaichi Takebayashi, Atibaia-SP, Brazil
52Embrapa Pantanal, Rua 21 de setembro 1880, Corumbá, Mato Grosso, Brazil
53Senckenberg Biodiversity and Climate Research Centre, Senckenberg Gesellschaft für Naturforschung, Frankfurt
(Main), Germany
54Department of Biological Sciences, Goethe University, Frankfurt (Main), Germany
55Natural Resources Canada, Canadian Forest Service, Northern Forestry Centre, Edmonton, Canada
56Centre for Conservation and Research, Kodigahawewa, Julpallama, Tissamaharama, Sri Lanka
57Anthropologisches Institut, Universität Zürich, Zürich, Switzerland
58Integrative Research Center, Field Museum of Natural History, Chicago Illinois, United States of America
59CONICET - Museo Argentino de Ciencias Naturales Bernardino Rivadavia
60Michigan Department of Natural Resources, Marquette, Michigan, United States of America
61Department of Economic Development, Environment, Conservation, and Tourism, North West Provincial
Government, Mmabatho, South Africa
62Department of Fish and Wildlife Sciences, University of Idaho, Moscow, Idaho, United States of America
63Department of Biology, University of Nebraska at Kearney, Kearney, Nebraska United States of America
64School of Animal and Veterinary Sciences, University of Adelaide, Roseworthy, SA, Australia
65BC Parks, British Columbia, Canada
66School of Animal, Rural and Environmental Sciences, Nottingham Trent University, Brackenhurst Campus,
Southwell, United Kingdom
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67Caribou Monitoring Unit, Biodiversity Pathways, University of British Columbia, Revelstoke, British Columbia,
Canada
681854 Treaty Authority, Duluth, Minnesota, United States of America
69Asociación Guyra Paraguay and CONACYT, Parque Ecológico Asunción Verde, Asunción, Paraguay
70Department of Environmental Science, Radboud University, Nijmegen, The Netherlands
71School of Natural Resources and the Environment, University of Arizona, Tucson, Arizona, United States of
America
72Department of Wildland Resources, Utah State University, Logan, Utah, United States of America
73Center for Advanced Systems Understanding (CASUS), Görlitz, Germany
74Helmholtz-Zentrum Dresden-Rossendorf (HZDR), Dresden, Germany
75U.S. Geological Survey, Wyoming Cooperative Fish and Wildlife Research Unit
76Department of Zoology and Physiology, University of Wyoming, Laramie, WY, USA
This draft manuscript is distributed solely for purposes of scientific peer review. Its content is
deliberative and predecisional, so it must not be disclosed or released by reviewers. Because the
manuscript has not yet been approved for publication by the U.S. Geological Survey (USGS),
it does not represent any official USGS finding or policy.
Summary
Animals moving through landscapes need to strike a balance between finding sufficient
resources to grow and reproduce while minimizing encounters with predators 1,2. Because
encounter rates are determined by the average distance over which directed motion persists 1,3–5,
this trade-off should be apparent in individuals’ movement. Using GPS data from 1,396
individuals across 62 species of terrestrial mammals, we show how predators maintained
directed motion ~7 times longer than for similarly-sized prey, revealing how prey species must
trade off search efficiency against predator encounter rates. Individual search strategies were also
modulated by resource abundance, with prey species forced to risk higher predator encounter
rates when resources were scarce. These findings highlight the interplay between encounter rates
and resource availability in shaping broad patterns mammalian movement strategies.
Main
As motile organisms move through landscapes in search of food, mates, and cover, they need to
strike a balance between finding sufficient resources to grow and reproduce, while also
minimizing the rate at which they encounter predators1,2. Because of the fitness consequences of
foraging success6,7 and predator-prey dynamics8,9, there should be strong selection pressure on
movement strategies that maximize resource encounter rates while minimizing encounters with
predators. Although it is well recognised that animals will adjust the size of their home-range
areas based on resource availability10–12, there remains the question of how to optimally find
resources within these ranges. In this context, random search models have proven influential in
understanding how individual movement strategies translate to encounter rates1,3,4,13. The
consensus from these models is that directed (i.e., ballistic) movement leads to higher encounter
rates than more tortuous (i.e., diffusive) movement1,3,4. This occurs because individuals that
exhibit tortuous movement will tend to repeatedly search over the same areas, whereas directed
motion allows individuals to search over a larger area within the same amount of time. The
average distance over which ballistic motion persists, lv (in m), is thus a key determinant of
encounter rates1 and a potent trait that individuals can optimize.
