Y Cherel
email: cherel@cebc.cnrs.fr

Revisiting taxonomy of cephalopod prey of sperm whales caught commercially in subtropical and Southern Ocean waters

Keywords: Antarctica, cetacean, Histioteuthidae, odontocete, squid, trophic relationships

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RESEARCH PAPER

Revisiting taxonomy of cephalopod prey of sperm whales caught commercially in subtropical and Southern Ocean waters Yves Cherel a, * a Centre d'Etudes Biologiques de Chizé (CEBC), UMR 7372 du CNRS-La Rochelle Université, 79360 Villiers-en-Bois, France

Introduction

The sperm whale Physeter macrocephalus is the largest of the toothed whales (odontocetes) and the commonest large cetacean today. It has a wide geographic range from the equator to high latitudes, where its diet consists almost exclusively of oceanic cephalopods, mainly oegopsids, with fish being a significant prey group in some areas [START_REF] Clarke | Cephalopods as prey. III. Cetaceans[END_REF]. The sperm whale is an apex predator that was estimated to consume ~110 million tons of cephalopods each year, thus highlighting its major role and the importance of cephalopods both as prey and as consumers within the trophic web of the pelagic ecosystem of the World Ocean [START_REF] Clarke | Beaks, nets and numbers[END_REF][START_REF] Santos | Assessing the importance of cephalopods in the diets of marine mammals and other top predators: problems and solutions[END_REF]. Since the sperm whale was historically heavily harvested, considerably more is known about its food than about other cephalopodeating whales (Clarke 1986b).

The initial step in studying the feeding habits of sperm whales was to identify cephalopods morphologically, with unfortunately no or little quantification of the species involved [START_REF] Kawakami | A review of sperm whale food[END_REF][START_REF] Mikhalev | To the problem of the feeding of sperm whales from the Southern Hemisphere[END_REF]. The second step was to use the cephalopod beaks that accumulate by hundreds and thousands in the whale stomach (over 18,000 beaks in a single stomach ;Clarke 1986b). Identification and quantification of cephalopod prey of marine predators by using the morphology of their sclerotized beaks was initiated in the 60s and subsequently developed with an initial focus on sperm whale food (Clarke 19862a,b, 1972(Clarke 19862a,b, , 1986a)). The method was at its best in a seminal and beautifully illustrated monography that depicts the feeding habits of sperm whales caught in the southern subtropics and the Southern Ocean [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF]. Tens of thousands of lower beaks were described, illustrated, numbered and measured, thus allowing detailed identification of the cephalopod prey of sperm whales in South Africa, western Australia and in the Antarctic. This and subsequent publications [START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF][START_REF] Pascoe | Cephalopod remains from the stomach of a sperm whale stranded off Patagonia[END_REF][START_REF] Clarke | Cephalopods represented by beaks in the stomach of a sperm whale stranded at Paekakariki, North Island, New Zealand[END_REF][START_REF] Evans | The diet of sperm whales (Physeter macrocephalus) in southern Australian waters[END_REF][START_REF] Gomez-Villota | Sperm whale diet in New Zealand. Master thesis, Auckland University of Technology Imber MJ (1973) The food of grey-faced petrels (Pterodroma macroptera gouldi (Hutton)), with special reference to diurnal vertical migration of their prey[END_REF] form the basis of our knowledge about the food of this overwhelmingly important cephalopod predator worldwide.

Unfortunately, several limitations now hinder an easy use of those data. Firstly, the initial monograph [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF] was published in an important journal that is now difficult to get access to a copy. Secondly, and more fundamentally, our knowledge of cephalopod taxonomy has developed over the last 40 years, thus obscuring the picture regarding beak names in previous investigations. Four features are notable within that context. Cephalopod taxonomy improved, thus inducing (i) new names for well-known species (e.g. Filippovia knipovitchi, formerly Moroteuthis knipovitchi; Bolstad 2010), and (ii) the description of new species to science (e.g. Asperoteuthis lui; Braid 2017). Moreover, improvement in the identification of lower beaks resolved (iii) previous mismatches between beak names and well-described species (e.g. ?Psychroteuthis, now Discoteuthis discus; Clarke and Roeleveld 1998), and (iv) the links between well-described beaks and the corresponding squid species (e.g. Moroteuthis A and Moroteuthopsis ingens; Clarke 1986a). Hence, a recent review of taxonomy and of the tracking of beak names over time increased substantially the diversity of pelagic squids in the Southern Ocean and underlined the importance of previously poorly known taxa as prey of seabirds and marine mammals [START_REF] Cherel | A review of Southern Ocean squids using nets and beaks[END_REF].

The main goal of the present work was to synthesize the dispersed information on cephalopod taxonomy and on identification of cephalopod beaks to upgrade the list of cephalopod prey of sperm whales in southern subtropical waters and in the Southern Ocean.

Its ultimate objective was to facilitate the use of this important scientific literature to researchers developing programs on cetaceans and on cephalopods, their trophic relationships, and on the functioning of the pelagic ecosystems of the Southern Hemisphere. Revisiting the food of sperm whales caught commercially brings up to date unique data sets that cannot be collected again, because commercial whaling has ceased and the species is protected worldwide. The sperm whale is today globally designated as Vulnerable on the IUCN Red List of Threatened species [START_REF] Taylor | Physeter macrocephalus (amended version of 2008 assessment). The IUCN Red List of Threatened Species 2019[END_REF].

Materials and methods

Study sites, physical oceanography and biogeography

The study focused on two sperm-whale dietary investigations that complement each other in terms of geographical coverage of the Southern Hemisphere, from the southwestern Atlantic to the southwestern Pacific Ocean, thus including the southern Atlantic and Indian Oceans [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF][START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF]. Food samples came firstly from three whaling stations that were located on the west coast (Donkergat) and on the east coast (Durban) of South Africa, and on the west coast of Australia (Albany) [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF].

Secondly, some samples were collected from pelagic factories operating in the Tasman Sea [START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF] and in the Antarctic, including South Georgia and the pelagic Antarctic (the South Shetland Islands and South Orkney Islands) [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF].

