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Biotic homogenization can decrease landscape-scale
forest multifunctionality
Fons van der Plas
a,b,1
, Pete Manning
a,b
, Santiago Soliveres
a
, Eric Allan
a
, Michael Scherer-Lorenzen
c
, Kris Verheyen
d
,
Christian Wirth
e,f
, Miguel A. Zavala
g
, Evy Ampoorter
d
, Lander Baeten
d,h
, Luc Barbaro
i,j
, Jürgen Bauhus
k
,
Raquel Benavides
c
, Adam Benneter
k
, Damien Bonal
l
, Olivier Bouriaud
m
, Helge Bruelheide
f,n
, Filippo Bussotti
o,2
,
Monique Carnol
p
, Bastien Castagneyrol
i,j
, Yohan Charbonnier
i,j
, David Anthony Coomes
q
, Andrea Coppi
o
,
Cristina C. Bestias
r
, Seid Muhie Dawud
s
, Hans De Wandeler
t
, Timo Domisch
u
, Leena Finér
u
, Arthur Gessler
v
,
André Granier
l
, Charlotte Grossiord
w
, Virginie Guyot
i,j,x
, Stephan Hättenschwiler
y
, Hervé Jactel
i,j
, Bogdan Jaroszewicz
z
,
François-xavier Joly
y
, Tommaso Jucker
q
, Julia Koricheva
aa
, Harriet Milligan
aa
, Sandra Mueller
c
,BartMuys
t
, Diem Nguyen
bb
,
Martina Pollastrini
o
, Sophia Ratcliffe
e
, Karsten Raulund-Rasmussen
s
, Federico Selvi
o
, Jan Stenlid
bb
,
Fernando Valladares
r,cc
, Lars Vesterdal
s
, Dawid Zielínski
z
, and Markus Fischer
a,b,dd
a
PlantEcology Group,Instituteof Plant Sciences, University of Bern,3013 Bern,Switzerland;
b
Senckenberg Gesellschaftfür Naturforschung,Biodiversityand Climate
Researc h Centre, 60325 Fr ankfurt, Germ any;
c
Facultyof Biology/Geobotany,University of Freiburg, 79104Freiburg, Germany;
d
Forest& Nature Lab, Department of
Forestand Water Management, Ghent University,9000 Ghent, Belgium;
e
Systematic Botanyand Functional BiodiversityStudy Group, University ofLeipzig, 04103
Leipzig,Germany;
f
German Centre for Integrative BiodiversityResearch (iDiv)Halle-Jena-Leipzig, 04103Leipzig, Germany;
g
ForestEcology and Restoration Group,
Departmentof LifeSciences, UniversitydeAlcalá,28805AlcaládeHenares,Madrid,Spain;
h
TerrestrialEcology Unit,DepartmentofBiology,GhentUniversity,9000
Ghent, Belgium;
i
Institut National de la Recherche Agronomique (INRA), UMR 1202, BiodiversitéGènesetCommunautés(BIOGECO),F-33610Cestas,France;
j
University
of Bordeaux, UMR 1202, Biodiversité Gènes et Communautés, F-33600 Pessac, France;
k
Faculty of Environment and Natural Resources, University of Freiburg, 79085
Freiburg, Germany;
l
Institut National de la Recherche Agronomique, UMR Ecologie et Écophysiologie Forestières, 54280 Champenoux, France;
m
Faculty of Forestry,
Stefan cel Mare University of Suceava, Suceava 720229, Romania;
n
Institute of Biology/Geobotany and Botanical Garden, Martin Luther University Halle-Wittenberg,
06108 Halle, Germany;
o
Laboratory of Applied and Environmental Botany, Department of Agri-Food Production and Environmental Science, University of Florence ,
50144 Firenze, Italy;
p
Laboratory of Plant and Microbial Ecology, Department of Biology, Ecology, Evolution,Unive rsityof Liège, 4000 Liège, Belgium;
q
Forest Ecology
and Conservation, Department of Plant Sciences, University of Cambridge, CB2 3EA Cambridge, United Kingdom;
r
Department of Biogeography and Global Change,
NationalMuseumof NaturalSciences(MNCN), ConsejoSuperior deInvestigacionesCientificas, 28006Madrid, Spain;
s
DepartmentofGeosciencesandNaturalResource
Management, University of Copenhagen, 1958 Frederiksberg C, Denmark;
t
Divisionof Forest, Nature, andLandscape, Department of Earthand Environmental
Sciences, KU Leuven, BE-3001 Leuven, Belgium;
u
Natural Resources Institute Finland, FI-80101Joensuu, Finland;
v
Swiss Federal Institutefor Forest, Snow, and
LandscapeResearch, CH-8903Birmensdorf, Switzerland;
w
Earth and EnvironmentalSciences Division,Los Alamos National Laboratory, Los Alamos, NM 87545;
x
InstitutNational dela Recherche Agronomique,UMR 1201, Dynamicsand Ecology ofForest Landscapes,F-31326 Castanet-Tolosan, France;
y
Centreof Evolutionary
and FunctionalEcology UMR 5175–University of Montpellier–University Paul-ValéryMontpellier–École Pratiquedes Hautes Études, 34293 Montpellier Cedex5,
France;
z
Białowie_
za GeobotanicalStation, Faculty of Biology, Universityof Warsaw, 17-230 Białowie_
za, Poland;
aa
Ecology, Evolution and Behaviour, School of
BiologicalSciences, Royal Holloway University of London,TW20 0EX Egham, Surrey, UnitedKingdom;
bb
Department ofForest Mycology and PlantPathology,
Swedish University ofAgricultural Sciences, SE-75007, Uppsala, Sweden;
cc
Departamento de Biologíay Geología, Escuela Superior de Ciencias Experimentales y
Tecnología, Universidad ReyJuan Carlos, 28933Móstoles,Spain; and
dd
OeschgerCentre forClimate ChangeResearch, University of Bern,CH-3012 Bern,Switzerland
Edited by William H. Schlesinger, Cary Institute of Ecosystem Studies, Millbrook, NY, and approved January 29, 2016 (received for review September 8, 2015)
Many experiments have shown that local biodiversity loss impairs
the ability of ecosystems to maintain multiple ecosystem functions at
high levels (multifunctionality). In contrast, the role of biodiversity
in driving ecosystem multifunctionality at landscape scales remains
unresolved. We used a comprehensive pan-European dataset,
including 16 ecosystem functions measured in 209 forest plots across
six European countries, and performed simulations to investigate
how local plot-scale richness of tree species (α-diversity) and their
turnover between plots (β-diversity) are related to landscape-scale
multifunctionality. After accounting for variation in environmental
conditions, we found that relationships between α-diversity and
landscape-scale multifunctionality varied from positive to negative
depending on the multifunctionality metric used. In contrast, when
significant, relationships between β-diversity and landscape-scale
multifunctionality were always positive, because a high spatial turn-
over in species composition was closely related to a high spatial
turnover in functions that were supported at high levels. Our find-
ings have major implications for forest management and indicate
that biotic homogenization can have previously unrecognized and
negative consequences for large-scale ecosystem multifunctionality.
