MARINE ECOLOGY PROGRESS SERIESMar Ecol Prog Ser

Vol. 436: 257–272, 2011doi: 10.3354/meps09236

Published August 31

INTRODUCTION

A permanent population of sperm whales Physetermacrocephalus Linneaus, 1758 inhabits the Mediter-ranean Sea, where they apparently constitute a genet-ically distinct stock from that of the neighbouringNorth Atlantic (Drouot et al. 2004, Engelhaupt 2004).Even though no overall abundance estimate is avail-able for this population, the comparison of recentsperm whale survey data to historical records suggeststhat, locally, encounter rates are declining; this has ledto its classification as ‘Endangered’ under the Interna-tional Union for the Conservation of Nature (IUCN) cri-teria (Reeves & Notarbartolo di Sciara 2006, Notarbar-tolo di Sciara & Birkun 2010). The presence of the

sperm whale has been historically reported in thewaters around the Balearic Islands in the westernMediterranean (e.g. Table 1 in Reese 2005), and recentsurveys have shown relatively high encounter ratesaround the archipelago (Gannier et al. 2002).

Sperm whales across the world have a distinctivesocial system, segregating into long-term social unitscontaining adult females and their immature offspring,and typically solitary maturing and mature males(Whitehead 2003). This picture seems to also broadlyapply to the Mediterranean (Drouot et al. 2004a,b).Together with the waters off Crete (Frantzis et al.2003), the Tyrrhenian Sea (e.g. Drouot et al. 2004a)and, recently, the Ligurian Sea (occurrences reviewedin Notarbartolo di Sciara & Birkun 2010), the Balearic

© Inter-Research 2011 · www.int-res.com*Email: pirotta.enrico@gmail.com

Modelling sperm whale habitat preference: a novelapproach combining transect and follow data

Enrico Pirotta1,*, Jason Matthiopoulos1,2, Monique MacKenzie2, Lindesay Scott-Hayward2, Luke Rendell1

1Sea Mammal Research Unit, Scottish Oceans Institute, School of Biology, University of St. Andrews, St. Andrews, Fife KY16 8LB, UK

2Centre for Research into Ecological and Environmental Modelling, University of St. Andrews, St. Andrews, Fife KY16 9LZ, UK

ABSTRACT: Sperm whale Physeter macrocephalus habitat preferences are still poorly understood inthe Mediterranean, despite the population being classified as ‘Endangered’ by the IUCN. Techniquesto make the best use of multiple data sources are important in improving this situation. This work pro-vides a detailed evaluation of sperm whale distribution and habitat use around the Balearic Islandsusing a novel analytical framework that combines transect and follow data while accounting for anyautocorrelation present. During dedicated research cruises (2003 to 2008), sperm whales werelocated by listening at regular intervals along a search track and subsequently followed acoustically.Sperm whales were encountered 56 times and followed for periods ranging from a few hours to 3 d.Logistic Generalized Additive Models were used to model the probability of whale presence acrossthe study area as a function of environmental variables, and Generalized Estimating Equations wereused to account for autocorrelation. The results suggest that sperm whales do not use the region uni-formly and that topography plays a key role in shaping their distribution. Moreover, solitary individ-uals were found to use the habitat differently from groups. This segregation appeared to be driven bywater temperature and might reflect different needs or intraspecific competition. By shedding lighton sperm whale habitat preference in such a critical area, this study represents an important steptowards the implementation of conservation measures for this population.

KEY WORDS: Habitat modelling · Cetacean · Distribution · Balearic Islands · GAM · GEE · Multi-scale

Resale or republication not permitted without written consent of the publisher

Mar Ecol Prog Ser 436: 257–272, 2011258

archipelago is one of the few areas in the Mediter-ranean Sea in which both social units and maturemales are observed consistently, suggesting a possiblyimportant role as breeding ground (Gannier et al.2002, Drouot-Dulau & Gannier 2007). Nevertheless, nolong-term study has been conducted to date to specifi-cally estimate the species distribution in this region,and thus little information exists on its space use andhabitat preferences around the archipelago.

Habitat preference modelling techniques representa useful tool to quantify the relationships between aspecies and its environment (Guisan & Zimmermann2000, Redfern et al. 2006, Matthiopoulos & Aarts2010). Knowing where the animals are, what environ-mental characteristics influence their choice of habitatand how this choice changes with time is crucial tounderstanding the species’ ecology, identifying theareas of critical importance, assessing the overlapwith human activities and, ultimately, guiding appro-priate conservation efforts (Redfern et al. 2006). Foodavailability is probably the main determinant of spaceuse by marine mammals (e.g. Benoit-Bird & Au 2003,Hastie et al. 2004, Frederiksen et al. 2006, Fried -laender et al. 2006). Other potentially important factors affecting habitat choice include behaviouralstate, the presence of calves, inter specific relation-ships (Cañadas & Hammond 2008), predation risk(e.g. Heithaus & Dill 2002), competition (e.g. Shane1995) and reproductive needs (e.g. Ersts & Rosen-baum 2003). Prey abundance and other factors areoften hard to measure directly (Guisan & Zimmer-mann 2000, Jaquet & Gendron 2002) and other easierto obtain environmental variables are thus used asproxies, even if they are not always directly andcausally related with animal presence (Redfern et al.2006). Several physiographic (e.g. depth, slope,aspect), oceanographic (e.g. sea surface temperature)and biological variables (e.g. chlorophyll a surfaceconcentration) have been successfully employed todescribe cetacean habitat preference indirectly (e.g.Cañadas et al. 2002, Davis et al. 2002, Hamazaki2002, Yen et al. 2004, Cañadas et al. 2005, Fergusonet al. 2006, Panigada et al. 2008, Praca & Gannier2008). There are however disadvantages of usingsuch proxy measures. Typically, they only explain asmall proportion of the observed variability in animaloccurrence, and their use limits the ability to extrapo-late to other areas because they replace unknowncombinations of direct predictors; the same proxymeasure might be caused by a different combinationof direct predictors in different geographical contexts,resulting in a different relationship with animal occur-rence (Guisan & Zimmermann 2000).

