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Abstract

Accurately quantifying species' area requirements is a prerequisite for effective area-based conservation. This typically involves collecting tracking data on species of interest and then conducting home-range analyses. Problematically, autocorrelation in tracking data can result in space needs being severely underestimated. Based on the previous work, we hypothesized the magnitude of underestimation varies with body mass, a relationship that could have serious conservation implications. To evaluate this hypothesis for terrestrial mammals, we estimated home-range areas with global positioning system (GPS) locations from 757 individuals across 61 globally distributed mammalian species with body masses ranging from 0.4 to 4000 kg. We then applied block cross-validation to quantify bias in empirical home-range estimates. Area requirements of mammals <10 kg were underestimated by a mean approximately15%, and species weighing approximately100 kg were underestimated by approximately50% on average. Thus, we found area estimation was subject to autocorrelation-induced bias that was worse for large species. Combined with the fact that extinction risk increases as body mass increases, the allometric scaling of bias we observed suggests the most threatened species are also likely to be those with the least accurate home-range estimates. As a correction, we tested whether data thinning or autocorrelation-informed home-range estimation minimized the scaling effect of autocorrelation on area estimates. Data thinning required an approximately93% data loss to achieve statistical independence with 95% confidence and was, therefore, not a viable solution. In contrast, autocorrelation-informed home-range estimation resulted in consistently accurate estimates irrespective of mass. When relating body mass to home range size, we detected that correcting for autocorrelation resulted in a scaling exponent significantly >1, meaning the scaling of the relationship changed substantially at the upper end of the mass spectrum.
Mathematisch-Naturwissenschaftliche Fakultät
Michael J. Noonan | Christen H. Fleming | Marlee A. Tucker |
Roland Kays | Autumn-Lynn Harrison | Margaret C. Crofoot |
Briana Abrahms | Susan C. Alberts | Abdullahi H. Ali | Niels Blaum
Effects of body size on estimation of
mammalian area requirements
Suggested citation referring to the original publication:
Conservation Biology 34 (2019) 4,
DOI https://doi.org/10.1111/cobi.13495
Postprint archived at the Institutional Repository of the Potsdam University in:
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaft-
liche Reihe 1206
ISSN: 1866-8372
https://nbn-resolving.org/urn:nbn:de:kobv:517-opus4-526824
DOI: https://doi.org/10.25932/publishup-52682
Conservation Methods
Effects of body size on estimation of mammalian area
requirements
Michael J. Noonan ,1,2 Christen H. Fleming,1, 2 Marlee A. Tucker,3,4,5 Roland Kays ,6,7
Autumn-Lynn Harrison,8Margaret C. Crofoot,9,10 Briana Abrahms,11 Susan C. Alberts,12
Abdullahi H. Ali,13 Jeanne Altmann,14 Pamela Castro Antunes,15 Nina Attias,16 Jerrold L. Belant,17
Dean E. Beyer Jr.,18 Laura R. Bidner,9,19 Niels Blaum,20 Randall B. Boone,21,22 Damien Caillaud,9
Rogerio Cunha de Paula,23 J. Antonio de la Torre,24 Jasja Dekker,25 Christopher S. DePerno,7
Mohammad Farhadinia ,26,27 Julian Fennessy,28 Claudia Fichtel,29 Christina Fischer,30
Adam Ford ,31 Jacob R. Goheen ,32 Rasmus W. Havmøller,9Ben T. Hirsch,33
Cindy Hurtado ,34,35 Lynne A. Isbell,9,19 René Janssen,36 Florian Jeltsch,20 Petra Kaczensky,37,38
Yayoi Kaneko,39 Peter Kappeler,29 Anjan Katna,40,41 Matthew Kauffman,42 Flavia Koch,29
Abhijeet Kulkarni,40 Scott LaPoint,43,44 Peter Leimgruber,1David W. Macdonald,26
A. Catherine Markham,45 Laura McMahon,46 Katherine Mertes,1Christopher E. Moorman,7
Ronaldo G. Morato,23,47 Alexander M. Moßbrucker,48 Guilherme Mourão,49
David O’Connor,4,50,51 Luiz Gustavo R. Oliveira-Santos,52 Jennifer Pastorini,53,54
Bruce D. Patterson,55 Janet Rachlow,56 Dustin H. Ranglack,57 Neil Reid,58
David M. Scantlebury,59 Dawn M. Scott,60 Nuria Selva,61 Agnieszka Sergiel,61 Melissa Songer,1
Nucharin Songsasen,1Jared A. Stabach,1Jenna Stacy-Dawes,50 Morgan B. Swingen,7,62
Jeffrey J. Thompson,63,64 Wiebke Ullmann,20 Abi Tamim Vanak,40,65,66 Maria Thaker,67
John W. Wilson,68 Koji Yamazaki,69,70 Richard W. Yarnell,71 Filip Zieba,72
Tomasz Zwijacz-Kozica,72 William F. Fagan,2Thomas Mueller,3,4 and Justin M. Calabrese1,2
1Smithsonian Conservation Biology Institute, National Zoological Park, 1500 Remount Road, Front Royal, VA 22630, U.S.A.
2Department of Biology, University of Maryland, College Park, MD 20742, U.S.A.
3Senckenberg Biodiversity and Climate Research Centre, Senckenberg Gesellschaft für Naturforschung, Senckenberganlage 25, Frank-
furt (Main), 60325, Germany
4Department of Biological Sciences, Goethe University, Max-von-Laue-Straße 9, Frankfurt (Main), 60438, Germany
5Department of Environmental Science, Institute for Wetland and Water ResearchRadboud University, P.O. Box 9010, Nijmegen, GL
NL-6500, The Netherlands
6North Carolina Museum of Natural Sciences, Biodiversity Lab, Raleigh, NC 27601, U.S.A.
7Fisheries, Wildlife, and Conservation Biology Program, College of Natural Resources Campus Box 8001, North Carolina State Uni-
versity, Raleigh, NC 27695, U.S.A.
8Migratory Bird Center, Smithsonian Conservation Biology Institute, Washington, D.C., 20013, U.S.A.
9Department of Anthropology, University of California, Davis, Davis, CA, 95616, U.S.A.
10Smithsonian Tropical Research Institute, Balboa Ancon, 0843-03092, Republic of Panama
11Environmental Research Division, NOAA Southwest Fisheries Science Center, Monterey, CA 93940, U.S.A.
12Departments of Biology and Evolutionary Anthropology, Duke University, Durham, NC 27708, U.S.A.
13Hirola Conservation Programme, Garissa, 1774–70100, Kenya
14Department of Ecology and Evolution, Princeton University, 106A Guyot Hall, Princeton, NJ 08544, U.S.A.
15Department of Ecology, Federal University of Mato Grosso do Sul, Campo Grande, MS 79070–900, Brazil
Address correspondence to Michael J. Noonan, email noonanm@si.edu
Article impact statement: Due to autocorrelation-induced bias, conventional methods severely underestimate the area requirements of GPS-
tracked large mammals.
Paper submitted September 9, 2019; revised manuscript accepted December 24, 2019.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction
in any medium, provided the original work is properly cited.