β-diversity
|
biodiversity
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ecosystem functioning
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FunDivEUROPE
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spatial scale
It is widely established that high local-scale biodiversity in-
creases levels of individual ecosystem functions in experimental
ecosystems (1–4), and that biodiversity is even more important
for the simultaneous maintenance of multiple functions at high
levels (i.e., ecosystem multifunctionality) (5–8). Because the ca-
pacity of natural ecosystems to maintain multiple functions
and services is crucial for human well-being (9), the positive
Significance
Numerous studies have demonstrated the importance of bio-
diversity in maintaining multiple ecosystem functions and services
(multifunctionality) at local spatial scales, but it is unknown
whether similar relationships are foundatlargerspatialscalesin
real-world landscapes. Here, we show, for the first time to our
knowledge, that biodiversity can also be important for multi-
functionality at larger spatial scales in European forest landscapes.
Both high local (α-) diversity and a high turnover in species com-
position between locations (high β-diversity) were found to be
potentially important drivers of ecosystem multifunctionality. Our
study provides evidence that it is important to conserve the
landscape-scale biodiversity that is being eroded by biotic ho-
mogenization if ecosystem multifunctionality is to be maintained.
Author contributions: F.v.d.P., P.M., S.S., E. Allan, M.S.-L., K.V., C.W., M.A.Z., and M.F. designed
research; F.v.d.P., E. Ampoorter, L. Baeten, L. Barbaro, J.B., R.B., A.B., D.B., O.B., H.B., F.B., M.C.,
B.C., Y.C., D.A.C., A.C., C.C.B., S.M.D., H.D.W., T.D., L.F., A. Gessler, A. Granier, C.G., V.G.,
S.H., H.J., B.J., F.-x.J., T.J., J.K., H.M., S.M., B.M., D.N., M.P., S.R., K.R.-R., F.S., J.S., F.V., L.V.,
and D.Z. performed research; F.v.d.P. and S.S. analyzed data; F.v.d.P. and P.M. wrote
the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
Data deposition: Data on forest plot locations, environmental variables, tree diversity
data, and values for all ecosystem functions are available at: https://figshare.com/
articles/PNAS_data_on_ecosystem_functions_tre_communities_and_multifunctionality/
3082180. German National forest inventory data is available at: forestportal.efi.int/
view.php?id=201&pl=01.20.
1
To whom correspondence should be addressed. Email: fonsvanderplas@gmail.com.
2
Present address: Department of Biology, University of Florence, 50121 Florence, Italy.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.
1073/pnas.1517903113/-/DCSupplemental.
www.pnas.org/cgi/doi/10.1073/pnas.1517903113 PNAS Early Edition
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ECOLOGY
diversity–multifunctionality relationship is often used as an ar-
gument to promote biodiversity conservation (6, 10). However, al-
though society seeks to maximize the delivery of potentially
conflicting ecosystem services, such as food production, bioenergy
generation, and carbon storage at the landscape scale (11–13), re-
search into the relationship between biodiversity and ecosystem
multifunctionality has been lar gely limited to local-scale studies,
where diversity is manipulated in experimental plant com-
munities. Although some studies have focused on more natural
communities distributed over larger spatial extents (e.g., 14–16),
they examined relationships between local-scale biodiversity and
local-scale multifunctionality. The only previous study to in-
vestigate multifunctionality at larger scales (17) simulated arti-
ficial landscapes using data from experimental grassland
communities. It showed that although different aspects of bio-
diversity affected multifunctionality, local-scale (α-) diversity was a
much stronger driver than the turnover of species between sites
(β-diversity). However, whether those findings can be extrapolated
to real-world (i.e., natural, seminatural) ecosystems, such as forests,
is unknown. As a result, we have a poor understanding of how
multifunctionality relates to biodiversity at the larger spatial scales
that are most relevant to ecosystem managers. This question is of
particular concern, given recent findings suggesting that human-
driven homogenization of communities [loss of β-diversity (18–21)]
may be just as widespread as α-diversity declines (22, 23).
Multifunctionality can be measured by a variety of methods,
and the most appropriate means of doing so remains unresolved
(24–27), particularly at larger scales, where the desired distri-
bution of ecosystem function across the landscape has not
been quantified. At local scales, one can quantify ecosystem
multifunctionality as the number of ecosystem functions that exceed
a given threshold value, where the threshold equals a certain per-
centage of the maximum observed value of each function (10, 24)
(hereafter “threshold-based multifunctionality”;Fig.1B). This
threshold reflects the minimum value of ecosystem functioning that
is deemed satisfactory. Because trade-offs between ecosystem
functions or services are commonplace (5, 7, 28, 29), it is often
impossible to maximize all of the desired functions in a local
community (6). However, when different species provide different
functions (5, 7) at larger spatial scales, a high spatial turnover in
community composition (i.e., a high β-diversity) across the land-
scape can cause different parts of the landscape to provide different
functions at high levels (defined as high threshold-based β-multi-
functionality; Fig. 1B). Therefore, high β-diversity might cause all
desired ecosystem functions to be provided at high levels in at least
one patch within a landscape [and hence promote threshold-based
landscape-scale or γ-multifunctionality (30)] (Fig. 1B), but only if
(i) species differ in the functions they support and (ii )thereis
no “superspecies”that supports the majority of functions. This
threshold-based γ-multifunctionality may be relevant for cases
where forest landscapes are managed for many different ser-
vices (e.g., timber production, limitation of nutrient runoff,
ecotourism), but where each of these services only needs to be
provided at high levels in a part of the landscape, not everywhere
(31). Alternatively, a manager may seek to promote the total
delivery of many summed individual ecosystem functions
across a landscape. We define this total delivery as sum-based
γ-multifunctionality (Fig. 1B). This metric may be a more ap-
propriate measure of multifunctionality in cases where the bene-
fits of ecosystem services are manifested at large scales, such as
carbon sequestration or water purification (32). In this case,
β-diversity might only promote sum-based γ-multifunctionality if
nonadditive diversity effects, such as resource partitioning, spe-
cies-environment matching, or spillover effects, operate at rela-
tively large spatial scales (33, 34). It is therefore likely that the
importance of β-diversity for γ-multifunctionality varies depending
on the desired pattern of ecosystem service provision.