According to physical oceanography, sperm whales were caught in subtropical waters and within the Southern Ocean. The latter is defined as water masses located south of the Subtropical Front (STF). The main marine fronts within the Southern Ocean are the Subantarctic and the Polar Fronts; they delineate the following oceanic zones, from North to South: the subantarctic Zone (SAZ), Polar Frontal Zone (PFZ) and Antarctic Zone (AZ) [START_REF] Pollard | Physical controls on biogeochemical zonation in the Southern Ocean[END_REF]. The oceanic zone north of the Southern Ocean (north of the STF) is the Subtropical Zone (STZ). Hence, sperm whales from Donkergat (western South Africa), Durban (eastern South Africa) and Albany (western Australia) [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF] were caught within the STZ of the eastern Atlantic, and of the western and eastern Indian Ocean, respectively. Whales from the Tasman Sea [START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF] were killed mainly within the STZ of the western Pacific, with some of them coming from the SAZ (to 47°S).

Finally, sperm whales from South Georgia, and from the South Orkney and South Shetland Islands [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF] were caught further south, within the AZ of the southwestern Atlantic.

Analysis and nomenclature

Cephalopod beaks that were identified in sperm whale food samples [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF][START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF] were listed and the validity of each taxon was thoroughly examined using various means (Table 1), including successive updates by M Clarke [START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF], Clarke 1986a[START_REF] Clarke | The diet of sperm whales (Physeter microcephalus Linnaeus 1758) off the Azores[END_REF][START_REF] Clarke | Cephalopods in the diet of sperm whales caught commercially off Durban, South Africa[END_REF][START_REF] Clarke | Cephalopods represented by beaks in the stomach of a sperm whale stranded at Paekakariki, North Island, New Zealand[END_REF][START_REF] Clarke | Description and analysis of cephalopod beaks from stomachs of six species of odontocete cetaceans stranded on Hawaiian shores[END_REF]. Synonymies of beak names were tracked over publications and time (details in Cherel 2020). The work also benefited from the opportunistic examination of beaks from Clarke's collection by the author, because beaks from sperm whale stomachs [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF] were deposited to several museums and scientific organizations, including the British Antarctic Survey (Cambridge, UK), and the Port Elizabeth Museum at Bayworld (South Africa). The work on beaks was completed by a review of articles and of recent grey literature (PhD) devoted to species, species groups and assemblages to complete and update both taxonomy and biogeography (e.g. [START_REF] Braid | Resolving the taxonomic status of Asperoteuthis lui Salcedo-Vargas, 1999 (Cephalopoda, Chiroteuthidae) using integrative taxonomy[END_REF][START_REF] Evans | A systematic review of the squid family Cranchiidae (Cephalopoda: Oegopsida) in the Pacific Ocean[END_REF][START_REF] Fernandez-Alvarez | An onto-phylogenetic journey through the life history of flying squids (Cephalopoda: Ommastrephidae)[END_REF][START_REF] Kelly | Systematics of the Octopoteuthidae Berry[END_REF].

The three following issues limited the retrospective analysis of dietary data on fresh items. Firstly, the lack of detailed information precludes knowing which cephalopods were caught within the STZ and/or within the SAZ of the Tasman Sea [START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF].

However, since only one whaling position lied within the SAZ, it was assumed that all the cephalopods from the Tasman Sea refer to the STZ (Tables 2 and3). Secondly, while it is expected that the southernmost caught fresh Octopoteuthis specimens in the Tasman Sea (in the SAZ, at 47°S) refer to Octopoteuthis fenestra (see below), it was not detailed how many individuals were eaten by the whales, thus explaining why O. fenestra was not listed in Table 2. Thirdly, I removed two Filippovia knipovitchi and added two Onykia robsoni amongst the fresh remains of cephalopods from South Georgia (Table 2), because (i) fresh remains of O. robsoni were identified from sperm whales caught at South Georgia, but no fresh specimens were recorded in the corresponding table [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF]), (ii) there was a mismatch in the number of fresh F. knipovitchi when comparing different tables (two more or less specimens), and (iii) beaks of the two species are closely-related and easy to confuse, thus likely explaining why their accumulated beaks were pooled [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF].

It is important to consider the following issues regarding data on accumulated beaks.

Retrospective analysis necessitated back calculation of the beak numbers of some species by using percentages that were indicated within the text and tables [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF]. There were also some limitations due to the initial data analysis (Table 3). Firstly, lower beaks of Liguriella podophtalma included those from Galiteuthis glacialis (see below). Secondly, beaks of Histioteuthis eltaninae at South Georgia and in the pelagic Antarctic were pooled with those of H. atlantica, as were beaks from O. robsoni with those of F. knipovitchi [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF]. Thirdly, according to beak size and location, Octopoteuthis spp. included two to three different taxa (see below) that were numbered in [START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF] but pooled in [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF]. Fourthly, beaks called "Others" included those from Discoteuthis discus at Donkergat and Durban [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF]. Finally, the lack of a database including detailed beak measurements (lower rostral length, LRL) precluded updating the estimation of cephalopod size (mantle length, body mass) and thus of the absolute and relative species-specific biomasses consumed by sperm whales.

Results

Overall, forty-five different beaks were identified and described in [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF] and [START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF]. Amongst those 45 cephalopod taxa (Table 1), the labelling of 11 (24.4%) beaks was right, three (6.7%) are still undetermined at the species level, and the name of the 31 (68.9%) remaining taxa had to be changed due to improvement in both taxonomy (n = 14, 31.1%) and beak identification (n = 12, 26.7%), and to initial misidentifications (n = 5, 11.1%).

Taxonomic updates and species notes

Most taxonomic updates were detailed in [START_REF] Cherel | A review of Southern Ocean squids using nets and beaks[END_REF], but some taxa required some additional information.

Chiroteuthidae

Five Chiroteuthis beaks, namely C. joubini, C. ?joubini, Chiroteuthis sp. A, Chiroteuthis sp. B and Chiroteuthis sp. C were described in [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF] and [START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF]. While Chiroteuthis sp. A and Chiroteuthis sp. C were subsequently synonymized with C. joubini and C. veranyi, respectively [START_REF] Clarke | The diet of sperm whales (Physeter microcephalus Linnaeus 1758) off the Azores[END_REF]), the species identification of C. ?joubini, and Chiroteuthis sp. B was problematic. The presence of luminous patches on eyes rather than photophores and its Antarctic location of capture suggests that the single head of Chiroteuthis sp. B corresponds to C. veranyi. C. ?joubini beaks are closely similar to those described as Chiroteuthis A from sperm whales caught off Peru [START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF]. Drawings of Chiroteuthis A beaks [START_REF] Clarke | Cephalopod remains from stomachs of sperm whales caught off Peru and Chile[END_REF]) look like those of C. veranyi, which is the single species of Chiroteuthis recorded in the area [START_REF] Nesis | Cephalopods of the world. Squids, cuttlefishes, octopuses and allies[END_REF], Alexeiev 1994). Overall, this suggests that C. ?joubini and Chiroteuthis sp. also correspond to C. veranyi.

