Ecography - Integrative Biogeography and Global Change Group

Ecography 34: 897908, 2011doi: 10.1111/j.1600-0587.2011.06919.x# 2011 The Authors. Ecography # 2011 EcographySubject Editor: Jens-Christian Svenning. Accepted 2 March 2011Using species co-occurrence networks to assess the impacts ofclimate changeMiguel B. Araújo, Alejandro Rozenfeld, Carsten Rahbek and Pablo A. MarquetM. B. Araújo (maraujo@mncn.csic.es), Depto de Biodiversidad y Biología Evolutiva, Museo Nacional de Ciencias Naturales, CSIC, Calle JoséGutiérrez Abascal, 2, ES-28006, Madrid, Spain. MBA also at: Rui Nabeiro Biodiversity Chair, CIBIO, Univ. of Évora, Largo dos Colegiais,PT-7000 Évora, Portugal, and Lab Internacional en Cambio Global, UC-CSIC, Depto de Ecología, Facultad de Ciencias Biológicas, PUC,Alameda 340, CP 6513677, Santiago, Chile. A. Rozenfeld and P. A. Marquet, Lab Internacional en Cambio Global, UC-CSIC, Depto deEcologiá, Facultad de Ciencias Biológicas, PUC, Alameda 340, CP 6513677, Santiago, Chile. AR also at: Inst. Mediterráneo de EstudiosAvanzados, CSIC, C/Miquel Marquès, ES-21-07190 Esporles, Mallorca, Spain. PAM also at: Inst. de Ecología y Biodiversidad (IEB), Casilla653, Santiago, Chile. C. Rahbek, Center for Macroecology, Evolution and Climate, Dept of Biology, Univ. of Copenhagen, Universitetsparken15, DK-2100 Copenhagen, Denmark.Viable populations of species occur in a given place if three conditions are met: the environment at the place is suitable;the species is able to colonize it; co-occurrence is possible despite or because of interactions with other species. Studiesinvestigating the effects of climate change on species have mainly focused on measuring changes in climate suitability.Complex interactions among species have rarely been explored in such studies. We extend network theory to the analysisof complex patterns of co-occurrence among species. The framework is used to explore the robustness of networks underclimate change. With our data, we show that networks describing the geographic pattern of co-occurrence among speciesdisplay properties shared by other complex networks, namely that most species are poorly connected to other species inthe network and only a few are highly connected. In our example, species more exposed to climate change tended to bepoorly connected to other species within the network, while species more connected tended to be less exposed. Such highconnectance would make the co-occurrence networks more robust to climate change. The proposed framework illustrateshow network analysis could be used, together with co-occurrence data, to help addressing the potential consequences ofspecies interactions in studies of climate change and biodiversity. However, more research is needed to test for linksbetween co-occurrence and network interactions.Assessments of the effects of climate change on thedistributions of species have typically been conducted usingbioclimatic modelling approaches that ignore local populationprocesses (but see Keith et al. 2008, Anderson et al.2009) and biotic interactions (but see Araújo and Luoto2007). By ignoring biotic interactions, an implicit assumptionis that responses of species to climate changes are‘individualistic’ (Pearson and Dawson 2003). However,interspecific interactions may structure biotic communitieseven at coarser spatial scales (Heikkinen et al. 2007, Gotelliet al. 2010). Thus, the ‘individualistic response’ assumptionis problematic because it fails to account for interdependenciesbetween species, whereby the removal of species orchanges in the density of individual species withinecosystems can have cascading effects giving raise, forexample, to secondary extinctions (for reviews see Ebenmanand Jonsson 2005, Tylianakis et al. 2008). The individualisticresponse approach may also fail by ignoring knownproperties of interaction networks, such as increasedresilience of assemblages with increasing connectance(Dunne et al. 2002b, Eklof and Ebenman 2006), and thelong-term co-occurrence of species enhanced by asymmetricalinteractions (Bascompte et al. 2006).The question then is: how can ecological interactions beaccounted for in predictions of the effects of climate changeon species distributions? One possible approach is toperform controlled experiments, whereby the anticipatedchanges in climate are simulated and the responses ofspecies under different treatments are recorded. The resultsof two recent studies using this approach reinforce thenotion that ecological interactions do affect species responsesto climate change and can even overturn pureclimatic effects (Suttle et al. 2007, Harmon et al. 2009).The problem is that while bioclimatic models often lackexplicit parameterization of biotic interactions (but seeAraújo and Luoto 2007, Heikkinen et al. 2007, Meier et al.2010), experimental approaches are generally not feasible.Here, we explore an alternative approach using matrices ofspecies spatial co-occurrences (the fundamental unit ofanalysis in community ecology and biogeography, Gotelli2000), derived from overlapping geographic distributionsto infer the consequences of climate change on assemblages897