Forests provide many ecosystem services, including wood pro-
duction, regulation of water quality and climate, and recreation
(35, 36). Most present-day European forests and almost all forest
plantations worldwide are dominated by only one or a few tree
species (15, 37), although their diversity could be promoted rela-
tively easily by planting more species or by encouraging natural
regeneration. This fact makes the understanding of diversity–
multifunctionality relationships in these ecosystems highly relevant
for forest management.
We therefore assessed the importance of α-andβ-diversity of
tree species in driving γ-multifunctionality in mature European
forests. To do so, we used data taken from a pan-European forest
dataset consisting of 209 forest plots, specifically selected to in-
vestigate relationships between tree diversity and ecosystem func-
tioning by maximizing variation in dominant “target”species
richness and minimizing (i) variation in other potential drivers
of ecosystem function (e.g., soil and climatic conditions) and
(ii) covariation between tree α-diversity, species composition, and
environmental variables as much as possible (38). Our plot se-
lection therefore aimed to mimic biodiversity experiments to in-
vestigate relationships between biodiversity and ecosystem
functioning in mature forests, which are difficult to undertake with
manipulative approaches due to the longevity of tree species. The
plots were widely distributed across six European countries,
spanning boreal to Mediterranean zones and representing six
major European forest types (38). In each plot, 16 ecosystem
processes, functions, or properties (termed “functions”hereafter)
were measured. These functions represented a wide range of
Fig. 1. Quantifying biodiversity and multifunctionality across
spatial scales. The light yellow areas represent hypothetical
landscapes, consisting of (white) local communities. In these
communities, some species are present (colored icons in Aand
C), whereas others are absent (gray icons). Similarly, some
functions are performing above a hypothetical threshold of
0.5 (colored icons in B), whereas others are not (gray icons).
Diversity and threshold-based multifunctionality are quantified
at (i) the local plot (α-) scale as the number of species present
(two and three in A) or functions performing above a given
threshold (two and three in B), (ii)theβ-scale as the turnover
in species composition [=1−logðða+b+2cÞ=ða+b+cÞÞ =1−log
ðð1+2+2Þ=ð1+2+1ÞÞ =0.90 in A(49)] or functions [=1−log
ðða+b+2cÞ=ða+b+cÞÞ =1−logðð1+2+2Þ=ð1+2+1ÞÞ =0.90
in B(49)] across plots, and (iii) the landscape (γ-) scale as the
number of functions (four in B) present in at least one plot. Sum-
based γ-multifunctionality is defined as the sum of all stan-
dardized ecosystem values in a landscape (=0.8 +0.2 +0.7 +
0.4 +0.9 +1.0 +0.1 +0.6 =4.7). In contrast to threshold-based multifunctionality, sum-based multifunctionality is not analogous to biodiversity (where
species are either present or absent), and can therefore not be partitioned into α-orβ-components. (C) This framework allows investigation of whether
γ-multifunctionality is promoted by α- and/or β-diversity.
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www.pnas.org/cgi/doi/10.1073/pnas.1517903113 van der Plas et al.
supporting, provisioning, regulating, and cultural ecosystem ser-
vices (sensu 9) (SI Appendix,TableS3). Next, we created simulated
landscapes by randomly drawing plots from a country to generate
a“landscape”of five plots, from which γ-multifunctionality
was calculated. We then explored relationships between α-and
β-diversity and different measures of γ-multifunctionality: thresh-
old-based γ-multifunctionality, quantified as the number of functions
with levels above a threshold [a certain percentage of maxi-
mum functioning observed across all plots (10)] in at least one plot
of the landscape (quantification is shown in Fig. 1B), and sum-based
γ-multifunctionality, quantified as the sum of scaled values of all
functions across all plots within a landscape (quantification is shown
in Fig. 1B). To demonstrate how α-andβ-diversity can promote
threshold-based γ-multifunctionality, we also measured the re-
lationships between both α-andβ-diversity and threshold-based
α-andβ-multifunctionality (quantification is shown in Fig. 1B).
Results and Discussion
Our analyses show that relationships between α-diversity and
threshold-based γ-multifunctionality varied from positive, when
moderate levels of ecosystem functioning were desired (40–70%
thresholds), to negative, when very high levels (90% threshold) of
ecosystem functioning were required (Fig. 2C;allP<0.05). In
contrast, relationships between β-diversity and threshold-based
γ-multifunctionality were, when significant, always positive, irre-
spective of the level of functioning desired (Fig. 2C;allP<0.05).
These positive relationships with β-diversity were generally con-
sistent throughout countries (Fig. 3C) and largely independent of
whether diversity was measured as total species richness or rich-
ness of abundant target species (SI Appendix, Fig. S3 and Tables
S5–S7) and the statistical approach used to investigate diversity–
multifunctionality relationships (SI Appendix,Figs.S5–S9). Thus,
landscapes with a high spatial turnover in species composition had
consistently more functions at high levels in at least some plots
than more biotically homogeneous landscapes. This finding indi-
cates that biotic homogenization can have detrimental conse-
quences for threshold-based γ-multifunctionality of ecosystems,
whereas management that promotes a higher spatial turnover in
species composition may reverse these detrimental effects. In
contrast, sum-based γ-multifunctionality was related to neither
α- nor β-diversity (Fig. 2Cand SI Appendix, Fig. S3).
