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Bayesian networks elucidate interactions between re and other drivers of terrestrial fauna distributions BRONWYN A. HRADSKY , 1,5,  TRENT D. PENMAN, 1 DAN ABABEI, 1,2 ANCA HANEA, 3 EUAN G. RITCHIE, 4 ALAN YORK, 1 AND JULIAN DI STEFANO 1 1 School of Ecosystem and Forest Sciences, University of Melbourne, 4 Water Street, Creswick, Victoria 3363 Australia 2 Light Twist Software, 115 Falconer Street, Fitzroy North, Victoria 3068 Australia 3 Centre of Excellence for Biosecurity Risk Analysis, School of BioSciences, University of Melbourne, Parkville, Victoria 3010 Australia 4 Centre for Integrative Ecology, School of Life and Environmental Sciences, Deakin University, 221 Burwood Highway, Burwood, Victoria 3125 Australia Citation: Hradsky, B. A., T. D. Penman, D. Ababei, A. Hanea, E. G. Ritchie, A. York, and J. Di Stefano. 2017. Bayesian networks elucidate interactions between re and other drivers of terrestrial fauna distributions. Ecosphere 8(8):e01926. 10.1002/ecs2.1926 Abstract. Fire is a major driver of community composition and habitat structure and is extensively used as an ecological management tool in ammable landscapes. Interactions between re and other processes that affect animal distributions, however, cause variation in faunal responses to re and limit our ability to identify appropriate re management regimes for biodiversity conservation. Bayesian networks (BNs) have not previously been used to examine terrestrial faunal distributions in relation to re, but offer an alterna- tive statistical framework for modeling complex environmental relationships as they explicitly capture interactions between predictor variables. We developed a conceptual model of the interactions between drivers of faunal distributions in re-affected landscapes, and then used a non-parametric BN modeling approach to describe and quantify these relationships for a suite of terrestrial native mammal species. We also tested whether BNs could be used to predict these speciesdistributions using only remote-sensed or mapped variables. Data were collected at 113 sites across 47,000 ha of continuous eucalypt forest in the Otway Ranges, southeastern Australia; time-since-re (TSF) ranged from six months to 74 yr. Habitat com- plexity increased with TSF and forest wetness. Critical-weight-range (355500 g) marsupials and rodents were generally more likely to occur at long unburnt sites with high habitat complexity, and in wetter forest types. In contrast, large grazers and browsers preferred less complex habitats and younger or drier forest. Species occurrences were more strongly affected by habitat complexity than TSF, coarse woody debris cover, or invasive predator (Vulpes vulpes or Felis catus) occurrence. Bayesian network models effectively discriminated between the presence and absence of most native mammal species, even when only pro- vided with data on remote-sensed or mapped variables (i.e., without eld-assessed data such as habitat complexity). Non-parametric BNs are an effective technique for explicitly modeling the complex and con- text-dependent inuence of re history on faunal distributions, and may reduce the need to collect exten- sive eld data on habitat structure and other proximate drivers. Key words: Australia; critical-weight-range mammal; disturbance; Felis catus; re management; forest; habitat complexity; non-parametric Bayesian network; predatorprey interaction; species distribution (niche) model; Vulpes vulpes. Received 11 July 2017; accepted 25 July 2017. Corresponding Editor: Debra P. C. Peters. Copyright: © 2017 Hradsky et al. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. 5 Present address: Quantitative and Applied Ecology Group, School of BioSciences, University of Melbourne, Parkville, Victoria 3010 Australia.  E-mail: [email protected] www.esajournals.org 1 August 2017 Volume 8(8) Article e01926

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Page 1: Bayesian networks elucidate interactions between fire … · Bayesian networks elucidate interactions between fire and other drivers of terrestrial fauna distributions ... regression

Bayesian networks elucidate interactions between fire and otherdrivers of terrestrial fauna distributions

BRONWYN A. HRADSKY ,1,5,� TRENT D. PENMAN,1 DAN ABABEI,1,2 ANCA HANEA,3 EUAN G. RITCHIE,4

ALAN YORK,1 AND JULIAN DI STEFANO1

1School of Ecosystem and Forest Sciences, University of Melbourne, 4 Water Street, Creswick, Victoria 3363 Australia2Light Twist Software, 115 Falconer Street, Fitzroy North, Victoria 3068 Australia

3Centre of Excellence for Biosecurity Risk Analysis, School of BioSciences, University of Melbourne, Parkville, Victoria 3010 Australia4Centre for Integrative Ecology, School of Life and Environmental Sciences, Deakin University, 221 Burwood Highway,

Burwood, Victoria 3125 Australia

Citation: Hradsky, B. A., T. D. Penman, D. Ababei, A. Hanea, E. G. Ritchie, A. York, and J. Di Stefano. 2017. Bayesiannetworks elucidate interactions between fire and other drivers of terrestrial fauna distributions. Ecosphere 8(8):e01926.10.1002/ecs2.1926