Seite 2 • Ausgabe 01/2013 LifeInhaltSeite 2• Überprüfung der versiegeltenFlächen durch Luftbildauswertung imStadtgebiet SiegenSeite 3• Feierliche Eröffnung der KläranlageIstanbul/AtaköyAusbaugröße 2.000.000 EWSeite 4• Erfahrungsbericht TAZV OderaueEuropäische Fördermittel für denAufbau von Kanal- und TrinkwasserdatenbankenSeite 5• INSPIRE-konforme GIS-DatenSeiten 6/7• Ganzheitliche NetzsanierungDas Anlagevermögen der Kommunenliegt zu einem großen Teil inForm von Kanalnetzen unter der ErdeSeite 8• Vorbeugende Instandhaltung alsInstrument zur Reduzierung vonReinvestitionenSeite 9• Betriebsführungsservice beimWasserwirtschaftsamt vorgestellt• WTEB auf der Fachausstellung• enertec und TerraTec – Branchenauftaktdes Jahres 2013Seiten 10/11• Erweiterung und Modernisierung derKläranlage in LarnacaSeite 12• 10 Jahre BetriebsführungsmodellKläranlage RHV ZellerbeckenImpressumHerausgeber:WTE Betriebsgesellschaft mbHHecklingenGaensefurth 7-1039444 Hecklingenphone: +49 3925 9269-0fax: +49 3925 282231web: http://www.wteb.deRedaktionsleitung: Martin KnustWTE-Life ist auf Envirostar (aus 100 %Altpapier) gedrucktÜberprüfung der versiegeltenFlächen durch Luftbildauswertungim Stadtgebiet SiegenSeit dem 01.01.1996 werden in Siegen getrennteGebühren für Schmutz- und Niederschlagswassererhoben.• Die Schmutzwassergebühr wird auf derGrundlage der bezogenen Trinkwassermengeabgerechnet.• Bemessungsgrundlage für die Niederschlagswassergebührist die an das Kanalnetzangeschlossene und versiegelte(bebaute und/oder befestigte) Fläche aufdem Grundstück.Diese Flächen wurden bisher einmal in einerBefragungsaktion im Jahr 1995 ermitteltund werden seitdem nur fortgeschrieben.Derzeit werden von der Stadt Siegen insgesamt6.071.878 m² befestigte einleitendeFlächen von privaten Grundstücken mitder Niederschlagswassergebühr veranlagt.Das kanalisierte Stadtgebiet hat sich seitdemvergrößert. Dieses Anwachsen derversiegelten und bebauten Flächen wurdein den vergangenen Jahren nicht immerder Stadt Siegen mitgeteilt. Daher ist einegrundlegende Überprüfung der Flächennotwendig geworden.Die WTE hat hierzu im ersten Schritt insgesamt26.172 Grundstücke ausgewertet,die auf Grund der vorliegenden Kanaldatenbankdie Möglichkeit haben, Niederschlagswasserin die öffentliche Kanalisationeinzuleiten.Aus der digitalisiertenGesamtflächeund unterZuhilfenahmevon Vergleichsprojektenwurdeeine Flächenmehrungermittelt.Basierend aufden von der StadtSiegen gewährtenAb schlägen fürGründächer von50 % und fürÖkopflaster von100 %, erhieltenwir für dasVergleichs projekteinen Einleitegradvon 58,1 %.Dieser wurde aufdie Stadt Siegenübertragen. Die damit ermittelte Flächebetrug 6.705.243 m². Die erreichte Flächenmehrungentspricht ca. 10,4 %.Auf Grund dieser Betrachtung erteilte dieStadt Siegen der WTEB den Auftrag zurkompletten Erfassung aller versiegeltenFlächen mittels Eigentümerbefragung aufder Grundlage von grafischen Daten.Um alle Flächen auf einen aktuellen Standzu bringen und ggf. bisher noch nicht erfassteFlächen einer Abrechnung zuzuführen,wurden ab 31.08.2012 Erfassungsbögenan alle Grundstückseigentümerverschickt.Eine erste Hochrechnung der einleitendenFlächen ergab für die Stadt Siegen eineMehrfläche von ca. 700.000 m², welche inetwa der Analyse aus dem ersten Schrittentsprach.Mit dieser Hochrechnung wurden durchdie Stadt Siegen die neuen Gebühren für2013 kalkuliert. Das Ergebnis war eineSenkung der Niederschlagswassergebührvon mehr als einem Euro auf 0,96 C.Da das Projekt noch nicht komplett abgeschlossenist, kann über die tatsächlicheFlächenmehrung noch keine Aussage getroffenwerden. Sobald alle Erkenntnissevorliegen, werden wir an dieser Stelle überdie konkreten Ergebnisse berichten.Die Luftbildfotografie ist die Basis zur Berechnung der befestigten Flächenauf Grundstücken.KontaktBeitrag: Überprüfung der versiegelten Flächen durch LuftbildauswertungKay Watermann • Gebühren- und BeitragsmanagementTelefon: +49 3925 9269-3 3 • E-Mail: watermann@wteb.de

shared non-random properties prevents the opposinginterpretation; that is, that species responses to climatechange are driven by species individual requirements ordispersal alone. The truth might lie between these twoextremes. Thus, rather than opposing the view of individualisticvs assemblage responses to climate change, a morefruitful discussion is one based on measurements of therelative importance of interdependencies in different assemblages.Such dependencies can be explored using networkanalysis.The critical question then is how to measure suchinterdependencies. Several studies have measured interactionsbetween pairs of species with well-known ecologies(Nilsson 1988, Johnson and Steiner 1997), while othershave measured interactions among species in simplecommunities (Colwell 1973). Only recently have researchersstarted measuring pairwise interactions for relativelylarger groups of species (Camacho et al. 2002, Dunne et al.2002a, Milo et al. 2002, Bascompte et al. 2003, Garlaschelliet al. 2003), but usually with a focus on a particular type ofbiotic interaction (e.g. predation, dispersal, pollination).Naturally, the sheer number and complexity of direct andindirect interactions linking species within ecosystems is sogreat that their complete documentation is beyond reach.Making progress in understanding the role of complexinteractions as drivers of species distributional dynamics,and their responses to climate change, requires theinvestigation of alternative approaches, such as the one weexplore in this contribution.MethodsThe proposed framework involves 1) building spatial cooccurrencenetworks from a species co-occurrence matrix;2) making inferences about network robustness; 3) modellingthe exposure of individual species to climate change;and 4) investigating the relationship between measurementsof network robustness and species exposure to climatechange. An application of the proposed framework isprovided using geographical distributions comprising allterrestrial vertebrates of Europe. The data are used forillustration of the framework, rather than testing it.Building spatial networks of co-occurrenceSpatial networks of co-occurrence were built in 4 steps. Inshort, the procedure consists in measuring the number ofsites where species co-occur (step 1), generating the cooccurrencenetwork based on the measured distributionaloverlap between species distributions (step 2), pruning thenetwork from spurious links using a null model of expecteddistributional overlap between pairs of species (step 3), anduse a known standard (the percolation threshold) foranalyzing and comparing network properties (step 4). Asynthetic description of this procedure is provided in Table1, where assumptions and shortcomings