The study area encompassed the entire Mediterranean Sea (from 6°W to 36°E and from 30°N to 46°N). The Mediterranean Sea is a distinctive ecosystem with a relatively small continental shelf and a mostly cyclonic circulation. The water column in the Mediterranean Sea is divided into distinct water masses: (1) the surface waters, which extend between 0 and 200 m in depth, originate from the Atlantic and enter the Mediterranean Sea via the Strait of Gibraltar; (2) underneath, the intermediate Levantine water circulates, on average between 200 and 600 m, this is the warmest and saltiest water of the Mediterranean Sea; (3) below 600 m, the deep waters originate in part from the intermediate Levantine water (Millot and Taupier-Letage, 2005). Even if dives made by sperm whales do not generally exceed 1,500–2,000 m (Amano and Yoshioka, 2003; Irvine et al., 2017; Towers et al., 2019), we chose to consider the entire water column, down to a depth of 4,100 m.

The ASI survey is the first survey carried out at the Mediterranean basin scale for all cetacean species. Acoustic surveys were conducted using hydrophone arrays towed by the R/V Song-of-the-Whale (Figure 1), a 21 m auxiliary-powered cutter-rigged sailing research vessel. A 400 m tow cable, close to the surface at a depth of less than 10 m, was used to isolate the array from any noise generated by the vessel. Acoustic data were collected 24 hours a day to maximise survey effort when water depth was appropriate (greater than 50 m). The vessel maintained a speed of 5 to 8 knots when surveying sperm whales to avoid bias due to animal movement by exceeding the speed of the target animals by 2-3 times (Buckland et al., 2015). The speed of sperm whales can vary between 2 and 6 knots (Arnbom et al., 1987), but they generally maintain an average speed of 2.1 knots (Whitehead, 2018). A pair of AQ-4 elements (Teledyne Benthos) was incorporated into the hydrophone array. They were characterised by a receiving sensitivity of -201 dB re 1V/µPa and a flat frequency response ( ± 1.5 dB) from 1 Hz to 30 kHz. Pre-amplifiers (29 dB gain) were use to prevent voltage-drop between the array and the vessel. A distance of 3 m separated each hydrophone element. A SAIL DAQ card (SA Instrumentation) digitised the array outputs at 48 kHz using a 10 Hz high pass filter and a 12 dB gain added to the signal. A click detector module was used to detect candidate sperm whale clicks in real time using PAMGuard (Gillespie et al., 2008). The click detector identified spectral properties, with most energy at or below 12 kHz (Watkins, 1980; Møhl et al., 2003).

A line transect distance sampling protocol was used during the survey and the perpendicular distances for each detection were estimated in PAMGuard using the target motion analysis tool. Sperm whale clicks were identified, analysed and validated by the Marine Conservation Research (MCR; Boisseau et al., this special issue).

The effort transects were linearised and segmented into 10 km segments for which the detection conditions were homogeneous. Each acoustic detection was then attributed to the effort segment on which the animals were detected (Figure 1).

During an at-sea survey, not all animals are detected acoustically; the probability of detecting an animal decreases with the distance from the transect and as detection conditions degrade. A detection function was therefore fitted to the acoustic data using Multiple Covariate Distance Sampling models (MCDS; Miller et al., 2019). The models were fitted considering two key distributions, half normal (hr) and hazard rate (hz) and different detection conditions (sea state, wave height in meters and wind speed in knots). The best model was selected according to the Kolmogorov-Smirnov and Cramer-von Mises goodness-of-fit tests and the Akaike information criterion (AIC; Buckland et al., 1993). The models were fitted using the ‘dfuncEstim’ function of the ‘Rdistance’ package (McDonald et al., 2019) and the two tests mentioned above were performed using the ‘gof_ds’ function of the ‘Distance’ package (Miller et al., 2019). Based on the detection function, ESWs were estimated for each class of the selected detection variable. An ESW is defined so that the number of objects detected beyond this distance is equal to the number of objects not detected before this limit (Buckland et al., 1993). ESWs were calculated using the ‘ESW’ function of the ‘Rdistance’ package (McDonald et al., 2019).

The number of individuals detected was determined by using a click detector module in PAMGuard (Gillespie et al., 2008) which was configured to identify potential sperm whale clicks. Field recordings were independently assessed in PAMGuard by two experienced analysts to identify potential sperm whale click sequences. Candidate clicks were identified when they formed part of a click sequence, characterised by consistent bearings and regularly spaced click intervals. Variations in bearing information were used to distinguish individual click sequences (Lewis et al., 2018). Consequently, acoustic detections were made at the individual level rather than at the group level, allowing the number of detected animals to be determined.