Sperm whale habitat use has been investigated bothwithin the Mediterranean (Cañadas et al. 2002, Gan-

nier & Praca 2007, Azzellino et al. 2008, Praca et al.2009) and worldwide (Waring et al. 2001, Davis et al.2002, Jaquet & Gendron 2002, Rendell et al. 2004,Embling 2008, Skov et al. 2008; studies before 1996have been reviewed by Jaquet 1996). Results have var-ied with some studies being able to draw direct rela-tionships between sperm whale presence and primaryproductivity, sea surface temperature or some aspectsof topography (such as slope or depth), and others find-ing relatively weak links at certain spatial and tempo-ral scales.

As for many cetacean species, modelling spermwhale habitat use is complicated by the dynamicnature of marine ecosystems and by the whales’ mobil-ity, complex life history, and inaccessibility (they areoften offshore and underwater; Redfern et al. 2006). Inaddition, other methodological issues become particu-larly challenging when assessing the habitat prefer-ence of this species. Firstly, distribution informationoften needs to be recorded in tandem with acoustic orphoto-identification data, meaning that detected ani-mals are followed for extended time periods of up toseveral days. Position data carry information relevantto habitat use so they should ideally be used in theanalysis, but advanced statistical techniques arerequired to correct for their inherent autocorrelation(Scott-Hayward 2006, Embling 2008). Secondly, therelationship between sperm whale occurrence andenvironmental covariates is dependent on the spatio-temporal scale at which it is evaluated (Jaquet 1996). Asubstantial temporal or spatial lag (several months andhundreds of kilometres), corresponding to the timeneeded for primary productivity to work through thetrophic web, might occur before top predator distribu-tion responds to variation in a particular proxy mea-sure (Jaquet 1996, Littaye et al. 2004, Croll et al. 2005).Such lags are likely to confound results, so a multi-scale approach is necessary (e.g. Jaquet 1996, Praca etal. 2009). Finally, social groups may have differenthabitat preferences compared to solitary individuals(e.g. mature males in the case of sperm whales) as aresult of their different ecological and biological needs.This difference has been recorded in other terrestrial(Jakimchuk et al. 1987, Litvaitis 1990) and marinemammal species (Stewart & DeLong 1995, Ersts &Rosenbaum 2003), and its evaluation can be particu-larly interesting in those areas that are identified bothas breeding and feeding grounds.

In this study we develop a novel analytical frame-work that can make use of combined acoustic andtracking data and account for autocorrelation in suchdata. We use a multi-scale approach to investigate thepattern of sperm whale distribution around theBalearic archipelago, and the potential differences inhabitat selection by single individuals versus groups.

Pirotta et al.: Modelling sperm whale habitat preference

MATERIALS AND METHODS

Study area. The study area ran from 38 to 41° N andfrom 0.5 to 5° E, enclosing the continental shelf, conti-nental slope and offshore waters around the Balearicarchipelago (Fig. 1a). The Balearic promontory is char-acterised by distinct topographic features (Acosta et al.2002). The narrow shelf to the north of Mallorca andMenorca islands breaks into a steep slope, incised byseveral gullies, while the southern part presents amore gentle depth gradient with 2 distinct canyon sys-tems (Acosta et al. 2003). At the south-western limit ofthis shelf, a south-west to north-east linear scarp (theEmile Baudot Scarp) is characterised by a steep slopeand numerous small canyon systems. Around the west-ern islands, Ibiza and Formentera, the shelf is charac-terised by a variable gradient that peaks on the steepwestern side. In terms of water circulation, the regionis an important transition area between the Balearic-Provençal basin and the Algerian basin (Pinot et al.2002). The interaction between colder, more salineMediterranean waters flowing from the north andwarmer, fresher Atlantic waters creates the BalearicFront over the northern slope of the islands (Garcia etal. 1994). Regional dynamics show a marked interan-nual and seasonal variability (Pinot et al. 2002).

Data collection. Dedicated summer research cruiseswere operated for 6 consecutive seasons (Table 1).Motor-sailing yachts (11–12 m length) were used asresearch platforms. Boat tracks were recorded throughthe data logging software Logger 2000 by the Interna-tional Fund for Animal Welfare (IFAW) that was con-nected to a global positioning system unit (GarminGPS12). Transects were not systematically designed,but the resulting route extensively covered the shelf-break region around Mallorca and Menorca as well assome areas south of Ibiza (Fig. 1a). A hydrophone wasdeployed to detect sperm whales; in 2003, a singlehydrophone (Sensor Technology of Canada; frequencyresponse 0.1–22 kHz) was used, while from 2004onward a dual-element hydrophone (Benthos AQ4;frequency response 0.1–22 kHz) towed at 100 m wasused because it allowed monitoring the sea withoutstopping the boat. Regular acoustic monitoring every30 min in waters deeper than 200 m checked for thepresence of vocalising animals in the area; this condi-tion was defined as ‘On-effort’. Anytime the hydro -phone was not deployed or no systematic listening wasconducted, the research status was considered to be‘Off-effort’. Constant visual scanning of the sea wasalso carried out during daylight hours to support theacoustic search for sperm whales. Because spermwhales are highly vocal, both when foraging andsocialising, they were mainly detected and followedacoustically. When whales were heard, they were

tracked and, during daylight hours, approached tomake visual contact. An encounter was defined as thetime spent in continuous acoustic contact with thewhales, from first hearing them to a loss of acousticcontact exceeding 1 h. A distinction was made be -tween encounters with single individuals, those thatperformed a stereotyped diving pattern and neverassociated with other individuals, and groups, i.e. moreindividuals (often including young animals) that wereshowing clear signs of direct interaction (e.g. socialvocalisations or surface behaviours) or ‘movingtogether in a coordinated fashion over periods of atleast hours’ (Whitehead 2003). The whales were leftwhen all the desired data (photo-identification pic-tures, acoustic recordings and sloughed skin forgenetic analysis) had been collected, unless contactwith them was lost or other conditions necessitated theboat’s departure (e.g. sea state, fuel shortage). Afterthe end of an encounter, the searching effort generallycontinued along the previously planned route.

Unit of analysis. Points corresponding to GPS fixesrecorded approximately every 20 min were used as theunit of analysis. ‘Off-effort’ fixes (i.e. those not with thewhales and not searching for them) were excluded.Each point was classified as a ‘presence’ if the re -searchers were in acoustic contact with the whales oran ‘absence’ if no whales were heard. The points werethen grouped into 2 types of blocks; a ‘follow’ wasdefined as the series of consecutive presence pointsthat formed each acoustic encounter with the whales,and a ‘searching transect’ was defined as the series ofconsecutive absence points that constituted each por-tion of the boat track travelled ‘On-effort’, i.e. between2 follows or ‘Off-effort’ intervals. These blocks wereused in the analysis to account for the autocorrelationbetween the residuals within blocks, while inde -pendence was assumed between blocks (see ‘Dataanalysis’).