Next, we investigated the mechanisms by which α-andβ-diversity
may affect threshold-based γ-multifunctionality by investigating re-
lationships between α-andβ-diversity and threshold-based α-and
β-multifunctionality (i.e., local multifunctionality and turnover in
functioning across plots; Fig. 1B). These analyses showed that the
aforementioned relationships between α-diversity and threshold-
based γ-multifunctionality were mediated by effects on threshold-
based α-multifunctionality: α-Diversity was positively related
to threshold-based α-multifunctionality when moderate levels
(40–50%) of functioning were desired [similar to most experimental
studies (8)], but negatively related when high levels (90%) of
functioning were required (Fig. 2A; all P<0.001), a finding that
was largely consistent throughout countries (Fig. 3A) and largely
independent of whether the richness of the dominant species or
the richness of all species (SI Appendix,Fig.S3) was used as
an α-diversity measure. This pattern may have been caused by
“statistical averaging”effects similar to the portfolio effects that
drive diversity–stability relationships (39): Without strong selection
or complementarity effects (40), mixed species plots will tend to
have intermediate, but never extremely high or low, ecosystem
function levels due to the averaging of individual species effects on
function. In line with this mechanism, α-diversity did not have sig-
nificant effects on sum-based γ-multifunctionality (Fig. 2C). These
results suggest that although function values were, on average, not
higher or lower in diverse communities than in monocultures, they
tended to be less extreme (never extremely high or low) (41). This
result contrasts with the results of other studies focusing on more
diverse and/or experimental grassland, aquatic, or soil communities.
In these studies, higher α-diversity enhances α-multifunctionality
even at very high thresholds (8, 24), possibly due to strong com-
plementarity effects. However, the diversity-ecosystem functioning
literature has tended to concentrate on particular ecosystems and
study designs. As a result, it is difficult to infer whether these con-
trasting results are caused by biological or methodological differ-
ences. In any case, our results indicate that in European forests at
least, the relationship between α-diversity and both α-andγ-multi-
functionality strongly depends on the desired level of functioning.
In our next analysis, we investigated the relationship between
β-diversity and γ-multifunctionality. In contrast to α-diversity, the
positive relationship between β-diversity and threshold-based
γ-multifunctionality was independent of the desired level of
ecosystem functioning. In almost all countries (Figs. 2Band 3C),
and irrespective of whether target ortotalspeciesrichnesswasthe
diversity metric used (SI Appendix,Fig.S3), β-diversity was posi-
tively related to threshold-based β-multifunctionality when mod-
erate or high levels of ecosystem functioning were desired, thereby
increasing the number of functions that were provided at high levels
in at least one part of the landscape (threshold-based γ-multi-
functionality; Fig. 2B). However, we did not detect a significant
relationship between β-diversity and sum-based γ-multifunctionality
(Fig. 2B). This finding was likely due to trade-offs between eco-
system functions: Of the 120 possible pairwise correlations among
functions, 50 were negative. This result made it impossible to
Fig. 2. Scale-dependent effects of biodiversity on forest ecosystem multi-
functionality. Bars represent the standardized regression coefficients of
α-diversity (light gray) and β-diversity (dark gray) in generalized LMMs explain-
ing α-(A), β-(B), or γ-(C) multifunctionality. Multifunctionality was quantified at
different scales using a threshold approach, with thresholds of 40%, 50%, 70%,
and 90%. In addition, sum-based γ-multifunctionality was calculated as the sum
of scaled (between 0 and 1) individual function values. Diversity measures were
calculated based on individuals of target tree species. *P<0.05; ***P<0.001;
****P<0.0001. NS, not significant.
Fig. 3. Scale-dependent effects of biodiversity on forest ecosystem multi-
functionality are generally consistent across countries. Bars represent the
standardized regression coefficients of α-diversity (blue) and β-diversity (red) in
LMMs explaining α-(A), β-(B), or γ-(C) multifunctionality. Multifunctionality
was quantified at different scales using a threshold approach, with thresholds
of 40%, 50%, 70%, and 90%. In addition, sum-based γ-multifunctionality was
calculated as the sum of scaled (between 0 and 1) individual function values.
Diversity measures were calculated based on individuals of target tree species.
van der Plas et al. PNAS Early Edition
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achieve very high levels of all functions across the entire landscape.
These results thus indicate that although β-diversity is not related to
higher average levels of ecosystem functions, it is positively related
to the number of functions that perform at high levels in at least
part of the landscape. Hence, positive relationships between
β-diversity and threshold-based β-multifunctionality (and hence
threshold-based γ-multifunctionality) are caused by the fact that
different species support different functions (5, 7). For example, in
Polish forests, monoculture plots of the conifer Picea abies are re-
lated to high levels of many functions relating to the production of
quality timber (e.g., timber quality, biomass production), whereas
plots of the deciduous tree Carpinus betulus were of higher recre-
ational and conservation value due to a high diversity of bats and
understory plants (SI Appendix,TableS8). Hence, forest landscapes
where some locations were dominated by P. abies and others by
C. betulus provided more functions at high levels than those forest
landscapes where all plots had thesametreespeciescomposition.
Our finding that the relationship between biodiversity and
European forest γ-multifunctionality depends strongly on the way
that multifunctionality is quantified has important implications for
European forest management. In short, our results suggest that
different patterns of tree species distribution would achieve dif-
ferent management goals (or “landscape multifunctionality sce-
narios”). The results of the threshold-based γ-multifunctionality
analysis would be most relevant to situations where managers
sought to promote forest landscapes with very high levels of eco-
system functioning in at least some (but not necessarily all) local
patches (sensu 30). As described earlier, this situation may
occur when managers seek to provide different ecosystem services
in different localities. An example of such a landscape is one
where some localities provide recreation or cultural services, such
as aesthetic beauty and a diversity of charismatic taxa (31) (SI
Appendix, section S3), whereas other localities maximize pro-
visioning services that are only cost-effective when delivered at
very high levels, such as production of high-value timbers (42),
or form hotspots of certain biogeochemical functions that
need to be strategically located, such as the minimization of nu-
trient runoff close to water bodies. In such scenarios, threshold-
based γ-multifunctionality could be promoted in forest landscapes
that possess a high turnover in community composition, but a low
α-diversity (top left landscape in Fig. 1C), by promoting a range of
different monocultures across the landscape. When the delivery of
provisioning services is cost-effective at lower levels or when cul-
tural or regulating services do not need to be at extremely high
levels, one could aim to promote landscapes with moderate levels
of many functions (40% or 50% threshold γ-multifunctionality). In
this scenario, threshold-based γ-multifunctionality is highest in
forests with both a high spatial turnover in community composi-
tion and a high local diversity of tree species (top right landscape
in Fig. 1C). This finding is in line with Gamfeldt et al. (15), who
hypothesized, based on local-scale analyses, that “adjacent stands,
each with multiple species but in different combinations, might be
the best way to provide multiple ecosystem services at the land-
scape scale.”A third hypothetical scenario would be to maximize
total delivery of services across the landscape (high sum-based
γ-multifunctionality), rather than having highly localized specialist
patches that deliver a limited number of services at very high
levels. This scenario may be most relevant to cases where the
primary goal of ecosystem management is to provide ecosystem
services whose benefits are manifested at large scales, such as
carbon sequestration (43). We found that neither α-diversity nor
spatial turnover in community composition (β-diversity) had sig-
nificant detectable relationships with γ-multifunctionality under this
scenario. In summary, we demonstrate that the importance of dif-
ferent components of diversity for promoting γ-multifunctionality is
likely to depend on management goals. Accordingly, stakeholder
engagement is required to see where these situations apply in real
forested landscapes. Further studies are also required to confirm
that tree α-andβ-diversity are causal drivers of the observed re-
lationships and to see how important they are in comparison to
other potentially important factors in driving ecosystem multi-
functionality in representative European forests.