Two recent taxonomic studies synonymized ?Mastigoteuthis A and ?Mastigoteuthis B [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF] with two species of the chiroteuthid genus Asperoteuthis, A. lui [START_REF] Braid | Resolving the taxonomic status of Asperoteuthis lui Salcedo-Vargas, 1999 (Cephalopoda, Chiroteuthidae) using integrative taxonomy[END_REF] and A. acanthoderma [START_REF] Cherel | is a junior synonym of Asperoteuthis acanthoderma[END_REF], respectively. ?Mastigoteuthis B beaks were erroneously named Mastigoteuthis A in Table 1, but not in the text of [START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF].

Cranchiidae

Lower beaks of Galiteuthis armata refer to three different species of cranchiids [START_REF] Cherel | A review of Southern Ocean squids using nets and beaks[END_REF], namely Galiteuthis suhmi in Clarke and[START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF]L. podophtalma andG. glacialis in Clarke (1980 Text-fig. 225). [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF] found two modes in beak size of G. armata, suggesting two species, the largest being G. armata (= L. podophtalma) and the smallest a second species he also found in albatross food samples. Indeed, lower beaks from L. podophtalma and G. glacialis are pretty similar, but those from L. podophtalma darken at, and reach, a larger size than those from G. glacialis, the latter species being one of the commonest cephalopod prey of albatrosses within the Southern Ocean [START_REF] Cherel | A review of Southern Ocean squids using nets and beaks[END_REF].

Confusion was increased when beaks named ?Taonius megalops (Clarke 1980 Text-fig. 209) were re-named G. armata, because one head was in sufficiently good condition to indicate that the species was not a Taonius but a Galiteuthis species [START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF]. Indeed, both ?Taonius megalops [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF]) and G. armata [START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF] now correspond to the rarely reported Galiteuthis suhmi [START_REF] Evans | A systematic review of the squid family Cranchiidae (Cephalopoda: Oegopsida) in the Pacific Ocean[END_REF][START_REF] Cherel | A review of Southern Ocean squids using nets and beaks[END_REF]. [START_REF] Voss | Systematics, biology and biogeography of the cranchiid cephalopod genus Teuthowenia (Oegopsida)[END_REF] synonymized Galiteuthis (= Teuthowenia) sp. B [START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF], misnamed as G. armata within the text p 33 but not in Tables 1 and2) with Teuthowenia pellucida (details in Cherel 2020).

The genus Liocranchia includes two species, with only one, L. reinhardti, living in subtropical waters where it is common [START_REF] Nesis | Cephalopods of the world. Squids, cuttlefishes, octopuses and allies[END_REF], thus explaining the shift here from Liocranchia sp. [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF] to L. reinhardti.

Cycloteuthidae

Beaks described as ?Large Psychroteuthis and ?Psychroteuthis [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF], and as ?Discoteuthis [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF][START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF] correspond to those of the two species of the genus Discoteuthis, D. discus and D. laciniosa, respectively [START_REF] Clarke | The diet of sperm whales (Physeter microcephalus Linnaeus 1758) off the Azores[END_REF][START_REF] Clarke | Cephalopods in the diet of sperm whales caught commercially off Durban, South Africa[END_REF][START_REF] Clarke | Description and analysis of cephalopod beaks from stomachs of six species of odontocete cetaceans stranded on Hawaiian shores[END_REF].

Octopoteuthidae

Two and three size modes of Octopoteuthis lower beaks were found in the diet of sperm whales caught at Donkergat and Durban [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF]), and at Albany and in the Tasman Sea [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF][START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF], respectively. Modes refer either to gender because females have larger beaks than males [START_REF] Kelly | Systematics of the Octopoteuthidae Berry[END_REF], or more likely to different taxa.

-The smallest Octopoteuthis species (mode at 8-9 mm LRL) from Donkergat, Durban and Albany remains undetermined. [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF] tentatively identified it as O.

sicula, but the species is endemic to the Atlantic and is not recorded from the Indian Ocean [START_REF] Kelly | Systematics of the Octopoteuthidae Berry[END_REF]).

-O. rugosa corresponds to the peak at 10-11 mm LRL, max 12.5 mm LRL (Donkergat, Durban and Albany) [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF]) and to beaks with LRL <11.5 mm (Tasman Sea) [START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF]. The species has a southern circumglobal distribution [START_REF] Kelly | Systematics of the Octopoteuthidae Berry[END_REF]).

-The third peak occurred at 13.0-14.5 mm LRL at Albany [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF]) and it corresponds to beaks with LRL>11.5 mm of Octopoteuthis sp. A in the Tasman Sea [START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF]. [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF] tentatively identified the corresponding species as O. longiptera, which is today a nomen dubium [START_REF] Kelly | Systematics of the Octopoteuthidae Berry[END_REF]). The species remains unidentified, but the newly described O. fenestra [START_REF] Kelly | Systematics of the Octopoteuthidae Berry[END_REF]) is a good candidate because: i) its maximum LRL is 13.6 mm, a larger size than that of all the other small Octopoteuthis species (Kelly 2019), (ii) O. fenestra has been collected south of Tasmania and in New Zealand waters [START_REF] Kelly | Systematics of the Octopoteuthidae Berry[END_REF], which fits well with its presence in the diet of sperm whales caught in Australian waters and not in South Africa [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF][START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF] ), and (iii) Octopoteuthis flesh recorded from sperm whales caught within the SAZ in the Tasman Sea [START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF] is likely to correspond to O. fenestra, which is the southernmost and single Octopoteuthis species living in the Southern Ocean [START_REF] Kelly | Systematics of the Octopoteuthidae Berry[END_REF]).

-In the Tasman Sea, large beaks with a LRL >15 mm were called Octopoteuthis sp.

(giant) B [START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF]. They correspond to the still undescribed giant Pacific Octopoteuthis sp. that lives in the western Pacific and possibly has a southern circumglobal distribution [START_REF] Kelly | Systematics of the Octopoteuthidae Berry[END_REF].