1017
Conservation Biology, Volume 34, No. 4, 1017–1028
© 2020 The Authors. Conservation Biology published by Wiley Periodicals LLC on behalf of Society for Conservation Biology
DOI: 10.1111/cobi.13495
1018
16Programa de Pós-Graduaçao em Biologia Animal, Universidade Federal do Mato Grosso do Sul, Cidade Universitária, Av. Costa e
Silva, Campo Grande, Mato Grosso do Sul, 79070-900, Brazil
17Camp Fire Program in Wildlife Conservation, State University of New York, College of Environmental Science and Forestry, Syra-
cuse, NY 13210, U.S.A.
18Michigan Department of Natural Resources, 1990 U.S. 41 South, Marquette, MI 49855, U.S.A.
19Mpala Research Centre, Nanyuki, 555–104000, Kenya
20University of Potsdam, Plant Ecology and Nature Conservation, Am Mühlenberg 3, Potsdam, 14476, Germany
21Natural Resource Ecology Laboratory, Colorado State University, Fort Collins, CO, 80523, U.S.A.
22Department of Ecosystem Science and Sustainability, Colorado State University, Fort Collins, CO, 80523, U.S.A.
23National Research Center for Carnivores Conservation, Chico Mendes Institute for the Conservation of Biodiversity, Estrada Munic-
ipal Hisaichi Takebayashi 8600, Atibaia, SP 12952-011, Brazil
24Instituto de Ecología, Universidad Nacional Autónoma de Mexico and CONACyT, Ciudad Universitaria, Mexico, D.F. 04318, Mexico
25Jasja Dekker Dierecologie, Enkhuizenstraat 26, Arnhem, WZ 6843, The Netherlands
26Wildlife Conservation Research Unit, Department of Zoology, University of Oxford, Tubney House, Oxfordshire, Oxford, OX13
5QL, U.K.
27Future4Leopards Foundation, Tehran, Iran
28Giraffe Conservation Foundation, PO Box 86099, Windhoek, Namibia
29German Primate Center, Behavioral Ecology & Sociobiology Unit, Kellnerweg 4, Göttingen, 37077, Germany
30Restoration Ecology, Department of Ecology and Ecosystem Management, Technische Universität München, Emil-Ramann-Straße 6,
Freising, 85354, Germany
31The Irving K. Barber School of Arts and Sciences, Unit 2: Biology, The University of British Columbia, Okanagan Campus, SCI 109,
1177 Research Road, Kelowna, BC V1V 1V7, Canada
32Department of Zoology and Physiology, University of Wyoming, Laramie, WY 82071, U.S.A.
33Zoology and Ecology, College of Science and Engineering, James Cook University, Townsville, QLD 4811, Australia
34Museo de Historia Natural, Universidad Nacional Mayor de San Marcos, Lima, 15072, Peru
35Department of Forest Resources Management, The University of British Columbia, Vancouver, BC V6T 1Z4, Canada
36Bionet Natuuronderzoek, Valderstraat 39, Stein, 6171EL, The Netherlands
37Norwegian Institute for Nature Research — NINA, Sluppen, Trondheim, NO-7485, Norway
38Research Institute of Wildlife Ecology, University of Veterinary Medicine, Savoyenstraße 1, Vienna, A-1160, Austria
39Tokyo University of Agriculture and Technology, Tokyo, 183–8509, Japan
40Ashoka Trust for Research in Ecology and the Environment (ATREE), Bangalore, Karnataka 560064, India
41Manipal Academy of Higher Education, Manipal, Karnataka 576104, India
42U.S. Geological Survey, Wyoming Cooperative Fish and Wildlife Research Unit, Department of Zoology and Physiology, University
of Wyoming, Laramie, WY, 82071, U.S.A.
43Max Planck Institute for Ornithology, Vogelwarte Radolfzell, Am Obstberg 1, Radolfzell, D-78315, Germany
44Black Rock Forest, 65 Reservoir Road, Cornwall, NY 12518, U.S.A.
45Department of Anthropology, Stony Brook University, Stony Brook, NY 11794, U.S.A.
46Office of Applied Science, Department of Natural Resources, Rhinelander, WI 54501, U.S.A.
47Institute for the Conservation of Neotropical Carnivores – Pró-Carnívoros, Atibaia, Sao Paulo 12945-010, Brazil
48Frankfurt Zoological Society, Bernhard-Grzimek-Allee 1, Frankfurt, 60316, Germany
49Embrapa Pantanal, Rua 21 de setembro 1880, Corumb´a, MS 79320–900, Brazil
50San Diego Zoo Institute of Conservation Research, 15600 San Pasqual Valley Road, Escondido, CA 92027, U.S.A.
51National Geographic Partners, 1145 17th Street NW, Washington, D.C. 20036, U.S.A.
52Department of Ecology, Federal University of Mato Grosso do Sul, Campo Grande, MS 79070–900, Brazil
53Centre for Conservation and Research, 26/7 C2 Road, Kodigahawewa, Julpallama, Tissamaharama, 82600, Sri Lanka
54Anthropologisches Institut, Universität Zürich, Winterthurerstrasse 190, Zurich, 8057, Switzerland
55Integrative Research Center, Field Museum of Natural History, Chicago, IL 60605, U.S.A.
56Department of Fish and Wildlife Sciences, University of Idaho, 875 Perimeter Drive MS 1136, Moscow, ID 83844-1136, U.S.A.
57Department of Biology, University of Nebraska at Kearney, Kearney, NE 68849, U.S.A.
58Institute for Global Food Security (IGFS), School of Biological Sciences, Queen’s University Belfast, Belfast, BT9 5DL, U.K.
59School of Biological Sciences, Queen’s University Belfast, 19 Chlorine Gardens, Belfast, Northern Ireland BT9 5DL, U.K.
60School of Life Sciences, Keele University, Keele, Staffordshire ST5 5BG, U.K.
61Institute of Nature Conservation, Polish Academy of Sciences, Mickiewicza 33, Krakow, 31–120, Poland
621854 Treaty Authority, 4428 Haines Road, Duluth, MN 55811, U.S.A.
63Asociación Guyra Paraguay – CONACYT, Parque Ecológico Asunción Verde, Asuncion, 1101, Paraguay
64Instituto Saite, Coronel Felix Cabrera 166, Asuncion, 1101, Paraguay
65Wellcome Trust/DBT India Alliance, Hyderabad, 500034, India
66School of Life Sciences, University of KwaZulu-Natal, Westville, Durban 4041, South Africa
67Centre for Ecological Sciences, Indian Institute of Science, Bangalore, 560012, India
68Department of Zoology & Entomology, University of Pretoria, Pretoria, 0002, South Africa
69Ibaraki Nature Museum, Zoological Laboratory, 700 Osaki, Bando-city, Ibaraki 306–0622, Japan
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70Forest Ecology Laboratory, Department of Forest Science, Tokyo University of Agriculture, 1-1-1 Sakuragaoka, Setagaya-Ku, Tokyo
156–8502, Japan
71School of Animal, Rural and Environmental Sciences, Nottingham Trent University, Brackenhurst Campus, Southwell, NG25 0QF,
U.K.
72Tatra National Park, Kúznice 1, Zakopane, 34–500, Poland
Abstract: Accurately quantifying species’ area requirements is a prerequisite for effective area-based conser-
vation. This typically involves collecting tracking data on species of interest and then conducting home-range
analyses. Problematically, autocorrelation in tracking data can result in space needs being severely underestimated.