In this study, some of the benefits of biodiversity for γ-mul-
tifunctionality may have been underestimated. Our study did not
consider some of the spatiotemporal processes that occur in real
forest landscapes [e.g., dispersal and movement of ecosystem
service providers, species-environment matching, large-scale
resource partitioning, spillover and subsidy of ecosystem services
between neighboring patches (13, 44)]. These processes could
promote ecosystem functioning in landscapes that possess a high
spatial turnover in species composition even more than was
detected here. For example, a forest resistant to herbivory might
also reduce pest damage in adjacent forests by lowering pop-
ulations of herbivores and preventing their movement into more
vulnerable areas, thus strengthening the relationship between
β-diversity and forest γ-multifunctionality. Future studies could
explore these ideas by studying ecosystem multifunctionality in
landscapes where ecological interactions between patches of dif-
fering diversity and composition are quantified.
Previous studies have demonstrated that local-scale (α-) bio-
diversity can boost multifunctionality in the real world, in addition
to experimental ecosystems (8, 14–16). Here, we add evidence that
both α-andβ-diversity can also drive ecosystem multifunctionality
at the landscape scale, and that the desired distribution of eco-
system functions across the landscape influences the importance of
this relationship. Biotic homogenization is occurring worldwide at
local, regional, and global scales (19–21). Similarly, current forest
management often results in large areas of low species turnover.
Our study is an important step forward in exploring the importance
of this biotic homogenization for γ-multifunctionality. It shows that
biotic homogenization may have negative, strong, far-reaching, and
so far overlooked impacts upon the ecosystem services on which
humanity depends, and that these impacts may be as strong as, or
even stronger than, the impacts of local diversity loss.
Methods
Plot Selection. In total, 209 forest plots (each measuring 30 ×30 m) were
established within the European FunDivEUROPE project (fundiveuropektp.
boku.ac.at/). Because we were interested in the effects of tree species diversity
on ecosystem functioning in mature forests (38), plot selection was aimed at
mimicking the design of a biodiversity experiment, in which variation in envi-
ronment is minimized and diversity is not confounded with composition, as in
most observational studies of diversity. Hence, the design aimed to bridge the
gap between controlled but very young tree diversity experiments and obser-
vational studies, where diversity can be strongly confounded with other factors.
Plots were located in six European countries, ranging from boreal to
Mediterranean zones, and with each representing a major European forest
type (38): Finland (28 plots, boreal forest), Poland (43 plots, hemiboreal
forest), Germany (38 plots, temperate deciduous forest), Romania (28 plots,
mountainous deciduous forest), Italy (36 plots, thermophilous deciduous
forest), and Spain (36 plots, Mediterranean mixed forest) (SI Appendix, Fig.
S1). Within countries, plots were located in a single region ranging in size
from 5 ×5 km (Romania) to 150 ×150 km (Finland). In each country, be-
tween three and five regionally common target species were selected, 15 in
total (SI Appendix, Table S1). Plots were then selected to differ as much as
possible in richness of target species and so that almost all possible combi-
nations of these target species were realized, a design that emulates the
designs of biodiversity experiments (38). Richness levels of one, two, three,
four, and five target species were replicated 56, 67, 54, 29, and 3 times,
respectively, across countries, and most possible target species compositions
were realized [additional details on the selection procedure are provided in
the study by Baeten et al. (38)]. To achieve this goal, some admixture of
nontarget species was unavoidable. However, on average, target species
accounted for 93.75% of the individuals and 91.39% of the basal area, and
they were always represented by more than two individuals (SI Appendix,
Fig. S2). We therefore focus on using the richness of target species in our
analyses, but we also tested for the effect of total (target +admixed) species
richness (SI Appendix). Plot selection strictly avoided correlations between
tree species richness and soil factors, as well as any spatial autocorrelation in
diversity (38), by choosing plots that differed as little as possible in envi-
ronmental factors (soil texture, depth, pH, and altitude) that could poten-
tially confound diversity effects on multifunctionality. The diversity gradient
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was therefore most likely a result of stochastic factors or differences in past
management between plots.
Tree Diversity and Community Composition Data. Within each plot, all tree
stems ≥7.5 cm in diameter at breast height were identified to the level of
species and mapped (12,939 stems in total). Species richness was defined as the
number of target species (SI Appendix,TableS1)withatleasttwoindividuals
in a plot. We also calculated Pielou’s evenness (45) for target tree species and
the proportion of coniferous target trees. Because plots were specifically se-
lected to have similar abundances of the target species, variation in evenness
values across plots was low, with values above 0.6 in >90% of plots. In addition
to richness, evenness, and the proportion of coniferous individuals of target
species, we calculated richness, evenness, and proportion of coniferous indi-
viduals of all tree species for the purpose of sensitivity analyses.
We recorded diameter to the nearest 0.1 cm of each individual tree stem
and measured height to the nearest 0.1 m. We used these diameter and
height measurements to estimate the aboveground biomass of each indi-
vidual tree, based on published allometric functions (ref. 46 and references
therein). These functions were species-specific, and, whenever possible,
functions developed for trees growing in forests similar to the forests of our
study were used. Plot-level biomass estimates were calculated by summing
the biomass of all individuals of the target tree species within a plot.