Abstract. Fire is a major driver of community composition and habitat structure and is extensively usedas an ecological management tool in flammable landscapes. Interactions between fire and other processesthat affect animal distributions, however, cause variation in faunal responses to fire and limit our ability toidentify appropriate fire management regimes for biodiversity conservation. Bayesian networks (BNs) havenot previously been used to examine terrestrial faunal distributions in relation to fire, but offer an alterna-tive statistical framework for modeling complex environmental relationships as they explicitly captureinteractions between predictor variables. We developed a conceptual model of the interactions betweendrivers of faunal distributions in fire-affected landscapes, and then used a non-parametric BN modelingapproach to describe and quantify these relationships for a suite of terrestrial native mammal species. Wealso tested whether BNs could be used to predict these species’ distributions using only remote-sensed ormapped variables. Data were collected at 113 sites across 47,000 ha of continuous eucalypt forest in theOtway Ranges, southeastern Australia; time-since-fire (TSF) ranged from six months to 74 yr. Habitat com-plexity increased with TSF and forest wetness. Critical-weight-range (35–5500 g) marsupials and rodentswere generally more likely to occur at long unburnt sites with high habitat complexity, and in wetter foresttypes. In contrast, large grazers and browsers preferred less complex habitats and younger or drier forest.Species occurrences were more strongly affected by habitat complexity than TSF, coarse woody debriscover, or invasive predator (Vulpes vulpes or Felis catus) occurrence. Bayesian network models effectivelydiscriminated between the presence and absence of most native mammal species, even when only pro-vided with data on remote-sensed or mapped variables (i.e., without field-assessed data such as habitatcomplexity). Non-parametric BNs are an effective technique for explicitly modeling the complex and con-text-dependent influence of fire history on faunal distributions, and may reduce the need to collect exten-sive field data on habitat structure and other proximate drivers.

Key words: Australia; critical-weight-range mammal; disturbance; Felis catus; fire management; forest; habitatcomplexity; non-parametric Bayesian network; predator–prey interaction; species distribution (niche) model; Vulpesvulpes.

Received 11 July 2017; accepted 25 July 2017. Corresponding Editor: Debra P. C. Peters.Copyright: © 2017 Hradsky et al. This is an open access article under the terms of the Creative Commons AttributionLicense, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.5 Present address: Quantitative and Applied Ecology Group, School of BioSciences, University of Melbourne, Parkville,Victoria 3010 Australia.� E-mail: [email protected]

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INTRODUCTION

Fire is a major driver of biome distribution andcommunity composition worldwide (Bond andKeeley 2005, Pastro et al. 2014) and is extensivelyused as an ecological management tool in flam-mable landscapes (Bowman et al. 2009, Penmanet al. 2011). Fire management objectives for bio-diversity conservation are commonly derivedfrom floral vital attributes; for example, manage-ment guidelines often include tolerable fire inter-vals that are based on the time-to-maturation orreproductive mechanisms of key plant species(Burrows 2008, Van Wilgen et al. 2011). Fauna,however, may require very different distribu-tions of post-fire age classes to flora (Di Stefanoet al. 2013), and their responses to fire often dif-fer between fire events and locations (Converseet al. 2006, Nimmo et al. 2014). Our ability topredict how fauna will respond to fire and sopromote animal diversity through fire manage-ment remains weak, partly because the interac-tions between fire and other drivers of speciesdistributions are poorly understood (Driscollet al. 2010, Spies et al. 2012).

Faunal responses to fire (positive and negative)are primarily driven by the effects of fire on habi-tat resources such as food and shelter, ratherthan direct mortality (Banks et al. 2011, Morriset al. 2011). Loss of vegetation cover after fire, forexample, can increase the vulnerability of smalland medium-sized mammals to predation,reduce prey abundance or survival, and attractpredators to recently burnt areas (Ogen-Odoiand Dilworth 1984, Barnard 1987, Morris et al.2011, Leahy et al. 2015, Hradsky et al. 2017).Large grazers may also be attracted to recentlyburnt habitats by a flush of palatable grasses andforbs (Gureja and Owen-Smith 2002, Kutt andWoinarski 2007). Spatial and temporal variationsin faunal responses to fire can arise, therefore,when post-fire habitats and processes developfrom different baselines or at different ratesacross the landscape or between fire events(Monamy and Fox 2000, Smucker et al. 2005).Our conceptual model (Fig. 1) summarizes thepotentially complex direct and indirect interac-tions between fire, habitat suitability, predators,vegetation communities, and environmental con-ditions that may influence faunal distributions infire-affected landscapes.

Such interactions are likely to be pervasive,and models that use habitat-related variables(such as habitat complexity or vegetation struc-ture) often provide better predictions of faunaloccurrence, abundance, or population growthrates than models that use fire-related variables(Di Stefano et al. 2011, Nimmo et al. 2014, Swanet al. 2015, Varner et al. 2015, Santos et al. 2016).Nonetheless, time-since-fire (TSF) and otherremote-sensed or mapped predictors that arerelatively simple to measure are more suitablemetrics for ecological fire management objectivesthan more proximate predictors such as habitatstructure. It is not logistically feasible, for exam-ple, to collect fine-scale vegetation structure dataacross large landscapes when interpolating spe-cies distributions; nor are such data availablewhen extrapolating future changes in speciesdistributions in response to proposed manage-ment or climate change scenarios. Consequently,there is a need for models that quantify therelationships between fauna populations, proxi-mate predictors, and variables that can beremotely sensed or mapped across fire-affectedlandscapes.Such relationships are difficult to capture in

regression-based species distribution models thatmust avoid collinear predictors, such as general-ized linear models (Elith and Leathwick 2009). Insome cases, researchers have used a series ofregression models to examine the relationshipsbetween interacting predictors such as TSF, habi-tat complexity, and vegetation type in a stepwisefashion (Sitters et al. 2014a); in others, variablesare so confounded that they preclude formalanalysis (Lindenmayer et al. 2008). For example,biotic interactions are usually excluded from spe-cies distribution models because predator, com-petitor, or mutualist data are confounded withenvironmental parameters (but see Ritchie et al.2008, Elith and Leathwick 2009). Over-fitting isanother potential problem that limits the numberof predictors that can be examined with manyecological data sets (Harrell et al. 1996).Bayesian networks (BNs) provide an alterna-

tive statistical framework for addressing thesechallenges. Bayesian networks explicitly includeinteractions between variables, and so are suit-able for modeling complex environmental sys-tems (McCann et al. 2006, Aguilera et al. 2011).There is a growing interest in the use of BNs to