Based on the previous work, we hypothesized the magnitude of underestimation varies with body mass, a rela-
tionship that could have serious conservation implications. To evaluate this hypothesis for terrestrial mammals,
we estimated home-range areas with global positioning system (GPS) locations from 757 individuals across 61
globally distributed mammalian species with body masses ranging from 0.4 to 4000 kg. We then applied block
cross-validation to quantify bias in empirical home-range estimates. Area requirements of mammals <10 kg were
underestimated by a mean approximately15%, and species weighing approximately100 kg were underestimated
by approximately50% on average. Thus, we found area estimation was subject to autocorrelation-induced bias that
was worse for large species. Combined with the fact that extinction risk increases as body mass increases, the
allometric scaling of bias we observed suggests the most threatened species are also likely to be those with the
least accurate home-range estimates. As a correction, we tested whether data thinning or autocorrelation-informed
home-range estimation minimized the scaling effect of autocorrelation on area estimates. Data thinning required
an approximately93% data loss to achieve statistical independence with 95% confidence and was, therefore, not
a viable solution. In contrast, autocorrelation-informed home-range estimation resulted in consistently accurate
estimates irrespective of mass. When relating body mass to home range size, we detected that correcting for
autocorrelation resulted in a scaling exponent significantly >1, meaning the scaling of the relationship changed
substantially at the upper end of the mass spectrum.
Keywords: allometry, animal movement, area-based conservation, autocorrelation, home range, kernel density
estimation, reserve design, scaling
Efectos del Tamaño Corporal sobre la Estimación de los Requerimientos de Área de Mamíferos
Resumen: La cuantificación precisa de los requerimientos de área de una especie es un prerrequisito para que
la conservación basada en áreas sea efectiva. Esto comúnmente implica la recolección de datos de rastreo de
la especie de interés para después realizar análisis de la distribución local. De manera problemática, la autocor-
relación en los datos de rastreo puede resultar en una subestimación grave de las necesidades de espacio. Con
base en trabajos previos, formulamos una hipótesis en la que supusimos que la magnitud de la subestimación varía
con la masa corporal, una relación que podría tener implicaciones serias para la conservación. Para probar esta
hipótesis en mamíferos terrestres, estimamos las áreas de distribución local con las ubicaciones en GPS de 757
individuos de 61 especies de mamíferos distribuidas mundialmente con una masa corporal entre 0.4 y 4,000 kg.
Después aplicamos una validación cruzada en bloque para cuantificar el sesgo en estimaciones empíricas de la
distribución local. Los requerimientos de área de los mamíferos <10 kg fueron subestimados por una media 15%
y las especies con una masa 100 kg fueron subestimadas en 50% en promedio. Por lo tanto, encontramos que
la estimación del área estaba sujeta al sesgo inducido por la autocorrelación, el cual era peor para las especies de
talla grande. En combinación con el hecho de que el riesgo de extinción incrementa conforme aumenta la masa
corporal, el escalamiento alométrico del sesgo que observamos sugiere que la mayoría de las especies amenazadas
también tienen la probabilidad de ser aquellas especies con las estimaciones de distribución local menos acertadas.
Como corrección, probamos si la reducción de datos o la estimación de la distribución local informada por la
autocorrelación minimizan el efecto de escalamiento que tiene la autocorrelación sobre las estimaciones de área.
La reducción de datos requirió una pérdida de datos del 93% para lograr la independencia estadística con un
95% de confianza y por lo tanto no fue una solución viable. Al contrario, la estimación de la distribución local
informada por la autocorrelación resultó en estimaciones constantemente precisas sin importar la masa corporal.
Cuando relacionamos la masa corporal con el tamaño de la distribución local, detectamos que la corrección
de la autocorrelación resultó en un exponente de escalamiento significativamente >1, lo que significa que el
escalamiento de la relación cambió sustancialmente en el extremo superior del espectro de la masa corporal.
Palabras Clave: alometría, autocorrelación, conservación basada en áreas, diseño de reserva, distribución local,
escalamiento, estimación de densidad del núcleo, movimiento de mamíferos
:,
,,
,,
Conservation Biology
Volume 34, No. 4, 2020
1020 Mammalian Area Requirements
0.4 4000 61757 (GPS)
,,,
10 15%, 10050%
,,
,,
,
93% 95% ,
,,,
1, 
:;:
:,,,,,,,
Introduction
Globally, human-altered landscapes are restricting animal
movement (Fahrig 2007; Tucker et al. 2018), and habi-
tat loss and fragmentation are the principal threats to
terrestrial biodiversity (Brooks et al. 2002; Wilson et al.
2016). A key component to conserving species in in-
creasingly human-dominated landscapes is understand-
ing how much space is required to maintain stable, in-
terconnected populations (Brashares et al. 2001; Pe’er
et al. 2014). Area requirements are typically quantified
via home-range analysis (Burt 1943). This routinely in-
volves collecting tracking data on species of interest
(Kays et al. 2015) and then applying a home-range esti-
mator to these data (Fleming et al. 2015; Noonan et al.
2019). These range estimates can then be used to inform
recommendations on reserve sizes (Linnell et al. 2001),
to advocate for specific land-tenure systems (Johansson
et al. 2016; Farhadinia et al. 2018), and to make con-
servation policy recommendations (Barton´ et al. 2019).
However, tracking data are often strongly autocorrelated,
whereas conventional home-range estimators are based
on the assumption of independent and identically dis-
tributed data (Noonan et al. 2019).
When data are autocorrelated, the total number of data
points does not reflect the total amount of information
in the data set (i.e., effective sample size) (Fleming &
Calabrese 2017). Although the idea that autocorrelation
may affect home-range estimates is not new (e.g., Swi-
hart & Slade 1985; Fieberg 2007; Fleming et al. 2015),
only recent analyses have demonstrated the seriousness
of the problem. Using the largest empirical tracking data
set assembled to date, Noonan et al. (2019) found con-
ventional estimators significantly negatively biased when
used on autocorrelated data. Although any form of bias
is undesirable, the systematic underestimation of home-
range areas is a worst-case scenario from a conserva-
tion perspective. Any policy or management decisions
informed by underestimated home-range estimates could
result in failed conservation initiatives (Brashares et al.
2001; Gaston et al. 2008) or exacerbate negative human–
wildlife interactions at reserve boundaries (Van Eeden
et al. 2018).
Noonan et al. (2019) noticed that large-bodied species
tended to exhibit more negatively biased conventional
home-range estimates than small-bodied species. How-
ever, the species included in their study were not se-
lected to provide the broad range of body masses re-
quired to investigate allometric trends. We compiled an
extensive empirical data set of global positioning system
(GPS) locations from 757 individuals across 61 terrestrial
mammalian species with body masses ranging from 0.4
to 4000 kg. We used these data to investigate whether
the underestimation of home-range size scales with body
mass. To see the potential for this, consider that large
species have large home ranges (Jetz et al. 2004) that
tend to take longer to cross than smaller home ranges
(Calder 1983). In addition, range crossing time (τp)in-
teracts with the sampling interval (dt) in determining
the amount of autocorrelation in tracking data (Fleming
& Calabrese 2017; Noonan et al. 2019). When dt τp,
the resulting data are autocorrelated, whereas dt τp
results in effectively independent data. Finally, the mag-
nitude of the negative biases in conventional home-range
estimates increases in proportion to the strength of auto-
correlation in the data (Noonan et al. 2019). Combining
these facts, we arrived at the hypothesis that an allometry
in τpdrives autocorrelation and negative estimation bias
to scale with body size.