of each one of thesteps are summarized.Step 1 a pairwise BrayCurtis distance matrix wasconstructed to measure the degree of geographical cooccurrencein the distributions of pairs of species (Bray andCurtis 1957), but any distance metric could be used.Distances ranged from 0 to 100, with 100 representingcompletely non-overlapping distributions and 0 representingcompletely overlapping ones.Step 2 a spatial network of co-occurrence with speciestreated as nodes was built with software programmed byAR. Each link joining pairs of species was labelled with theBrayCurtis distance among them.Step 3 several connections between species may be dueto chance alone (Connor and Simberloff 1979). In order toremove these links from the network a null model wasgenerated. The general principle is that overlaps that areequal or lower from that expected by chance should bediscarded. Rather than generating the null model from arandomized experiment (Blick and Burns 2009, Kones et al.2009), we addressed the problem analytically. Consider agiven geographical space occupied by randomly locatednon-overlapping individuals, regardless of whether theypertain to the same species or not. Suppose we representthis environment by a two dimensional regular lattice of sizeANM. Then the probability P a of finding anindividual of species a in any randomly chosen site can becalculated as P a N a /A, where N a is the number of sitesoccupied by species a. In this same context one can calculatethe probability of finding individuals of species a and bsimultaneously,P a&b P a P bTable 1. Stepwise approach for building networks of interactions using large scale species distributions. A discussion of the majorassumptions and caveats with each step in the framework is provided.Step Approach Assumptions Caveats1 Build pair wise geographicaldissimilarity matrix2 Construct unweighted or weightednetwork of interactions ingeographical space3 Remove interactions that are notmore likely than expected bychance4 Prune network of interactions byidentifying the percolation pointThe degree of spatial overlap in species distributionsindicates degree to which species can potentiallyinteract.If assumption 1 is correct, then distances can beconverted in network interactions.Pairwise interactions not greater than expected bychance are not ecologically meaningful.At large geographical scales all species interactdirectly or indirectly with one another, thus forminga connected network.Species may overlap but do not interacteither directly or indirectly.The same as in 1.Interactions may be no greaterthan expected by chance and still bemeaningful.Procedure with untested properties inecological systems. Needs empiricalvalidation.899

of finding just one species,P aORb P a (1P b )(1P a )P b P a P b 2P a P band of finding neither species a or b in a randomly chosensiteP a&b (1P b )(1P a )1P a P b P a P bThen it follows thatP a&b P aORb P a&b 1Consider now a multinomial random variable X(a,b) withthree possible states S{(i) site contains both species a andb, (ii) site contains one of the species a or b, (iii) sitecontains neither of the species, neither a nor b}. So it isexpected to find in average B(i)AP a&b sites in state(i), B(ii)AP aORb sites in state (ii) and B(iii)AP a&b sites in state (iii); with a variance of Var(i)A P a&b (1P a&b ), Var(ii)AP aORb (1-P aORb ) andVar(iii)AP a&b (1-P a&b ) respectively.In order to identify links between species that aredifferent from that expected by chance, we retain linksbetween pairs of species whose number of co-ocurrences iseither above B(i)2(Var(i)) 1/2 (attractive overlap) orbelow B(i)2(Var(i)) 1/2 (repulsive overlap).Step 4 once the network has been pruned from nonsignificantlinks, further removal of links is done afteridentification of the network’s percolation threshold. Thepercolation threshold is a mathematical term related topercolation theory, which is the formation of long-rangeconnectivity in random systems (Stauffer and Aharony1992). The percolation threshold is the critical value of theoccupation probability, or more generally a critical surfacefor a group of parameters, such that infinite connectivity(percolation) first occurs. As such, it is a particularly usefulpoint at which to examine networks as it represents theminimal set of links underlying network connectivity andprovides a standard for comparing networks of different sizeand type. Below this threshold, a network is thought to loseits integrity and collapse into small clusters. In ourapplication, co-occurrence among species in the networkwas expected for connections representing BrayCurtisdistance just below the percolation threshold (Rozenfeldet al. 2008), standing for geographical overlapping above aminimal cut-off. The precise location of this threshold ismade with a standard methodology adapted for finitesystems (Stauffer and Aharony 1992), i.e. by calculatingthe average size BS * of the clusters excluding the largestone:ŽS 1 Xs 2 n s (1)N sBS maxas a function of the last distance value removedand identifying the critical distance with the one at whichBS * has a maximum. N is the total number of nodes notincluded in the largest cluster and n s is the number ofclusters containing s nodes.Making inferences about ecological networkrobustnessStarting with the working premise that co-occurrencenetworks provide a surrogate for potential interactionsamong species (but see summary of caveats in Table 1),three measures of robustness can be investigated (Table 2):species contributions to network robustness; species sensitivityto the loss of network nodes (i.e. species); and overallnetwork robustness or network resistance to species loss.Species contributions to network robustnessThe species contributions to network robustness are oftenexamined as a function of species degree k i ; that is, thenumber of species a given species interacts with. Theassumption is that the greater the