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4
An individual's ballistic length scale, l
v
, is a function of the spatial variance of their movement
(
σ
p
, in m
2
) and their positional and velocity autocorrelation timescales (
τ
p
and
τ
v
respectively, in
sec), given by
Because directed movement is the more efficient search strategy
1,4,5
, bottom-
up pressure exerted
by the need to encounter resources should select for more ballistic movement. Importantly,
however, increasing l
v
will also increase the rate at which individuals encounter predators
1
. Top
-
down predation pressure should thus select for shorter ballistic length scales. Prey species
searching for immobile vegetation must therefore optimize their movement against the opposing
forces of their energetic requirements selecting for longer l
v
,
and predation pressure selecting for
shorter l
v1
. Predators also benefit from maintaining longer ballistic length scales
1
, but without the
intense top-down predation pressure experienced by prey species. The combination of bottom-
up
and top-down regula
tion is thus expected to select for longer ballistic length scales in predators,
versus more diffusive movement in prey species, all else being equal
1
(Fig. 1).
Figure 1 Selection pressures on predator and prey ballistic length scales. Schematic representation of bottom-
up
energetic requirements selecting for longer ballistic length scales in mammalian movement paths, and top-
down
nt
in
ed
ly,
-
ies
ng
for
he
up
rs,
up
wn
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5
predation pressure selecting for shorter
ballistic length scales. The simulated prey movement path (blue) has a
ballistic length scale of 10m, whereas the predator's movement (orange) has a ballistic length scale of 100m.
Notably, ‘all else’ is rarely equal in ecological systems, and the relative importance of bottom-
up
versus top-down regulation is expected to be context specific. In resource-
poor ecosystems,
individuals need to spend a substantial amount of time searching for food and moving between
patches
6,14
. The bottom-up driven need to f
ind sufficient resources to survive should outweigh
top-down pressure when resources are scarce. In productive environments, in contrast, bottom-
up
pressure on resource acquisition rates should be relaxed
12
, providing individuals with the
capacity to respond more directly to top-
down pressure and maintain relatively more diffusive
movement. These considerations lead to the expectation of a negative relationship between l
v
and
environmental productivity.
Although the importance of l
v
in governing encounter rates is suggested by theoretical models
1,5
,
there has, to date, been no empirical demonstration of systematic differences in l
v
between
comparably sized predators and prey for any taxonomic group. Here, we leverage the rapid
advances in the capacity to collect
15
and work with
16,17
animal movement data that have enabled
l
v
to be estimated for a broad range of species. We annotated Global Positioning System (GPS)
location data on 1,396 individuals from 62 species of terrestrial mammals (Fig. 2a
) with mean
adult body size and trophic group (prey n = 41, and predator n
= 21). We restricted our analyses
to range-resident animals and used continuous-time stochastic models
16
to estimate l
v
for each
individual (Fig 2b). We also annot
ated each data point with the mean Normalized Difference
Vegetation Index (NDVI), a satellite-derived measure of resource abundance
18
, to which each
individual was exposed. Finally, as measures of habitat permeability we quantified the mean
percent forest cover, terrain roughness, and human footprint index at each sampled location.
Figure 2 The distribution of mammalian movement data. In a
, the GPS locations of 1,396 prey (blue) and
predatory (orange) mammals across 62 species are plotted on the global map of Normalized Difference Vegetation
Index ranging from low (-1) to high (1) productivity; and b shows the median ballistic length scales, l
v
, for each
species.
Our analyses revealed allometric scaling in ballistic length scales, with larger mammals tending
to have more directed movement, all else being equal (P < 10
-7
; Fig. 3a
). The parameters of the
body-mass scaling relationships are shown in Table S2
. The residuals of the body mass
relationship followed theoretical predictions, with predator l
v
being 7.1 times longer than that of
a
up
s,
en
gh
up
he
ve
nd
,
en
id
ed
S)
an
es
ch
ce
ch
an
nd
on
ch
ng
he
ss
of
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6
comparably sized prey species (P < 10
-6
; Fig. 3b). Least-
squares regression also revealed a strong
negative correlation between NDVI and the residuals of the allometric relationships in l
v
for prey
species (P < 10
-6
; Fig. 3c
). In other words, when resource abundance was ignored, predictions
from the simple body-size relationships tended to under-estimate observed l
v
in low-
productivity
ecosystems, and over-estimate l
v
in highly productive ecosystems. That bottom-
up pressures
appear to outweigh top-down pressure for prey species living in resource-poor ec
osystems is
made all the more poignant when contrasted against known patterns in trophic structure scaling.
Resource-
poor environments tend to be more trophically top heavy than productive
ecosystems
19
, effectively increasing the number of predators per
individual prey on the
landscape. Nonetheless, prey species living in resource-
poor ecosystems exhibited significantly
longer ballistic length scales than those in resource-
rich environments, on average. Because
predation rates depend on numerous factors b
eyond encounter rates, (e.g., capture efficiency,
predator hunger levels at the time of the encounter, the presence of suitable cover, prey defenses,
etc.
20
), we would expect prey species to respond more directly to bottom-
up factors than
predators. In l
ine with this expectation, we found no evidence that predators adjusted their
ballistic length scales as a function of NDVI (P = 0.26; Fig. 3C).
Figure 3 Trends in mammalian ballistic length scales. Mammalian l
v
scales with body size, but predators exhibit
more ballistic motion than prey, and search behavior is modulated by environmental productivity. The scatterplot in
a show the allometric scaling of the ballistic length scale, l
v
for prey (blue), as well as pr
edatory (orange) mammals.