Knowing the ESWs and the number of individuals detected, it was possible to estimate the density of individuals along the transects. This density was then multiplied by the total area sampled during the survey (here 1,312,625 km²) to obtain the total abundance of sperm whales and the associated confidence intervals (Buckland et al., 1993).

In total, 13,806 km of transects were conducted by boat during the ASI survey, of which 97.17% were carried out in good conditions (Beaufort sea state ≤ 4). The final dataset included 284 acoustic detections of sperm whales. The majority of these detections were recorded in the western Mediterranean basin and along the Hellenic Trench.

The wind speed variable associated with a hazard rate key function best explained the distribution of sperm whale detections as a function of distance from the transect (Appendix 2, 3). The qqplot suggested a good fit.

As the distance from the transect increased, the probability of detecting sperm whales decreased more rapidly as wind speed increased (Figure 2). Consequently, as the wind speed increased, the estimated ESWs decreased (Figure 3). When the wind speed was < 5 knots, the estimated ESW was 4.88 km, while when the wind was > 25 knots the estimated ESW was 3.14 km.

Based on the detection function and the ESWs, the abundance of sperm whales in the surveyed blocks was estimated at 2,959 individuals [2,077 - 4,265]. It was a global estimate produced for the sampled areas of the Mediterranean Sea (i.e., in the Western Mediterranean Sea and in the Ionian Basin).

The ASI survey filled gaps in the overall summer distribution of sperm whales in the Mediterranean Sea, as it was the first to be conducted at such a large scale (Mannocci et al., 2018). We obtained maps of the summer distribution with a low error rate.

As sperm whales are deep divers that spend most of their time underwater foraging (dives of up to 138 minutes during foraging; Watwood et al., 2006), they are more easily detected by passive acoustics thanks to the echolocation clicks they emit almost permanently while diving. Indeed, during the vessel survey, only 26 visual detections were recorded compared to 284 acoustic detections. Although the detection rate was ten times higher using acoustic techniques, all animals were not detected because sperm whales typically do not vocalise when at the surface (Watwood et al., 2006; Fais et al., 2016) and/or individuals may have been beyond the detection range of the hydrophone array. On average, sperm whales dive for 45 minutes and emit sounds and clicks for 81% of the dive, making them easy to detect acoustically (Watwood et al., 2006; Fais et al., 2016). Furthermore, as they emit clicks at relatively low frequencies (≤12 kHz), they can be detected over long distances. The ESW was estimated to be between 0.5 and 1.7 km visually (Virgili et al., 2019), whereas acoustically it was estimated to be between 3.14 and 4.88 km. The detection capabilities of the acoustic platform are significantly higher.

The total abundance of sperm whales was estimated at 2,959 individuals [2,077 - 4,265] in the surveyed blocks (i.e., in the Western Mediterranean Sea and in the Ionian Basin). It was similar to or greater than the estimates obtained in previous studies. Lewis et al. (2018) have acoustically detected 194 sperm whales in the entire Mediterranean Sea. The various surveys took place in 2004 in the western basin and spread over several years, 2003, 2007 and 2013 in the entire eastern basin. They estimated an abundance of 1,842 sperm whales [842 – 2,842] in the entire Mediterranean Sea. Poupard et al. (2022) have acoustically detected 422 sperm whales in the Pelagos sanctuary over 147 days of recording. They estimated a density of 0.00169 individuals.km^-2 in the sanctuary. Our model predicted average sperm whale densities of 0.03 individuals.km^-² throughout the western Mediterranean basin. Gannier (2018) have visually (from 1988 to 2012) and acoustically (since 1994) recorded 157 detections of sperm whales in the western Mediterranean basin. They estimated a population size between 200 and 1,000 individuals in the North-Western Mediterranean Sea.

Using acoustics to detect sperm whales is therefore an effective method to estimate their abundance. In the future, it would be interesting to develop more systematic acoustic surveys when targeting deep divers (mainly sperm whales and Cuvier’s beaked whale Ziphius cavirostris), while continuing to use visual observation for other species.

However, the main limitation associated with the use of acoustic detection is the estimation of the number of individuals (Kimura et al., 2010; Marques et al., 2013). It is difficult to distinguish individuals that emit sounds at similar frequencies in an acoustic recording unless they emit a sound simultaneously. This can lead to an underestimation of the abundance.

