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Basic and Applied Ecology 13 (2012) 188–195

ehavioural context of multi-scale species distribution models assessed byadio-tracking

athieu G. Lundya,b,∗, Daniel J. Buckleya,c, Emma S.M. Bostona,c, David D. Scotta,b,aulo A. Prodöhla,b, Ferdia Marnelld, Emma C. Teelinga,c, W. Ian Montgomerya,b

Centre for Irish Bat Research, IrelandSchool of Biological Science, Queen’s University Belfast, 97 Lisburn Road, Belfast BT9 7BL, United KingdomSchool of Biology and Environmental Science, University College Dublin, Belfield, Dublin 4, IrelandNational Parks and Wildlife Service, Department of the Environment, Heritage and Local Government, 7 Ely Place, Dublin, Ireland

eceived 5 April 2011; accepted 2 December 2011

bstract

Incorporating ecological processes and animal behaviour into Species Distribution Models (SDMs) is difficult. In speciesith a central resting or breeding place, there can be conflict between the environmental requirements of the ‘central place’ and

oraging habitat. We apply a multi-scale SDM to examine habitat trade-offs between the central place, roost sites, and foragingabitat in Myotis nattereri. We validate these derived associations using habitat selection from behavioural observations ofadio-tracked bats. A Generalised Linear Model (GLM) of roost occurrence using land cover variables with mixed spatial scalesndicated roost occurrence was positively associated with woodland on a fine scale and pasture on a broad scale. Habitat selectionf radio-tracked bats mirrored the SDM with bats selecting for woodland in the immediate vicinity of individual roosts butvoiding this habitat in foraging areas, whilst pasture was significantly positively selected for in foraging areas. Using habitatelection derived from radio-tracking enables a multi-scale SDM to be interpreted in a behavioural context. We suggest thathe multi-scale SDM of M. nattereri describes a trade-off between the central place and foraging habitat. Multi-scale methodsrovide a greater understanding of the ecological processes which determine where species occur and allow integration ofehavioural processes into SDMs. The findings have implications when assessing the resource use of a species at a singleoint in time. Doing so could lead to misinterpretation of habitat requirements as these can change within a short time periodepending on specific behaviour, particularly if detectability changes depending on behaviour.

usammenfassung

Es ist schwierig die ökologischen Prozesse und das Verhalten von Tieren in Modellen der Artverbreitung (speciesistribution model: SDM) zu berücksichtigen. Bei Arten, die einen zentralen Ruhe- oder Brutplatz haben, kann es einenonflikt zwischen den Umweltanforderungen an diesen zentralen Platz und dem Nahrungshabitat geben. Wir wendenin SDM auf multiplen Skalen an, um die “trade offs” in Bezug auf das Habitat zwischen dem zentralen Ort, den

astplätzen und dem Nahrungshabitat bei Myotis natteri zu untersuchen. Wir validieren die abgeleiteten Beziehungen

∗Corresponding author at: School of Biological Science, Queen’s University Belfast, 97 Lisburn Road, Belfast BT9 7BL, United Kingdom.el.: +44 2890972281; fax: +44 2890975877.

E-mail address: m.lundy@qub.ac.uk (M.G. Lundy).

439-1791/$ – see front matter © 2011 Gesellschaft für Ökologie. Published by Elsevier GmbH. All rights reserved.oi:10.1016/j.baae.2011.12.003

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M.G. Lundy et al. / Basic and Applied Ecology 13 (2012) 188–195 189

ndem wir die Habitatselektion auswerten, die wir durch Verhaltensbeobachtungen an besenderten Fledermäusen feststellen. Eineneralisiertes lineares Modell (GLM) der Rastvorkommen, das die Variablen der Flächenanteile auf gemischten räumlichenkalen auswertet, war auf der feinen Skala mit Waldvorkommen und auf der großen Skala mit Weidelandvorkommen positivssoziiert. Die Habitatselektion der besenderten Fledermäuse spiegelte das SDM wider, da die Fledermäuse Waldvorkommenn der unmittelbaren Umgebung der individuellen Rastplätze wählten, dieses Habitat jedoch in den Nahrungsgebieten mieden,nd Weideflächen bei den Nahrungsgebieten signifikant positiv ausgewählt wurden. Die Verwendung der Habitatselektion auf-rund der Telemetrie ermöglicht es, ein SDM auf multiplen Skalen in einem Verhaltenskontext zu analysieren. Wir schlagenor, dass das SDM auf multiplen Skalen für M. natteri einen “trade off” zwischen dem zentralen Platz und den Nahrungshabi-aten beschreibt. Multiskala-Methoden ermöglichen ein besseres Verständnis der ökologischen Prozesse, die bestimmen worten auftreten, und erlauben es, Verhaltensprozesse in ein SDM zu integrieren. Die Ergebnisse haben Auswirkungen, wenn