The boxplots in b show the residuals of the body-mass scaling of l
v
for predators and prey. When body size is
accounted for, predatory species have longer ballistic length scales on average (P < 10
-5
). The scatterplot in c
show
the body mass residuals as a function of the normalized difference vegetation index (NDVI). The solid lines in
c
show how prey adjusted their ballistic length scales based on NDVI (P < 10
-6
), whereas predators did not (P
= 0.26).
Although predation
pressure and resource abundance will influence the relative importance of
search times and movement rates
6,12,14,21
, they are not the only factors that will influence animal
movement. For instance, memory
22
, socially transmitted information
23
, and the ‘patchiness’
of
resources
6,14
have all been shown to influence foraging behavior. Similarly, landscape
permeability can impact the capacity for individuals to maintain directed motion, with
implications for foraging efficiency
24
. Indeed, we found complex, non-
linear and heteroskedastic
relationships between habitat structure and l
v
(Fig. S2
). Yet, even with all of these other factors at
play within the individual datasets we analyzed, our capacity to identify a clear signal for t
he
interplay between encounter rates and resource availability in shaping mammalian movement
strategies highlights just how important risk-reward trade-offs are to animals.
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7
One question that arises from these results is ‘Why don't predators have longer ballistic length
scales?’. Without top-down regulation, there should be little preventing longer lv in predators, yet
we found that predator lv was only ~7 times longer than that of comparably sized prey on
average. There are two main reasons why predator ballistic length scales are not longer than
observed. The first is that individuals need to perceive resources within the area they travel
through, and while more directed motion might be the more efficient movement strategy, it does
not necessarily imply that animals will perceive their targets. Individuals are thus constrained by
their perceptual range1,13 and the time and effort required to find resources in the landscapes they
move through20. Increasing lv thus only benefits predators up to a certain point, and beyond some
optimal value encounter rates may actually decrease4,5,14. The second reason is that while many
adult mammalian predators have few predators themselves, their movement can be constrained
by intra-guild and conspecific encounters25,26, or parasite avoidance27. Longer lv in predators
might increase prey encounter rates, but at the expense of increasing the rates at which they
encounter these negative factors.
Conclusions
The behavioral consequences of foraging within a landscape of fear have been theorized about
extensively28,29, yet demonstrated for only a handful of systems, such as elephant seals
(Mirounga angustirostris), which optimize their diving behavior against predation risk and their
energetic state2. Here, we demonstrate how the optimization of search strategies and encounter
rates underpin broad patterns in the movement of terrestrial mammals spanning orders of
magnitude in body size and distributed in multiple different ecosystems around the world. Prey
species searching for immobile vegetation under the threat of predation must trade off the
efficiency of their search strategies against the risk of encountering predators. However, ballistic
length scales were negatively correlated with resource abundance, revealing how prey species
are forced to risk higher predator encounter rates when resources are scarce. In contrast, the
ballistic length scales of predatory species searching for mobile prey experience less top-down
selection pressure, allowing them to maintain more efficient search behavior. These results
highlight the interplay between encounter rates and resource availability in shaping mammalian
movement strategies.
Methods
Empirical analyses
Tracking data analysis
To investigate pattern in the ballistic length scales of terrestrial mammals, we compiled openly
available GPS tracking data from the online animal tracking database Movebank30, or from co-
authors directly. Individual datasets were selected based on the criterion of range resident
behavior, as evidenced by plots of the semi-variance in positions as a function of the time lag
separating observations (i.e., variograms) with a clear asymptote at large time lags16,31. All data
from migratory, or dispersing periods were excluded as their measured movement strategies
would not be representative of the normal foraging dynamics we aimed to describe. The visual
verification of range-residency via variogram analysis31 was conducted using the R package
ctmm (version 1.1.0)16.
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8
As noted in the main text, the average length scale over which ballistic motion is maintained (lv,
in m) is a function of the spatial variance of an animal's movement (
σ
position, in m2) and its
positional and velocity autocorrelation timescales (
τ
position and
τ
velocity respectively, in sec). While
σ
p can be well estimated from coarse data32, autocorrelation structures are only revealed when
the time scale of measurement is less than or equal to the autocorrelation timescales 33. In
particular,
τ
v tends to be on the order of minutes to hours for medium to large terrestrial
mammals32,34. Estimating lv for these data thus first required estimating the autocorrelation
structure in each of the individual tracking datasets and identifying those for which there was
sufficient information to estimate
σ
p,
τ
p, and
τ
v. To do this, we fit a series of range-resident,
continuous-time movement models to the data. The fitted models included the Independent and
Identically Distributed IID process, which features uncorrelated positions and velocities; the
Ornstein-Uhlenbeck (OU) process, which features correlated positions but uncorrelated
velocities35; and an OU-Foraging (OUF) process, featuring both correlated positions, and
correlated velocities31,36. We then employed AICc based model selection to identify the best
model for the data36,37, from which the
σ
p,
τ
p, and
τ
v parameter estimates were extracted. To fit
and select the movement models, we used the R package ctmm, applying the workflow described
by16. Because only the OUF process included information on all of the parameters required to
estimate lv, we further restricted our analyses to only those individuals for which the OUF model
was selected. This latter threshold was based on the sampling resolution of the GPS data, as only
data of a sufficiently fine sampling resolution allow for the estimation of lv. In other words, we
used AICc based model selection to identify the individual datasets with data of sufficient
resolution to allow for an estimate of lv, rather than relying on an arbitrary sampling threshold.