Two size modes of Taningia danae lower beaks were found in the diet of sperm whales caught at Donkergat and Durban [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF], and in the Tasman Sea [START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF], thus suggesting that the genus Taningia is composed to two species [START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF]. Indeed, a recent taxonomic revision split the monotypic T. danae into five different taxa, including the cosmopolitan tropical-subtropical T. danae and the newly described Southern Hemisphere T. fimbria [START_REF] Kelly | Systematics of the Octopoteuthidae Berry[END_REF]. The correspondence between beak size and species is not established but available information suggest that the large and the small LRL peaks correspond primarily to T. danae and T. fimbria, respectively.

Ommastrephidae

Beaks of Todarodes sp. were collected at Donkergat, Durban, Albany and in the Tasman Sea [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF][START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF]. Morphology and biogeography indicate that they were either T. angolensis, T. filippovae or a mix of both. The picture is even more complicated because firstly, the taxonomic status of T. angolensis outside South African waters needs to be investigated [START_REF] Cherel | A review of Southern Ocean squids using nets and beaks[END_REF], and secondly, beaks from the Ommastrephes bartramii species complex that occurs in the area (Fernandez-Alvarez 2018) are morphologically similar to those of the genus Todarodes [START_REF] Cherel | A review of Southern Ocean squids using nets and beaks[END_REF]. Indeed, a subsequent analysis of new material that included whole specimens from sperm whales caught at Durban found two O. bartramii (now O. cylindraceus, Fernandez-Alvarez 2018) and showed that all Todarodes specimens were T. filippovae [START_REF] Clarke | Cephalopods in the diet of sperm whales caught commercially off Durban, South Africa[END_REF].

Pholidoteuthidae

According to size and morphology, beaks of P. massyae eaten by sperm whales clustered into three groups [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF](Clarke , 1986a)), including P. boschmai (= massyae) A and B [START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF], thus suggesting that there may well be three species in the Southern Hemisphere (Clarke 1986a).

Alloposidae

Alloposus mollis [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF][START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF] is a junior synonym of Haliphron atlanticus [START_REF] Kristensen | A catalogue of the type specimens of Cephalopoda (Mollusca) in the Zoological Museum, University of Copenhagen[END_REF].

Cephalopods in the diet of sperm whales

A total of 1991 fresh remains were identified either morphologically or from beaks that were sorted from buccal masses (Table 2). Most of them (70%) came from Durban, which was the most investigated locality by far [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF][START_REF] Clarke | Cephalopods in the diet of sperm whales caught commercially off Durban, South Africa[END_REF]. Two oegopsid families dominated by number the diet of sperm whales in the southern subtropics, the octopoteuthids (25.0%) and histioteuthids (21.3%), while onychoteuthids (59.1%) and cranchiids (32.6%) were the two most important families within the Southern Ocean. Six squids totalled >5% by number of fresh items in the STZ, by decreasing order of importance:

T. filippovae/angolensis > O. rugosa > Ancistrocheirus lesueurii > Histioteuthis bonnellii corpuscula > H. miranda > G. suhmi. In contrast, only three species dominated the whale diet in the Antarctic, M. longimana > Mesonychoteuthis hamiltoni > F. knipovitchi.

A total of 131,577 lower beaks were sorted from the stomach of 237 sperm whales (Table 3). Thirty-six taxa from 16 families were identified, almost all oegopsids, but two species of Octopodiformes, the vampire squid Vampyroteuthis infernalis and the incirrate seven-arm octopus H. atlanticus. The number of taxa ranged from 26 (Albany) to 32 (Donkergat and Durban), thus depending on localities. There was a strong difference in the main squid prey in the AZ and STZ, and items were locality-specific in the subtropics. In Antarctic waters, three families including four species overall dominated the whale diet, the onychoteuthids (58.5% by number) with F. knipovitchi (39.4%) and M. longimana (16.8%), the cranchiids (17.5%) with M. hamiltoni (15.5%), and the histioteuthids (10.5%) with S. arcturi (8.8%).

Within the STZ, histioteuthids ranked first at Donkergat (37.5%), Durban (44.7%) and Albany (41.4%) and second in the Tasman Sea (30.5%). H. atlantica was important everywhere, but H. b. corpuscula, H. macrohista, H. miranda, and S. hoylei were notably abundant at Durban, Donkergat, Albany and in the Tasman Sea, respectively (Table 3, Fig. 2).

Octopoteuthids ranged from 8.8% in Albany to 33.7% in the Tasman Sea, the only locality where they dominated and where they were detailed at the species level, in the decreasing order: O. ?fenestra (11.7%) > T. danae/fimbria (10.5%) > O. rugosa (10.0%) > giant Pacific Octopoteuthis sp. (1.5%). Cranchiids were important at Donkergat (20.0%) with G. suhmi and in the Tasman Sea (10.9%) where Megalocranchia sp. was a significant prey item. Other squids that amounted to >5% by number were O. robsoni at Donkergat, A. lesueurii and Chiroteuthis spp. (pooled C. joubini and C. veranyi) at Durban, T. filippovae at Albany, and P. massyae at Donkergat, Albany and in the Tasman Sea (Table 3).

Many more beaks were analyzed at Donkergat and Durban than elsewhere, with the same 32 taxa being identified at the two South African localities (Table 3). Statistical analyses (equality of two proportions tests) showed that proportions significantly differed (all p ≤ 0.460, with p < 0.0001 in 27 comparisons) for almost all taxa but three, the numerically important H. atlantica (Z = 0.24, p = 0.814), and the occasional M. ingens (Z = 0.23, p = 0.816), and Others (including D. discus) (Z = 1.00, p = 0.319).

Discussion

Revisiting taxonomy changed considerably the species list of cephalopods initially identified from stomachs of sperm whales commercially hunted in the southern Atlantic, Indian and Pacific Oceans. This greatly improves our knowledge on cephalopod biodiversity and on trophic relationships within the deep-sea ecosystems of the subtropics and the Southern Ocean. By reviewing the existing literature, the study also highlights the marked contrast in the dietary habits of sperm whales caught within the STZ and AZ, which is related to the different teuthofaunas inhabiting temperate and cold waters of the Southern Hemisphere.