degree of a species, thegreater its contribution to network robustness. In additionto k i , we also calculate a weighted measure of interactionintensity (Barrat et al. 2004), known as species strength(Bascompte et al. 2006). Species strength s i is a quantitativeextension of species degree, and can be defined as the sumof dependences d ij (or co-occurrence, see below) betweenpairs of species i and js i XNj1a ij d ij (2)where a ij determines whether species i and j are connected(a ij 1) or not (a ij 0). The loss of a species linked withseveral highly dependent species is considered to affectnetwork robustness more than a species with fewer linksTable 2. Measured network properties and their ecological interpretations.Indicator Measure DefinitionPairwise sensitivity to species loss Symmetry The degree to which the dependence of species A on species B isequal to the dependence of species B on the species A.Network robustness to species loss Degree distribution The frequency distribution of the individual species degree for theentire network.Strength distributionThe frequency distribution of the individual species strength (in) forSpecies contribution to networkrobustnessSpecies degreeSpecies strength (in)the entire network.The number of links that connect the focal species to the otherspecies. Assumes symmetrical interactions.A quantitative extension of species degree accounting for asymmetricalinteractions. It provides a weighted sum of the proportion of thegeographical distribution of B 1..n that overlaps with species A.Species sensitivity to network loss Species strength (out) A quantitative extension of species degree but accounts forasymmetrical interactions. It provides a weighted sum of theproportion of the geographical distribution of A that overlaps withB 1..n .900

with less dependent species. In practice, measures ofstrength and degree tend to be correlated (Barrat et al.2004, Bascompte et al. 2006), but degree assumes dependenciesbetween species to be symmetrical whereas themeasure of strength incorporates the more realistic idea ofasymmetry between species dependences.The critical issue for measuring strength is to quantifythe level of dependence between pairs of species (d ij ). Innetworks of co-occurrence, species strength may be calculatedby first quantifying the proportion of the geographicaldistribution of species A that overlaps with species B andvice versa. The underlying ideas are that 1) the proportionof the geographical distribution of A that overlaps with Bprovides a surrogate of interaction intensity of species Awith B; and 2) this proportion is asymmetrical, such that,for example, the geographical distribution of A may overlapwith B to a greater extent than B overlaps with A (Fig. 1).Quantitatively, the degree of overlapping between A and Bis defined as O(A,B)(aSb)/a as the proportion of a (A’sarea) that overlaps b (B’s area). The degree of symmetry ofthe link is then calculated asS in (A) Xn iO(B i ; A) (4)Species sensitivity to the loss of links in the networkThe previous measures of degree (k) and strength (S in )provide indices allowing the quantification of the robustnessof small sets of interacting species to the loss of highlyconnected species. A third measure, herein termed strengthout (s out ), measures the sensitivity of individual species tothe loss of nodes in the network. Strength out does notcontribute to measuring network robustness; it measureshow dependent a species might be, given the potentialinteractions with other species: a high s out implies that thetarget species is highly dependent on other species, whilelow s out implies the opposite. Strength out can be measuredas the weighted sum of the proportion of the geographicdistribution of species A that overlaps with B 1..nS out (A) Xn iO(A; B i ) (5)½O(A; B) O(B; A)½Sim(A; B)Max[O(A; B); O(B; A)]where Sim(A,B) can get values in the interval [0,1]. In oneextreme of the interval (Sim0), the link is completelysymmetric. In the other (Sim1), the link is completelyasymmetrical so that, for example, A is fully nested in B.It follows that if O(A,B) is understood as a measure ofinteraction intensity (either direct or indirect) betweenspecies A and B, then we can define a measure of strengthsummarising how strongly other species may potentiallyinteract with A, measured as the weighted sum of theproportion of the geographical distribution of B 1..n thatoverlaps with species A. Thereafter, this measure will betermed strength in (S in )(3)Network robustnessThe former measures are focused on the properties ofsummed pairs of interacting species. To assess the overallrobustness of networks we need to investigate the collectiveproperties of degree (k) and strength (s in ). Following Dunneet al. (2002b), network robustness can firstly be investigatedby examination of the frequency distribution of the speciesdegree k i . That is, the frequency distribution of the numberof species a given species interacts with. Formally, thedistribution P(k) gives the proportion of species in thenetwork having degree k. Typically P(k) follows anexponential or power law (scale-free) distributions. Scalefreedistributions depict networks in which most species arepoorly connected with one another whereas a few species arewell connected. In the ecological literature, such wellconnectedspecies are termed keystones, whereas in thenetwork literature they are termed hubs. Scale-free degreefrequency distributions are expected to be very robust torandom loss of species, because most species are poorlyconnected in the network thus being unlikely removed bychance. However, they are very sensitive to the chirurgicremoval of species with high k degree (Albert et al. 2000).In contrast, networks with exponential degree distributions,whereby a great proportion of species is highly connectedwith other species, are more sensitive to random removal ofspecies.Secondly, network robustness was investigated by examinationof the frequency distribution of the speciesstrength s i . That is, the frequency distribution of the sum ofdependencies between pairs of species (our measure of S in ).The distribution of P(s in ) is expected to generally have thesame properties as P(k) (Barrat et al. 2004).Figure 1. Graphical representation of symmetry in the geographicaldistribution between pairs of species: (a) species A dependsstrongly on species B, but species B does not depend strongly onspecies A; (b) species A and B depends moderately and equally onone another.Modelling exposure of individual species to climatechangeSpecies exposure to climate change was measured as dr i t future r i t baseline , where r is the distributional range ofspecies i at time t. In order to calculate d, individual species901