The final dataset included data from 62 species, comprising a total of 8,613,485 locations for
1,396 individuals. Finally, lv was calculated from the parameter estimates for each of these
individuals as
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Covariate data
For each of the species in our dataset we compiled covariate data on that species' mean adult
mass, in kilograms, and diet taken from the EltonTraits database38. This dataset includes species
with body masses covering five orders of magnitude (0.4 – 4000 kg). Dietary class was then used
to categorize species as being either a predator or prey species. Predators were species that
specialized primarily on mobile animal prey, whereas prey were herbivores and frugivores that
specialized primarily on sessile vegetation. A summary of the dataset is shown in Table S1. To
assess ecological factors that may have influenced lv, we also annotated each estimate with four
satellite-derived habitat metrics: i) mean Normalized Difference Vegetation Index (NDVI), as a
measure of local resource abundance18; ii) percent forest cover39; iii) terrain roughness40; and iv)
machine-learning human footprint index (ml-HFI)41, as measures of habitat permeability. Details
on the annotation process for the habitat covariate data were as follows:
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1. NDVI. To annotate the location data with NDVI we first compiled NDVI data from the
publicly accessible NASA MODIS archive. We used global NDVI rasters sampled at a
250m resolution at 16-day intervals between 2000-2022 (i.e., a total of 518 raster layers).
For each individual GPS location in the dataset, we identified the point in time and space
that was closest to the sampled location and extracted the NDVI value. Once each
location was annotated with the appropriate NDVI value, we calculated the geometric
mean value of NDVI to which each individual was exposed.
2. Percent forest cover. Consensus land cover data at a 1-km resolution were obtained
from the EarthEnv data repository based on the methods presented in39. These data were
available as 12 raster layers containing percentages on the prevalence of one of 12 land-
cover classes. From these individual raster layers we quantified the percent forest cover
as the summation of five layers containing information on the prevalence of
evergreen/deciduous needleleaf trees, evergreen broadleaf trees, deciduous broadleaf
trees, mixed/other trees, and shrubs. Following a similar process as the NDVI annotation,
we identified the point in space that was closest to each sampled GPS location and
extracted the percent forest cover value and calculated the geometric mean value to
which each individual was exposed.
3. Terrain roughness. Terrain roughness data at a 1-km resolution were obtained from the
EarthEnv data repository based on the methods presented in40. Terrain roughness
represents a measure of topographic heterogeneity, and was quantified as the largest
inter-cell difference in elevation between a focal cell and its 8 surrounding cells. Here
again we identified the point in space that was closest to each sampled GPS location and
extracted the roughness value and calculated the geometric mean value to which each
individual was exposed.
4. ml-HFI. The machine-learning-based human footprint index (ml-HFI)41 is an index of
human pressure on the landscape that is derived from remotely sensed surface imagery
and ranges on a scale between 0 (no human impact), and 1 (high human impact). Briefly,
convolutional neural networks, are used to identify patterns of human activity from the
Hansen Global Forest Change imagery version 1.7 (GFCv1.7). The raster is available at
an approximately 1-km resolution. We identified the point in space that was closest to
each sampled GPS location and extracted the ml-HFI value and calculated the geometric
mean value to which each individual was exposed.
Table S1 Data summary table. Summary statistics on the GPS tracking data used in the analyses presented in the
main text. Values include the species binomial, including subspecies where appropriate, the number of individuals
per species (n), body mass, trophic group, the median spatial variance of the animals' movement (
σ
p), the median
positional (
τ
p) and velocity (
τ
v) autocorrelation timescales, and the median ballistic length scale (lv).