Revisiting cephalopod taxonomy

Dietary investigations from the 1970s to 1990s contain out-of-date scientific names of prey species and include initial misidentifications, because identifying cephalopods from their beaks is challenging [START_REF] Cherel | A review of Southern Ocean squids using nets and beaks[END_REF]. This is especially problematic in pioneer studies that are either impossible (e.g. Imber 1973) or difficult (e.g. [START_REF] Rodhouse | Cephalopod prey of the wandering albatross Diomedea exulans[END_REF][START_REF] Ridoux | The diets and dietary segregation of seabirds at the subantarctic Crozet islands[END_REF] to use, including the seminal works on the cephalopod prey of sperm whales [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF][START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF]. Taxonomic updating of the latter studies changed the name of a majority (69%) of the 45 different cephalopods that were identified morphologically and/or from their lower beaks (Table 1). Shifts from one family to another family are restricted to four species that were not major prey of sperm whales (Table 3), namely the chiroteuthids A. lui and A. acanthoderma (formerly mastigoteuthids), the cycloteuthid D. discus (formerly a psychroteuthid) and the neoteuthid A. antarcticus (formerly a cranchiid). Hence, the relative importance of cephalopod families in the diet of sperm whales remains essentially unchanged [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF][START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF] and conclusions about them worldwide are likely valid today (Clarke 1986b[START_REF] Clarke | Cephalopods as prey. III. Cetaceans[END_REF].

In contrast, within-families changes at the species level are substantial (Table 1).

Three issues are especially relevant: (i) the importance of H. macrohista (formerly H.

?meleagroteuthis) in the diet of whales at Donkergat; (ii) the disentangling of the beaks previously named ?Taonius megalops and G. armata adds significant new records and trophic information about the two rarely reported cranchiids G. suhmi and L. podophtalma, the former species being one of the main prey of sperm whales at Donkergat; and (iii), improving beak identification overall increases our knowledge on squid biodiversity and biogeography (e.g. the poorly-known A. lui and A. acanthoderma). Despite these changes, the initial analysis of lower beaks is remarkable and the hypothesis that various LRL modes of fully darkened beaks within a given taxa represent different species was validated (e.g. G. armata that corresponds to G. suhmi/G. glacialis) or in the process of being validated (e.g. Octopoteuthis spp. and Taningia danae/fimbria). However, the absence of some beaks is puzzling and suggests that at least some of them were not recognized morphologically as distinct from others and, hence, that some taxa are a diverse mix of different species. Within the STZ and Southern Ocean, relevant missing species include Batoteuthis skolops, Mastigoteuthis psychrophila, the neoteuthid Nototeuthis dimegacotyle, the onychoteuthids Moroteuthopsis sp. B (Imber) and Notonykia africanae, and the recently described cranchiids Taonius expolitus and possibly T. tanuki [START_REF] Evans | A systematic review of the squid family Cranchiidae (Cephalopoda: Oegopsida) in the Pacific Ocean[END_REF][START_REF] Cherel | A review of Southern Ocean squids using nets and beaks[END_REF]. Indeed, B. skolops was subsequently identified amongst fresh items in the stomach of sperm whales caught within the AZ [START_REF] Lubimova | Results of Soviet investigation of the distribution and ecology of pelagic squids (Oegopsida) in the Southern Ocean[END_REF].

Cephalopod prey within the Subtropical Zone (STZ)

Fresh remains of 10 squids were identified at all the four subtropical localities (A. lesueurii, A. dux, C. sirventi, H. atlantica, H. miranda, L. grimaldii, O. rugosa, T. danae/fimbria, O. robsoni and P. massyae), thus indicating they form the basis of cephalopod prey of sperm whales within the STZ circumglobally (Table 2). Accumulated beaks confirmed that general pattern with the diet being dominated by histioteuthids and to a lesser extent octopoteuthids, while A.dux, C. sirventi and L. grimaldii were not numerically important (<3%) (Table 3). Histioteuthids also accounted for 54.7% and 60.6% of accumulated beaks in stranded individuals from Tasmania and New Zealand, respectively [START_REF] Evans | A systematic review of the squid family Cranchiidae (Cephalopoda: Oegopsida) in the Pacific Ocean[END_REF]Hindell 2004, Gomez-Villota 2007), thus highlighting the importance of this family in the diet of sperm whales within the STZ (Fig. 1). Five species were involved and H. atlantica ranked first or second everywhere (Fig. 2). Moreover, it is likely that numerous H. atlantica beaks from Tasmania were misidentified as H. eltaninae [START_REF] Evans | The diet of sperm whales (Physeter macrocephalus) in southern Australian waters[END_REF], because LRL measurements are too large for the latter species and fit well with the former.

The four other histioteuthids are H. miranda (1.1%-11.5%), H. b. corpuscula (1.1%-21.6%, excluding New Zealand), H. macrohista at Donkergat, and finally S. hoylei in the western Pacific (3.1%-9.0% in Tasmania, the Tasman Sea and New Zealand). All the above species were commonly recorded in nets in subtropical waters and at the Subtropical Front [START_REF] Voss | The cephalopod family Histioteuthidae (Oegopsida): systematics, biology, and biogeography[END_REF]. Elsewhere, histioteuthids are dominant numerically (73.2%-76.9% ) in the diet of sperm whales from the northern Atlantic and the Mediterranean Sea, where H. b. bonnellii is the main prey item [START_REF] Clarke | The diet of sperm whales (Physeter microcephalus Linnaeus 1758) off the Azores[END_REF][START_REF] Spitz | Prey preferences among the community of deep-diving odontocetes from the Bay of Biscay, Northeast Atlantic[END_REF][START_REF] Foskolos | A taste for squid : the diet of sperm whales stranded in Greece, Eastern Mediterranean[END_REF].

At the family level, octopoteuthids, cranchiids and onychoteuthids are also important food items of sperm whales within the STZ (Fig. 1). Octopoteuthids dominated numerically in the Tasman Sea, ranked second at Durban, and third at Donkergat and Albany, with Octopoteuthis spp. being more abundant than T. danae/fimbria at every locality (Table 3).

Cranchiids ranked second at Donkergat and in Tasmania [START_REF] Evans | The diet of sperm whales (Physeter macrocephalus) in southern Australian waters[END_REF] and New Zealand (Gomez-Villota 2007), and third at Albany and in the Tasman Sea. Several species were involved but G. suhmi and Megalocranchia sp. were notably abundant (>5%) at Donkergat, and in the Tasman Sea and New Zealand, respectively. Finally, onychoteuthids amounted to >5% everywhere, mainly due to the abundance of O. robsoni circumglobally and of the subantarctic endemic M. ingens in New Zealand waters (Gaskin and Cawthorn 1967a,b, Clarke and Roper 1998[START_REF] Gomez-Villota | Sperm whale diet in New Zealand. Master thesis, Auckland University of Technology Imber MJ (1973) The food of grey-faced petrels (Pterodroma macroptera gouldi (Hutton)), with special reference to diurnal vertical migration of their prey[END_REF]. Onychoteuthids also included the two Southern Ocean endemics F. knipovitchi and M. longimana, which indicate a recent northward migration of some of the whales (see below).