bgeschätzt wird, welche Ressourcen eine Art zu einem Zeitpunkt nutzt. Bei dieser Vorgehensweise können Fehlinterpretationenn Bezug auf die Habitatansprüche auftreten, da diese innerhalb einer kurzen Zeitperiode vom spezifischen Verhalten abhängen,esonders wenn sich die Erfassbarkeit mit dem Verhalten verändert.

2011 Gesellschaft für Ökologie. Published by Elsevier GmbH. All rights reserved.

eywords: Central place forager; Habitat selection; Multi-scale modelling; Myotis nattereri; Radio telemetry; Species Distribution Modelling

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Species distribution models (SDMs) offer an alternativeo direct mapping, allowing the prediction of species’ cur-ent, future and past distributions (Guisan & Zimmermann000; Thomas, Cameron, Green, Bakkenes, & Beaumont004). SDMs are used to assess a species’ conservation statusCabeza, Araújo, Wilson, Thomas, & Cowley 2004; Thomast al. 2004), describe and predict changes in species’ dis-ribution in response to environmental change (e.g. Lundy,

ontgomery, & Russ 2010), identify sites for reintroductionse.g. Wilson & Roberts 2010), and define priority con-ervation areas (e.g. Fiorella, Cameron, Sechrest, Winfree,

Kremen 2010). For a comprehensive review of currentssues and applications of mapping species distributions seeranklin (2009). The predictions of SDMs are based on cor-elations with environmental variables. The suitability of anrea is not solely related to the availability of habitat but to theontext of the surrounding landscape habitat structure, sizend shape (Virkkala 1991; Jokimäki & Huhta 1996; Bennett,adford, & Haslem 2006). Species respond to heterogeneous

andscapes at multiple scales which combine to determineresence and population processes (e.g. Fryxell et al. 2005).sing a multi-scale approach allows the immediate habitat toe placed in the context of the surrounding landscape (Wiens989; Jokimäki & Huhta 1996). Multi-scale methods candentify species-specific relationships with aspects of habi-at spatial scale (McAlpine, Rhodes, Callaghan, Bowen, &unney 2006; Lundy & Montgomery 2010).Central place foragers utilise a defined location, which

rovides suitable conditions to rest or protect juveniles andake repeated trips to foraging areas. A central place is

elected to minimise the energetic cost of travel to forag-ng areas (Rosenberg & McKelvey 1999). The character of a

entral place and foraging area may contrast in some species.pecies distribution can also change significantly during the

ife cycle in response to changed resource requirements (Law

nSo

Dickman 1998). Jaberg and Guisan (2001) demonstratedseasonal contrast in the habitat associations and predicted

hat the distribution of the Greater mouse-eared bat (Myotisyotis) in Switzerland would shift from low elevation during

ummer to higher elevation with structured vegetation coverutside the breeding period.

Defining the geographical ranges in bats is difficult due toheir nocturnal behaviour (Walsh & Harris 1996; Vaughan,ones, & Harris 1997) and, hence, SDMs are particularly use-ul for examining the ecology of bat species (Jaberg & Guisan001; Rebelo & Jones 2010). Roosts are crucial in bat ecologynd distribution (Kunz & Lumsden 2003; Findley 1993), withifferent species having specific roost requirements (Marnell

Presetnik 2010). Roosts are considered ‘central places’articularly during the maternity period (Daniel, Korine,

Pinshow 2008). Roost choice is associated with thermalonditions (Lourenco & Palmeirim 2004; Smith & Racey005) and predator avoidance (Jones & Rydell 1994). WhilstDMs allow predictions of occurrence across a landscape,ehavioural observations contribute to understanding habitatelection of bat species (Fenton 1997; Bontadina, Schofield,