Binomial n Mass (kg) Trophic Group
σ
p
(km
2
)
τ
p
(hrs)
τ
v
(min)
l
v
(m)
Acinonyx jubatus
1 46.7 Predator 14.882 190.21 98.05 357.58
Aepyceros melampus
20 52.5 Prey 0.229 33.43 8.05 31.12
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Alces alces
56 541.46 Prey 8.56 706.57 31.62 76.29
Antidorcas marsupialis
10 31.5 Prey 66.451 345.81 42.96 338.58
Antilocapra americana
46 46.08 Prey 20.41 264.17 31.75 215.78
Beatragus hunteri
4 79.13 Prey 4.888 128.43 20.38 101.8
Blastocerus dichotomus
3 86.67 Prey 0.929 145 13.45 37.97
Brachylagus idahoensis
3 0.42 Prey 0.002 13.18 35.18 8.93
Canis latrans
49 13.41 Predator 2.981 17.6 6.18 115.15
Canis lupus
128 32.18 Predator 58.427 88.49 27.43 542.95
Capra ibex
39 85.17 Prey 4.155 353.57 25.02 74.6
Cerdocyon thous
19 5.24 Predator 0.156 7.43 1.63 21.62
Cervus canadensis
14 200 Prey 67.242 1636.76 27.93 167.19
Chlorocebus pygerythrus
10 4.99 Prey 0.024 11.05 3.35 9.94
Connochaetes taurinus
35 180 Prey 41.062 490.7 12.12 118.85
Cuon alpinus
11 14.17 Predator 5.589 51.68 33.05 244.06
Elephas maximus indicus
24 3500 Prey 50.144 1375.75 48.63 124.34
Elephas maximus maximus
51 3750 Prey 12.971 202.4 64.2 232.89
Elephas maximus sumatranus
9 3000 Prey 26.06 1013.66 51.66 177.53
Equus hemionus hemionus
18 240 Prey 1129.502 4715.34 14.21 234.94
Equus quagga
9 400 Prey 463.718 930.14 34.95 494.23
Eulemur rufifrons
3 2.25 Prey 0.029 7.03 10.83 24.01
Euphractus sexcinctus
4 4.78 Prey 0.024 4.85 1.19 11.23
Felis catus
53 2.88 Predator 2.05 74.06 8.72 80.7
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Felis silvestris
3 5.1 Predator 2.634 30.4 23.67 108.93
Giraffa camelopardalis antiquorum
17 899.99 Prey 48.821 676.22 28.25 210.75
Giraffa camelopardalis camelopardalis
51 899.99 Prey 18.352 195.06 33.92 232.42
Giraffa camelopardalis peralta
17 899.99 Prey 66.868 253.61 33.64 346.69
Giraffa giraffa angolensis
72 899.99 Prey 39.839 303.38 36.98 255.91
Giraffa giraffa giraffa
31 899.99 Prey 6.082 118.25 34.9 183.03
Giraffa reticulata
35 899.99 Prey 20.083 191.98 31.17 211.52
Giraffa tippelskirchi
18 899.99 Prey 9.298 157.74 27.83 172.82
Hyaena brunnea
3 42.98 Predator 19.798 44.85 25.77 425.29
Lagostrophus fasciatus
1 1.7 Prey 0.005 6.1 34.35 21.17
Leopardus pardalis
3 11.9 Predator 0.246 7.66 9.85 72.59
Loxodonta africana
22 3940.03 Prey 242.666 1025.23 34.06 309.1
Lycalopex culpaeus
8 8.62 Predator 0.505 5.26 5.65 95.17
Lynx rufus
13 8.9 Predator 0.506 22.71 2.19 28.56
Madoqua guentheri
15 7.5 Prey 0.003 2.96 1.69 4.86
Neogale vison
5 1.15 Predator 0.548 127.94 53.65 44.45
Odocoileus hemionus
5 54.21 Prey 26.912 1734.41 23.69 91.76
Odocoileus virginianus
33 55.51 Prey 0.187 12.04 16.09 69.39
Oreamnos americanus
4 72.5 Prey 4.618 48.56 53.35 318.42
Oryx dammah
38 200 Prey 38.379 265.81 20.29 203.16
Ovis canadensis
3 74.64 Prey 10.951 822.88 47.67 114.35
Ovis dalli
66 55.65 Prey 23.112 524.31 61.06 204.6
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12
Panthera leo
3 161.5 Predator 31.722 57.14 65.13 748.76
Panthera onca
105 100 Predator 11.749 126.68 45.69 254.45
Panthera pardus pardus
7 48.75 Predator 29.444 359.11 13.47 101.31
Panthera pardus saxicolor
6 52.04 Predator 15.643 185.1 30.3 221.34
Pekania pennanti
17 4 Predator 0.707 20.18 2.93 35.31
Propithecus verreauxi
7 3.48 Prey 0.006 < 0.01 < 0.01 6.11
Puma concolor
31 51.6 Predator 46.227 428.86 52.92 264.8
Rangifer tarandus
19 86.03 Prey 55.734 1521.59 62.11 182.18
Rangifer tarandus tarandus
8 86.03 Prey 285.467 1749.55 72.86 402.56
Sus scrofa
23 96.12 Prey 0.234 7.53 2.18 43.85
Syncerus caffer
6 580 Prey 23.035 255.58 29.75 240.2
Tapirus terrestris
41 207.5 Prey 0.367 9.11 21.41 117.39
Tremarctos ornatus
1 140 Prey 15.035 258.17 35.41 185.38
Ursus arctos horribilis
18 212.5 Predator 30.3 249.65 40.92 253.13
Vulpes lagopus
18 3.58 Predator 1.289 4.42 0.81 64.09
Vulpes vulpes
20 5.48 Predator 1.39 5.89 13.04 199.24
Assessing trends in lv
The resulting dataset of ballistic length scales was then analyzed to test for differences in lv
between predators and prey, and for any effects of NDVI or forest cover on lv. Because lv was
correlated with body size (Fig. 3A), we controlled for mass by regressing lv against body size on
a log10-log10 scale using generalized least-squares fitting with Gaussian distributed errors. Due to
phylogenetic autocorrelation42, closely related species may exhibit similarities in movement due
to common descent. Accordingly, we did not treat species data records as independent, but rather
corrected for this inertia by adjusting the variance-covariance matrix in our regression model
based on the phylogenetic relationships using the R package nlme43. Phylogenetic relationships
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13
between the mammalian species in our dataset were obtained from the VertLife repository44. We
sampled 1,000 trees and estimated the consensus tree using the R package phytools, version
1.0-345. Several of the species and subspecies included in our analyses were not included in the
VertLife repository. These were manually inserted into the phylogeny using the most recent
estimates of divergence times from the closest related species found in the VertLife repository.