We examined this hypothesis in 2 ways. First, we
tested whether the chain of relationships that would
drive bias to scale with mass holds for empirical track-
ing data. Second, we explored how well 2 methods of
home-range estimation for autocorrelated data eliminate
the scaling of home-range estimation bias. These meth-
ods were model-informed data thinning, which removes
autocorrelation from the data prior to home-range es-
timation, and autocorrelation-informed home-range esti-
mation, which statistically accounts for autocorrelation
in movement data. We then used model selection to de-
termine whether significant allometry bias remains in
the data for each approach and identified whether one
of these corrections offers improved performance over
the other. Finally, in light of our findings, we revisited
Conservation Biology
Volume 34, No. 4, 2020
Noonan et al. 1021
−50
0
50
−100 0 100
Longitude
Latitude
Figure 1. Distribution of study sites for the empirical
global positioning system tracking data set spanning
757 individuals across 61 mammalian species.
the concept of home-range allometry (e.g., McNab 1963;
Jetz et al. 2004; Tucker et al. 2014). Mammalian home-
range area (H) scales positively with body mass (M)as
H=B0Mb,whereB0is a normalization constant and b
is the scaling exponent (McNab 1963). Despite decades
of research, however, there has been little consensus
on whether the allometry is linear (i.e., M1), or super-
linear (i.e., M>1). Historically, this scaling relationship
has been calculated by compiling home-range areas esti-
mated via conventional estimators, which are subject to
varying levels of autocorrelation-induced bias (Noonan
et al. 2019), whereas no one has assessed this relation-
ship directly from tracking data. Although consistent bias
across the mass spectrum would lead only to a change
in the normalization constant, differential bias across the
mass spectrum could alter the scaling exponent, funda-
mentally changing the properties of the relationship. As
such, we tested for any significant deviations from linear
(M1) scaling.
Methods
All analyses were based on precollected tracking data
sets obtained under appropriate permits and that were
based on Institutional Animal Care and Use Committee
approved protocols.
Data Compilation
To investigate whether biases in home-range estimation
scale with body size, we compiled GPS tracking data
for 61 globally distributed terrestrial mammalian species,
comprising 6.94 ×106locations for 757 individuals col-
lected from 2000 to 2019 (Fig. 1). Individual data sets
were selected based on the criterion of range resident
behavior (i.e., area-restricted space use), as evidenced
by plots of the semivariance in positions as a function
of the time lag separating observations (i.e., variograms)
with a clear asymptote at large lags (Calabrese et al.
2016). When data do not indicate evidence of range res-
idency, home-range estimation is not appropriate (Cal-
abrese et al. 2016; Fleming & Calabrese 2017), so we
excluded data from migratory or nonrange resident in-
dividuals. The visual verification of range residency via
variogram analysis was conducted using the R package
ctmm (version 0.5.3) (Calabrese et al. 2016). Further de-
tails on these data are given in Supporting Information.
For each of the species in our data set, we compiled
covariate data on that species’ mean adult mass in kilo-
grams. We also identified the main food source for each
species and classified them as carnivorous or omnivorous
or frugivorous or herbivorous. Data from these 2 dietary
classes were analyzed separately. Mass and dietary data
were from the EltonTraits database (Wilman et al. 2014).
Tracking-Data Analyses
Our conjecture that the underestimation of home-range
areas increases as body size increases was based on 2
well-established biological and one methodological rela-
tionship: the positive correlation between body mass and
home-range area (Jetz et al. 2004); the positive correla-
tion between home-range area and range crossing time,
τp(Calder 1983); and the negative correlation between
range crossing time and the effective sample size for area
estimation, Narea (i.e., equivalent number of statistically
independent locations [Noonan et al. 2019]). We hypoth-
esized that these conspire to drive 2 previously untested
relationships: a potential negative correlation between
body mass and Narea and a potential negative correlation
between body mass and home-range estimator accuracy.
Testing for these relationships first required estimating
the autocorrelation structure in each of the individual
tracking data sets. To accomplish this, we fitted a series
of range-resident, continuous-time movement models to
the data with the estimation methods developed by Flem-
ing et al. (2019). The fitted models included the indepen-
dent and identically distributed process, which features
uncorrelated positions and velocities; the Ornstein–
Uhlenbeck (OU) process, which features correlated po-
sitions but uncorrelated velocities (Uhlenbeck & Orn-
stein 1930); and an OU-foraging (OUF) process, featuring
both correlated positions and velocities (Fleming et al.
2014). We used model selection to identify the best fit-
ting model given the data (Fleming et al. 2014) from
which τpand Narea were extracted. To fit and select the
movement models, we used the R package ctmm and ap-
plied the workflow described by Calabrese et al. (2016).
We estimated home-range areas for each of the 757
individuals in our tracking database via kernel density
estimation (KDE) with Gaussian reference function band-
width optimization because this is one of the most com-
monly applied home-range estimators in ecological re-
search (Noonan et al. 2019). The KDE home ranges were
estimated via the methods implemented in ctmm, and
Conservation Biology
Volume 34, No. 4, 2020
1022 Mammalian Area Requirements
the further small-sample-size bias correction that was
introduced in area-corrected KDE (Fleming & Calabrese
2017).
Our primary aim was to determine the extent to which
autocorrelation-induced bias in conventional home-range
estimation might increase with body size. This required
an objective and statistically sound measure of bias. We
applied the well-established technique of block cross-
validation (Noonan et al. 2019) to quantify bias in em-
pirical home-range estimates.
By determining the extent to which the results of an
analysis generalize to a statistically independent data set,
cross-validation is an effective tool for quantifying bias
(Pawitan 2001). For this approach, each individual data
set was split in half, and a home-range area was esti-
mated from the first half of the data only (i.e., training
set). Next, the percentage of observations in the second
half of the data (i.e., held-out set) that fell within the
specified contour (here 50% and 95%) of the estimated
home range was calculated. If the percentage of points
included came out consistently higher or lower than the
specified contour, then it would suggest positive or neg-
ative bias, respectively.
As a further measure of bias, we identified the con-
tour of the home range estimated from the training set
that contained the desired percentage of locations in the
held-out set (i.e., 50% and 95%) and compared the area
within that contour to the estimated area at the specified
quantile. For example, consider that the 95% area esti-
mated on the training data contained only 90% of the
locations in the held-out set, whereas the 97% contour
contained 95% of the locations. To measure bias, we
would take the ratio between the 97% area and the 95%
area. Cross-validating home-range estimates in this way
can also be seen as providing a measure of how well a
home-range estimate can be expected to capture an ani-
mal’s future space use, assuming no substantial changes
in movement behavior.
Block cross-validation is based on the assumption that
data from the training and held-out sets are generated
from the same processes. To confirm this assumption, we
used the Battacharryya distance implementation in ctmm
(Winner et al. 2018) as a measure of similarity (range 0–
) between the mean area and covariance parameters of
movement models fitted to the training and held-out data
sets and determined whether the confidence intervals on
this distance contained 0 (details are given in Appendix
S1 in Noonan et al. [2019]). Using this method, we deter-
mined that 160 of 757 individuals had movement models
with significantly different parameter estimates between
the first and second halves of the data, so we excluded
these from our cross-validation analyses. We found no
significant relationship between whether or not a data
set was excluded from our analyses and which species
the data were from (p=0.52) or between exclusion
and how long an individual was tracked (p=0.39). This
confirmed that the subsampling required to meet the as-
sumptions of half-sample cross-validation did not bias our
sample.