Environmental Data. We recorded the altitude of each plot as a proxy for
variation in local climate. Soil pH was also measured because it is an important
driver of numerous other soil properties (47). Between May and October
2012, forest floor litter (in nine 25 ×25-cm patches) and mineral soil (using a
cylindrical metal corer from 0–10 cm in all countries and from 10–20 cm in all
countries except Spain) were sampled for pH measurements, which were
then measured using standard protocols (SI Appendix). Soil texture was also
estimated using expert assessment as the abundance of sand (size), silt (size),
and clay (size) content. Measurements were done on an ordinal scale, with
values ranging from 1 (absent) to 3 (very common). Finally, soil depth
(centimeter depth to bedrock) was measured in each plot using a soil auger.
Measurement of Ecosystem Functions and Properties. In each plot, 16 ecosystem
processes, functions, or properties (termed functions hereafter) were measured
between 2012 and 2014: timber quality, timber production, tree regeneration, root
biomass, litter decomposition, wood decomposition, microbial biomass, soil carbon
stock, resistance to drought, resistance to insect herbivory, resistance to mammal
browsing, resistance to pathogens, bird diversity, bat diversity, understory plant
diversity, and earthworm biomass. All measured ecosystem functions have estab-
lished links to supporting, provisioning, regulating, or cultural services (sensu 9).
Details about function measurements are available in SI Appendix,sectionS2,and
details on the services they provide are available in SI Appendix,sectionS3.Toallow
comparison of the different ecosystem functions, they were scaled between 0 and 1:
SEFi=EFi−minðEFÞ
maxðEFÞ−minðEF Þ,
with SEF indicating the final (scaled) ecosystem value; EF indicating raw
(unscaled) ecosystem function values; and min/max(EF), respectively, in-
dicating the minimum/maximum raw values of the ecosystem function.
Simulating Artificial Forest Landscapes. To analyze diversity and multi-
functionality at different spatial scales, ranging from plots (α), to species
turnover between plots (β), to landscape scales (γ), we simulated artificial
forest landscapes from the observed forest plots. Within each country, we
randomly selected, without replacement, five plots to create an artificial
landscape and repeated this process 1,000 times. With six countries, we
therefore created 6,000 artificial forest landscapes, with 5,981 unique plot
combinations. The number of unique dominant tree species within countries
was relatively small (up to five), and few plots contained all of these species;
hence, creating landscapes from a relatively low number of plots ensured
that landscapes varied as much as possible in both α- and β-diversity. Addi-
tional analyses showed that the compositions of these simulated landscapes
are likely to be realized at the local regional scale (SI Appendix, section S5).
Within each of these 5,981 unique landscapes, we then calculated tree di-
versity at two spatial scales. α-Diversity was defined as the average target
species richness value across the plots. Turnover in tree community compo-
sition [i.e., β-diversity (48)] was calculated for each of the 10 pairs of plots
within a landscape as follows: βdiv =1−ðlogðA+B+2CÞ=ðA+B+CÞÞ
logð2ÞÞ,whereAand Bare the number of target species unique to each
plot and Cis the number of target species shared by the plots (49). This
measure is bound between 0 (no turnover) and 1 (complete turnover).
Landscape-level β-diversity was then calculated as the average of all 10
β-diversity values of pairwise plot combinations. γ-Diversity was calculated as
the richness of all the target species present in at least one plot within the
landscape. Note that γ-diversity (or threshold-based γ-multifunctionality; see
below) is not strictly additively or multiplicatively partitioned into α-and
β-diversity (or threshold-based α-orβ-multifunctionality; see below), so that
α-, β-, and γ-diversity can, to some extent, vary independent of one another.
For sensitivity analyses, we also calculated α-, β-, and γ-diversity based on all
tree species present (rather than target species only).
In the 5,981 artificial landscapes, we used two approaches to calculate mul-
tifunctionality measures, which correspond to different hypothetical manage-
ment objectives. We calculated threshold-based α-, β-, and γ-multifunctionality in
a way that is analogous to calculating α-, β-, and γ-diversity (Fig. 1) and also
broadly analogous to a recent method for quantifying the temporal stability of
ecosystem functioning at different spatial scales (50). Within plots, threshold-
based multifunctionality was defined as the number of ecosystem function
values that exceeded a minimum threshold:
MF =X
n
i=11 SEFi≥T
0 SEFi<T
(10), in which nis the number of functions and Tis the performance
threshold value. Threshold values were defined as a certain percentage of
the 95th percentile of maximum functioning (10) from the country in which
plots were located. We chose to investigate diversity–multifunctionality re-
lationships at four different multifunctionality thresholds: 40%, 50%, 70%,
and 90%. In plots with one (n=28), two (n=1), or three (n=1) missing
ecosystem function values, threshold-based multifunctionality scores were
corrected by accounting for the proportion of nonmissing functions:
TMF = X
n
i=11 SEFi≥T
0 SEFi<T!·n
nc,
where TMF is threshold-based multifunctionality, n_c is the number of
nonmissing functions, and nis the total number of functions measured in
this study. Threshold-based α-multifunctionality was then calculated as the
average TMF value across the five plots comprising a landscape. Threshold-based
β-multifunctionality was calculated as the turnover in ecosystem functions pre-
sent (i.e., exceeding a threshold) across plots comprising a landscape, with the
same formula as was used for β-diversity (see above), but this time with Aand B
representing functions exceeding the threshold in either the first or second plot
and Crepresenting the ecosystem functions that exceed the threshold in both
plots. Lastly, threshold-based γ-multifunctionality was measured as the number
of ecosystem functions exceeding a 40%, 50%, 70%, or 90% threshold value in
at least one of the five plots within each landscape.
In addition to the threshold-based approach, we calculated γ-multi-
functionality based on a summing approach [broadly similar to the ap-
proach used by Maestre et al. (14)]. To calculate sum-based γ-multifunctionality,
we first summed the five plot-level values for each function. These
summed landscape-level function values were then scaled between
0and1ðEF −minðEFÞ=maxðEFÞ−minðEFÞ.Tocalculatesum-based
γ-multifunctionality, we then summed the scaled values of the 16 functions.
In contrast to biodiversity and threshold-based multifunctionality, sum-based
multifunctionality is quantified using continuous variation in function values,
rather than “presence/absence data”(of species or functions passing a thresh-
old), making it impossible to partition it into α-andβ-components.