potential distributions were modelled with ensemble forecasting(Araújo and New 2007) based on four widely-usedbioclimatic envelope modelling techniques: 1) generalizedlinear models assuming a binomial error distribution(GLM, McCullagh and Nelder 1989); 2) mahalanobisdistance (MD, Farber and Kadmon 2003); 3) maximumentropy (MaxEnt, Phillips and Dudík 2008); and 4) geneticalgorithm for rule prediction (GARP, Stockwell and Peters1999). Maximum entropy and GARP were parameterisedusing the default options in MaxEnt and Open ModellerGARP. Internal evaluation of the models was performedwith a data split procedure, whereby 70% of the occurrencedata was randomly split and used for calibration of themodels and the remaining 30% were used for crossevaluationof the models; this procedure was repeated 50times thus generating a 50-fold cross-validation of modelresults. For species with range size B10 cells, rather thanperforming a 50-fold cross validation, each of the n cellswith presence records were deleted once and the analyseswere repeated n times. Model accuracy was measured usingthe average True Skill Statistic (Allouche et al. 2006). Thisanalysis was performed to check if grossly implausibleprojections were being made (i.e. TSSB0.3). No specieswas removed based on this criterion and because measuresof accuracy on non-independent data do not provide areliable benchmark for evaluation of projections of speciesdistributional changes under climate change (Araújo et al.2005a), we instead used an unweighted consensus of thefour modelling techniques. Projections agreeing at least halfof the times were retained. With such approach potentialerrors associated with individual model projections are thussmoothed out in the consensus (Araújo et al. 2005b,Marmion et al. 2009). Nevertheless, final projections forcurrent and future periods were obtained with all knownrecords of occurrence, because bioclimate envelope modelshave been shown to be extremely sensitive to incompletenessof data in the calibration set (Araújo et al. 2009).Models were fitted with the BIOENSEMBLES software(Diniz-Filho et al. 2009).Assessing co-variation between robustness andexposure to climate changeThe two measures of network robustness can be comparedagainst measures of exposure of species to climate change.Such comparison allows addressing the question of whetherspecies with disproportionate contribution to networkrobustness, or species that are particularly sensitive to theloss of links in the network, are less or more exposed toclimate change than species with minor contributions tonetwork robustness or with small dependence on networkstructure.The case studyThe species distributions used to illustrate the frameworkincluded records of presence and absence for 58 amphibians,91 reptiles (Gasc et al. 1997), 233 breeding birds(Hagemeijer and Blair 1997), and 186 mammals (Mitchell-Jones et al. 1999). Data represents the majority of terrestrialvertebrates of Europe (only mammals and birds with lifecycleshighly dependent on water bodies were removed).The geographic grid used is based on that of the AtlasFlorae Europaeae (Lahti and Lampinen 1999), with cellboundaries typically following the 50 km lines of theUniversal Transverse Mercator (UTM) grid, except near theborder of the six-degree UTM zones and at coasts. Datawere converted to the AFE grid system by identifyingunique (although sometimes approximate) correspondencebetween cells in these grids. The mapped area (2089 gridcells) excludes most of the eastern European countries(except for the Baltic States) because of low recordingefforts in these areas (Williams et al. 2000).The bioclimate envelope models were constructed withthree variables (mean temperature of the coldest month(8C), mean temperature of the warmest month (8C), andmean annual summed precipitation (mm)) thought toreflect two properties of the climate temperature andwater that have known roles in imposing constraints uponspecies distributions as a result of widely shared physiologicallimitations (Hawkins et al. 2003, Whittaker et al.2007). Variables were also checked for collinearity usingprincipal components analysis (PCA). The mean temperatureof the warmest month (highest loading in PCA 1) wasnearly orthogonal with mean summed precipitation (highestloading in PCA 2). The mean temperature of the coldestmonth was characterised with a vector 45 degrees from PCA1 and 2.Climate parameters were derived from an updatedversion of climate data provided by New et al. (2000).The updated data provides monthly values for the years19012000 in a 10? grid resolution (Schroter et al. 2005).Average monthly temperature and precipitation in grid cellscovering the mapped area of Europe were used to calculatemean values of three different climate parameters for theperiod 19611991 (referred to as ‘baseline data’). Futureprojections for 20202050 (referred to as the 2050scenario) were based on climate model outputs fromHadCM3 and made available through the IntergovernmentalPanel on Climate Change (IPCC) Data DistributionCentre (Bipcc-ddc.cru.uea.ac.uk). The modelledclimate anomalies were scaled based on the A1FI scenario(Nakicenovic and Swart 2000).ResultsNetwork structureCo-occurrence networks in the four groups of terrestrialvertebrates reveal different biogeographical structures(Fig. 2). Amphibians (median range size79) have a cooccurrencenetwork hub (i.e. with species highly connectedto other species) in the Iberian Peninsula and anothercentred in central Europe. Reptiles (median range size86)have two Mediterranean hubs (Iberian and Balkan peninsulas)and third centred in central Europe. Birds andmammals (median range sizes389 and 187 respectively),have a slightly more diffuse network structure with a mainhub in central Europe. Nevertheless, for birds, two smallerhubs are detected in the SW Mediterranean (including partsof the Iberian Peninsula and islands west of Italy) and902