Naef-Daenzer 2002). Radio-tracking individual bats elu-idate behavioural patterns such as roost switching, foragingabitat selection and home ranges (Fenton 1997; Bontadinat al. 2002; Russo, Cistrone, Jones, & Mazzoleni 2004). Inontrast to predictive modelling, radio-tracking is applied onsmaller scale, assessing habitat selection of a small propor-

ion of a population.Myotis nattereri is a foraging generalist, hunting in a vari-

ty of habitats utilising gleaning and aerial hawking (Arlettaz996; Siemers, Kaipf, & Schnitzler 1999; Siemers & Swift006; Smith & Racey 2008). However, it emerges fromoosts later than other species. This is considered as preda-or avoidance behaviour related to the slow flight of M.

attereri (Jones & Rydell 1994). We develop a multi-scaleDM (McAlpine et al. 2006) to examine habitat associationsf M. nattereri maternity roosts at a landscape scale. We

190 M.G. Lundy et al. / Basic and Applied Ecology 13 (2012) 188–195

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ig. 1. (A) Myotis nattereri maternity roost records used in the cotudy (*); (B) the habitat surrounding the roost at which radio-tracksing the 50% kernel density areas (Hooge & Eichenlaub 1997).

ypothesise that there will be a positive association withabitats providing cover on a small spatial scale, an asso-iation which diminishes with distance and is replacedy selection for foraging habitat. Multi-scale analysis ofabitat selection based on radio-tracking is used to cor-oborate the results of the SDM. The combination of aulti-scale SDM and radio-tracking indicates that continued

onservation of roosts and their immediate habitat facilitatexploitation of a relatively common habitat by foraging by. nattereri.

aterials and methods

onstruction of a multi-scale SDM

The study was carried out in Ireland using all known M.attereri maternity roosts (N = 22) records spread across thetudy region (Fig. 1; O’Sullivan 1994; BCI 2008). Pseudo-bsence roost records (N = 22) were generated, at random,n a Geographical Information System (GIS; ArcMap 9.2,SRI). The foraging areas of M. nattereri can be up tokm from roosts (Siemers et al. 1999). Hence, we used

his distance as the upper limit of spatial scales to modeloost occurrence, delineating available habitat in sequen-ial tori starting at roosts with limits at; 0.25 km 0.5 km,.75 km, 1 km, 2 km, 3 km and 4 km. The area of land coverlasses, derived from CORINE (EEA 2002), was calculatedithin each torus (Table 1). Independent Generalised Lin-

ar Models (GLM) were applied, with arcsine square-rootransformed area of habitat types within each torus and roostresence (56 models). GLMs with a first order response pro-

ide parameter estimate which can be compared to habitatelection ratios derived from radio-tracking. Confidence inhe parameter estimates was assessed by examination of theegression coefficient and associated standard error. The most

adfia

ion of the Species Distribution Model (SDB) and a radio trackings conducted within tori; (C) area utilised by tracked bats delineated

elevant spatial extent for each land cover variable waselected using Akaike Information Criterion, corrected forample size (AICc; Burnham & Anderson 2002).

abitat selection of radio-tracked bats

A maternity roost of M. nattereri was selected in southast Ireland on the basis of size and accessibility (N◦52.64;◦6.34). This roost was not used in the analysis of roost

abitat associations but was characteristic of M. nattererioosts across the region, with approximately 60 bats roostingn an open attic of a stone building. The surrounding habi-at was dominated by pasture with small woodland blocksispersed across the landscape characteristic of the predomi-antly agricultural, rural landscape. The bats roosted openlyithin the attic allowing selective capture of a small num-er of individuals. Radio tracking was conducted duringay and June 2010, avoiding periods when bats were in

ate stages of pregnancy or carrying dependent young. Batsere removed from the roost during day time and radio trans-itters (0.35 g, LB-2N; Holohil Ltd, Canada) attached using

urgical adhesive between the shoulder blades, before beingeturned to the roost. Bats were tracked in the pre-partum andost-partum periods. All procedures were carried out undericence from the National Parks and Wildlife Service (NPWS;icence No.74C/2008). Tracking continued for a seven-nighteriod, during which up to seven individuals were tracked atne time. Locations of each individual were assessed usingimultaneous triangulation from multiple positions every0 min. The locations of these fixes were calculated usingocate (http://www.locateiii.com) using maximum likeli-ood to allocate fix locations from multiple bearings. This

llows an error to be attributed to each fix. Fixes with a stan-ard error of less than 100 m on either axis were retained. Allxes more than 50 m from the maternity roost were classifieds representing part of the range of individuals (Fig. 1).