Environmental covariates. The variables used topredict sperm whale presence comprised depth, slopegradient, slope aspect, chlorophyll a (chl a) surfaceconcentration, sea surface temperature (SST), sea sur-face height (SSH) deviation, and surface wind direc-tion (Table 2).

Depth was expressed as a negative value in metresand taken from the ETOPO2v2 dataset (resolution 2arc minutes; NOAA 2006). Slope gradient (hereafter‘slope’) was defined as the maximum rate of change indepth in a given grid cell and expressed as percentslope. These data were computed from the ETOPO2v2data using GIS software (Manifold 8.0) at 3 differentspatial scales averaged over progressively larger gridsat resolutions of 2 × 2 n miles (1×), 10 × 10 n miles (5×)and 20 × 20 n miles (10×). Slope aspect (hereafter‘aspect’) was defined as the compass orientation of the

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41.1°N

40.8°

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0.6°E 0.9° 1.2° 1.5° 1.8° 2.1° 2.4° 2.7° 3.0° 3.3° 3.6° 3.9° 4.2° 4.5° 4.8° 5.1°

0.3°E 0.6° 0.9° 1.2° 1.5° 1.8° 2.1° 2.4° 2.7° 3.0° 3.3° 3.6° 3.9° 4.2° 4.5° 4.8° 5.1°

b

a

0 25

n mile

Depth (m)

0 25 n mile

Fig. 1. (a) Study area in the Balearic Islands showing the distribution of effort and whale encounters. Prediction maps for (b) theentire data set; (c) the group subset; and (d) the singleton subset. Projection: UTM 31; Datum: WGS84; Coastline data source:Global Self-consistent Hierarchical High-resolution Shorelines, available at www.ngdc.noaa.gov/mgg/shorelines/gshhs.html;

bathymetry source: 2-minute Gridded Global Relief Data ETOPO2v2 from NOAA

Pirotta et al.: Modelling sperm whale habitat preference 261

c

d

0.6°E 0.9° 1.2° 1.5° 1.8° 2.1° 2.4° 2.7° 3.0° 3.3° 3.6° 3.9° 4.2° 4.5° 4.8° 5.1°

0.6°E 0.9° 1.2° 1.5° 1.8° 2.1° 2.4° 2.7° 3.0° 3.3° 3.6° 3.9° 4.2° 4.5° 4.8° 5.1°

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Fig. 1 (continued)

Mar Ecol Prog Ser 436: 257–272, 2011

slope, ranging from –180 to +180° with respect to truenorth, and also computed from the ETOPO2v2 data seton a scale of 2 n miles. Chlorophyll a surface concen-tration (hereafter ‘chl a’) is a proxy of primary produc-tivity and phytoplankton biomass in the surface layer.We used Moderate Resolution Imaging Spectrora-diometer (MODIS) data from NASA’s Aqua satellite,pre-processed by the NASA’s Goddard Space FlightCenter (GSFC) using the SeaWiFS Data Analysis Sys-tem (SeaDAS) software (Fu et al. 1998). The data wereavailable as monthly concentrations (mg m–3) at a res-olution of 0.05° lon gitude × 0.05° latitude from theNOAA CoastWatch program (http://coastwatch. pfeg.noaa. gov/ index.html). Some of the downloaded datawere incomplete with missing data generally in theform of stripes in the maps that were filled with theinterpolation tools in the Manifold GIS system. Sincetime is necessary for changes in primary production tofilter through the trophic levels to whales, the effect ofthis covariate was evaluated over different temporalscales. We did not know in advance how long this lagwas, so we considered the concentrations of chl aaround 3 different peak months (February, April and

June). The value of chl a for eachperiod was calculated as a weightedaverage of the monthly chl a valuesaround the peak, with the peak monthhaving the largest weight and themonths further away from the peakhaving less weight. To allow for uncer-tainty in the precise way primary pro-duction affects higher trophic levels,we tested 3 candidate weighting func-tions (all Gaussian kernels), centred oneach of the 3 peak months and withstandard deviations (SDs) correspond-ing to 1/2, 1/5 and 1/10 of the timeinterval between the peak month andthe research month (i.e. July, exceptfor 2003, when the survey was con-ducted in August). The different SDsdetermined how fast the influence ofthe monthly chl a values declinedaround each peak. As a result, 9 differ-ent chl a maps (3 peak maps, each with3 SDs of the distribution of the weights)were obtained, with grid resolutions of0.05° (≈ 3 n miles). Each temporal scalewas then evaluated on 2 different spatial scales, corresponding to reso -lutions of 0.05 and 0.5°, the latterachieved by averaging chl a concen-trations over larger grid cells. We thenselected which of these 18 spatio-tem-poral scales could best predict whale

presence using an information criterion approachdetailed below. For SST (°C), we used data collectedby NOAA’s Advanced Very High Resolution Radiome-ter (AVHRR) aboard NOAA’s Polar Operational Envi-ronmental Satellites. We used the Path finder Version5.0 Sea Surface Temperature data set (Kilpatrick et al.2001) as processed by the University of Miami’s Rosen-stiel School of Marine and Atmospheric Science andNOAA’s National Oceanographic Data Center. Thedata were downloaded at a resolution of 0.05° longi-tude × 0.05° latitude from the NOAA CoastWatch pro-gram website (see above). Monthly and weekly valuesof SST were associated with each data point, togetherwith the variability in weekly SST (expressed as slopeof the relative surface and calculated in the ManifoldGIS system) and the deviation of the SST in each 0.05 ×0.05° cell from the monthly median. This latter wasimplemented to allow whale presence to respond torelative rather than absolute temperatures, becausethe median SST varied substantially between years.SSH deviation (hereafter ‘SSH’) was the differencebetween the measured height of the sea surface andthe expected mean height, calculated by reviewing

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Year Research Searching Encounters No. of encounters period effort (km) (km) Overall Group

2003 1–28 Aug 2467 141 3 22004 10 Jul–6 Aug 2070 310 9 32005 9 Jul–5 Aug 1992 392 12 52006 14–28 Jul 1702 270 9 22007 3–28 Jul 1835 374 11 02008 15–27 Jul 1033 233 12 5