Correction Factors
We explored 2 potential solutions to the allometric scal-
ing of autocorrelation and home-range estimation bias:
thinning data to minimize autocorrelation and using
autocorrelation-informed home-range estimation.
Conventional kernel methods are based on an assump-
tion of independence; however, they can provide ac-
curate estimates for autocorrelated processes when the
sampling is coarse enough that the data appear uncor-
related over time (Hall & Hart 1990). Thus, data thin-
ning presents a potentially straightforward solution to
autocorrelation-induced bias, but requires a balance be-
tween reducing autocorrelation and retaining sample
size. We, therefore, explored model-informed data thin-
ning as a means of mitigating size-dependent home-range
bias. As noted above, the parameter τprelates to an indi-
vidual’s range-crossing time and quantifies the time scale
over which positional autocorrelation decays to insignif-
icance. More specifically, because positional autocorrela-
tion decays exponentially at rate 1/τp,thetimerequired
for the percentage of the original velocity autocorrela-
tion to decay to αis τα=τpln(1/α). Conventionally, data
are thinned to independence with a 95% level of con-
fidence, and approximately3τpis the time it takes for
95% of the positional autocorrelation to decay. Conse-
quently, we thinned each individual’s tracking data to a
sampling frequency of dt =3τp. We then used autocor-
relation functions to quantify how much autocorrelation
remained in the thinned data and evaluated the perfor-
mance of KDEs on these thinned data.
As opposed to manipulating the data to meet the as-
sumptions of the estimator, the second potential solu-
tion was to use an estimator that explicitly modeled the
autocorrelation in the data. Autocorrelated-KDE (AKDE)
is a generalization of Gaussian reference function KDE
that conditions upon the autocorrelation structure of
the data when optimizing the bandwidth (Fleming et al.
2015). Following the workflow described by Calabrese
et al. (2016), AKDE home-range areas were estimated
conditioned on the selected movement model for each
data set, via the methods implemented in ctmm, with
the same small-sample-size bias correction applied to the
conventional KDE area estimates (Fleming & Calabrese
2017). The AKDE is available via the web-based graphical
user interface at ctmm.shinyapps.io/ctmmweb/(Dong
et al. 2017).
Correction Factor Performance
To test for body-size-dependent biases in cross-
validation success, we fitted 3 regression models to the
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Volume 34, No. 4, 2020
Noonan et al. 1023
cross-validation results as a function of log10-scaled mass.
The models included an intercept-only model (i.e., no
change in bias with mass), linear model, and logistic
model. We then identified the best model for the data
via small-sample-size corrected quasi-Akaike information
criterion (Burnham et al. 2011).
Species may exhibit similarities in traits due to phy-
logenetic inertia and the constraints of common ances-
try; thus, controlled comparisons are required (Harvey
& Pagel 1991). Accordingly, we did not treat species data
records as independent; rather, we used the phyloge-
netic distances among species to construct a variance–
covariance matrix and defined the correlation structure
in our allometric regressions with the R package nlme
(version 3.1-137) (Pinheiro et al. 2018). Phylogenetic re-
lationships between eutherian mammalian orders were
based on genetic differences and taken from Liu et al.
(2001). Intraorder relationships were taken from more
targeted studies aimed at resolving species-level rela-
tionships, including Price et al. (2005) for Artiodactyla,
Matthee et al. (2004) for Lagomorpha, Steiner and Ryder
(2011) for Perissodactyla, Barriel et al. (1999) for Pro-
boscidea, Perelman et al. (2011) for Primates, and Agnars-
son et al. (2010) for Carnivora. For Canidae, however,
we took relationships from Lindblad-Toh et al. (2005),
due to better coverage of the species in our data set.
The phylogenetic tree was built with the R package ape
(version 5.2) (Paradis & Schliep 2019), and branch
lengths were computed following Grafen (1989). Phylo-
genies are given in Supporting Information.
Results
Allometric Scaling of Bias
Out of 757 data sets, only one was independent and
identically distributed and free from significant autocor-
relation. Conventional KDE 95% home-range areas cross-
validated at a median rate of 88.3% (95% CI 87.2–90.1),
which was below the target 95% quantile and demon-
strated a tendency to underestimate home-range areas
on average. Similarly, KDE 50% home-range areas cross-
validated at a median rate of 41.5% (95% CI 39.4–43.3),
which was again below the target 50% quantile. The
magnitude of KDE’s underestimation worsened as body
mass increased (t=2.30, p=0.02) (Fig. 2a), carnivores
and herbivores did not differ significantly (t=0.31; p=
0.75). Cross-validation success of 50% home-range areas
across the mass spectrum was best described by a lin-
ear decay model with an intercept of 47.2 (95% CI 39.9–
54.5) and a slope of –3.9 (95% CI –7.0 to –0.8). In other
words, for every order of magnitude increase in body
mass, home-range estimates captured approximately4%
less of an individual’s future space use.
When comparing the 95% area estimates with the
area estimates for the contours that contained 95% of
0
20
40
60
80
1 10 100 1000
Mass (kg)
Relocations included (%)
(a)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1 10 100 1000
Mass (kg)
95% Home range area accuracy
(b)
Figure 2. Cross-validation of conventional kernel
density estimation (KDE) across the mammalian
body-mass spectrum: (a) percentage of locations from
the second half of the data (held-out set) included in
KDE 50% home ranges estimated from the first half of
the data (training set) as a function of body mass
(dashed line, target 50% quantile; solid line,
phylogenetically controlled regression model fit to
cross-validation results; shading, 95% CI of the fit) and
(b) regression model describing the accuracy of 95%
KDE area estimates across the mass spectrum.
Accuracy was quantified as the ratio between
estimated 95% area of the training set and the area
contained within the contour that encompassed 95%
of locations in the held-out set. The horizontal dashed
line represents an unbiased area estimate. The x-axes
in are log scaled.
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Volume 34, No. 4, 2020
1024 Mammalian Area Requirements
0.01
0.1
1
10
100
1000
0 0.1 1 10 100 1000 10000
Home range area (km2)
p(days)
(b)
(a)
1
10
100
1000
1 10 100 1000
Mass (kg)
NArea
(d)
1
10
100
1000
0 0.1 1 10 100 1000
p(days)
NArea
(c)
Figure 3. Mechanisms driving body-size-dependent estimation bias: (a) positive allometry of home-range areas,
(b) correlation between home-range area and range-crossing time (τp), (c) negative correlation between τpand
effective sample size (Narea) governed by duration of observation period (T)andτpsuch that Narea T/τp,and
(d) resulting negative allometry of Narea (axes, log scaled; lines, phylogenetically controlled fitted regression
models). From (a) to (d), 1 axis is preserved from the previous panel to demonstrate the inherent link between
each of these relationships (arrows, visual aid of link; top-left arrow, end of the chain).
locations, KDE accuracy across the mass spectrum was
best described by linear decay (Fig. 2b). Consequently,
whereas the home-range areas of mammals weighing
<10 kg were underestimated by 13.6% (95% CI 6.3–
18.6), those of species weighing >100 kg were under-
estimated by 46.0% on average (95% CI 36.7–51.4).