M.G. Lundy et al. / Basic and Applied Ecology 13 (2012) 188–195 191

Table 1. Habitats used in developing a Spatial Distribution Model (SDM) of maternity roost occurrence of Myotis nattereri. Habitats deemedto have a consistent effect by inspection of their regression coefficients and standard errors are marked (a). The most relevant distance for eachhabitat is determined using Akaike weights for Generalised Linear Models (GLMs). Habitats which occurred within the Minimum ConvexPolygon (MCP) of foraging bats from a radio-tracked roost are marked (b). The selection ratio (wi) of available habitats utilised by foragingbats is shown at both the SDM selected distance and that of the strongest selection.

Habitat Description SDM model Habitat selection

Coefficient (se) Selecteddistance

Akaikeweight

Strongest selectionratio and (distance)

Selection ratioat SDM distance

Developmenta,b Urban fabric −21.8 (12.5) 3 km .212 1.37 (0.75 km) 0.38Pasturea,b Permanent grassland 5.21 (1.9) 2 km .712 1.25 (2.0 km) 1.25Woodlanda,b Broad leaf and

mixed woodland485 (286) 0.5 km .452 1.72 (0.5 km) 1.72

Arableb Arable crops andmixed cultivation

−31.5 (42.6) 2 km .162 1.09 (0.25 km) 0.85

Bog Peat and heath 1.86 (2.8) 3 km .164 – –Conifer Conifer woodland 3.13 (32.3) 1 km .410 – –Freshwater Water body and −769 (553) 2 km .240 – –

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water courseatural grassland Natural grassland −6.03 (32.6)

A Minimum Convex Polygon (MCP) bounding all fixesas created. Land cover was digitised from aerial pho-

ographs using categories of CORINE land cover (EEA,002; Table 1). The limits of MCP defined the available areaSmith & Racey 2008). This was delineated within sequen-ial tori starting at roost with limits; 0.25 km 0.5 km, 0.75 km,km, 2 km, 3 km and 4 km. Kernel analysis, using theawth’s tools extension for ArcMap 9.2 (version 3.27) was

pplied to the location of fixes for bats, with the core area cal-ulated as the 50% kernel area (Hooge & Eichenlaub 1997).ernel analysis is a probabilistic method which accounts notnly for the location of radio fixes but also density providingprobability of occurrence in an area (Worton 1989). The

umber of fixes required to accurately calculate core areasas examined by calculating the core area for each individ-al using increasing number of fixes. The proportional areahange of core area was calculated with additional fixes and

lotted against number of fixes (Fig. 2). The change in corerea stabilised when approximately 25 fixes were used.

ig. 2. Change in core range area (%) with increasing number ofxes used. Vertical bars are standard deviation for change of all

ndividual core range areas.

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Selection ratios (ωi) allow preference for habitats to bealculated (Manly 2002). These are based on the amount ofabitat used in proportion to habitat availability. Preferenceor a habitat is reflected by a ωi of greater than 1, whereasvoidance is assumed with ratios below 1. We calculated ωior each habitat type within each torus assuming a singlevailable area and summed area for all individuals (Manly002). The significance of selection ratios was calculatedsing Chi-square tests with Bonferroni correction (Desbiez,odmer, & Santos 2009). The pattern of the selection ratio

or each land cover category with distance was compared tohe regression coefficients of the SDM.

esults

abitat association of the multi-scale SDM

The results of the SDM and the patterns of habitat selectionerived from tracking observations are presented in Table 1nd Fig. 3. Four land cover classes were utilised withinhe core home ranges of tracked bats; developed, pasture,oodland and arable. Patterns of selection and modelled

ssociation with these land cover types over distance arellustrated (Fig. 3).