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model species distributions and compare alterna-tive management options (Marcot et al. 2001,Smith et al. 2007, Johnson et al. 2010, Douglasand Newton 2014). In relation to fire and fauna,BNs have recently been used to investigatewildfire scenarios such as salmonid responses toclimate change (Roberts et al. 2013, Falke et al.2015), and the potential ecological risks to awatershed (Ayre and Landis 2012). To ourknowledge, however, BNs have not previouslybeen used to model terrestrial faunal distribu-tions in fire-affected landscapes.In this study, we used a BN modeling

approach to investigate the drivers of nativemammal distributions in a heterogeneous, fire-affected landscape. This approach enabled us tosimultaneously quantify the interdependenciesof key drivers depicted in our conceptual model(Fig. 1). Our secondary objective was to examinethe potential relevance of these models for con-servation management, by reducing the need forintensive collection of fine-scale data when pre-dicting fauna distributions at a landscape scale.

METHODS

Study areaWe collected data on habitat structure and

native mammal and invasive predator occur-rence across 47,000 ha of continuous eucalyptforest in the Otway Ranges, southeastern Aus-tralia. The region has a temperate climate, withcool wet winters and dry warm summers. Thereis an elevation and rainfall gradient across theregion, from the relatively flat, dry northeast(150–250 m a.s.l; 800–1000 mm average annual

Fig. 1. Factors that influence fauna distributions infire-affected landscapes. Fire can directly kill individ-ual animals [1, 2], but faunal occurrence and abun-dance in fire-affected landscapes is more oftenstrongly associated with the availability of key habitatresources such as food, den sites, water, and densevegetation cover [3–10]. These habitat resources are, inturn, influenced by the interactive effects of fire [8, 9,11–14], environmental conditions such as rainfall andtopographic position [7, 11], and vegetation type orcommunity [8, 9, 12, 15]. By altering a prey species’vulnerability to predators, habitat structure can affectpredator–prey interactions [16, 17]. Predation ratesmay also change if predators are attracted to or avoidrecently burnt areas [18–21] or if fire affects the avail-ability of alternative prey species [22, 23]. The com-bined effects of these numeric and functionalpredation responses can impact faunal survival ormortality rates in burnt landscapes [1, 16, 24]. Bothpredators [20, 25] and prey [6, 8, 26] often also use dif-ferent vegetation communities selectively, which mayaffect their interactions. Fire severity, frequency, andextent are influenced by environmental conditionssuch as rainfall, geology, and topographic position[27–29], as well as the type and age of the vegetationcommunity [27, 28, 30]. Finally, the vegetation commu-nity is a product of environmental conditions such aselevation, temperature, and annual rainfall [31], aswell as long-term fire regimes [32]. References are asfollows: 1, Conner et al. (2011); 2, Cross et al. (2015); 3,Clark et al. (2014); 4, Gureja and Owen-Smith (2002);5, Letnic et al. (2005); 6, Nimmo et al. (2014); 7, Plavsic

(2014); 8, Swan et al. (2015); 9, Sitters et al. (2014a); 10,Varner et al. (2015); 11, Banks et al. (2011); 12, Haslemet al. (2011); 13, Smucker et al. (2005); 14, Aponte et al.(2014); 15, Keeley et al. (2005); 16, Leahy et al. (2015);17, McGregor et al. (2015); 18, Barnard (1987); 19, Ebyet al. (2013); 20, McGregor et al. (2014); 21, Ogen-Odoiand Dilworth (1984); 22, Green and Sanecki (2006); 23,Dawson et al. (2007); 24, Sokos et al. (2016); 25, Bondet al. (2009); 26, Kelly et al. (2011); 27, Bradstock et al.(2010); 28, Collins et al. (2013); 29, Smit et al. (2013);30, Banks et al. (2011); 31, Begon et al. (1996); 32, Bondand Keeley (2005).

(Fig. 1. Continued)

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rainfall) to the wetter, steeper southwest (400–550 m a.s.l; 1300–1600 mm average annual rain-fall). The region encompasses four main foresttypes: tall mixed forest, foothills forest, forby for-est, and wet forest (Fig. 2). These represent broadgroupings of vegetation with similar ecologicalcharacteristics and fire responses (Cheal 2010)and are ranked in order from the open, dry “tallmixed” forest that occurs at low-elevation loca-tions, to the tall, dense “wet” forest that occurs athigh-elevation, high-rainfall locations; detaileddescriptions are provided in Appendix S1:Table S1. The forests were extensively burnt bywildfires in 1939 and 1983, and numerous smal-ler planned burns have subsequently been con-ducted across the region, particularly in the lastdecade.

Study designWe used a space-for-time approach, assessing

native mammal and invasive predator occurrence

and habitat variables at 113 sites along a 74-yrpost-fire chronosequence. Sites were spatiallynested within 23 100-ha circular units (mosaics;Fig. 2). We located three to six (generally five)sites in each mosaic using a stratified randomapproach to ensure that sites were at least 100 mapart, more than 50 m from roads and the bound-aries of neighboring vegetation types and fire ageclasses, and that different vegetation types andfire age classes were adequately represented. Ulti-mately, sites within mosaics were 103–955 mapart and mosaics were separated by ≥2.7 km.Details of the site selection procedure are pro-vided in Sitters et al. (2014b), but note that ourstudy did not include their heathland sites. Sur-veys were conducted between September andNovember 2012.Native mammal distributions.—We used digital

motion-sensing cameras (Reconyx HyperfireHC500; www.reconyx.com) to survey native ter-restrial mammals. These cameras capture images

Fig. 2. Locations of 113 study sites, Otway Ranges, southeastern Australia. Sites were distributed within 23sampling units (mosaics). Shading indicates the four major forest types.