This included the Persian leopard (Panthera pardus saxicolor), with divergence time of 0.297
Ma from the African leopard (P. pardus pardus)46, the Sumatran elephant (Elephas maximus
sumatranus), with divergence time of 190,000 years from the Indian elephant (E. maximus
indicus)47, the Sri Lankan elephant (E. maximus maximus), with divergence time of 43,000 years
from the Indian elephant47, elk (Cervus canadensis), with divergence time of 20 million years
from Rangifer tarandus48, and Norwegian reindeer (R. tarandus tarandus) with a divergence
time from R. tarandus of 115,000 years49. Divergence times for all of the species of Giraffa were
taken from50. The species G. camelopardalis was assigned a divergence time from G. giraffa of
0.37 Ma. G. tippelskirchi was assigned a divergence time from G. giraffa of 0.23 Ma, and G.
reticulata a divergence time from G. camelopardalis of 0.26 Ma. The subspecies G. giraffa
angolensis and G. giraffa giraffa had a divergence time of 0.04 Ma. G. camelopardalis
antiquorum was assigned a divergence time from G. camelopardalis peralta of 0.15 Ma and G.
camelopardalis camelopardalis from G. camelopardalis peralta of 0.12 Ma. The resulting
phylogenetic tree is shown in figure S1.
The final step in our analyses was to determine whether individual deviations from the allometric
relationship in lv could be described by trophic group, ecosystem productivity, or habitat
permeability. We regressed the residuals of the phylogenetically controlled allometric model
described above against trophic group, NDVI, percent forest cover, terrain roughness, and ml-
HFI using generalized least-squares fitting with Gaussian distributed errors. The relative support
for these models was then assessed by comparing the AICc values of the fitted models against
intercept only models. We chose to work with the residuals as it allowed for like-to-like
comparisons across all of the individuals in our dataset and clearer visualisations of the partial
effects, while still correcting for differences in body sizes and phylogenetic inertia. The
parameters of the body-mass scaling relationships in lv are shown in Table S2. Results of the
trophic group and NDVI regressions are presented in the main text and the model selection
results are presented in Table S3. The R scripts used to produce the results presented in this work
are openly available on GitHub at https://github.com/NoonanM/BallisticMotion.
Table S2. Observed scaling relations of ballistic length scales in terrestrial mammals. All three of the scaling
relations had the general form lv =
β
0 mass
α
.
β
0
95% CI
α
95% CI
All taxa 4.67 1.34 — 15.72 0.30 0.19 — 0.41
Prey 0.84 0.22 — 3.22 0.42 0.30 — 0.53
Predators 1.26 0.19 — 8.56 0.51 0.32 — 0.71
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14
Figure S1
Phylogenetic relationships of the Mammalian species analysed in the main text with species labels
coloured by trophic guild (prey in blue, predators in orange).
Table S3.
Table showing the model selection results for the effect of NDVI on the residuals of the body mass
relationship in ballistic motion length scales, l
v
, for predators and prey.
Model AICc
∆
AICc
Prey l
v
residuals
-23.0 - 95.7 x NDVI
10552 0
-21.4
10577 25
Predator l
v
residuals
172.9 - 41.8 x NDVI
7145 0
els
ss
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15
165.3
7153 8
When corrected for body size, mammalian ballistic length scales, l
v
, show mixed responses to
measures of habitat permeability. We found no relationship between the l
v
body mass residuals
and percent tree cover within each individual's habitat for prey (P = 0.06) nor predators (P
=
0.92), but both trophic groups exhibited
exponentially variable heteroskedasticity with changing
forest cover (Fig. S2a, table S4). We also found no relationship between the l
v
body mass
residuals and terrain roughness for prey (P
= 0.06), but there was a positive relationship for
predators (P
= 0.001). Here again both trophic groups exhibited exponentially variable
heteroskedasticity with changing terrain roughness (Fig. S2b, table S5
). Finally, both predators
and prey living in human modified landscapes had shorter ballistic length scales tha
n those living
in more natural environments, but these relationships were non-
linear and heteroskedastic (Fig.