Figure 2. Spatial networks of co-occurrence among the European amphibians, reptiles, birds and mammals after removal of nonsignificantlinks (step 3 of the methods), and setting a threshold just below the percolation point (step 4 of the methods, Supplementarymaterial Fig. A1). Circles represent the centroids of species distributions in a lat long coordinate system, and their sizes are proportional tothe species degree (i.e. the number of links every species makes with other species). Lines represent the links between species. From top leftto bottom right: amphibians; reptiles; birds; and mammals.Scandinavia. Mammals have a more diffuse central Europeannetwork structure extending to parts of Scandinaviawith a small hub recorded in the Iberian Peninsula. Noticethat Fig. 2 plots nodes (species) and links (level of cooccurrencejust below the percolation threshold, Supplementarymaterial Fig. A1), with nodes being located at thecentre of each species range. Because species with restrictedranges are mainly in the south and to a smaller extent in thenorth, and species with wide ranges occur throughout mostof Europe, central European hubs mainly represent thecentroids of species that are widespread across Europe,whereas southern or northern hubs represent faunas nestedin smaller regions.Network robustnessEven though the spatial distribution of nodes and linksvaries between the four taxonomic groups, the empiricaldegree distribution P(k) (for definitions see Table 2)displays a power-law-like distribution that is typical ofmany complex networks (Fig. 3). Departures to a perfectpower law distribution do exist in our results, however. Thisis particularly true for birds and, to smaller extent,mammals since both taxa have more species with highdegree k i than expected. In other words, they have morespecies well connected in the network than expected from atypical power law distribution.The frequency distribution of species strength P(s in ) (fordefinitions see Table 2) also reveals a power-law-likedistribution for amphibians, reptiles and mammals, withthe distribution of strength (in) for birds displaying no clearstructure (Fig. 3). Inspection of the frequency distributionof the pairwise symmetries of co-occurrence between species(the measure used to calculate measures of strength, Table2), further reveals the existence of a left-skewed distributionfor most pairwise combinations of species (Fig. 4). In otherwords, most pairwise interactions (of co-occurrence) betweenspecies are asymmetrical.Species sensitivity to network lossStrength (out) is best characterised by a bell-shapedlikedistribution (Fig. 4). The distribution of s out foramphibians is slightly skewed to the left, meaning that agreat proportion of species are expected to be sensitiveto the loss of nodes in the network. The tendency forleft (negative) skews is recorded also for birds and mammalsbut the degree of skewness is generally low for all taxa(Fig. 4).Network properties and climate changeThe two measures of species’ contribution to networkrobustness, degree (k) and strength (s in ), display similar903

Figure 3. Distribution of degree (left panel), as defined by the probability of one species interacting with k species, and strength (in) (rightpanel) values, as defined by the sum of dependencies between the set of species B 1,n with species A. In the panels: a) stands for amphibians;b) for reptiles; c) for birds; and d) for mammals. In random networks the degree and strength (in) distributions follows a Poissondistribution (or exponential if the number of nodes keeps growing), but in complex networks nodes tend to have few interactions and fewnodes are more connected than expected by chance. This heterogeneous distribution of degree and strength (in) is often described by apower law function. In a loglog plot, such as that above, this relationship is given by a linear slope for the entire range of degree andstrength (in) values. The distribution of degree and strength (in) values was processed using a standard rebinning procedure described byAdami and Chu (2002). The distributions of strength (in) for birds does not follow a power-law like distribution, thus we show the resultswithout log-scaling the x axis.properties when compared against species’ exposure to 21stcentury climate change (Fig. 5). Essentially, amphibians,birds and mammals display a triangular relationship withover-dispersion of range-change values (d) for species withlow contribution to overall network robustness (low k ands in ). Species with high k degree and s in strength tend tocovary near the horizontal line of no-range-change, whichmeans that as species become more important to overallnetwork robustness they are also projected to be lessimpacted by climate change. This relationship is particularlymarked for birds and mammals and for themeasure of strength (s in ). For reptiles the pattern is slightlydifferent with a clear tendency for species gainingrange as a consequence of climate change being also thespecies that contribute more to robustness of the networks(Fig. 5).When examining the measure