Table 1. Research effort and encounters with sperm whales

Covariate Unit Spatial scale(s) Temporal scale(s)

Depth m 2 × 2 arcmin –

Slope % 2 × 2 arcmin 10 × 10 arcmin –20 × 20 arcmin

Aspect ° 2 × 2 arcmin –

Chl a mg m–3 0.05 × 0.05° 1 mo lag (Jun); SD: 1/2, 1/5, 1/100.5 × 0.5° 3 mo lag (Apr); SD: 1/2, 1/5, 1/10

5 mo lag (Feb); SD: 1/2, 1/5, 1/10

SST °C 0.05 × 0.05° Weekly, monthly

SST slope % 0.05 × 0.05° Weekly

SST deviation °C 0.05 × 0.05° Monthly(from median)

SSH m 0.25 × 0.25° Monthly

Surface wind ° 0.25 × 0.25° Monthlydirection

Table 2. Environmental covariates considered in the analysis and their scales. SST: sea surface temperature; SSH: sea surface height

Pirotta et al.: Modelling sperm whale habitat preference 263

historic altimetry data. This is generally influenced ona daily basis by the tidal cycle and, on a longer term, bythe overall water circulation. We used data from theAVISO (Archiving, Validation and Interpretation ofSatellite Oceanographic data) program, which wasavailable at a resolution of 0.25° longitude × 0.25° lati-tude from the NOAA CoastWatch program website(see above). Finally, surface wind direction data,expressed as an angle from 0° to 359° where 0° corre-sponds to the north, were also available from theNOAA CoastWatch program website (see above), originating from the SeaWinds sensor on NASA’sQuikSCAT satellite and processed using NASA- developed algorithms (Freilich 2000). The data weredownloaded at 0.25° resolutions in the form of the 2components of wind velocity: the zonal wind (W-Ecomponent) and the meridional wind (S-N compo-nent), which were then combined to obtain overallwind direction.

Other variables. In order to assess potential differ-ences in the probability of encountering sperm whalesbetween the different research seasons, year was alsoincluded as a factor in the models. Additionally, the lat-itude and longitude of each location were included;these are generally used to account for unknown pre-dictors and, consequently, they compete with the avail-able ones in trying to explain whale distribution. In thiscase, their inclusion had the effect of making eachpoint unique. Each point was thus visited only once, sono offset term was required in the model to account foreffort. Because of this convenience, latitude and longi-tude were not subjected to model selection and wereretained in the models regardless of their significance.

Data analysis. A Generalized Additive Model (GAM)framework was used to model the relationship be -tween sperm whale presence/absence at each GPS fixand the predictors described above (Hastie & Tibshi-rani 1990, Wood 2006). This flexible, data-driven ap-proach has already been extensively used in the studyof cetacean distributions (e.g. Forney 2000, Hastie etal. 2005, Ferguson et al. 2006). Specifically, a binomial-based GAM with a logit link function was employed tomodel sperm whale probability of presence.

Whale follows lasted from a few hours up to 3 d. Dur-ing these periods, the whales were always on themove, sometimes zigzagging and other times movingrectilinearly but generally displacing consistentlyaway from the position where they were initiallyencountered (Whitehead 2003) and thereby typicallytraversing a range of environmental conditions. A tra-ditional approach would entail substantial subsettingof the data to reduce serial autocorrelation betweensuccessive points; for instance, only the initial, final ormiddle positions would generally be considered as apresence point in the analysis (e.g. Gannier & Praca

2007). This approach has the disadvantage of discard-ing information on which habitat whales were select-ing during the follow period. Using all the data pointsto account for the occurrence of the animals over thewhole habitat where they were tracked is therefore apreferable approach (Embling 2008). The problem isthat GAM inference relies upon independence be -tween model residuals, an assumption that is violatedby using all the points within a follow or searchingtransect because the conditions at each location will besimilar to those at the previous location. This spatialautocorrelation leads to the underestimation of theuncertainty associated with model estimates. Data sub-sampling and the use of a coarser analysis resolutionare potential solutions, but they also reduce samplesize (Embling 2008). An alternative way to deal withthis issue while retaining all the information from eachfollow or searching transect is to relax the indepen-dence assumption and explicitly model the correlationbetween the residuals using Generalized EstimatingEquations (GEEs; Liang & Zeger 1986). Under thisapproach, data points are grouped in blocks withinwhich residuals are allowed to be correlated, whileindependence is assumed between separate blocks. Acorrelation structure may be specified for the errorswithin each block that can accommodate both spatialand temporal dependence. Several options are avail-able for the definition of the correlation structure, butGEEs are quite robust to misspecifications (Liang &Zeger 1986, Pan & Connett 2002). When unsure aboutthe true underlying structure of the dependencebetween the residuals, the use of a simple workingindependence model is advisable (Pan 2001). There-fore, a working independence model was preferredover the specification of a correlation structure in thepresent study. This approach generally leads to effi-cient estimates for model coefficients (McDonald 1993,Pan & Connett 2002) and uses robust, modified sand-wich variance estimators to produce realistic standarderrors. These models combine the ‘variance estimatefor the specified model with a variance matrix con-structed from the data’ (Hardin & Hilbe 2003), thusaccounting for the observed lack of independencebetween the residuals within blocks and inflating thestandard errors to make robust inference. Sharples(1989, in McDonald 1993) showed by means of a simu-lation study that this so-called empirical variance esti-mator performs well when compared to other estima-tors that assume a specific model for the correlation.This approach has already been successfully applied tothe study of cetacean habitat preference by Panigadaet al. (2008).