Cephalopod prey within the Southern Ocean

Three Southern Ocean endemics form the bulk (90.7% by number of fresh items) of the cephalopod diet of sperm whales in the Antarctic, the colossal squid M. hamiltoni and the two onychoteuthids F. knipovitchi and M. longimana (Table 2), which is in general agreement with qualitative information collected from Soviet and Japanese factories [START_REF] Mikhalev | To the problem of the feeding of sperm whales from the Southern Hemisphere[END_REF][START_REF] Nemoto | Squid as predators on krill (Euphausia superba) and prey for sperm whales in the Southern Ocean[END_REF][START_REF] Filippova | Review of Soviet/Russian studies on squids in the Antarctic Ocean[END_REF]. The other squids eaten within the AZ include G. antarcticus and two other Southern Ocean endemics (A. lui and P. glacialis). A review of the literature adds four species, again all endemics, to the squid prey of sperm whales in the Antarctic (B. skolops, G. glacialis, A. antarcticus, and M. ingens), and six species to the prey taken further north within the Southern Ocean (A. dux, C. sirventi, H. atlantica, H. eltaninae, P. massyae and H. atlanticus) [START_REF] Vovk | Distribution of deep sea cephalopods in the South Atlantic and adjacent waters (mainly analyses of sperm whales feeding)[END_REF][START_REF] Mikhalev | To the problem of the feeding of sperm whales from the Southern Hemisphere[END_REF][START_REF] Lubimova | Results of Soviet investigation of the distribution and ecology of pelagic squids (Oegopsida) in the Southern Ocean[END_REF][START_REF] Filippova | Review of Soviet/Russian studies on squids in the Antarctic Ocean[END_REF]. Comparing fresh remains of cephalopods from sperm whales caught within the AZ and the STZ highlights the dietary importance of different squids living in these two contrasting oceanic environments (Table 2). Twenty-three species occurred in the STZ only, six in the AZ only, and three were recorded in the two zones. The latter species (T. danae/fimbria, T. filippovae/angolensis and O. robsoni) are primarily subtropical species whose distribution extends to the northern Southern Ocean [START_REF] Cherel | A review of Southern Ocean squids using nets and beaks[END_REF], where, accordingly, they are minor prey items for sperm whales.

Analysis of accumulated beaks fit well with quantification of fresh items, with the three same species (M. hamiltoni, F. knipovitchi and M. longimana) accounting together for 71.6% of the total number of lower beaks within the AZ (Table 3). This proportion is lower than for fresh items, however, which is the consequence of the much larger diversity of cephalopods identified from beaks than from fresh items, since most beaks were found in whales caught in both subtropical and Antarctic waters. Fresh items are indicative of local food, while the much larger number of beaks results primarily from their progressive accumulation in the stomach over time (maximum ~10 days; Clarke 1980). Male sperm whales migrate back and forth over years between their main feeding zone in cold waters and the reproductive zone in warmer waters where females and juveniles live all year-round. Hence, the presence of beaks of subtropical cephalopods in the stomach of adult males caught in the Antarctic indicates a recent southward migration, and vice-versa [START_REF] Clarke | New technique for the study of sperm whale migration[END_REF][START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF]. Within that context, the puzzling large number of eroded lower beaks of S. arcturi in two whales caught in the pelagic Antarctic (South Shetlands) likely results from their southward migration [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF], since S. arcturi does not occur within the Southern Ocean [START_REF] Cherel | A review of Southern Ocean squids using nets and beaks[END_REF], but it was recorded in subtropical waters of the southwest Atlantic [START_REF] Voss | The cephalopod family Histioteuthidae (Oegopsida): systematics, biology, and biogeography[END_REF].

Predators, trophic niches, and the pelagic ecosystems

Within the STZ and AZ, sperm whales are apex predators that feed almost exclusively on medium-to large-sized cephalopods [START_REF] Clarke | Cephalopoda in the diet of sperm whales of the Southern Hemisphere and their bearing on sperm whale biology[END_REF][START_REF] Mikhalev | To the problem of the feeding of sperm whales from the Southern Hemisphere[END_REF], with the Patagonian toothfish being a significant prey item in some areas [START_REF] Vukhov | The range of fish of the genus Dissostichus (Fam. Nototheniidae) in Antarctic waters of the Indian Ocean[END_REF]. To my knowledge, only two other apex predators feed significantly on the same squids as the sperm whale, the Antarctic sleeper shark Somniosus antarcticus and large Diomedea albatrosses.

The sleeper shark lives in slope waters surrounding subantarctic and Antarctic islands where it has a catholic diet including large M. longimana, M. hamiltoni and T. danae/fimbria [START_REF] Cherel | Antarctic jaws: cephalopod prey of sharks in Kerguelen waters[END_REF]. Diomedea albatrosses are endemic from the Southern Ocean and southern subtropical waters where they prey on large fish and squids, which include mainly adult onychoteuthids (M. longimana), histioteuthids (H. atlantica, H. eltaninae) and cranchiids (G. glacialis) [START_REF] Xavier | Cephalopod fauna of South Pacific waters: new information from breeding New Zealand wandering albatrosses[END_REF][START_REF] Cherel | Feeding ecology, isotopic niche, and ingestion of fishery-related items of the wandering albatross Diomedea exulans at Kerguelen and Crozet Islands[END_REF]. The sperm whale and sleeper shark feed in the deep-sea, but the former catch live prey, while the latter both predates and scavenges. Diomedea albatrosses are also scavengers that feed at the sea surface, where they catch dead or dying post-spawning squid species that have positive buoyancy [START_REF] Cherel | Spawning cycle of onychoteuthid squids in the southern Indian Ocean: new information from seabird predators[END_REF]. Hence, each apex consumer occupies a unique trophic niche, thus limiting or avoiding direct competition within the oceanic ecosystems of the Southern Ocean and subtropics.

Conclusion

Revisiting taxonomy of cephalopod prey of sperm whales improved our knowledge on their feeding habits and on cephalopods from the southern subtropics and the Southern Ocean.

It reveals how important previously poorly known squid species are, as the histioteuthid H. macrohista, and the cranchiids G. suhmi and Megalocranchia sp. The study highlights the need to continue improving both the taxonomy of cephalopods and the description of their sclerotinized beaks, with the ecologically-fruitful outcome of using the numerous beaks of rarely net-caught species and adults of cephalopods that accumulate in predators' stomachs.