Mechanisms Driving Body Size-Dependent Estimation Bias
We found significant positive relationships between body
mass and home-range area (regression parameter: β=
1.18, 95% CI 0.92–1.43, t=9.09, p<0.0001) (Fig. 3a)
and between home-range area and range crossing time,
τp(β=7.09, 95% CI 4.78–9.41, t=6.00, p<0.0001)
(Fig. 3b) and a negative relationship between τpand the
effective sample size, Narea (β=−0.65, 95% CI –0.70 to
–0.60, t=25.46, p<0.0001) (Fig. 3c). The former 2 scal-
ing relationships differed significantly between carnivo-
rous and herbivorous mammals (t=3.08, p<0.005 and
t=2.37, p=0.02, respectively). Carnivores tended to
have larger home ranges and shorter range crossing times
than comparably sized herbivores, and herbivores tended
to have longer range crossing times. The relationship
between Narea and mass did not differ between dietary
classes (t=0.82, p=0.06). The Narea was governed by
both τpand sampling duration, T,suchthatNarea T/τp.
Although we noted a positive correlation between body
mass and Tin the studies we sampled (β=0.24, 95%
CI 0.09–0.39, t=3.17, p<0.005), this was not enough
to counter the positive correlation between mass and τp.
Consequently, the net result was a negative relationship
between body mass and Narea (β=0.23, 95% CI –0.39
to –0.08, t=2.98, p<0.005) (Fig. 3d).
Correction Factors
Model-informed data thinning served to reduce the mean
autocorrelation at lag 1 from 0.96 (95% CI 0.96–0.97)
to 0.32 (95% CI 0.30–0.35) (Fig. 4). Hence, an indepen-
dent and identically distributed model was the best fit
for 167 of the 463 individuals for which sufficient data
(>2 locations) remained after data thinning. The remain-
ing individuals were best described by OU and OUF pro-
cesses whose autocorrelation parameters were not sig-
nificant. Although thinning mitigated the correlation be-
tween bias and body mass (β=–2.41, 95% CI –6.08 to
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Volume 34, No. 4, 2020
Noonan et al. 1025
0
50
100
150
0.00 0.25 0.50 0.75 1.00
Autocorrelation at lag 1
Frequency
Full dataset
Thinned dataset
Figure 4. Frequency of amounts of autocorrelation at
lag 1 in the full tracking data sets for each of the 757
individuals used to estimate home ranges via
conventional kernel density estimation (KDE),
compared with the thinned data sets for individuals
for which sufficient data remained after thinning to
apply KDE.
1.26, t=1.29, p=0.20), the median cross-validation
rate of 95% home ranges estimated using the thinned
data was only 85.1% (95% CI 83.6–86.5). This approx-
imately3% decrease in performance, as compared with
conventional KDE on the full data, was likely the result
of the small sample size. Model-informed data thinning
resulted in a mean data loss of 93.2% (95% CI 92.1–94.3),
and the median number of approximately independent
locations left in each data set after thinning was only
23 (95% CI 18–26). Furthermore, in approximately20%
of the individuals, 2 locations remained after thinning,
making it impossible to estimate a home-range area on
the thinned data.
Autocorrelation-Informed Home-Range Estimation
Like model-informed data thinning, autocorrelation-
informed home-range estimation via AKDE also elimi-
nated the correlation between cross-validation success
and body mass (β=–0.51, 95% CI –1.88 to 0.86, t=
0.73, p=0.47). However, without the data loss required
by the thinning approach, AKDE resulted in a median
cross-validation rate of 95.2% (95% CI 94.2–95.9) for 95%
home ranges and 51.3% (95% CI 49.26–54.36) for 50%
home ranges. In other words, AKDE exhibited consistent
accuracy across species, irrespective of the allometries
in autocorrelation time scales and effective sample sizes.
Table 1. Estimates of the scaling exponent (b) of mass to home-range
area relationship.
Category KDE (95% CI) AKDE (95% CI)
All mammals 1.20 (0.95–1.45) 1.28 (1.01–1.54)
Herbivores and frugivores 1.26 (0.99–1.52) 1.38 (1.09–1.66)
Carnivores and omnivores 1.23 (0.95–1.50) 1.27 (1.01–1.56)
Abbreviations: KDE, kernel density estimation; AKDE,
autocorrelated-kernel density estimation.
Scaling of Mammalian Space Use
When regressing home-range area against mass with con-
ventional KDE estimates, we documented no significant
difference from linear scaling for either herbivores or
carnivores (Table 1). For AKDE-derived area estimates,
however, we detected that the scaling exponent was
significantly >1 for both taxonomic groups, suggesting
home-range area scales with mass according to a power
function.
Discussion
The importance of autocorrelation in animal-tracking
data has been an active area of research for decades
(Swihart & Slade 1985; Fieberg 2007; Fleming et al.
2015). We, however, are the first to demonstrate
that mass-specific space requirements driven by
autocorrelation-induced underestimation of home-range
areas are worse for larger species. From a fundamental
perspective, the continuous nature of animal movement
means quantities, such as positions, velocities, and
accelerations, are necessarily autocorrelated (Fleming
et al. 2014). Autocorrelation time scales (τ) should,
therefore, be viewed as explicit attributes of an
animal’s movement process (Gurarie & Ovaskainen
2015) that are revealed when the temporal resolution of
measurement becomes τ. As technological advances
continue to permit ever-finer sampling (Kays et al. 2015),
persistent autocorrelation is likely to become the norm
in animal-tracking data. Pairing data from inherently
autocorrelated processes with statistical approaches that
ignore autocorrelation not only risks biasing any derived
quantities, but also effectively negates the technological
advances that are improving data quality. Unless analyses
that are informed by autocorrelation become adopted
by movement ecologists and conservationists, the issue
of autocorrelation-induced bias will only worsen. Con-
versely, properly harnessing the wealth of information
provided by autocorrelation can dramatically improve
the accuracy of tracking-data-derived measures (see
also Fleming & Calabrese 2017; Winner et al. 2018;
Noonan et al. 2019). Our findings, therefore, highlight
the need for more statistical estimators that can handle
biologically induced variance without introducing bias.
Conservation Biology
Volume 34, No. 4, 2020
1026 Mammalian Area Requirements
Implications of Size-Dependent Bias
From a conservation perspective, the underestimation of
home-range areas is a worst-case scenario. When reserves
are too small, relative to their target species’ area require-
ments, the probability of local populations undergoing
declines or extirpations increases significantly (Brashares
et al. 2001; Gaston et al. 2008). Undersized protected ar-
eas resulting from poorly estimated space needs also risk
exacerbating the issue of negative human–wildlife inter-
actions at reserve boundaries (Van Eeden et al. 2018) as
animals move beyond reserve boundaries to meet their
energetic requirements (Farhadinia et al. 2018). It is thus
of critical importance that policy actions be well in-
formed about species’ spatial requirements. To this end,
we analyzed a broad taxonomic and geographic range of
data and identified a strong correlation between home-
range underestimation and body size when autocorrela-
tion was ignored; average bias was approximately 50%
at the upper end of the mass spectrum. In this regard,
the majority of home ranges are estimated via methods
based on the assumption of statistically independent data
(Noonan et al. 2019). Combined with the facts that hu-
mans are the dominant mortality source for terrestrial
vertebrates globally (Hill et al. 2019), that this mortality is
higher for large-bodied species (Hill et al. 2020), and that
megafauna are experiencing more severe range contrac-
tions (Tucker et al. 2018) and extinction risk (Cardillo
et al. 2005), the most threatened species are also likely to
be those with the least accurate home-range estimates, a
worrying combination.