The geepack library (Yan et al. 2010) in R (R Devel-opment Core Team 2009) was used to fit binomial-based GEE-GLMs with a logit link and a working cor-

Mar Ecol Prog Ser 436: 257–272, 2011

relation structure defined by block (i.e. the followsand the searching transects). The splines library (RDevelopment Core Team 2009) then allowed us tobuild cubic B-splines within the GEE-GLM, thus lead-ing to a GEE-GAM. All the covariates were consid-ered either as linear terms or as 1-dimensional smoothterms (4 degrees of freedom), modelled as cubic B-splines with one internal knot positioned at the aver-age value of each variable. The best subset of vari-ables to retain in the model was identified by meansof an approximate form of the quasi-likelihood underthe independence model criterion (QIC; Pan 2001), amodified version of the Akaike Information Criterion(AIC) that accounts for the fact that GEEs are basedon quasi-likelihood. The approximation is called QICu

(Hardin & Hilbe 2003), and it can be employed tocompare models in a stepwise selection. The QICu

score is provided by the R library yags (Carey 2004).Including all the covariates at the different scales inthe same model would have caused instabilitybecause of the strong collinearity between them. Thisnecessitated the development of an ad hoc procedureto carry out variable selection. Each covariate wasfirst evaluated at its different spatial and temporalscales in order to select only one to be tested in thefull model. This was done by comparing the QICu

score of a null model (i.e. containing only latitude andlongitude) with the score of a series of models, eachadditionally containing the covariate in question atone of the scales under examination. Because thepackage splines does not allow the selection of theappropriate degree of smoothness, the inclusion ofeach covariate as a linear term was also evaluated.Once the most appropriate spatial and temporal scaleand form (linear or smooth) were identified, a fullmodel was fitted, containing all the covariates sel -ected by the above procedure together with the onesavailable at a single scale. First, the QICu score wasused to select the best form (linear or smooth) inwhich to incorporate these latter single-scale covari-ates. Then, a manual stepwise selection was carriedout, where a series of reduced models was fitted ateach step, containing all the terms but one, and themodel with the lowest QICu was used in the followingstep. This procedure was continued until each of thecovariates, if removed, caused the QICu score toincrease. Year was evaluated as a factor, and latitudeand longitude were not subject to model selection(see ’Other variables’). Repeated Wald’s tests (anova.geeglm function in the geepack library) were carriedout on the final model to determine the significance ofeach covariate (Hardin & Hilbe 2003). Non-significantvariables were removed one by one, and the signifi-cance of the others was re-tested until all the associ-ated p-values were smaller than 0.05. At this point,

the final model was obtained. Our aim in the studywas to accurately understand the factors drivingsperm whale distribution, for which the inclusion ofunnecessary predictors would be confusing ratherthan maximising model fit. We thus adopted thisintentionally conservative 2-step model selection pro-cedure because some of the predictors selected usingthe QICu returned high p-values under the Wald’stests. The entire procedure was applied to the fulldataset and repeated on 2 subsets, one only contain-ing the follows of single individuals (hereafter ‘single-ton subset’) and the other only the groups (‘groupsubset’) in order to assess any potential variation inthe habitat use by whales showing different groupingbehaviours.

The contribution of the explanatory variables in thefinal model was visualised by means of partial residualplots of the estimated relationship between the res -ponse (on the link scale) and each predictor coupledwith confidence intervals based on the GEE standarderrors. The package ggplot2 (Wickham 2009) was usedfor this purpose. We evaluated model performancewith confusion matrices, which compare the binarypredictions to the observed values and report the trueand false presences and the true and false absences,thus summarising the goodness-of-fit of the model(Fielding & Bell 1997). In order to build a confusionmatrix, an appropriate cut-off probability value has tobe chosen, beyond which a prediction is considered asa presence. Rather than selecting arbitrary cut-offsthat could introduce a bias, if inappropriate (Boyce etal. 2002), a Receiver Operating Characteristic (or ROCcurve) can be used (library ROCR in R; Sing et al.2009); this curve plots the sensitivity (or true positiverate, i.e. the proportion of correctly classified pres-ences) versus the specificity (or false positive rate, i.e.the proportion of incorrect presence classifications) fora binary response as the cut-off probability is varied(e.g. Zweig & Campbell 1993). The best cut-off proba-bility for the observed data corresponds to the pointwhere the distance between the ROC curve and the45° diagonal is maximised, which was identified bycalculating the perpendicular distance of each point ofthe ROC plot from the line of slope 1. Additionally, thearea under the curve (AUC) can be used as an indica-tion of the model performance (the closer to 1, the bet-ter the model; Boyce et al. 2002); this was also com-puted using the ROCR library.

A grid of cells 2 × 2 n miles was created and thecentroids used for prediction. To avoid extrapolations,only points within the margins of the study area wereincluded. GIS tools were used to return the values ofthe covariates for each point. For the time-varyingvariables (e.g. SST), average values were computed.When year was kept in the model, the average year

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was used (2005) and the values of thetime- varying covariates were averagedacross this time period. The probabilityof whale presence in each location wasthen predicted in R using the finalmodel. All predictions were made onthe response scale (i.e. a value of prob-ability between 0 and 1). The pre-dicted values were finally visualised ina map, where a gradation of colourshelped to locate the areas of higherpredicted probability of encounteringthe whales.

The annotated R code developed forall the analysis is made available as anelectronic supplement at www.int-res.com/articles/suppl/m436p257_supp/.

RESULTS

A total distance of 11 099 km was cov-ered in acoustic search mode across the6 yr. Sperm whales were encountered56 times (of which 17 were sightings ofgroups), for a total of 1720 km ofacoustic contact (Table 1; Fig. 1a).

Entire data set

The selected chl a covariate was the April peak withSD of the weights equal to 1/10 of the lag on a spatialscale of 20 × 20 n miles and in a linear form. For SST,weekly values (in a linear form) were retained. Slopewas selected on the 20 × 20 n mile spatial scale, againas a linear term. These covariates were then enteredin the full model with those remaining. The finalmodel after variable selection retained depth, slope,aspect, weekly SST and chl a as predictors of whalepresence. Wald’s tests for the significance of thesecovariates excluded slope, SST and chl a so that thefinal model only included depth (p = 0.0165) andaspect (p = 0.0002) in addition to latitude and longi-tude. The realistic modelling of the autocorrelation inour data means that the confidence intervals aroundthe modelled relationships remain wide (Fig. 2).Therefore, the detailed form of the best fit relation-ships must be interpreted with caution. Nevertheless,our conservative model selection procedure ensuresthat the retained variables are genuinely importantpredictors of sperm whale distribution because ourmodel performed well in terms of its fit to the data.The cut-off for the construction of the confusionmatrix was chosen at a probability of 0.2516, as indi-

cated by the ROC curve. The resulting matrix sug-gested that the model predicts correctly 72% of thepresences and 67% of the absences. The area underthe ROC curve (AUC) was equal to 0.77 (SD = 0.007),confirming a good model performance and providingfurther assurance that the model was not overfitted.The probability of sperm whale occurrence declineswith decreasing depth (i.e. approaching the coast)with a second peak around 500 m depth (Fig. 2c).Additionally, sea floor oriented eastward and south-ward (i.e. aspect > 0 and <–150) seemed to be pre-ferred (Fig. 2d). The prediction map showed that themodel correctly identified the area north of Mallorcaand Menorca and west of Mallorca as a region wherethe probability of encountering sperm whales is low(no encounters across the 6 yr), while defined hot-spots are located south, east and north-east of these 2islands and south of the 2 western islands (Fig. 1b).Despite its overall close fit to the data, the modelfailed to recognise some regions around Menorca assuitable habitat for the species; whales were encoun-tered closer to the coast both to the south and to thenorth-east of this island, but low probabilities werepredicted here.