In the landscapes, we also quantified factors that potentially affect rela-
tionships between diversity and multifunctionality: average values of target
species evenness, the proportion of coniferous tree individuals, sand content,
clay content, soil depth, soil pH, and altitude. In addition, we calculated envi-
ronmental heterogeneity in two steps. First, we quantifiedthe heterogeneityof
individual abiotic factors (altitude, pH, and soil texture) as the coefficient of
variation (CV) ofvalues acrossplots within a landscape.In the case of soiltexture,
heterogeneity was quantified as the sum of CV values of clay, silt, and sand
content. Next, these three heterogeneity measures were Z-transformed and
summed toproduce a single measure of environmental heterogeneity. By using
Z-scores, we ensured that each abiotic variable had an equal impact on total
environmental heterogeneity. All analyses were done with R version 3.0.2 (48).
Statistical Analyses. We first investigated whether α-andβ-diversity in simulated
forest landscapes was associated with γ-multifunctionality using linear mixed
models (LMMs). Although we designed our study to minimize variation in en-
vironmental factors, completely eliminating any variation in these environmen-
tal factors was impossible (SI Appendix,sectionS3). Hence, to avoid the detection
of spurious diversity–multifunctionality relationships, we included these
van der Plas et al. PNAS Early Edition
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ECOLOGY
environmental factors as covariates in the LMMs. We performed three differ-
ent LMM analyses. In the first, we investigated how α-multifunctionality was
driven by α-diversity, using an LMM with α-multifunctionality as the response
variable, species richness as the focal fixed factor, species evenness, proportion
of evergreen trees, altitude, soil depth, soil pH, soil sand and clay content, and
their two-way interactions as covariates, and with country as a random factor.
In the second analysis, we investigated the relationship between β-multi-
functionality and β-diversity, using an LMM with β-multifunctionality as the
response variable, β-diversity as the focal fixed factor, environmental hetero-
geneity asa covariate, and country as a random factor. In the third analysis, we
investigated how γ-multifunctionality was affected by both α-andβ-diversity,
by first constructing a full LMM with γ-multifunctionality as the response var-
iable; α-andβ-diversity as the focal fixed factors; species evenness, proportion
of evergreen trees, altitude, soil depth, soil pH, soil sand and clay content,
environmental heterogeneity, and their bivariate interactions as covariates;
and country as a random factor. As a result of the careful study design, diversity
measures were largely independent of the covariates (38): Correlations be-
tween focal predictors and covariates were always <0.230, whereas the
correlation between α-andβ-diversity was moderate (R
2
=0.316, P<0.0001);
hence, there was no strong indication of multicollinearity. In all three analyses,
we used a backward model-selection analysis to remove covariates sequen-
tially (based on ratio-likelihood tests with a Bonferroni correction) until
we reached a final model with only the focal fixed factor(s) and signifi-
cant covariates. From this final model, we quantified the significance ofα-and
β-diversity in driving multifunctionality using likelihood ratio tests, and we also
quantified their standardized regression coefficients. All analyses were per-
formed for all different threshold-based and sum-based multifunctionality
variables. As a robustness check, we also repeated all these analyses with
predictors and covariates based on all tree species, rather than on target
species only (SI Appendix). In addition, to investigate how general the main
patterns were across countries, we ran linear models for each country sepa-
rately, with the same fixedfactors in models as in the finally selected LMMs. All
analyses were performed using R version 3.0.2 (51). LMMs were fitted using
the “lmer”function of the “lme4”library (52). Given that effects of covariates
were variable and complex, and that the main focus of this study was on
biodiversity effects, the effects of covariates are not presented here (effect
sizes of all covariates are shown in SI Appendix,TablesS2–S4).
In addition to LMMs, we used structural equation models to investigate re-
lationships betweenbiodiversity and multifunctionality, to test thesensitivity of
our results tothestatistical method used, and to test for indirect relationships
between biodiversity and multifunctionality (SI Appendix,sectionS4).
ACKNOWLEDGMENTS. We thank the Hainich National Park administration as
well as Felix Berthold and Carsten Beinhoff for support of this study and Gerald
Kaendler and the Johann Heinrich von Thünen-Institut for providing access
to the German National Forest Inventory data. The research leading to these
results received funding from the European Union Seventh Framework
Programme (FP7/2007-2013) under Grant Agreement 265171.
1. Hooper DU, et al. (2005) Effects of biodiversity on ecosystem functioning: A consensus
of current knowledge. Ecol Monogr 75(1):3–35.
2. Balvanera P, et al. (2006) Quantifying the evidence for biodiversity effects on eco-
system functioning and services. Ecol Lett 9(10):1146–1156.
3. Cardinale BJ, et al. (2011) The functional role of producer diversity in ecosystems. Am J
Bot 98(3):572–592.
4. Handa IT, et al. (2014) Consequences of biodiversity loss for litter decomposition
across biomes. Nature 509(7499):218–221.
5. Hector A, Bagchi R (2007) Biodiversity and ecosystem multifunctionality. Nature
448(7150):188–190.
6. Zavaleta ES, Pasari JR, Hulvey KB, Tilman GD (2010) Sustaining multiple ecosystem
functions in grassland communities requires higher biodiversity. Proc Natl Acad Sci
USA 107(4):1443–1446.
7. Isbell F, et al. (2011) High plant diversity is needed to maintain ecosystem services.
Nature 477(7363):199–202.
8. Lefcheck JS, et al. (2015) Biodiversity enhances ecosystem multifunctionality across
trophic levels and habitats. Nat Commun 6:6936.
9. Millennium Ecosystem Assessment (2005) Ecosystems and Human Well-Being: Synthesis
(Island Press, Washington, DC).
10. Gamfeldt L, Hillebrand H, Jonsson PR (2008) Multiple functions increase the impor-
tance of biodiversity for overall ecosystem functioning. Ecology 89(5):1223–1231.
11. Green RE, Cornell SJ, Scharlemann JPW, Balmford A (2005) Farming and the fate of
wild nature. Science 307(5709):550–555.
12. Goldstein JH, et al. (2012) Integrating ecosystem-service tradeoffs into land-use de-
cisions. Proc Natl Acad Sci USA 109(19):7565–7570.
13. Manning P, Taylor G, Hanley ME (2015) Bioenergy, food production and biodiversity–
an unlikely alliance? Glob Change Biol Bioenergy 7(4):570–576.
14. Maestre FT, et al. (2012) Plant species richness and ecosystem multifunctionality in
global drylands. Science 335(6065):214–218.
15. Gamfeldt L, et al. (2013) Higher levels of multiple ecosystem services are found in
forests with more tree species. Nat Commun 4:1340.
16. Allan E, et al. (2015) Land use intensification alters ecosystem multifunctionality via
loss of biodiversity and changes to functional composition. Ecol Lett 18(8):834–843.