Based on these findings, we suggest that any conserva-
tion initiatives or policy based on home-range estimates
derived from estimators based on the assumption of sta-
tistically independent data be revisited, especially where
large-bodied species are involved. To facilitate this, we
developed HRcorrect, an open-access application that al-
lows users to correct a home-range area estimate for their
focal species’ body-mass-specific-bias with a correction
factor calculated from our cross-validation regression
models. The current version of HRcorrect is freely avail-
able from https://hrcorrect.shinyapps.io/HRcorrect/.
However, there are numerous factors beyond body
mass that influence an individual’s home-range size. For
instance, mammalian home-range areas are well known
to covary with the spatial distribution of resources
(Litvaitis et al. 1986; Boutin 1990), social structure
(Lukas & Clutton-Brock 2013), sex (Cederlund & Sand
1994; Lukas & Clutton-Brock 2013; Noonan et al. 2018),
age (Cederlund & Sand 1994), population density
(Adler et al. 1997), and reproductive status (Rootes
& Chabreck 1993; Noonan et al. 2018). Furthermore,
if an individual’s space use changes over time (e.g.,
interseasonal and -annual variation), a home-range area
estimated from a single observation period may not be
representative of its long-term area requirements. As
such, the deterministic trend-based correction provided
by HRcorrect is not a substitute for more rigorous data
collection and home-range estimation and should only be
used for cases where the underlying tracking data are not
accessible.
Allometries and Conservation Theory
The metabolic theory of ecology (West et al. 1997) sug-
gests that body mass represents a super trait that governs
a wide range of ecological processes. Prime among these
is the relationship between body mass and home-range
area, an allometry that has guided ecological theory for
more than 50 years (McNab 1963; Calder 1983; Jetz et al.
2004). More recently, attempts have been made to in-
tegrate this allometry into conservation theory. For in-
stance, Hilbers et al. (2016) incorporated the home-range
allometry into a method for quantifying mass-specific ex-
tinction vulnerability, and Hirt et al. (2018) highlighted
how allometries in movement and space use can be used
to make testable predictions of movement and biodiver-
sity patterns at the landscape scale. Similarly, Pereira et al.
(2004) used allometries of space use and movement rates
to predict species-level vulnerability to land-use change.
If the underlying allometries are biased, however, hy-
pothesis testing and conservation planning in this con-
text can fail even if the logic behind the experimental
design is perfectly sound. Although the earliest deriva-
tion of the home-range allometry proposed a metabol-
ically determined M0.75 allometry (McNab 1963), subse-
quent revisions showed no support for a purely energetic
basis for home-range scaling (Calder 1983; Kelt & Van
Vuren 2001; Jetz et al. 2004; Tucker et al. 2014; Tambu-
rello et al. 2015). Although all these studies concluded
that home-range area should scale with an exponent
greater than the 0.75 predicted by metabolic require-
ments alone, there has been little consensus on whether
the allometry is linear (M1) or superlinear (M>1). Our
results suggest that at least part of the confusion can
be attributed to the increasing bias in underestimating
home ranges with increasing body size. Ours is the first
study to estimate this relationship directly from track-
ing data by applying a consistent estimator across all
individuals and, crucially, correcting for any potential
autocorrelation-induced bias (Noonan et al. 2019). In
doing so, we documented a super-linear relationship
between body mass and home-range area (exponent of
approximately 1.25 for M). This shift from linear to
power-law scaling fundamentally changes the behavior
of the relationship, particularly at the upper end of the
mass spectrum. Although we did not investigate the
mechanisms behind the deviation from the metabolically
determined M0.75, we encourage future work on this
subject be based on the assumption of a superallom-
etry, as opposed to linear allometry. Accurately quan-
tifying species’ area requirements is a prerequisite for
Conservation Biology
Volume 34, No. 4, 2020
Noonan et al. 1027
successful, area-based conservation planning. Our results
highlight an important yet hitherto unrecognized aspect
of home-range estimation: autocorrelation-induced neg-
ative bias in home-range estimation that is systemati-
cally worse for large species. Crucially, however, our
findings also outline a readily applicable solution to the
problem of size-dependent bias. We demonstrated that
home-range estimation that properly accounts for the
autocorrelation structure of the data is currently the
only consistently reliable solution for eliminating allo-
metric biases in home-range estimation (see also Noo-
nan et al. 2019). We emphasize that the differential
scaling of autocorrelation across the mass spectrum
be a key consideration for movement ecologists and
conservation practitioners and suggest avoiding home-
range estimators that assume statistically independent
data.
Acknowledgments
This work was supported by a Smithsonian Institution
Scholarly Studies Award to M.J.N., J.M.C., and A.L.H. and
by the U.S. NSF Advances in Biological Informatics pro-
gram (ABI-1458748 to J.M.C., W.F.F., and C.H.F.). N.B.,
F.J., and W.U. were supported by Deutsche Forschungs-
gemeinschaft in the framework of the BioMove Research
Training Group (DFG-GRK 2118/1). T.M. and M.T. were
funded by the Robert Bosch Foundation. S.L. was sup-
ported by Animals on the Move (NNX15AV92A), a NASA
Arctic Boreal Vulnerability Experiment-funded project.
This work was supported in part by the Wellcome
Trust/DBT India Alliance Fellowship to A.T.V. (grant
IA/CPHI/15/1/502028) and an IISc-ISRO Space Technol-
ogy Cell Grant to M.T. Any use of trade, firm, or product
names is for descriptive purposes only and does not im-
ply endorsement by the U.S. Government.
Supporting Information
Data set summary statistics (Appendix S1), individual
tracking data set summaries (Appendix S2), and mam-
malian phylogenetic relationships (Appendix S3) are
available online. The authors are solely responsible for
the content and functionality of these materials. Queries
(other than absence of the material) should be directed
to the corresponding author.
Supplementary Material
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Conservation Biology
Volume 34, No. 4, 2020
... For example, we hypothesized that all antelope species are attracted to termite mounds by the localized availability of high-quality forage, but that the strength of selection for mounds scales negatively with body size, because small animals can (and may need to) subsist on high-quality diets, whereas larger individuals can (and may need to) tolerate lower quality diets (Bell, 1971;Clauss et al., 2013;Jarman, 1974;. Conversely, home-range sizes and step lengths should scale positively with body size, because localized resource hotspots are sufficient to fulfill the dietary requirements of small animals, whereas larger individuals require more food and must range farther to get it (Harestad & Bunnell, 1979;Illius & Gordon, 1987;Noonan et al., 2020). For similar reasons, we expected the scaling of several behaviors to differ between wet and dry F I G U R E 1 Study site and associated habitat layers. ...
... The relationship between home-range area and body size in mammals is the focus of a large body of literature and a long-standing debate over whether and when scaling should be sublinear, linear (isometric), or superlinear (Calder III, 1983;Harestad & Bunnell, 1979;Haskell et al., 2002;Jetz et al., 2004;Kelt & Van Vuren, 2001;Mcnab, 1963;Tamburello et al., 2015). Our finding that home-range size increased as a concave-up function of body mass accords with the most recent and taxonomically inclusive analysis, involving 61 globally distributed mammal species (Noonan et al., 2020); indeed, our scaling exponent in the dry season, when sample size and tracking duration were greatest (b = 1.40), almost perfectly matches the one reported for herbivores in that study (b = 1.38). This consistency is noteworthy in light of the observation that ecological patterns in global syntheses may not "scale down" to the community level . ...