Pirotta et al.: Modelling sperm whale habitat preference 265

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Mar Ecol Prog Ser 436: 257–272, 2011

Analysis by grouping behaviour: groups and single individuals

For the subset of data originating from social groups,the preliminary investigation on the multi-scale covari-ates retained slope on the 2 × 2 n mile scale and SST ona weekly scale, both as smooth terms (i.e. non-linear).The February peak of chl a with standard deviation ofthe weights equal to 1/10 of the lag and spatial scale20 × 20 n miles was also selected for the full model as asmooth term. The subsequent variable selection, basedfirst on QICu scores and then on Wald’s tests, produceda final model with latitude, longitude, weekly SST (p =0.02) and slope (2 × 2 n mile resolution; p = 8.155 × 10–8)as cubic B-splines with 4 degrees of freedom (Fig. 3).The considerations about confidence intervals notedwith respect to the overall analysis above also apply tothese results. While sperm whale groups seemed toprefer colder waters (Fig. 3c), they also tended to occurwith lower probability in areas with intermediate slopegradients (Fig. 3d). The ROC curve selected a cut-offprobability of 0.2205 for the construction of the confu-sion matrix; the model correctly predicted 67% of thepresences and 89% of the absences. The AUC was0.85 (SD = 0.009), again showing good model perfor-

mance. The prediction map (Fig. 1c) was broadly com-parable to the one obtained from the model fitted onthe entire data set; some areas south, east and north-east of the islands were identified as suitable habitatfor sperm whale groups, even though the southern hot-spots appeared to be more restricted. Interestingly, themodel performed better on the north-eastern side ofMenorca where the previous one predicted whalepresence poorly.

For the singleton subset (i.e. including only the fol-lows of single individuals), the investigation of multi-scale covariates selected monthly values of SST (as alinear term) and slope on the 20 × 20 n mile scale (as asmooth term). For chl a, in this case, variable selectionidentified 2 different temporal peaks on the 2 spatialscales, so that both of them were kept in the subse-quent analysis; the April peak (SD of the weights: 1/10of the lag) was retained as a smooth term on the 20 ×20 n mile scale, while the June peak (SD of theweights: 1/5 of the lag) was selected as a smooth termon the 2 × 2 n mile scale. The final model after variableselection contained latitude, longitude, year (p =0.016), monthly SST (p = 0.02) and aspect (p = 2.163 ×10–7), the latter as a smooth term with 4 degrees offreedom (Fig. 4). Single individuals concentrated in

areas with high monthly average sur-face temperatures (Fig. 4d). Therewere significant differences betweenyears (Fig. 4c) with higher sightingprobability in 2007. Aspect showed asimilar pattern to the analysis of thecomplete dataset, albeit with muchmore associated uncertainty. Again,confidence intervals were wide aroundmost of the modelled relationships,but the selected model performed well.The cut-off probability selected throughthe ROC was 0.1162. The confusionmatrix showed that the model pre-dicted correctly 91% of the presencesand 65% of the absences. As in the 2previous cases, the AUC was quitehigh (0.83; SD = 0.007). The predictivemap (built with 2005 as the year factorand the relative values of SST) differedfrom the previous 2 (Fig. 1d); singleindividuals only used the area off thesouthern and south-eastern coast of theislands, while low probabilities werepredicted for the eastern and north-eastern sides (where only one individ-ual was ever encountered). Al thoughnot shown here, 5 additional mapswere drawn using the other years (i.e.not 2005) and the associated average

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the actual data values is also shown

Pirotta et al.: Modelling sperm whale habitat preference

value of SST; despite some small-scale differences, thegeneral pattern was consistent, suggesting that thesegregation of single whales in a smaller portion of thestudy area is not an artefact.

DISCUSSION

Our data show that in the period from 2003 to 2008sperm whales did not use the study area uniformly butwere concentrated in the southern, eastern and north-eastern waters of the Balearic archipelago. No whalewas ever encountered in the region north and west ofthe archipelago, and the final model correctly associ-ated this area with low occurrence probabilities. Thispreference seems to be quite stable across time; thevisual inspection of yearly data shows that the whaleswere consistently encountered mainly in those areasthat have been identified as hot-spots. In addition, no

differences in sighting probability were found be -tween research seasons.

Gannier et al. (2002) and Gannier & Praca (2007)hypothesised a spatially bimodal distribution for thisspecies in the western basin, an idea that was subse-quently supported by Azzellino and colleagues (2008)in the Pelagos Sanctuary (Ligurian Sea). As a result oftheir opportunistic feeding strategy, Mediterraneansperm whales were found both over the continentalslope, where habitat selection is believed to be drivenmainly by bathymetric features, and in the offshorewaters (i.e. far from topographic singularities) wherethe animals appear to respond to the position of ther-mal fronts (Gannier & Praca 2007). This was explainedas the result of the positive influence of both complextopography (steep slopes, seamounts and canyons) anddownwelling/upwelling water movements (associatedwith frontal zones) on high trophic level biomass. Eventhough the prey targets might change, sperm whales

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Fig. 4. The presence of singletons modelled as a function of (a)latitude, (b) longitude, (c) year, (d) monthly sea surface tem-perature (SST) and (e) aspect. Shaded areas (or grey seg-ments in the case of year) represent 95% CIs (GEE-based).