of species sensitivity tonetwork loss (s out ) against projected climate change impactson species, no clear pattern emerges (Fig. 5). If anything,there is a tendency for species with intermediate strengths(s out ) to over-disperse towards intermediate values, but thismay well be a consequence of the quasi-random distributionof strength (s out ) values (Fig. 4). Nevertheless there seems tobe a tendency for amphibian and reptile species with highdependence on network structure (high s out ) to be generallypositively affected by climate change (a few exceptions foramphibians). In contrast, the bird and mammal species thatgaining or losing more with climate change tend to havelow dependences on network structure.DiscussionThis study provides an approximation to using networkanalysis for assessments of climate change impacts onspecies. If one accepts that broad-scale interactions arereflected in patterns of overlapping distributions betweenspecies, then results invite the interpretation that 1) mostpairs of interacting species had asymmetrical interdependencies,2) most species displayed weak links thus atendency for individualistic behaviour, and 3) networksdescribing the geographic pattern of co-occurrence amongEuropean vertebrate species displayed general propertiesshared by other complex networks, namely a power-law (i.e.scale free) distribution of degree (k) and strength (s in ), withthe notable exception of networks for birds and mammals(the latter departing from scale free distribution only for k)(see also Azaele et al. 2010). Networks with scale-freedistributions are particularly robust to random losses ofnodes (Albert et al. 2000, Kaiser-Bunbury et al. 2010),while being sensitive to losses of well-connected hubs in thenetwork (Albert et al. 2000). Having characterised thetypology of the networks and identified the hubs that gluethem together the question that follows is whether withclimate change, such hubs would be affected. Here, speciesmore exposed to climate change tended to be poorlyconnected to other species within the network (low k ands in ), while the more connected species tended to be lessexposed to climate change. Low connectance for highlyexposed species and high connectance for species with lowexposure to climate change is good news. Poor connectance,904

Figure 4. Frequency distribution of asymmetry values betweenpairs of species, and strength (out), as defined by the sum ofdependencies between species A and B 1,n. . In each panel from topleft to bottom right: amphibians, reptiles, birds and mammals.or low distributional overlap, makes the networks speciesbelong to more robust to climate change because species areunlikely to be strongly associated with the distribution ofother species in the network. It also indicates that whileprojections assuming individualistic responses of species toclimate change are warranted for most cases, the generalproperties of interaction networks must be examined inorder to anticipate which species would exert greaterinfluence on the others and which would be moredependent on linkages with other species in the network.In other words, while most species display low connectanceor overlap with other species, some species do have a highdegree of connectance, thus supporting the hypothesis thatstrong interdependencies exist between species (but see thecautionary note below). Our framework provides one wayto begin exploring the consequences of climate change onFigure 5. Species degree (k), strength (sin) (degree to which focal species are needed by other species), and strength (sout) (degree to which focal species needs other networked species), plotted againstthe projected change (d) in the potential distribution of species under climate change. When d values are 0 the species are projected to expand their ranges under climate change; when d values areB0 contractions are projected. In each panel from top left to bottom right: amphibians, reptiles, birds and mammals.905

complex networks of co-occurring species. The criticalquestion is whether co-occurrence networks provide inferencesabout functional properties of networks that would beuseful for biodiversity assessments of climate changeimpacts.The proposed framework rests on several assumptionsthat are largely untested and obviously are debatable; forexample, that the strength of the interactions between twospecies can be inferred from the number of sites where bothspecies coexist. Although co-occurrence networks are blindto the specific types of interactions involved, they docapture the essential fact that in order to interact, speciesmust typically coexist. One exception is competitiveexclusion, whereby spatial non-overlap is the outcomeof strong negative interactions. Spatial networks of cooccurrencemay thus be interpreted as summarizingpotential interactions between species rather than actualones. All other things being equal, one would expect regionswith highly spatially dependent faunas to indicate theexistence of functional interactions between species more sothan faunas with lower spatial interdependences.To avoid amalgamating likely and the unlikely interactions,as inferred from patterns of co-occurrence amongspecies, we proposed a methodology based on 1) removal oflinks that may arise by chance alone, and 2) further removalof links preventing the emergence of clear network structurethrough inferences based on percolation theory (Table 1).The proposed methodology rests on the assumption that allspecies are either directly or indirectly connected inecological systems and that spatial co-occurrence amongspecies is, at partly, a consequence of functional interactions.Obviously, this is not always the case and speciesmight co-occur due to shared physiological limitations orshared historical contingencies. For example, interactionhubs among amphibians and reptiles in the Mediterraneanare likely to reflect mechanisms of parapatric