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of passing animals using a passive infraredmotion detector and infrared flash array. At eachsite, we fastened one camera 30 cm up a tree andfaced it toward a bait station 1.6 m away. Cam-eras were set to maximum sensitivity, and pro-grammed to record images continuously whilemovement was detected, with five photographsper trigger event. The bait station comprised fivetea-strainers (each containing a mix of peanutbutter, golden syrup, oats, and pistachio essence)and was tied to a picket approximately 30 cmabove the ground. We clipped understory vege-tation around the bait station to ensure that ani-mals would be clearly visible. Cameras weredeployed for 18 full days at each site, and tworesearchers with similar levels of experienceidentified fauna from the photographs. Animalswere identified to species level where possible,but Antechinus agilis and Antechinus swainsoniicould not reliably be distinguished and so thesespecies were grouped as Antechinus spp. Specieswere considered to occur (be present) at a site ifthey were recorded at least once during the sur-vey period.

Interspecific interactions.—Records of predatoroccurrence (presence/absence) from camera sur-veys at each site were used to represent preda-tion in our model. Information on competitive orother interactions between native species wasinsufficient to model these effects. A pilot studyindicated that the peanut butter-based lures usedin this study were at least as effective at attract-ing invasive predators as a more typical predatorlure, which comprised tuna oil, feathers, and anaudio lure (B. Hradsky, unpublished data).

Detection probabilities.—We did not incorporateimperfect detection in the BN models. As an indi-cator of survey efficacy for each species, however,we calculated the probability that each specieswould be detected at least once during thesurvey period given that it was present as1 � (1 � p)18, where p is the overall detectabilityestimate for the species. We calculated p for eachspecies by fitting the single season occupancymodel of MacKenzie et al. (2002) using theunmarked package (Fiske and Chandler 2011) inR version 3.2.3 (R Core Team 2015).

Habitat survey.—We derived two measures ofhabitat structure for each site: understory habitatcomplexity and coarse woody debris cover(CWD). Both measures were assessed along a

60-m transect, centered on the camera station,and established along a randomly oriented bear-ing. To quantify habitat complexity, we adaptedthe approach developed by Newsome andCatling (1979). That is, we assessed the presenceof understory vegetation cover in three verticalstrata (20–50, 50–100, and 100–200 cm) at 20evenly spaced points along a 60-m transect usinga height pole. We gave each stratum at the site ascore from 0 to 3 (corresponding to 0%, 1–30%,31–70%, or 71–100% vegetation cover, respec-tively), and summed these scores to give an over-all habitat complexity score for the site, rangingfrom 0 to 9. In our study region, vegetation coverin the 0–20 cm height class is often uniformlyhigh and so it is not an informative predictor(B. Hradsky, unpublished data). Coarse woodydebris cover was quantified by measuring thecross-sectional width of each piece of wood(>5 cm diameter and >50 cm in length) thatintersected the 60-m transect, summing alllengths and then dividing the sum by the totaltransect length.Mapped and remote-sensed variable.—Fire maps

dating back to 1939 were used to derive the TSFhistory of each site. These values were then con-verted to a time-since-fire index (TSFI) to reflectdifferences in post-fire growth rates in each vege-tation type (Cheal 2010). We calculated the indexby deriving a relationship between the rate ofsuccession (x-axis) and a synthetic index rangingbetween 0 (renewal immediately post-fire) and 1(waning or senescence) for each vegetation type.This allowed us to model TSF as a continuousvariable, and account for different developmen-tal rates in the four vegetation types. A BN mod-eling approach is capable of incorporatingmultiple, correlated fire history attributes. How-ever, fire severity data were only available for themost recent fires and so were not included in themodel. Fire frequency was also not includedbecause only a narrow range exists within thestudy area (more than 90% of sites have beenburnt no more than three times since 1939).Other variables that represented the environ-

mental conditions at each site (elevation, averageannual rainfall, productivity [normalized differ-ence vegetation index], aspect, slope, and topo-graphic wetness index) were extracted fromspatial databases. Data sources, descriptions, andranges are provided in Appendix S1: Table S2.

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Bayesian network developmentNon-parametric BNs were used to analyze the

relationships presented in the conceptual model.Bayesian networks are directed acyclic graphsthat depict logical or causal relationships among anetwork of variables. Nodes in the BN representvariables, while directed links (arcs) connect input(parent) nodes to response (child) nodes, indicat-ing the direction of influence (Nyberg et al. 2006).Changes to one node can influence all connected(direct and indirect) nodes. We constructed theinitial BN based on our conceptual model (Fig. 1),using the variables listed in Appendix S1:Table S2 as nodes. Initially, the model containedall arcs that seemed logical, based on the pub-lished literature and our understanding of thestudy system. After refining the BN structure (seeModel construction and refinement), we used the BNto model the distribution of each of the sevennative mammal species separately, with the modeloutput (or terminal node) being the probability ofspecies occurrence at each site.