S2c, table S6
). Although this latter result is somewhat surprising given some empirical studies'
findings that the structure present in natural e
cosystems can impact the capacity for individuals
to maintain directed motion
24
,
it is in line with the reductions in mammalian movement observed
in human modified environments generally
21
.
Figure S2 Relationship between mammalian ballistic length scales and habitat permeability.
When corrected
for body size, mammalian ballistic length scales, l
v
, show mixed responses to measures of habitat permeability. The
scatterplot in a shows the residuals of the allometric scaling of the ballistic length scale, l
v
for prey (blue), as well as
predatory (orange) mammals as a function of the percent tree cover. In b the residuals of the body mass scaling of l
v
for predators and prey are shown as a function of terrain roughness. The scatterplot in c
depicts the body mass
residuals as a function of the human footprint index, a satellite derived measure of human disturbance ranging on a
scale between 0 and 1. Each point is an individual (n = 1,396)
representing 62 species. The solid lines depict the
selected regression models and the shaded areas the 95% confidence intervals around the mean trend. Trends are not
shown for cases where the intercept-only model was selected.
Table S4. Table showing the
model selection results for the effect of percent forest cover on the residuals of the
body mass relationship in ballistic motion length scales, l
v
, for predators and prey.
Model AICc
∆
AICc
Prey l
v
residuals
-14.5 +
ε
~ N(0,
σ
2
x e
-
0.004 x
forest cover
)
10574 0
to
als
=
ng
ss
for
le
rs
ng
ig.
es'
als
ed
ted
he
as
v
ss
a
the
ot
the
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16
-53.0 + 0.5 x forest cover +
ε
~ N(0,
σ
2 x e-0.004 x forest cover)
10574 0
-52.7 + 0.5 x forest cover +
ε
~ N(0,
σ
2)
10577 3
-21.4 +
ε
~ N(0,
σ
2)
10577 3
Predator lv residuals
158.7 +
ε
~ N(0,
σ
2 x e0.014 x forest cover)
7145 0
163.7 - 0.1 x forest cover +
ε
~ N(0,
σ
2 x e0.014 x forest cover)
7145 0
156.6 + 0.1 x forest cover +
ε
~ N(0,
σ
2)
7154 9
165.3 +
ε
~ N(0,
σ
2)
7154 9
Table S5. Table showing the model selection results for the effect of terrain roughness on the residuals of the body
mass relationship in ballistic motion length scales, lv, for predators and prey.
Model AICc
∆
AICc
Prey lv residuals
-37.4 +
ε
~ N(0,
σ
2 x e-0.02 x roughness)
10504 0
-11.8 - 0.6 x roughness +
ε
~ N(0,
σ
2 x e-0.02 x roughness)
10505 1
-5.1 - 1.1 x roughness +
ε
~ N(0,
σ
2)
10563 59
-21.4 +
ε
~ N(0,
σ
2)
10577 73
Predator lv residuals
106.4 + 4.9 x roughness +
ε
~ N(0,
σ
2 x e0.02 x roughness)
7127 0
130.9 +
ε
~ N(0,
σ
2 x e0.02 x roughness)
7138 11
102.2 + 4.3 x roughness +
ε
~ N(0,
σ
2)
7141 14
165.3 +
ε
~ N(0,
σ
2)
7154 27
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17
Table S6. Table showing the model selection results for the effect of the human footprint index on the residuals of
the body mass relationship in ballistic motion length scales, lv, for predators and prey.
Model AICc
∆
AICc
Prey lv residuals
-1095.4 - 1876.4 x HFI + 1180.6 x eHFI +
ε
~ N(0,
σ
2 x e-2.8 x HFI)
10487 0
-972.6 - 1630.8 x HFI + 1040.8 eHFI +
ε
~ N(0,
σ
2)
10512 25
11.5 - 189 x HFI +
ε
~ N(0,
σ
2 x e-2.4 x HFI)
10512 25
23 - 219.3 x HFI +
ε
~ N(0,
σ
2)
10531 44
-66.6 +
ε
~ N(0,
σ
2 x e-2.7 x HFI)
10535 48
-21.4 +
ε
~ N(0,
σ
2)
10577 90
Predator lv residuals
262.1 - 198.0 x HFI - 39.1 x eHFI +
ε
~ N(0,
σ
2 x e-3.5 x HFI)
7094 0
227.7 -262.8 x HFI +
ε
~ N(0,
σ
2 x e-3.5 x HFI)
7105 11
778.2 + 684.9 x HFI - 598.2 x eHFI +
ε
~ N(0,
σ
2)
7115 21
97.1 +
ε
~ N(0,
σ
2 x e-3.0 x HFI)
7123 29
201.5 - 152.3 x HFI +
ε
~ N(0,
σ
2)
7129 35
165.3 +
ε
~ N(0,
σ
2)
7154 27
Acknowledgments: The full list of funding sources for this work is provided in Appendix S1.