Declaration of competing interest

The author declare that he has no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. (1980), [START_REF] Clarke | Cephalopod remains from the stomachs of sperm whales caught in the Tasman Sea[END_REF], [START_REF] Evans | The diet of sperm whales (Physeter macrocephalus) in southern Australian waters[END_REF] and [START_REF] Gomez-Villota | Sperm whale diet in New Zealand. Master thesis, Auckland University of Technology Imber MJ (1973) The food of grey-faced petrels (Pterodroma macroptera gouldi (Hutton)), with special reference to diurnal vertical migration of their prey[END_REF]

CRediT authorship contribution statement Not applicable

(n) (%) (n) (%) (n) (%) (n) (%) (n) (%) (n) (%)

Figure 1 Figure 2

 12 Figure 1 Numerical importance of the four main families of cephalopods in the diet of sperm whales caught in the southern subtropics. The

Table 1

 1 Improvement in cephalopod identification and taxonomy over time: revisiting and 584 updating cephalopod prey of sperm whales from the Southern Hemisphere

	585
	Previous taxonomy

Table 3

 3 Accumulated cephalopod beaks identified from stomach contents of sperm whales caught in the Southern Hemisphere.

	590
	Location	Donkergat	Durban	Albany	Tasman Sea	South Georgia	Pelagic Antarctic
	Number of whales	89	72	6	30	28	12
		Clarke (1980)	Clarke (1980)	Clarke (1980)	Clarke and MacLeod (1982)	Clarke (1980)	Clarke (1980)
	Species

Acknowledgements Not applicable

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.


domain: spi chim phys

text:
Alessandro Nardecchia

Vincent Motto-Ros

Ludovic Duponchel

Saturated signals in spectroscopic imaging: why and how should we deal with this regularly observed phenomenon?

Keywords: saturated signal, imaging spectroscopy, statistical imputation

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Saturation is a phenomenon regularly observed in spectroscopy. Its presence can be linked to various factors such as sample preparation, specific photon-matter interactions or even instrumental limitations in the detection chain. For example, too high extinction coefficients and/or too high pathlengths in the mid-infrared spectral range reduce so much the number of non-absorbed photons arriving at the detector that the absorbance levels are infinitely high, values that cannot of course be transcribed in a spectrum, 2 or by default in the form of a plateau. On the other hand, in the case of scattering or emission measurements as in Raman, fluorescence or LIBS (laser-induced breakdown spectroscopy), the number of photons collected by the measurement chain can be sometimes so important that it cannot be transcribed into the spectrum. Again in this case, a clipping effect is observed which does not allow to observe the real values to be measured. Generally speaking, we can say that a saturation may occur when a signal is recorded by a detector that has constraints on the range of data it can measure. This can therefore be the case when a signal is digitized using an analog-to-digital converter, or any other time an analog or digital signal is transformed, particularly in the presence of gain.

When a saturation phenomenon is observed on a spectrum acquired for bulk analysis of a single sample, the analysts know that they have has to reconsider the preparation of their samples or the acquisition parameters depending of course on the constraints related to the experiment under consideration.

The newly acquired spectrum then has every chance this time to present values that are representative of the analytical reality of the sample. The situation is quite different when we have to do bulk analyses on a set of samples with the final objective of comparing their spectra. For this specific purpose, we must then set unique experimental conditions that will be applied to all samples. We could then easily observe perfectly exploitable spectra next to others that are potentially saturated. This is a situation that often occurs in spectroscopic imaging when exploring a single and complex heterogeneous sample. Indeed, for given acquisition conditions, hundreds, thousands or even hundreds of thousands of spectra are acquired in a region of interest of the sample. Since each spectrum corresponds to a specific micro-surface of the sample with a potentially different molecular distribution, it is quite likely that some of them are saturated. If we are lucky we might be able to find experimental conditions that remove these saturations. Nevertheless, we must not lose sight of the fact that it is not always possible to reproduce the experiment a second time, for example when the technique is destructive as in LIBS.

In general, we can say that we always try to avoid the saturation phenomenon as much as possible.

Unfortunately, it is observed in many cases and it is necessary to deal with these data as they are. The question that then arises is the following: what should we do with saturated values that we know to be systematically erroneous? Figure 1a gives a schematic representation of a dataset with six spectra of which three contain saturations highlighted in red. We can notice first that it is not always the same bands that are saturated in this dataset used as a toy example. Second, the number of saturations in a given spectrum is quite variable. Figure 1b presents the two strategies typically used to manage potential spectral saturation in a dataset. The idea is finally very simple since knowing that saturated values do not represent the true values, it seems logical to remove them from the acquired dataset. We then have a first possibility which is to remove all the spectra as soon as they contain at least one saturated spectral variable also known as row-wise deletion. This strategy might seem satisfactory because it is simple to implement, but it is not flawless. Indeed, we could then remove a spectrum made up of several hundreds of spectral variables and thus potentially a very large amount of molecular/atomic information just because a single variable would be saturated, for example. We would then have a significant loss of chemical information as in the present case study where only 50% of the spectra would be kept for multivariate analysis. In the specific case of spectroscopic imaging, we would then end up with areas of the image without defined chemical information. From a more statistical point of view, we would also have a biased analysis since we would no longer have the initial population of acquired spectra. In a second strategy known as column-wise deletion, we could suppress a spectral variable in the data set as soon as at least one of the spectra of the dataset presents a saturation on this same variable. This strategy is no more satisfactory because a significant loss of information would still be observed. In the case of the presented example, we notice that such a strategy would remove almost all the spectral information from the dataset. Thus even if these two strategies are regularly exploited in spectroscopy, we see that they are unsatisfactory on different aspects.

Starting from the observation that a saturated value in a spectrum is an erroneous one, we propose in this work to consider it as a missing value. It is indeed more relevant to say that a value could not be measured than to exploit a value that finally does not represent a reality. Thus in the matrix representation of the data set in Figure 1b, red boxes that were initially saturated values will become missing ones.