speciation andlong-term population persistence in glacial refugia that werenot followed by inter-glacial expansion, possibly due tophilopatry and limited dispersal (Gasc et al. 1997, Holman1998, Araújo et al. 2008). The use of co-occurrencenetworks for practical assessments of biodiversity andclimate change would thus require that an additional step3) is implemented to screen for the ecological realism of theinferred interactions. Such screening would involve basicconsiderations of scale (e.g. what is the minimum spatialresolution required to infer interactions from co-occurrencepatterns for particular groups of organisms?), as well asconsideration of relevant aspects of the auto-ecology of thespecies (e.g. what organisms are likely to interact with oneanother?).Previous attempts to factor biotic interactions intoassessments of climate change impacts on species distributionsare difficult to generalize as they typically involved alimited number of species in experimentally controlledenvironments (Davis et al. 1998, Suttle et al. 2007,Harmon et al. 2009), or use modelling approaches thatrequire information that is generally unavailable for mostspecies (Araújo and Luoto 2007), or tools that areconceptually incapable of handling interactions wherethey operate, i.e. in geographical space (see for discussionBaselga and Araújo 2009, 2010).The proposed framework is a first attempt to handle acomplex problem using the theoretical framework andanalytical toolboxes of network analysis and bioclimaticmodelling. We hope our contribution will motivate othersto test the predictions and assumptions of the frameworkherein proposed, particularly the proposed inferences aboutnetwork robustness and species sensitivity to loss of networklinks using co-occurrence networks. It is clear that not allpotential interactions are real, and in some cases it may bemore useful to explore bipartite networks that restrictanalysis to co-occurrence of preselected taxa based onknown functional relationships (Bascompte et al. 2006,Berg et al. 2009). But the important question is whether thegeneral patterns emerging from coarse biogeographicalanalysis of networks reflects underlying patterns in nature.In other words, if the general structure of hubs and links inthe network is maintained when actual interactions, ratherthan potential ones, are considered. A recent paper, showedthat patterns of species co-occurrence at coarse geographicalcontinental scales exhibit strong signals of interspecificinteractions (Gotelli et al. 2010). The authors revealed thatcommunity-wide patterns of spatial segregation amongDanish breeding birds could not be attributed to the patchydistribution of habitat, or to gross differences in habitatutilization among ecologically similar species. They proposedthat conspecific attraction in concert with interspecificterritoriality may result in spatially segregateddistributions of ecologically similar species at larger spatialscales when habitat patch size is limited. Finally, they alsoshowed that the effects of species interactions on communityassembly were pervasive and could be discerned at grainsizes up to four orders of magnitude larger than those ofindividual territories. More examples support the view thatspatial co-occurrence allows inferences to be about interactionsamong species. For example, Azeaele et al. (2010)demonstrated the usefulness of examining co-occurrencenetworks to uncover functional relationships between plantsin forest ecosystems. Another study empirically investigatedthe extent to which trophic relationships between speciescould be uncovered through the analysis of bipartitepredator-prey co-occurrence networks (Bell et al. 2010).The results of Bell et al. (2010) are encouraging in that thefeeding behaviour of the studied polyphagous beetles andspiders could be inferred with their particular implementationof co-occurrence networks. More studies investigatingthe extent to which co-occurrence networks can help inferfunctional interactions among species are obviously needed(see also Heikkinen et al. 2007, Meier et al. 2010), but ourprediction is that if errors arising from the simplifiedassumptions of co-occurrence networks are randomlydistributed across taxa and regions, then functional networksbased on verifiable interactions between specieswould not change the overall patterns emerging from cooccurrencenetworks. This should be particularly true atcoarse resolutions where ‘ecological noise’ is reduced(Lawton 1999).ConclusionThe challenges posed by a rapidly changing climate and itsconsequences on biodiversity, requires a concerted effort of906

scientists in different disciplines. In this paper we haveadvanced an idea that builds on the interaction betweennetwork theory and bioclimatic modelling to generate asimple framework that can be use as a first approximationto tackle this challenge. We believe that network theoryprovides a suitable and powerful framework to address thecomplexities of climate change impacts on biodiversity,which in concert with simple co-occurrence matrices (thefundamental unit of analysis in community ecology andbiogeography, Gotelli 2000) can pave the way to incorporatespecies interactions into the analysis of species responsesto climate change and further our understanding of theeffects of climate change on biodiversity.Acknowledgements This study is part of a broader researchprogram sponsored by the CSIC-PUC International Laboratoryfor Global Change (LINC-Global); MBA is also funded by ECFP6 ECOCHANGE project (036866-GOCE) and by the SpanishMinistry of Science and Innovation (CGL2008-01198-E/BOS);CR thanks the Danish National Research Foundation for itssupport of the Center for Macroecology, Evolution and Climate.PAM acknowledges support from FONDECYT-FONDAP 1501-0001, ICM P05-002 and CONICYT PFB-23.ReferencesAdami, C. and Chu, J. 2002. 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