Any use of trade, firm, or product names is for descriptive purposes only and does not imply
endorsement by the U.S. Government.
Author contributions: MJN and JMC conceived the manuscript; MJN conducted the analyses.
MJN, JMC, RMG, CHF, and WHF wrote the first manuscript draft. Co-authors contributed data
and assisted with writing the final version of the manuscript.
Competing interests: Authors declare that they have no competing interests.
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18
Data and materials availability: The data reported in this paper and the R scripts used to carry
out this study are openly available on GitHub at https://github.com/NoonanM/BallisticMotion.
Materials & Correspondence: Data and/or methods request should be sent to Michael Noonan.
Supplementary Materials
Figs. S1 to S2
Tables S1 to S6
Appendix S1: Extended List of Acknowledgements and Funders
Data S1: Data used to generate the results presented in the main text.
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Appendix S1: Extended List of Acknowledgements and Funders
MJN was supported by an NSERC Discovery Grant RGPIN-2021-02758. This work was
partially funded by the Center of Advanced Systems Understanding (CASUS) which is financed
by Germany’s Federal Ministry of Education and Research (BMBF) and by the Saxon Ministry
for Science, Culture and Tourism (SMWK) with tax funds on the basis of the budget approved
by the Saxon State Parliament. CHF, WFF, and JMC were supported by NSF IIBR 1915347.
R.M.-G. was supported by FAPESP through grant no. ICTP- SAIFR 2016/01343-7; Programa
Jovens Pesquisadores em Centros Emergentes through grant nos. 2019/24433-0 and 2019/05523-
8, and the Simons Foundation through grant number 284558FY19; BGF was supported by
FAPESP through grant 2019/26736-0; R.M.-G and B.G.F were supported by Instituto
Serrapilheira through grant no. Serra-1911-31200. The procurement of the collars in Ecuador
was funded by the International Climate Initiative of the German Federal Ministry for the
Environment, Nature Conservation, and Nuclear Safety with support of KfW Development Bank
(BMZ project no. 2098 10 987). MSF was supported by a research fellowship from the
University of Oxford and the Iranian Department of Environment approved permits for the work
conducted (93/16270). Financial support was provided by the People’s Trust for Endangered
Species (PTES), Zoologische Gesellschaft für Arten und Populationsschutz (ZGAP), Iranian
Cheetah Society, IdeaWild and Association Francaise des Parcs Zoologiques (AFdPZ) to the
leopard collaring project in Iran. RGM was supported by FAPESP grants 2013/10029-6 and
2014/24921-0. RK was supported by USA NSF grants 2206783, 1914928, 1754656 and NASA
Ecological Forecasting Program Grant 80NSSC21K1182. DB was supported by Canada
Foundation for Innovation (grant no. 38881), Natural Sciences and Engineering Research
Council of Canada (grants no. 509948-2018, RGPIN-2019-0592, RGPNS-2019-305531), and
Network of Centers of Excellence of Canada ArcticNet. LAI thanks the US National Science
Foundation (grant nos. BCS 99-03949 and BCS 1266389), L.S.B. Leakey Foundation, and
Committee on Research, University of California, Davis, for financial support, the Kenya
Government (NACOSTI permit No. P/15/5820/4650) for research permission, and the Kenya
Wildlife Service for local affiliation. The Dutch Wildcat data was obtained in a project for ARK
Nature with funding of the province of Limburg. JJT, RTM, and MV were supported by
PROCIENCIA project 14

INV

208 from the Consejo Nacional de Ciencia y Tecnología of
Paraguay with the permission of the Ministerio del Medio Ambiente y Desarrollo Sostenible of
Paraguay under research permits 124/2017 and 155/2018. Funding for research on introduced
predators was provided by supporters of Australian Wildlife Conservancy with additional
support from the Australian Government’s National Environmental Science Program through the
Threatened Species Recovery Hub. Movement data for scimitar-horned oryx were obtained
through a reintroduction project in Chad: this project is a joint initiative of the Government of
Chad and the Environment Agency - Abu Dhabi, implemented in Chad by SaharaConservation
in partnership with the Ministry for the Environment, Fisheries and Sustainable Development,
with technical support from the Zoological Society of London, Fossil Rim Wildlife Center, Saint
Louis Zoo, and other key partners. Movement data for the four giraffe species was funded by the
Giraffe Conservation Foundation and its supporters, and the collaborative efforts of government,
academic and NGO partners. Funding for this project was provided by the U.S. Department of
Defense through the Wildlife Branch at Fort Bragg Military Installation and Fisheries, Wildlife,
and Conservation Biology Program at North Carolina State University. Funding was provided by
the National Science Foundation (DEB-1146166, to J.L. Rachlow) Funding was provided by the
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22
Austrian Science Fund (P18624). Funding was provided by the Utah Division of Wildlife
Resources.
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