Model construction and refinement.—All BN anal-yses were conducted using the engine of Uninet(Cooke et al., 2017; www.lighttwist.net/wp/uninet), via R version 3.4.0 (R Core Team 2017),using the package RDCOMClient (Lang 2014).Uninet constructs non-parametric BNs by quanti-fying nodes using marginal distributions (contin-uous and/or discrete) and arcs using normalcopulas (Nelsen 2006). We manually built theBN, using arcs between nodes to indicate poten-tial relationships between key predictors as iden-tified from the literature (Fig. 1). We thenpopulated the model with data from our 113sites and used this data to learn relationshipsbetween the remote-sensed variables (e.g., eleva-tion, aspect, rainfall, slope, and TSF) to avoidover-saturating the model. We removed arcsbetween these nodes when the empirical normalrank correlation of the two nodes was <0.1;Uninet calculates these correlations from the dataunder the assumption of a Gaussian dependencestructure (Hanea et al. 2015).

The clustered design of our study (Fig. 2) meantthat many data were spatially auto-correlated atdistances <2500 m. We therefore calculated a spa-tially lagged response variable (SLRV; as definedby Haining 2003) for the occurrence of each nativemammal species at each site, and added this as anode to the BN. We calculated SLRVas:

SLRVi ¼PjðWijYjÞPj Wij

where i is the site of interest, j is a site within2500 m of i, W is the inverse distance betweensites i and j (the weighting), and Y is the response(i.e., presence or absence of the species) at site j.To enable the SLRV node to be estimated by theBN if species occurrence data from surroundingsites were not available, the node was connectedto the elevation, rainfall, topographic wetness,and productivity nodes (Fig. 3).We redefined each continuous node of the BN

as a beta distribution with parameter estimates(alpha and beta) derived from the raw data usingin-built functions in Uninet. The beta distributionmodel was then used to quantify the influence ofpredictor variables and assess the fit of predicteddistribution models for each species.Model verification.—Model verification was con-

ducted as per Hanea et al. (2015) using the built-infunctions in Uninet. Uninet can test whether jointnormal copulas adequately represent the originaldata by comparing the empirical correlation struc-tures to correlation structures under the normalcopula assumption; however, this test is highlyconservative. As correlation matrices revealedmaximum (element-wise) differences in the orderof 0.01, we concluded that the correlation matrixunder the normal copula assumption provided anadequate approximation of the empirical correla-tion matrix. A comparison of the similarity of thecorrelation matrix of the model to the correlationmatrix of the data smoothed by the normal copulaassumption indicated that the model provided anacceptable approximation of the smoothed data.Model inference.—Conditionalization is the pro-

cess of setting the value of one or more inputnodes within a BN to infer how it/they affect thestate of other nodes (e.g., if CWD cover is 3%and forest type is tall mixed forest, what is theprobability of Rattus fuscipes occurrence?). Con-ditionalizing one (or more) nodes allows theother (unconditionalized) nodes to vary, basedon the relationships defined within the network,and provides uncertainty estimates around thesevalues.We conducted all model inferences within each

forest type, as forest type strongly influenceshabitat structure and the distribution of some

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native mammals in our study area (Swan et al.2015). This involved first conditionalizing the for-est type node in the model to one of the fourtypes, running all the other conditionalizationanalyses and then repeating the process for eachof the other forest types.

To examine how fire affected habitat structureand predator occurrence within each forest type,

we conditionalized the TSFI node across a rangeof values from the 5% to the 95% quantiles of ourfield data (at 10% intervals), and recorded thevalue of the node of interest. We conducted simi-lar conditionalization analyses to compare howthe probability of native mammal occurrencewas affected by habitat complexity (scores 1–9),CWD cover (5–95% quantiles), and the

Fig. 3. The final Bayesian network. Arrows indicate the direction of influence from input to response nodes.Colors are consistent with Fig. 1; descriptions of the nodes are provided in Appendix S1: Table S2.

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occurrence of each predator species (absent/pre-sent), within each forest type. All values in thetext and figures are presented as means withupper and lower 95% confidence limits, whichwere estimated from the model standard devia-tion using a sample size of 113. We conserva-tively considered that there was a substantialrelationship between an input and a responsenode if the confidence intervals around the esti-mated response did not overlap at the minimumand maximum input values. When there wasmarginal overlap in the confidence intervals andhence some (but not strong) evidence for a rela-tionship, this is indicated in the text.

To assess the ability of our BN models to pre-dict native mammal distributions, we used oursurvey data to conditionalize the predictornodes, determined the probability of speciesoccurrence at each site, and then assessed modelfit using the area under the receiver-operatingcharacteristic curve (AUROC) using the R pack-age pROC (Robin et al. 2011). Area under thereceiver-operating characteristic curve comparesthe true-positive rate to false-positive rate andranges between 0.5 (indicating no discriminationability) and 1 (perfect discrimination; Swets1988). We calculated AUROC separately for eachspecies, conditionalizing all nodes.

To understand the potential for these models tobe applied by conservation managers in broad-scale land management, we also assessed themodel fit when the model was conditionalizedonly with data on mapped and remote-sensed

nodes for each species. When data on vegetationcover, habitat complexity, CWD cover, and preda-tor occurrence are not provided to the model, theBN estimates a mean and uncertainty distributionfor each of these variables based on rank correla-tions calculated from the data during model con-struction. The effectiveness of these models wasassessed by comparing the partially conditional-ized AUROC to the AUROC of the full model.

Ethics statementOur study did not involve direct contact with

the study species as data were collected usingmotion-sensing cameras. All research was con-ducted with the approval of the VictorianDepartment of Environment and Primary Indus-tries (research permit numbers 10005514 and10006882).