In this study, we were able to predict the summer sperm whale distribution throughout the Mediterranean Sea. However, to highlight a change in species distribution throughout the year, the same survey should be conducted at least in winter. Lack of data is a recurrent problem in cetacean habitat modelling; there are very few surveys conducted outside the summer periods creating seasonal gaps (Mannocci et al., 2018). Although we showed that sperm whale detection was influenced by wind speed, the estimated ESW with a wind speed of 25 knots was high (3.14 km), so sperm whales would probably be well detected even in winter conditions. However, detection rates for other species, such as dolphins, may decrease in elevated sea states. Shabangu et al. (2022), for example, suggest that high wind speeds induce a decrease in cetacean acoustic detectability due to increased ambient noise. Such a large-scale survey targeting only sperm whales would therefore not be cost-effective. However, other possibilities exist, such as deploying passive acoustic hydrophones on moorings, buoys, or vessels, which would record sounds throughout the year. Fixed buoys are very effective at assessing the seasonal presence of species at local scales (Mellinger et al., 2007; Stafford et al., 2007). However, they are less suitable for studying animal habitat use, at least at a large scale. This would require the installation of extensive buoy networks, which are very costly and require regular calibration to ensure accurate results (Shabangu and Findlay, 2014). In this case, a large-scale survey using towed acoustics seems more appropriate.

Although we predicted the sperm whale distribution in the entire Mediterranean Sea, the sampling effort was not uniform throughout the area. The gap analysis identified the eastern part of the Mediterranean basin, especially the Levantine basin, as an extrapolation area. This suggests that the sampling effort was not sufficient in this area and a more intensive sampling effort could help better describe the habitat used by sperm whales in the eastern Mediterranean Sea. More research is needed in the east as anthropogenic pressures are high for sperm whales (e.g., ship strike risk in the Hellenic Trench) and therefore we need to improve our understanding of distribution and seasonal variation.

We expected Beaufort sea state to be selected in the detection function because cetacean detection, notably visual detection, is often affected by sea state. Here, the wind speed was selected as the variable most affecting the acoustic detection; the higher the wind speed the lower the detection probability. This is consistent with the fact that Beaufort sea state is a subjective measure of wind speed as perceived by a visual appreciation of the effect of wind on the water surface (Barlow, 2015). Ambient noise, generated by the boat, but also by all processes other than cetacean sounds, would probably be a more important factor to consider when assessing the acoustic detectability of cetaceans. We encourage the systematic recording of ambient noise levels in future acoustic surveys.

We choose to use GAMs in this study because of their ability to handle non-linear and non-monotonic relationships; GAMs are relevant for modelling ecological relationships (Booth and Hammond, 2014). In GAMS, the explained deviance is an indicator of model quality. Deviance is rarely high for cetaceans because the variables used do not fully explain the distribution of animals, as they are proxies of prey distribution. In contrast, a high deviance would have indicated an over-fitting of the relationships to the data. The value of the selected model was 38.8%, which is a good result, similar to other studies (Bailey and Thompson, 2009; Tepsich et al., 2014; Virgili et al., 2017; Virgili, 2018; Virgili et al., 2019). We were rather confident in the model as the explained deviance was quite high but not too high and the NRMSE calculation gave a result of 5.4% error, indicating a low prediction error rate.

The good performance of the model may be related to the use of proxies that are probably more direct than the commonly used surface variables. Environmental variables were separated according to the water masses of the Mediterranean Sea, which were assumed to be homogeneous. However, as sperm whales can dive much deeper than 1,000 m (Whitehead, 2018), we might have considered other depth classes. Particularly, the 600-4,100 m layer may not have been sufficiently precise for a deep-diver that feeds in this layer depth. We might consider splitting the deepest layer to be consistent with the depths used by the sperm whales. However, this would lead to a considerable increase in the number of variables and calculation time, as well as a possible lack of variation between depth classes, as water masses tend to be more homogeneous at greater depths.

In addition, other environmental and biological variables could have been considered. Some studies use other variables to study cetacean distribution such as the distribution and concentration of prey species (Pendleton et al., 2020; Virgili et al., 2021) or canyon areas, because submarine canyons are widely recognised as hotspots in cetacean distribution (Tepsich et al., 2014). Pendleton et al. (2020) suggested that using modelled prey availability, rather than oceanographic proxies, could be important to forecast species distributions. In contrast, in Virgili et al. (2021), the model that used prey distributions obtained from the SEAPODYM model did not accurately model the prey of deep-diving cetaceans, the simulated prey mostly corresponded to the prey of the prey targeted by deep-divers. The SEAPODYM model is a tool for simulating the three-dimensional distributions of prey species in marine ecosystems. It considers various factors such as physical oceanography, prey behaviour, and predator-prey interactions to estimate the spatial distribution of prey. To study the distribution of deep divers, it therefore seems more relevant to use proxies that characterise the water column rather than the distribution of their prey, which is not modelled well enough.