A rug plot with the actual data values is also shown

Mar Ecol Prog Ser 436: 257–272, 2011

would therefore be able to exploit profitable foodresources in both habitats (Gannier et al. 2002). Simi-larly to other studies where the research effort waslikewise focused on the continental slope and adjacentwaters (e.g. Cañadas et al. 2002), topography was thusfound to be the driving factor affecting sperm whaledistribution in the study area. Although physiographicvariables were competing with spatial covariates (lati-tude and longitude) in model selection and despite therobust standard errors used in the hypothesis tests, thepresent analysis provides compelling evidence thatbottom depth and aspect are significantly influencingthe presence of sperm whales in the Balearic region.Specifically, sperm whales seem to prefer watersdeeper than 2000 to 2500 m, but they are also presentover the 500 to 1000 m contour. Additionally, they con-centrate in areas where the bottom aspect is approxi-mately between 0° and 210°, i.e. where the seafloor isoriented north-eastward, eastward or southward.Depth might be associated with the bathymetric zona-tion of cephalopod assemblages (Quetglas et al. 2000),and a comparable range has been identified by otherstudies both within the Mediterranean (e.g. Cañadaset al. 2002 in the Alboran Sea) and outside the basin(e.g. Davis et al. 2002 in the Gulf of Mexico or Embling2008 off the west coast of Scotland). Slope aspect couldinteract with water circulation to determine the down-welling/upwelling movements that are believed toinfluence the availability and concentration of spermwhale prey, giving the significant relationship wefound. In contrast with other studies, we found no rela-tionship with the steepness of the slope, which hasbeen deemed crucial in aggregating prey (e.g. Praca etal. 2009), even though we tested for its potential effectat 3 different spatial scales. In short, a steep slopealone might be insufficient to support sperm whalepresence if it is not oriented correctly, possibly in relation to the directionality of the main water cur-rents. This idea could help to reconcile the contra -dictory results regarding the role of slope as a pre -dictor of sperm whale presence in the Mediterranean(see, for example, Praca & Gannier 2008 versusCañadas et al. 2002). The interaction between waterflow and complex seafloor characteristics appears to berelevant to the species’ distribution in other areas(e.g. Jaquet 1996, Davis et al. 2002, Tynan et al. 2005,Skov et al. 2008). The combination of oceanographicand topographic features is likely to promote verticaland horizontal water movements that enhance primaryproductivity and thus sustain a richer biomass alongthe entire trophic web (Tynan et al. 2005). Con -sequently, these areas become centers of trophic trans-fer where dense patches of food are predictably avail-able to all top predators (Davis et al. 2002, Yen et al.2004).

While groups were distributed throughout the pre-ferred areas identified by the overall model, the hot-spots in the southern waters were smaller and differentvariables were retained by model selection. Groupsshowed a bimodal relationship with slope gradient ona small scale (2 n miles) with a preference for eithersteep or flat bottom gradients. This pattern may reflecta short-term bimodality in their habitat use resultingfrom different habitat preferences associated with dif-ferent activities, such as foraging and socialising. Forexample, Lusseau & Higham (2004) found that bot-tlenose dolphins use a different habitat when involvedin social activities. We did not have enough data to partition by activity, so further research is requiredto assess this hypothesis. In addition, sperm whalegroups appeared to prefer cooler waters. A negativerelationship with temperature has already been docu-mented (Jaquet 1996, Rendell et al. 2004, Embling2008), and Rendell et al. (2004) speculated that lowertemperatures might correspond to a better habitat forsperm whale prey. A more direct effect on the prey(rather than the enhancement of primary productivity)would also justify the small temporal scale (weekly values) that was found to best predict sperm whalepresence.

In contrast, single animals were encountered in alimited portion of the area identified by the modelusing the overall data set, being restricted to 2 mainregions south and south-east of the islands. These soli-tary individuals showed a stereotyped diving patternfor long time spans, a behaviour that is typically asso-ciated with foraging males, although the sex of theseindividuals was not verified. Their probability of pres-ence varied significantly between years, possibly sug-gesting a variable profitability of the area as a feedingground. Males are known to move between this regionand other parts of the western basin (Drouot-Dulau &Gannier 2007) so that alternative areas might be cho-sen to forage according to variation in resource avail-ability. In contrast to groups, we found an increasedprobability of presence for singletons associated withhigher monthly SST. This was unexpected, given theliterature listed above, but a segregation from socialgroups might help to explain the discrepancy.

In summary, the habitat exploited by sperm whalegroups and solitary individuals appeared to differ. Thissegregation appears to be mainly described by con-trasting responses to sea surface temperature, withgroups less frequently found in warm waters where,conversely, the probability of sighting single individu-als was higher. The reasons for this separation areunknown, but different ecological requirements mayrepresent one potential explanation. While single ani-mals can focus the choice of their habitat on prey avail-ability, groups might have to make a trade-off between

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contrasting needs, such as the search for food andsocial interactions or the presence of immature indivi -duals, which are known to heavily affect the behaviourof adults (Whitehead 1996). This could also lead indi-viduals in groups to target other prey species with different spatial distributions (Whitehead 2003). Alter-natively, groups could outcompete singletons, forcingthem to use suboptimal warmer waters (Whitehead etal. 1989). Whitehead (2003) hypothesised that a re -duced feeding success of adult males in those placeswhere they overlap with groups could be due to thecompetition with groups of smaller individuals. De -mon strating that a sexual segregation exists on smallerscales could offer interesting insights into the mecha-nisms that have led to its development at a large scale.These findings also have important methodologicalimplications, as they point out that a distinction be -tween groups and single animals is necessary for anaccurate evaluation of sperm whale space use. Whilein the southern waters pooling all the encounters in asingle data set only resulted in the identification oflarger hot-spots, fitting a separate model for groupsdetermined a better goodness-of-fit on the eastern sideof Menorca where the overall model performed poorly.Some contradictory results available in the literaturecould also derive from pooling the observations fromsperm whales in different behavioural or social states;for instance, no relationship with surface temperaturewould have been found in this work if the data werenot split into the 2 subsets.