No single distance was selected as most relevant for alland cover classes. Regression coefficients and their standardrrors revealed consistent associations with roost presenceor woodland, developed and pasture habitats (Table 1).ositive associations were observed with the area of wood-

and and pasture, being strongest at 0.5 km and 2 km fromoosts, respectively. Variation in regression coefficients gen-rally declined for all land covers with distance from theoosts (Fig. 3). There was a decline in the strength of the

192 M.G. Lundy et al. / Basic and Applied Ecology 13 (2012) 188–195

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ig. 3. Associations of Myotis nattereri maternity roosts with four hn a Species Distribution Model (grey) (Table 1). Habitat selection raeriod.

ositive association with woodland with distance from theoost, becoming negative in torus greater than 3 km. Devel-ped habitats were negatively associated with the presencef maternity roosts across all distances.

abitat selection of radio-tracked bats

Sixteen bats were tracked, of which fifteen returned to thenitial study roost. A single bat roosted 1.2 km from the studyoost and remained throughout. The core foraging area ofhis individual was not included in analysis of habitat selec-ion. The average core foraging area was 58.1 ± 6.4 ha, withndividuals travelling 200–3800 m to core areas (Table 2).o ensure that habitat use was comparable between the pre-nd post-parturition period, Wilcoxon signed-rank tests werepplied to core foraging area and foraging distance. There waso significant difference between foraging area, in terms ofize of core foraging area (W = 37, df = 1, p = 0.64) or distanceravelled to core area (W = 39, df = 1, p = 0.51). Furthermore,here was no difference in body mass (W = 29, df = 1, p = 0.79)n the pre- and post-parturition period.

Selection ratios changed with distance from the roostFig. 3). Woodland and developed land cover in the immedi-te vicinity of the roost were positively selected but selectioneclined and became negative with increasing distance. Thereas selection against arable habitat across distance classes

rom the roost. Pasture was avoided at extremes of the

istance range but selected for at intermediate distances.trongest selection ratios for both woodland and developmentere observed at 0.5 km and 0.75 km respectively. Avoidancef arable habitats was strongest at 0.75 km. The strongest

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ypes deemed to have a consistent relationship with roost occurrencelack) derived from radio-tracking M. nattereri during the maternity

election for pasture occurred at a distance of 2 km. Selectionatios and the associations derived from regression modelsere in agreement at distances identified as most relevant

Table 1).

omparison of habitat associations from SDMnd radio-tracking

General patterns were consistent between both selectionatios of radio-tracking and coefficients of the SDM (Table 1;ig. 3). Agreement in trend with distance between SDMabitat associations and selection ratios of tracked bats wasbserved for woodland (Fig. 3B). There was little change withistance in the relationship with arable, which was avoidedcross all distances by tracked bats, although a non-consistentelationship with the occurrence of roosts was defined byhe SDM (Table 1; Fig. 3D). Selection for developed areasy tracked bats declined with distance, a relationship whichas within the error estimates of the SDM regression coeffi-

ients derived. However, the SDM coefficient and selectionatio disagreed for development land cover within 1 km ofhe roosts. This may reflect the position of the roost at theeriphery of a small urban area (Figs. 1 and 3A). The rela-ionship of selection for pasture can be superimposed onto theattern of the SDM coefficients, although the high degree ofariation in association with pasture suggests that high levelsf grassland cover occur in the immediate vicinity of some

. nattereri roosts (Fig. 3C). The proportion of fixes which

ell within pasture and woodland was plotted against time ofight (Fig. 4). A bimodal pattern emerged for woodland at thetart and end of night relating directly to emergence and bats

M.G. Lundy et al. / Basic and Applied Ecology 13 (2012) 188–195 193

Table 2. Tracking details of 16 adult female bats. Foraging area is determined as 50% kernel density area for all foraging fixes recorded foran individual. A single individual (*) utilised a second roost other than the roost at which it was first captured. Time with signal contact withat least one of the receiver positions is shown as the percentage of time from emergence to dawn return. The number of triangulated locationsused to calculate foraging areas is given.

Bat Nights tracked Mass (g) Pre/post parturition Signal contact (%) Fixes Foraging area (ha) Commuting distance (m)

1 5 10.5 POST 86.2 56 13.9 384.92 5 8.8 POST 84.6 55 70.8 1022.03 3 8.7 POST 44.6 37 21.4 284.54 4 10.0 POST 76.9 48 95.5 2972.85 5 9.0 POST 84.4 54 72.5 615.26 5 8.3 POST 73.4 47 44.4 709.47 5 9.2 POST 84.6 54 60.1 1076.68 3 8.5 POST 80.0 27 74.1 3676.9