... We hope that future work succeeds in discovering size-structured traits and processes that underpin our results. We also note that, even for the best-studied relationships in our study such as those between body size and home-range area (Haskell et al., 2002;Jetz et al., 2004;Noonan et al., 2020) and diet quality Müller et al., 2013), there is no firm consensus about the exact functional form of the relationships, much less their mechanistic basis. ...
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1.Technological advances have steadily increased the detail of animal tracking datasets, yet fundamental data limitations exist for many species that cause substantial biases in home‐range estimation. Specifically, the effective sample size of a range estimate is proportional to the number of observed range crossings, not the number of sampled locations. Currently, the most accurate home‐range estimators condition on an autocorrelation model, for which the standard estimation frame‐works are based on likelihood functions, even though these methods are known to underestimate variance‐and therefore ranging area‐when effective sample sizes are small. 2.Residual maximum likelihood (REML) is a widely used method for reducing bias in maximum‐likelihood (ML) variance estimation at small sample sizes. Unfortunately, we find that REML is too unstable for practical application to continuous‐time movement models. When the effective sample size N is decreased to N ≤ O(10), which is common in tracking applications, REML undergoes a sudden divergence in variance estimation. To avoid this issue, while retaining REML's first‐order bias correction, we derive a family of estimators that leverage REML to make a perturbative correction to ML. We also derive AIC values for REML and our estimators, including cases where model structures differ, which is not generally understood to be possible. 3.Using both simulated data and GPS data from lowland tapir (Tapirus terrestris), we show how our perturbative estimators are more accurate than traditional ML and REML methods. Specifically, when O(5) home‐range crossings are observed, REML is unreliable by orders of magnitude, ML home ranges are ~30% underes‐timated, and our perturbative estimators yield home ranges that are only ~10% underestimated. A parametric bootstrap can then reduce the ML and perturba‐tive home‐range underestimation to ~10% and ~3%, respectively. 4.Home‐range estimation is one of the primary reasons for collecting animal tracking data, and small effective sample sizes are a more common problem than is currently realized. The methods introduced here allow for more accurate movement‐model and home‐range estimation at small effective sample sizes, and thus fill an important role for animal movement analysis. Given REML's widespread use, our methods may also be useful in other contexts where effective sample sizes are small. This article is protected by copyright. All rights reserved.
Article
Home range estimation is routine practice in ecological research. While advances in animal tracking technology have increased our capacity to collect data to support home range analysis, these same advances have also resulted in increasingly autocorrelated data. Consequently the question of which home range estimator to use on modern, highly autocorrelated tracking data remains open. This question is particularly relevant given that most estimators assume independently sampled data. Here, we provide a comprehensive evaluation of the effects of autocorrelation on home range estimation. We base our study on an extensive dataset of GPS locations from 369 individuals representing 27 species distributed across 5 continents. We first assemble a broad array of home range estimators, including Kernel Density Estimation (KDE) with four bandwidth optimizers (Gaussian reference function, autocorrelated‐Gaussian reference function (AKDE), Silverman's rule of thumb, and least squares cross‐validation), Minimum Convex Polygon, and Local Convex Hull methods. Notably, all of these estimators except AKDE assume independent and identically distributed (IID) data. We then employ half‐sample cross‐validation to objectively quantify estimator performance, and the recently introduced effective sample size for home range area estimation (N̂area) to quantify the information content of each dataset. We found that AKDE 95% area estimates were larger than conventional IID‐based estimates by a mean factor of 2. The median number of cross‐validated locations included in the holdout sets by AKDE 95% (or 50%) estimates was 95.3% (or 50.1%), confirming the larger AKDE ranges were appropriately selective at the specified quantile. Conversely, conventional estimates exhibited negative bias that increased with decreasing N̂area. To contextualize our empirical results, we performed a detailed simulation study to tease apart how sampling frequency, sampling duration, and the focal animal's movement conspire to affect range estimates. Paralleling our empirical results, the simulation study demonstrated that AKDE was generally more accurate than conventional methods, particularly for small N̂area. While 72% of the 369 empirical datasets had >1000 total observations, only 4% had an N̂area >1000, where 30% had an N̂area <30. In this frequently encountered scenario of small N̂area, AKDE was the only estimator capable of producing an accurate home range estimate on autocorrelated data. This article is protected by copyright. All rights reserved.
Article
Integrating mechanistic models of movement and behavior into large-scale movement ecology and biodiversity research is one of the major challenges in current ecological science. This is mainly due to a large gap between the spatial scales at which these research lines act. Here, we propose to apply trait-based movement models to bridge this gap and generalize movement trajectories across species and ecosystems. We show how to use species traits (e.g., body mass) to generate allometric random walks and illustrate in two worked examples how this facilitates general predictions of species-interaction traits, meta-community structures, and biodiversity patterns. Thereby, allometric random walks foster a closer integration of movement ecology and biodiversity research by scaling up from small-scale mechanistic measurements to a predictive understanding of movement and biodiversity patterns in different landscapes.
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After more than fifteen years of existence, the R package ape has continuously grown its contents, and has been used by a growing community of users. The release of version 5.0 has marked a leap towards a modern software for evolutionary analyses. Efforts have been put to improve efficiency, flexibility, support for 'big data' (R's long vectors), ease of use, and quality check before a new release. These changes will hopefully make ape a useful software for the study of biodiversity and evolution in a context of increasing data quantity. Availability: ape is distributed through the Comprehensive R Archive Network: http://cran.r-project.org/package=apeFurther information may be found athttp://ape-package.ird.fr/.
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1.Despite the routine nature of estimating overlapping space use in ecological research, to date no formal inferential framework for home range overlap has been available to ecologists. Part of this issue is due to the inherent difficulty of comparing the estimated home ranges that underpin overlap across individuals, studies, sites, species, and times. Because overlap is calculated conditionally on a pair of home range estimates, biases in these estimates will propagate into biases in overlap estimates. Further compounding the issue of comparability in home range estimators is the historical lack of confidence intervals on overlap estimates. This means that it is not currently possible to determine if a set of overlap values are statistically different from one another. 2.As a solution, we develop the first rigorous inferential framework for home range overlap. Our framework is based on the AKDE family of home range estimators, which correct for biases due to autocorrelation, small effective sample size, and irregular sampling in time. Collectively, these advances allow AKDE estimates to validly be compared even when sampling strategies differ. We then couple the AKDE estimates with a novel bias‐corrected Bhattacharyya Coeffcient (BC) to quantify overlap. Finally, we propagate uncertainty in the AKDE estimates through to overlap, and thus are able to put confidence intervals on the BC point estimate. 3.Using simulated data, we demonstrate how our inferential framework provides accurate overlap estimates, and reasonable coverage of the true overlap, even at small sample sizes. When applied to empirical data, we found that building an interaction network for Mongolian gazelles (Procapra gutturosa) based on all possible ties, versus only those ties with statistical support, substantially inuenced the network's properties and any potential biological inferences derived from it. 4.Our inferential framework permits researchers to calculate overlap estimates that can validly be compared across studies, sites, species, and times, and test whether observed differences are statistically meaningful. This method is available via the R package ctmm. This article is protected by copyright. All rights reserved.