Similarly, it might have been relevant to study anthropogenic pressures such as the impact of noise pollution on sperm whale distribution in order to find out whether these have a direct negative effect on sperm whale distribution. Poupard et al. (2022) analysed the ambient noise recorded by two hydrophones on a 25 m depth buoy to identify the impact of noise pollution (high or low ambient noise) on sperm whales. They showed that sperm whales were present all year round in the Mediterranean Sea, but their abundance decreased when the ambient noise was high due to the presence of ships such as ferries. This is particularly true near the coast where the anthropogenic noise is very high (Buscaino et al., 2016; Pieretti et al., 2020). Poupard et al. (2022) suggested that sperm whales do not come close to ships because ambient noise masks their echolocation when foraging. In addition, many studies have shown that cetaceans would modify their vocalisations in the vicinity of vessels and increase their sound level to maintain acoustic contact with other individuals (Castellote et al., 2012; Melcón et al., 2012; Shabangu et al., 2022).

Sperm whales were predicted in areas associated with high gradients of temperatures at the surface, strong variations in the current velocity between 200 and 600 m, low variations in sea bottom temperatures and rather low chlorophyll-a concentrations in the surface layer. In the literature, sperm whales have often been associated with bathymetric features, such as depth, continental slopes or canyons and seamounts, as well as frontal systems and other mesoscale features such as cyclonic eddies (Virgili et al., 2019; Pirotta et al., 2020). Recently, Virgili et al. (2022) have shown that other parameters influence the distribution of sperm whales at the surface and at depth, such as temperatures and eddies at depth. We also showed that two of the selected variables in the model characterised the water column and not the surface (the standard deviation of the sea floor temperature and the standard deviation of the eddy kinetic energy between 200 and 600 m). For species such as sperm whales, it is therefore relevant to consider the whole environment and not only the surface.

The model predicted average sperm whale densities around 0.03 individuals.km^-² in the entire western Mediterranean basin, with maximum densities predicted in the Algerian and Ligurian-Provençal basins, more precisely in the Ligurian Sea and off the Gulf of Lion continental slope. The highest densities were predicted in the protected area of the Pelagos sanctuary (Ligurian Sea). In comparison, Lewis et al. (2018) predicted 2,12.10^-3 individuals per km² in the southern part of the western Mediterranean Sea and 0,12.10^-3 individuals per km² in the eastern Mediterranean Sea (with, however, high densities in the Aegean Sea, the Hellenic Trench and the northern Ionian Sea). Our predictions in the southern part of the western Mediterranean Sea coincide with their results.

In summer, sperm whales seemed to concentrate mainly in continental slope areas, whether off the Gulf of Lion, the Liguro-Provençal Sea, the Algerian Coast or around Corsica, frequenting depths above 2,000 m (Gannier, 2018; Laran et al., 2018). This suggests the existence of an east-west gradient of sperm whale densities, with higher abundances in the west. Indeed, from summer to autumn, the northern part of the western basin is a major concentration and feeding area for sperm whales (Drouot et al., 2004). Other studies indicate that the presence of sperm whales extends further east along the Hellenic Trench from south-west Kefallonia Island to central south Crete (Frantzis et al., 2014) and even to the Turkish coast as far as the western part of Antalya Bay (Öztürk et al., 2010). From a single survey performed at the scale of the Mediterranean Sea, we were able to predict hotspots observed at more local scales.

The high presence of sperm whales in the southeast of the Gulf of Lions and in the Ligurian Sea could be explained by the presence of numerous canyons (Harris et al., 2014). Submarine canyons act as a connecting corridor between continental shelf areas and deep waters. As a result, they are widely recognised as cetacean concentration areas (Tepsich et al., 2014). The high densities of sperm whales in the Ligurian Sea can be explained by the presence of numerous canyons in this geographical area. A large-scale study revealed the presence of sperm whales along the Hellenic Trench and the west coast of Greece, and in the north-western Mediterranean Sea from the Gulf of Lion to the Ligurian Sea (Lewis et al., 2018), providing support for the model results.

In addition, sperm whales are often observed in the channel between Mallorca and Ibiza, an area characterised by the presence of three seamounts. The Balearic Archipelago is one of the few areas in the Mediterranean Sea where females, juveniles and single males are regularly observed (Pirotta et al., 2020). This is due to the critical role of the area as a breeding and feeding ground for the threatened Mediterranean population (Rendell and Frantzis, 2016).