RESULTS

We recorded 11 native terrestrial mammal spe-cies and two invasive predator species across our113 study sites, as well as four native arborealmammal and two invasive herbivore species (a fullspecies list is provided in Appendix S1: Table S3).We developed BN models for the seven native ter-restrial mammal species that occurred at morethan 15% of sites. With the exception of Tachyglos-sus aculeatus, the cumulative detection probabili-ties for these species were all >0.70 (Table 1). Theinvasive predators, Vulpes vulpes and Felis catus,occurred at 12% and 14% of sites, respectively.

Table 1. Species included in the Bayesian network distribution modeling.

Scientific name Common name Sites recorded (n = 113) Pr (detection|present)

Small native mammals (<500 g)Antechinus spp. Antechinus spp. 54 1.00 (0.99, 1.00)Rattus fuscipes Bush rat 81 1.00 (1.00, 1.00)

Medium-sized native mammals (0.5–5 kg)Potorous tridactylus Long-nosed potoroo 21 1.00 (1.00, 1.00)Perameles nasuta Long-nosed bandicoot 34 0.74 (0.61, 0.86)Tachyglossus aculeatus Short-beaked echidna 25 0.33 (0.12, 0.60)

Large native mammals (>10 kg)Wallabia bicolor Swamp wallaby 85 0.99 (0.98, 0.99)Macropus giganteus Eastern gray kangaroo 19 0.80 (0.65, 0.92)

Invasive predatorsVulpes vulpes Red fox 13 0.28 (0.08, 0.72)Felis catus Feral cat 16 0.39 (0.17, 0.72)

Notes: Sites recorded is the number of sites where the species was recorded; Pr (detection|present) is the cumulative proba-bility of detection over the 18-d survey period, given the species was present. Numbers in brackets show the lower and upper95% confidence limits.

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There was high uncertainty around the predators’cumulative detection probabilities (Table 1), buttheir occurrences were included as nodes in theBN as indicators of potential predation risk. Habi-tat complexity across the sites ranged from 1 (at arecently burnt site) to the maximum score of 9(>85% cover in all three height strata). Coarsewoody debris cover ranged from <1% to 12%.

The final BN contained 17 nodes (Fig. 3; nodesare described in Appendix S1: Table S2). Modelinference showed that habitat complexity waspositively associated with time-since-fire (TSFI;Fig. 4a), but that CWD cover did not changewith post-fire age (Fig. 4b). Forest type stronglyinfluenced both habitat variables, with valuesbeing substantially higher in the wetter foresttypes (Fig. 4a, b). Time-since-fire, habitat com-plexity, and forest type did not affect V. vulpesoccurrence (Fig. 4c, d). There was some evidencethat F. catus occurrence was positively associatedwith TSF and negatively associated with habitatcomplexity; F. catus was also more likely to occurin the wetter forest types (albeit confidence inter-vals marginally overlapped; Fig. 4e, f).

Terrestrial native mammals showed threebroad types of responses to fire, habitat complex-ity, and forest type. The four small and medium-sized (<5 kg) marsupial and native rodent spe-cies had weak positive responses to TSF (exceptPotorous tridactylus), strong positive responses tohabitat complexity, and were generally morelikely to occur in the wetter forest types (Fig. 5).Tachyglossus aculeatus, a mid-sized (2–7 kg)monotreme, showed little response to the TSF orhabitat variables, but tended to be more likely tooccur in the drier forest types (Fig. 6a). The twolarge (≥10 kg) macropod species (Wallabia bicolorand Macropus giganteus) were more likely tooccur at sites with lower habitat complexity;W. bicolor also tended to prefer younger forests,while M. giganteus was more common in thedrier forest types (Fig. 6b, c).

The occurrence of all native mammal specieswas more strongly affected by habitat complexitythan TSF or CWD cover. The probability of Rattusfuscipes occurrence in foothills forest, for example,increased by 31% along the TSFI gradient and34% along the CWD gradient, but by 291% alongthe habitat complexity gradient (Fig. 5a). Simi-larly, M. giganteus occurrence was not affected by

TSF or CWD, but decreased by 85% along thehabitat complexity gradient (Fig. 6c).There was some evidence that R. fuscipes was

less likely to occur when V. vulpes was present,particularly in tall mixed forest, where the proba-bility of occurrence decreased from 0.53 (0.44,0.62) to 0.39 (0.30, 0.47) when V. vulpes was pre-sent. In contrast, T. aculeatus was more likely tooccur when F. catus was present, with the proba-bility of occurrence in tall mixed forest increasingfrom 0.31 (0.22, 0.40) to 0.49 (0.40, 0.58). For theother native mammal species, estimates aroundthe effects of invasive predator occurrence wereassociated with large uncertainty, and few con-sistent patterns could be discerned. Full resultsare presented in Appendix S1: Fig. S1.Area under the receiver-operating characteris-

tic curve values indicated that models discrimi-nated between the presence and absence ofterrestrial native mammal species with reason-able to good ability when conditionalized usingthe full data set (AUROC range: 0.69–0.86;Fig. 7). Using only mapped and remote-senseddata reduced the discriminative ability of themodels by 5.3–16.4%, but AUROCs remained≥0.70 for R. fuscipes, M. giganteus, Peramelesnasuta, and P. tridactylus (Fig. 7).