17. Pasari JR, Levi T, Zavaleta ES, Tilman D (2013) Several scales of biodiversity affect
ecosystem multifunctionality. Proc Natl Acad Sci USA 110(25):10219–10222.
18. McKinney ML, Lockwood JL (1999) Biotic homogenization: A few winners replacing
many losers in the next mass extinction. Trends Ecol Evol 14(11):450–453.
19. Dornelas M, et al. (2014) Assemblage time series reveal biodiversity change but not
systematic loss. Science 344(6181):296–299.
20. Vellend M, et al. (2013) Global meta-analysis reveals no net change in local-scale plant
biodiversity over time. Proc Natl Acad Sci USA 110(48):19456–19459.
21. McGill BJ, Dornelas M, Gotelli NJ, Magurran AE (2015) Fifteen forms of biodiversity
trend in the Anthropocene. Trends Ecol Evol 30(2):104–113.
22. Murphy GEP, Romanuk TN (2014) A meta-analysis of declines in local species richness
from human disturbances. Ecol Evol 4(1):91–103.
23. Newbold T, et al. (2015) Global effects of land use on local terrestrial biodiversity.
Nature 520(7545):45–50.
24. Byrnes JEK, et al. (2014) Investigating the relationship between biodiversity and eco-
system multifunctionality: Challenges and solutions. Methods Ecol Evol 5(2):111–124.
25. Bradford MA, et al. (2014) Discontinuity in the responses of ecosystem processes and
multifunctionality to altered soil community composition. Proc Natl Acad Sci USA
111(40):14478–14483.
26. Byrnes J, et al. (2014) Multifunctionality does not imply that all functions are posi-
tively correlated. Proc Natl Acad Sci USA 111(51):E5490.
27. Bradford MA, et al. (2014) Reply to Byrnes et al.: Aggregation can obscure under-
standing of ecosystem multifunctionality. Proc Natl Acad Sci USA 111(51):E5491. (lett).
28. Lavorel S, et al. (2011) Using plant functional traits to understand the landscape
distribution of multiple ecosystem services. J Ecol 99(1):135–147.
29. Grigulis K, et al. (2013) Relative contributions of plant traits and soil microbial
properties to mountain grassland ecosystem services. J Ecol 101(1):47–57.
30. Brandt J (2003) Multifunctional landscapes–perspectives for the future. J Environ Sci
(China) 15(2):187–192.
31. Chan KMA, Shaw MR, Cameron DR, Underwood EC, Daily GC (2006) Conservation
planning for ecosystem services. PLoS Biol 4(11):e379.
32. Trumper K, et al. (2009) The Natural Fix? The Role of Ecosystems in Climate Mitigation. A
UNEP Rapid Response Assessment. United Nations Environment Programme (United Na-
tions Environment Programme-World Conservation Monitoring Centre, Cambridge, UK).
33. Loreau M, Mouquet N, Gonzalez A (2003) Biodiversity as spatial insurance in het-
erogeneous landscapes. Proc Natl Acad Sci USA 100(22):12765–12770.
34. Cardinale BJ, Ives AR, Inchausti P (2004) Effects of species diversity on the primary
productivity of ecosystems: Extending our spatial and temporal scales of inference.
Oikos 104(3):437–450.
35. Aerts R, Honnay O (2011) Forest restoration, biodiversity and ecosystem functioning.
BMC Ecol 11:29.
36. Fares S, Mugnozza GS, Corona P, Palahí M (2015) Sustainability: Five steps for man-
aging Europe’s forests. Nature 519(7544):407–409.
37. Bauhus J, van der Meer P, Kanninen M (2010) Ecosystem Goods and Services from
Plantation Forests (Earthscan, London).
38. Baeten L, et al. (2013) A novel comparative research platform designed to determine
the functional significance of tree species diversity in European forests. Perspect Plant
Ecol Evol Syst 15(5):281–291.
39. Tilman D, Lehman CL, Bristow CE (1998) Diversity-stability relationships: Statistical
inevitability or ecological consequence? Am Nat 151(3):277–282.
40. Loreau M, Hector A (2001) Partitioning selection and complementarity in biodiversity
experiments. Nature 412(6842):72–76.
41. Loreau M (1998) Biodiversity and ecosystem functioning: A mechanistic model. Proc
Natl Acad Sci USA 95(10):5632–5636.
42. Phalan B, Onial M, Balmford A, Green RE (2011) Reconciling food production and biodiversity
conservation: Land sharing and land sparing compared. Sc ience 333(6047):1289–1291.
43. Canadell JG, Raupach MR (2008) Managing forests for climate change mitigation.
Science 320(5882):1456–1457.
44. Tscharntke T, Klein AM, Kruess A, Steffan-Dewenter I, Thies C (2005) Landscape
perspectives on agricultural intensification and biodiversity–ecosystem service man-
agement. Ecol Lett 8(8):857–874.
45. Pielou EC (1966) The measurement of diversity in different types of biological col-
lections. J Theor Biol 13:131–144.
46. Jucker T, Bouriaud O, Avacaritei D, Coomes DA (2014) Stabilizing effects of diversity
on aboveground wood production in forest ecosystems: Linking patterns and pro-
cesses. Ecol Lett 17(12):1560–1569.
47. White RE (2005) Principles and Practice of Soil Science: The Soil as a Natural Resource
(Wiley–Blackwell, Oxford, UK), 4th Ed.
48. Whittaker RH (1960) Vegetation of the Siskiyou Mountains, Oregon and California.
Ecol Monogr 30(3):279–338.
49. Lennon JJ, Koleff P, Greenwood JJD, Gaston KJ (2001) The geographical structure of
British birddistributions: Diversity, spatial turnover and scale. JAnimEcol70(6):966–979.
50. Wang S, Loreau M (2014) Ecosystem stability in space: α,βand γvariability. Ecol Lett
17(8):891–901.
51. R Core Team (2013) R: A Language and Environment for Statistical Computing
(R Foundation for Statistical Computing, Vienna, Austria).
52. Bates D, Maechler M, Bolker B, Walker S (2014) lme4: Linear mixed-effects models
using Eigen and S4, R package version 1.1-7. Available at cran.r-project.org/web/
packages/lme4/index.html. Accessed February 16, 2015.
6of6
|
www.pnas.org/cgi/doi/10.1073/pnas.1517903113 van der Plas et al.