Sperm whales were predicted to occur in the Ionian Sea (0.03 individuals.km^-², mainly off the Italian and Greek coasts), which was consistent with the literature. For example, Lewis et al. (2007); Lewis et al. (2018) found densities 0.24.10^-3 individuals.km^-² in the Ionian Sea and 0.12.10^-3 individuals.km^-² in the eastern Mediterranean Sea (similar results to Frantzis et al., 2014). Sperm whales appear to prefer the underwater relief of the sides of the Hellenic Trench at depths between 500 and 1,500 metres (Frantzis et al., 2003). However, densities were comparatively lower than in the western basin. There were two possible explanations for this: either there was less effort in the Ionian Sea, or, as suggested by Lewis et al. (2007), density estimates in the Ionian Sea were underestimated because sperm whales tend to congregate in large groups along the Hellenic Trench, skewing the count results. Even if densities were underestimated, the Ionian Sea appeared to be important for the species as it may be a breeding ground according to Drouot et al. (2004).

The eddy kinetic energy was one of the main variables that explained the distribution of sperm whales in our model. Biggs et al. (2000) showed that sperm whales are mainly distributed in cyclonic eddies, which are proxies for prey distribution. Cyclonic eddies are mesoscale structures that induce a locally increased concentration of plankton in response to the upwelling of nutrient-rich water. The abundance of plankton would induce the strong presence of prey for deep-diving cetaceans, through a trophic cascade mediated by vertically migrating micronekton. Sperm whales are large warm-blooded mammals not physiologically limited by water temperature or other hydrographic features; hence their spatial distribution would be primarily driven by the distribution of their prey, such as squid, supposedly concentrated in cyclonic oases (Biggs et al., 2000). The eddies present at a depth of 200 m can strongly modify the mixing and dispersion of organic matter and thus lead to a concentration of many prey species (Pingree and Le Cann, 1992; Koutsikopoulos and Le Cann, 1996).

Statistic modelling allows the prediction of the number and distribution of animals, their physiological status, demographic rates and interactions between individuals and species (Grimm and Railsback, 2013). This information allows more effective conservation measures to be taken.

The Mediterranean sperm whale population is particularly exposed to various anthropogenic pressures, such as high-intensity noise activities, fishing activities, ship strikes, plastic ingestion, or exposure to chemical pollution (Aguilar et al., 2002; Reeves and Notarbartolo di Sciara, 2006; Notarbartolo-Di-Sciara, 2014). To mitigate the impact of these activities, management measures need to be implemented, based on knowledge of the distribution of sperm whales. Our study shows that in the western basin, sperm whales are found in the east of the Corsican coast and in the north of the Balearic Sea, but also in the Liguro-Provençal, Ionian, and Algerian basins where sperm whale densities reached 0.05 individuals.km^-². A high density of sperm whales has been estimated in the Pelagos sanctuary, mainly in the east of Corsica but also in the south of France in the Ligurian Sea, but a large area where sperm whales were predicted is not protected by the sanctuary, mainly south-east of Gulf of Lion. Since this species has been considered endangered by the International Union for Conservation of Nature’s Red List (IUCN; Notarbartolo di Sciara et al., 2012) for several years, it may be relevant to extend this marine protected area to provide better protection. High densities of sperm whales were also predicted in the Balearic Sea. This area became a marine protected area (MPA) in 2018, as it has been recognised as a corridor for cetaceans. In the model, about 0.06 individuals.km^-² were predicted in the north of the MPA, which is higher than the average density in the whole area (0.03 individuals.km^-²). It would be necessary to extend this MPA to the east to protect sperm whales more effectively.

Even though the MPAs do not fully encompass the distribution areas of sperm whales, three Important Marine Mammals areas (IMMAs) have been identified within these regions: the Northwest Mediterranean Sea IMMA, the Shelf of the Gulf of Lion IMMA, and the Western Ligurian Sea and Genoa Canyon IMMA. These protected areas represent a discrete portion of crucial marine mammal habitat and have the potential to be earmarked and administered for conservation purposes. The identification of IMMAs is intended to raise awareness among policy and decision makers regarding the urgent need to ensure the favourable conservation status of marine mammals in these specific regions through the implementation of appropriate management measures.

However, the model only predicts the summer distribution and not the annual distribution, which may be different in other seasons. It is therefore essential to conduct winter surveys and incorporate the results from these surveys into our results.