DISCUSSION

Faunal distributions in fire-affected landscapesare potentially influenced by numerous interact-ing factors (Fig. 1) and can be difficult to predictusing fire-related metrics such as TSF or fireseverity alone (Nimmo et al. 2014, Varner et al.2015). A non-parametric BN approach explicitlycaptured the relationships between multiple,often correlated, drivers of native mammal distri-butions within a single model. This holistic anal-ysis enabled us to predict native mammaloccurrences with reasonable to good accuracy.Moreover, the distributions of four of the sevenspecies could be predicted with reasonable accu-racy using only data from remote-sensed andmapped variables such as TSF, vegetation type,and elevation. Further verification with an inde-pendent data set is required, but our findingssuggest that BNs provide an efficient way ofmodeling faunal distributions across heteroge-neous, fire-affected landscapes, and may reduce

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Fig. 4. Interactions between potential drivers of native mammal occurrence in a fire-affected landscape. Theinfluence of time-since-fire on (a) habitat complexity, (b) coarse woody debris (CWD) cover, (c) Vulpes vulpesoccurrence, (e) Felis catus occurrence, and the influence of habitat complexity on (d) V. vulpes occurrence and (f)F. catus occurrence. Results were derived from non-parametric Bayesian networks of data collected at 113 sites,Otway Ranges, Australia. Responses are shown for four different forest types: wet forest (dotted), forby forest(dot-dashes), foothills forest (short dashes), and tall mixed forest (long dashes). Shading indicates 95% confidenceintervals.

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Fig. 5. Influence of time-since-fire, habitat complexity, and coarse woody debris cover (CWD) on the occur-rence of critical-weight-range marsupials and rodents. Results were derived from non-parametric Bayesian net-works of data collected at 113 sites, Otway Ranges, Australia. Responses are shown for four different foresttypes: wet forest (dotted), forby forest (dot-dashes), foothills forest (short dashes), and tall mixed forest (longdashes). Shading indicates 95% confidence intervals. Note difference in scale for Rattus fuscipes.

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the need to collect extensive field data on habitatstructure and other proximate drivers.

The importance of habitat structure for mam-mal persistence in fire-affected landscapes is wellestablished (Monamy and Fox 2010, Plavsic 2014,

Leahy et al. 2015). Habitat structure changesthrough time after a fire (Coops and Catling2000, Haslem et al. 2011), but also varies withnumerous other factors including topographyand rainfall (Keeley et al. 2005, Plavsic 2014).

Fig. 6. Influence of time-since-fire, habitat complexity, and coarse woody debris cover (CWD) on the occur-rence of (a) Tachyglossus aculeatus and (b, c) large macropods. Results were derived from non-parametric Bayesiannetworks of data collected at 113 sites, Otway Ranges, Australia. Responses are shown for four different foresttypes: wet forest (dotted), forby forest (dot-dashes), foothills forest (short dashes), and tall mixed forest (longdashes). Shading indicates 95% confidence intervals.

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Bayesian network analysis showed that habitatcomplexity increased with TSF and forest wet-ness and strongly influenced the distributions ofnative mammal species in our study landscape.

The direction in which habitat complexity influ-enced native mammal occurrences concurredwith current knowledge of the species’ biology.All four small and medium-sized marsupial androdent species had strong positive associationswith habitat complexity and were generally morelikely to occur in wetter and long unburnt forests.These taxa are depredated by invasive and nativepredators (Bilney et al. 2010, Doherty et al. 2015b)and preferentially shelter and/or forage in densevegetation (Hughes and Banks 2010, Norton 2010,MacGregor et al. 2013, Fordyce et al. 2016). Theyalso fall within the 35–5500 g critical weight rangeof Australian native mammals that have beenmost prone to extinction, partly as a result ofVulpes vulpes and Felis catus predation (Burbidge

and McKenzie 1989, Johnson and Isaac 2009,Chisholm and Taylor 2010).In contrast, Tachyglossus aculeatus (a mono-

treme) showed very little association with habitatstructure or TSF. Although T. aculeatus is med-ium-sized and preyed upon by V. vulpes (Hrad-sky et al. 2017), its spiny coat and ability to digrapidly means that it does not require dense veg-etation cover to escape from predators. Instead,its occurrence is more likely to reflect the distri-bution of shelter sites under CWD and the avail-ability of ants (Smith et al. 1989). The lowdetection rate for this species means that falseabsences may have contributed to the weaknessof its relationships with predictor variables suchas CWD in our study.The large herbivore (macropod) species were

negatively associated with habitat complexity,and had neutral or negative associations with TSFand forest wetness. Although young macropodsare vulnerable to foxes (Banks et al. 2000), thesespecies generally forage in open areas (Banks2001, Swan et al. 2008) and may be attracted torecently burnt sites by the growth of palatablegrasses and herbs after fire (Styger et al. 2011,Tuft et al. 2012).The relationships between native mammal

occurrence, habitat complexity, and fire identifiedby the BN analyses were qualitatively similar tothose from previous regression analyses of speciesdistributions in the same landscape, indicatingthat BNs represented these relationshipsappropriately. Swan et al. (2015) used a series ofgeneralized additive mixed models (GAMMs) todetermine the relationships between TSFI, vegeta-tion structural variables, and terrestrial nativemammal occurrence in the same study area, basedon data collected in spring/summer of 2010–2011and 2011–2012. Key similarities in our findingsinclude the importance of habitat structural vari-ables for native mammals relative to TSFI, positiverelationships between Perameles nasuta and Potor-ous tridactylus occurrence and dense vegetationcover, and negative relationship betweenMacropusgiganteus and understory vegetation.One substantial difference between the BN

and GAMM results, however, was that theGAMMs showed strong interactions betweenforest type and TSFI for habitat structural vari-ables. Coarse woody debris cover, for example,was not associated with TSFI in tall mixed forest

Fig. 7. Area under the receiver-operating curve(AUROC) for Bayesian network models of native mam-mal distributions. AUROC (full data set) shows the fit ofmodels conditionalized using the full data set; AUROC(mapped variables) shows the fit of models conditional-ized using only mapped and remote-sensed variables.An AUROC of 0.5 indicates that the model has nodiscrimination ability, and a model with AUROC = 1discriminates perfectly between species presence andabsence. The further the point is from the 1:1 line, thegreater the loss of discrimination ability when data onproximate drivers (such as habitat complexity andpredator occurrence) were not provided in the model.