The present study contributes to the development ofa modelling framework for the analysis of sperm whalehabitat use in 3 specific ways. (1) The non-linear rela-tionships between whale probability of presence andmost environmental predictors suggests that GLMsmay be insufficient to capture the species’ habitat pref-erence correctly; the importance of environmentalvariables could have been missed or misinterpreted ifunderlying shapes of their influence were assumed(Hastie et al. 2005). The selection we performed onhow each variable should enter the model settled onnon-linear forms for all except SST for singleton ani-mals, which supports this view. (2) Although the detailsof the smooth terms employed here could not be opti-mised as suggested by Wood (2006), the use of one-dimensional B-splines allowed autocorrelation to beaccounted for via the GEEs (as in Panigada et al. 2008).Cetacean observations are often spatially and tem -porally autocorrelated. In particular, sperm whaleacoustic and tracking data are unavoidably so, be -cause the same individual or group is generally fol-lowed over consequent sampling points (Embling2008). Correcting for this dependence is thus critical tocorrectly estimate uncertainty (Redfern et al. 2006).These data are expensive and time-consuming to col-

lect and so discarding intermediate data points toobtain independence is undesirable because it reducesthe already limited effective sample size (Redfern et al.2006). Our study confirms that GEEs are an appropri-ate tool to deal with this issue. (3) The effect of some ofthe covariates was evaluated at different spatial andtemporal scales in order to account for a potentialdelay in sperm whale responses to oceanographic andphysical processes, such as the increase in chl a sur-face concentration, SST or and the effects of sea floorsteepness on water circulation. The choice of an arbi-trary scale at which to investigate the significance ofthese factors can lead to confusing and contradictoryresults, so a multi-scale approach is required (Jaquet1996). For example, we found that the presence ofsperm whale groups was influenced by SST on aweekly scale, while single individuals appeared torespond to monthly averages of the same variable. Weused a multi-scale approach based on a series ofweighted averages to model lags of approximately 5, 3and 1 mo between the peak in chl a surface concentra-tion and whale occurrence (4 mo is the time lag gener-ally recognised to exist between phytoplankton andcephalopods; Jaquet 1996). Despite the evaluation ofmultiple scales and the correlation that previous stud-ies have found outside the Mediterranean (Jaquet1996), chl a did not show any significant relationshipwith the species in the area. Possibly, this factor affectssperm whale presence at much larger spatial scales,which might include the entire region of the Balearics.Indeed, Jaquet & Whitehead (1996) recorded a correla-tion in the Pacific at a scale of more than 320 n miles(i.e. about twice the size of our entire study area).

On the whole, these analytical techniques gave goodpredictions of sperm whale presence around theBalearic Islands both when the entire data set was con-sidered (70% of the points were correctly classified)and when it was split into the 2 subsets (78% correctclassifications were obtained for both the group andthe singleton subsets). Nonetheless, our approachalmost certainly oversimplifies the complex relation-ships between whale presence and indirect environ-mental variables, not least by the exclusion ofunknown relevant covariates. Direct information onthe availability and movements of sperm whale preywould thus be beneficial for a better understanding ofthe relationship of this species with its environment(Jaquet & Gendron 2002, Friedlaender et al. 2006).

The identification of sperm whale key areas is thefirst step in developing specific conservation measuresfor the Balearic archipelago. For instance, habitat mod-elling results could help define the boundaries of can-didate Marine Protected Areas (MPAs) by providing abetter description of the species distribution comparedto other simple measures of occurrence (e.g. encounter

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rates; Cañadas et al. 2005). The establishment of a net-work of MPAs encompassing the identified hot-spots inthis important feeding and breeding ground wouldprobably have beneficial effects on the entire ‘Endan-gered’ stock of Mediterranean sperm whales (Reeves& Notarbartolo di Sciara 2006, Notarbartolo di Sciara &Birkun 2010). Evaluating the stability of the specieshabitat preference in time and space and validating itwith independent data is however necessary beforethe effective implementation of any measure. Particu-larly, further research is needed in the regions at thenorth-eastern and at the south-western ends of thestudy area, which were identified as important hot-spots of whale presence. The searching effort was lim-ited in both of these areas and additional evidence isrequired to exclude any edge effects (e.g. resultingfrom their extreme values of depth or latitude and lon-gitude). The high probability of presence predictedhere must therefore be interpreted with caution. More-over, no extrapolation outside the survey region isadvisable until the mechanisms underlying the ob -served use of space are rigorously tested (Ferguson etal. 2006, Panigada et al. 2008). Similar habitats or pro-cesses may be characterised elsewhere by differentindirect variables (Hamazaki 2002), and the effect ofthe identified predictors could also differ outside thesampled area (Panigada et al. 2008).

Future research should aim to improve the analyticalframework presented here. For instance, testing moresophisticated correlation structures for the GEEswould be interesting; a user-defined correlation matrixthat better reflects the true structure of the autocorre-lation could increase the efficiency of model estimates,although the issue is controversial (Pan & Connett2002). Moreover, the interactions among the availablecovariates (e.g. between seafloor characteristics andthe processes affecting water circulation, such as themain winds or currents) should be included in themodels to better describe the complex underlying rela-tionships between environmental proxies and whalepresence. The role of other ecologically relevant pro-cesses in shaping habitat use also remains to be tested(e.g. the interspecific competition with other squid- eating cetaceans, as in Waring et al. 2001).

In parallel to the refinement of the analytical tech-niques, an extensive research effort is required to pro-vide new systematic data for the construction of aglobal model of sperm whale distribution coveringboth offshore and continental slope regions of theMediterranean and other ocean basins. Basin-widedata would also offer reliable indications on the densi-ties, movements, site fidelity and habitat segregationof single males and social groups. We have shown hownew analytical approaches can offer robust insightsinto the factors driving the distribution of this species

in the critical region of the Balearic archipelago, usingthe kind of data that are commonly collected duringsurveys at sea. This information is increasingly neededto improve our limited understanding of the speciesecology in the Mediterranean Sea, assess the currentstatus of this population and inform effective conserva-tion and management efforts.

Acknowledgements. This work uses the data collected duringthe Balearics Sperm Whale Project, a research programstarted in 2003 by L.R. in collaboration with A. Cañadas (Alni-tak, Spain) and C. Mundy (One World Wildlife, UK) to inves-tigate the biology and ecology of sperm whales around theBalearic Islands. We are grateful to One World Wildlife andthe Whale and Dolphin Conservation Society for financialsupport. Our fieldwork was invaluably supported by theBalearic Government Office of Fisheries Management, espe-cially by J. M. Brotons of that office. We thank all the volun-teer assistants who took part in data collection, C. Booth foradvice on GEEs, A. Cañadas for providing information on theenvironmental covariates and C. Blight for help with GISanalysis.

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Editorial responsibility: Matthias Seaman, Oldendorf/Luhe, Germany

Submitted: February 25, 2011; Accepted: May 31, 2011Proofs received from author(s): August 23, 2011