*9 5 8.3 PRE 89.7 37 14.5 199.810 5 9.2 PRE 60.0 32 34.0 743.811 5 10.3 PRE 96.9 62 77.9 620.112 5 9.7 PRE 96.9 61 84.6 1698.213 3 9.9 PRE 69.3 26 73.3 3777.414 5 8.5 PRE 90.8 56 79.0 1750.115 5 8.5 PRE 96.9 62 52.6 1951.51

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eturning to roost, with pasture predominating at other times.small increase in the proportion of fixes occurring in wood-

and and a similar decline in those in pasture was observed inhe middle of the night, which may result from night roostingats utilising woodland patches during this period.

iscussion

A multi-scale SDM of roost occurrence identifies theelevant spatial scale of specific habitats related to roostccurrence. Using telemetry data we place the results ofhe multi-scale SDM in the context of habitat use relatedo emergence and foraging behaviours. The predictions ofDMs require validation by comparison with independent

est datasets (Vaughan & Ormerod 2005). We demonstratehat a multi-scale SDM can be interpreted through observa-

ional studies of animal behaviour and habitat selection.

The SDM applied to maternity roosting in M. nattererievealed complex patterns of habitat associations. There were

ig. 4. Proportion of fixes located in pasture (solid line) and wood-and (broken line) against time.

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arked differences in the most relevant spatial scales forpecific habitat types. We argue that these are related to arade-off between habitat selection for roosting and habi-at selection for foraging, supported by examining changen habitat use during the night. Comparing the results of theDM and radio-tracking also allows the assessment of site-pecific factors to be addressed. This is highlighted by anpparent selection for development and arable land coverlose to the roost by tracked bats. When examined in theontext of the SDM developed for all roosts, this pattern wasdentified as being an individual character of the study roost.dentification of this deviation from a SDM allows assess-ent of behavioural plasticity.There is a nightly, temporal shift between two behaviours

n bats, emergence and foraging. Across their range, M. nat-ereri is regarded as a foraging generalist, gleaning prey fromegetation and aerial hawking insects close to vegetationArlettaz 1996; Siemers et al. 1999; Siemers & Swift 2006;mith & Racey, 2008) and as a species which emerges rela-

ively late from roosts (Jones & Rydell, 1994). We predictedoosting would be associated with habitats providing coverrom predators. Woodland provides this and was selected inhe immediate vicinity of the roost, but this selection declinedith distance. In contrast, pasture was avoided close to the

oosts and selected within the core foraging areas. These con-itions provide M. nattereri with the desired level of covern brighter periods (dusk and dawn) and access to foragingabitat, in this case, grassland.

The strong behavioural association with different habitats

t different times and scales may lead to misinterpretation ofabitat requirements for central place foragers. For example,f the presence of M. nattereri was assessed in the emergenceeriod, it may be concluded that there is a high dependence on

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94 M.G. Lundy et al. / Basic and

oodland habitat. However, observing the species foragingin grassland) would detract from the importance of wood-and close to a roost. During the maternity period it is likelyhat the effects of spatial scale in habit at association will be

ost pronounced. At this time, maternity roosts must providepecific thermal conditions for developing young (Lourenco

Palmeirim 2004; Smith & Racey 2005) and females musteturn to these roosts to provision their young. During theon-maternity period, opportunistic roosting may be in lesspecific conditions and strong changes in habitat associationselated to behaviour may not be observed.

SDMs may be perceived as static generalisations ofpecies occurrences. In the face of global environmen-al change, SDMs have increasingly become essential toredict distributional responses at species and communityevels. Mechanistic models of occurrence are used to predictange of species with respect to physiological parametersKearney, Wintel, & Porter 2010). The use of multi-scaleechniques to construct SDMs facilitates more than staticredictions of species’ occurrence. These methods are par-icularly relevant for central place foragers which occupyatchy environments and can deliver invaluable insights foranagement.

cknowledgements

The Centre of Irish Bat Research is funded by the Nationalarks and Wildlife Service. The comments of Prof. Paulacey and Dr. Manuel Ruedi on study design were ofreat benefit. We are grateful to the owners of Leskinferehurch or Ireland, Gorey, Co. Wexford for allowing access

o roosting bats and to Fionn Clissmann for assistance inhe field. We thank three anonymous reviewers for theirelpful comments and suggestions for improvements to theanuscript.

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