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but was positively associated with TSFI in wetforest (Swan et al. 2015). In contrast, the BNmodeled forest type (which was categorical) asan ordinal variable and found similar relation-ships between TSFI and habitat structural vari-ables in each vegetation type (Fig. 4a, b). This islikely to be an artifact of the non-parametric BNstructure. Alternate model structures could beexplored using a larger data set with more sam-ples from each forest type. Fauna distributionsmay also differ between seasons and years (Haleet al. 2016); further surveys would help clarifythis potential source of variation.

Predators are rarely included among the poten-tial drivers of species occurrence or abundance inmodels of faunal distributions in fire-affectedlandscapes (although see Arthur et al. 2012),despite their important role in post-fire popula-tion dynamics (Morris et al. 2011, Leahy et al.2015). Our data on the interactions betweenpredators, prey, and fire were limited as they onlycaptured species occurrence (rather than abun-dance or behavior) and predator detection rateswere low. Nonetheless, we found some evidencethat F. catuswas more likely to occur in wet forest,particularly as TSF increased and habitat com-plexity decreased. The majority of feral cat studiesindicate that F. catus selects for structurally com-plex habitats (Doherty et al. 2015a); however,high-resolution telemetry has shown that feralcats select for open habitats in their fine-scalemovements (McGregor et al. 2014). A differencein spatial scale of selection may therefore explainthe seemingly contradictory preference of F. catusfor low habitat complexity and wet forests in ourstudy (given that wet forests generally had highhabitat complexity)―wet forests also supportedmore potential prey species. Similarly, differencesin temporal scale may explain why broad-scalecorrelative analyses of V. vulpes distributions infire-affected landscapes such as ours and those ofPayne et al. (2014) and Southgate et al. (2007)have found weak or no relationships between foxoccurrence and fire history, vegetation type, and/or habitat structure, but telemetry studies haveshown that V. vulpes uses burnt forest and heath-land intensely immediately after fire (Meek andSaunders 2000, Hradsky 2016).

The native rodent Rattus fuscipes was less likelyto occur when V. vulpes was present, perhapsreflecting its avoidance of this predator. Overall,

however, we found little consistent evidence ofassociations between invasive predator and nativeprey occurrence, and the strength of associationsdid not reflect the relative prevalence of theseprey species in the diet of V. vulpes in the OtwayRanges (Hradsky et al. 2017). Surprisingly, T.aculeatus was positively associated with F. catusoccurrence―this relationship should be inter-preted cautiously given the low detection rates ofboth species. Predator manipulation experimentsand more detailed data on predation risk arerequired to better understand the influence ofinvasive predators on native mammal distribu-tions in fire-affected landscapes. The role of otherinterspecific interactions also needs further inves-tigation. For example, high levels of herbivory cannegatively impact small mammals through theeffects on vegetation structure (Foster et al. 2014),and interact with both fire and predators (Dexteret al. 2013, Colman et al. 2015).The BNs discriminated between the presence

and absence of most native mammal species rea-sonably well, particularly when models were con-ditionalized using the full variable set. For fourspecies, discrimination was also reasonable whenmodels were conditionalized with only mappedand remote-sensed data, indicating that the BNseffectively captured relationships between proxi-mate and ultimate drivers of distributions forthese species. Bayesian networks might thereforebe used to predict the distributions of these spe-cies at a landscape scale. However, our samplesizes were too small to enable cross-validationtesting, and additional testing with independentdata sets from the same and other regions is nec-essary. Fine-scale habitat data sets (and perhapsdifferent survey methods) will be required to pre-dict the distributions of some species such asT. aculeatus and Antechinus spp. Habitat structuresurveys will also continue to be important forunderstanding how fine-scale habitat complexityand vegetation mosaics influence species distribu-tions, abundance, and behavior.

CONCLUSIONS

Bayesian networks can be useful for modelingcomplex systems, but have not been routinelyapplied in the environmental sciences to date(Aguilera et al. 2011). Recent developments innon-parametric continuous BNs further increase

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the potential applicability of BNs for ecologicalproblems, as they reduce the need for large samplesizes and discretization of continuous variables(Aguilera et al. 2011, Hanea et al. 2015). We foundthat non-parametric BNs provided an effectiveand efficient method for modeling and predictingnative fauna distributions across a heterogeneouslandscape, while explicitly incorporating the inter-actions between habitat structure, fire, invasivepredators, and other environmental conditions.Further research and replication is needed to testthe ability of BNs to predict species occurrences atinterpolated or extrapolated sites. Bayesian net-works are likely to be a useful tool for predictingspecies responses to fire management and identi-fying appropriate fire regimes for biodiversity con-servation in an increasingly fire-prone world.

ACKNOWLEDGMENTS

We thank Peter Barrow, Eryl Jones, Bert Hommel,Marney Hradsky, Karl Hradsky, John Loschiavo, andCallam Reynolds for helping with fieldwork; AmandaAshton for assisting with image processing; HollySitters for guidance on graphing in R; and Matt Swanand anonymous reviewers for helpful comments on themanuscript. Funding was provided by the VictorianGovernment Department of Environment, Land, Waterand Planning (Hawkeye), the Holsworth WildlifeResearch Endowment, and the Australian Govern-ment’s National Environmental Science Programmethrough the Threatened Species Recovery Hub.

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