In statistics, the art of dealing with missing values in a matrix is called imputation [START_REF] Van Buuren | Flexible Imputation of Missing Data[END_REF]. It is in fact the process of replacing missing data with substituted values. By approaching the problem of saturation in this way, we see that we can then work on a data set while keeping its initial dimensions, i.e. with the initial number of spectra and spectral variables resulting from the acquisition. Thus in this work, three different spectroscopic imaging datasets will first be used to show the need to manage saturations present in the spectra at the risk of seeing many artifacts during multivariate analyses generating biased chemical images and extracted spectral profiles. The principle of imputation will of course be explained and the analysis of the corrected datasets will allow us to demonstrate the benefits of this concept to find chemical images and corresponding spectroscopic information representative of the analytical reality of complex samples.

MATERIAL AND METHODS

Imputation

Imputation is a field of statistics. The great idea in imputation is to fill gaps in the data with plausible values, the uncertainty of which is coded in the data itself. There are many ways of doing data imputation today [START_REF] Van Buuren | Flexible Imputation of Missing Data[END_REF]. However, we will use in this work the so-called 'multiple imputation' now considered as the best general method to deal with incomplete data (i.e. containing missing values) in many scientific domains [START_REF] Scheuren | Multiple Imputation: How It Began and Continues[END_REF][START_REF] Rubin | Multiple Imputation for Nonresponse in Surveys[END_REF][START_REF] Rubin | Multiple Imputation After 18+ Years[END_REF]. Our goal here is of course not to redo a whole development of the theory of imputation but to explain some general principles in order to understand the results presented in this work. Readers who would nevertheless like to have all the details on this topic are invited to read other works specifically dedicated to statistic [START_REF] Van Buuren | Flexible Imputation of Missing Data[END_REF][START_REF] Rubin | Multiple Imputation for Nonresponse in Surveys[END_REF]. The two main approaches for imputing multivariate data are called joint modeling [START_REF] Schafer | Analysis of Incomplete Multivariate Data[END_REF] (JM) and fully conditional specification (FCS), also known as multivariate imputation by chained equations (MICE) [START_REF] Van Buuren | mice: Multivariate Imputation by Chained Equations in R[END_REF]. As the JM approach is often more constraining from a statistical point of view to be applied, the MICE method has been considered in this work. MICE specifies the multivariate imputation model on a variable-by-variable basis by a set of conditional densities, one for each incomplete variable (i.e. containing missing values). In this work, a regression model is developed using the complete variables of the matrix as input and a given incomplete variable as output. Once this model is established, we can then use it to predict missing values of spectra at this specific spectral variable based on known values in the matrix. We will thus have as many regression models developed as spectral variables containing missing values in the considered dataset. At the end of this imputation procedure, we then find a full matrix free of missing values that we can then explore with usual multivariate methods.

In this work, all imputation calculations have been done under the R environment using MICE, an open source R package. Source code and documentation can be found at https://github.com/amices/mice.

Multivariate data analysis

Principal component analysis (PCA) is one of the most flexible and effective chemometric method for exploratory data analysis applied to hyperspectral imaging [START_REF] Moncayo | Exploration of megapixel hyperspectral LIBS images using principal component analysis[END_REF]. It is indeed very sensitive and thus allows the detection of very low variance levels. Its use will first of all allow to see artifacts generated during a direct use of saturated spectral datasets but also to estimate in a second time the efficiency of the corrections brought by our imputation strategy. All PCA calculations were performed under the Matlab 2016b environment.

Dataset #1: a simulated sample

The first hyperspectral imaging dataset consists of synthetic spectra that could have been acquired using LIBS. The advantage of using such simulations lies in the fact that all the parameters potentially influencing a given problem are under controlled. In this way, we often have a less biased view of the phenomena and a real generalization is possible. As we will see further on, it will also be a way to vary the importance of the saturation phenomenon. On the basis of the spectroscopic information given by the Kurucz database [START_REF] Kurucz | Atomic Line Data, Atomic Line Data[END_REF], we first simulated the emission spectra of silver, aluminum and arsenic by considering a typical plasma temperature and electron density (9000 K and 5.1016 cm -3 respectively). In order to be the most faithful with the spectral reality, we then applied a Lorentzian profile with a linewidth of 0.15 nm to each emission line, corresponding to the resolution of classical spectrometer used in LIBS [START_REF] Motto-Ros | Investigation of signal extraction in the frame of laser induced breakdown spectroscopy imaging[END_REF]. In the considered spectral range (250-350 nm), several emission lines of Ag, Al, and As were observed with various intensity ranges. On the basis of these three pure spectra, it was then possible to generate by linear combination 62880 spectra of mixtures in percentages ranging from 100 to 0 for each of them. A white noise of 5 % has also been added to each spectrum. In this way, we obtained a hyperspectral data cube defined by 131 pixels x 480 pixels x 2018 wavelengths. Figure 1S in supplementary material presents the three element spectra, all the generated spectra of mixtures in overlay mode as well as the spatial distribution of the different elements in this synthetic sample.

Dataset #2: a lung biopsy

The second dataset used in this work corresponds to a LIBS imaging experiment conducted on a lung biopsy of a patient with severe emphysema [START_REF] Busser | LIBS Imaging Is Entering the Clinic as a New Diagnostic Tool[END_REF]. Note that the patient signed informed consent, and the clinical procedure was approved by the local ethics committee. The LIBS imaging has been conducted with a protocol dedicated to paraffin-embedded tissues, as described in a previous work [START_REF] Moncayo | Multi-elemental imaging of paraffin-embedded human samples by laser-induced breakdown spectroscopy[END_REF]. The aim of such application was to characterize the distribution of metallic particles (from nanometric to micrometric size) in tissue biopsies, which represent a precious help for clinicians to diagnose the cause of the exposition (i.e. environmental and/or occupational). This spectroscopic experiment is a good example of a case where saturated spectra cannot be avoided. Since the concentration, composition, location and size of the particles are not known prior the experiment, the measurement system requires an extremely large dynamic in term of detection, typically from few ppm to a few percent in mass. Despite our efforts to set up the experimental parameters as optimized as possible, it is not uncommon to have a significant number of spectra showing saturations on a LIBS image as in this case. The size of the analyzed area of the biopsy was 5.42 mm long by 3.18 mm wide with a spatial resolution of 20 µm. We have thus acquired 43089 spectra over a spectral range from 282.01 to 310.03 nm and an approximate spectral resolution of 0.04 nm. The hyperspectral data cube was therefore defined by 271 pixels x 159 pixels x 644 wavelengths.

Dataset #3: a rock section

The third dataset was also acquired using a LIBS imaging instrument on a banded iron formation rock consisting of alternating layers of iron oxides and silicates. We selected this sample because it somehow allowed us to find approximately the same chemical distributions for two contiguous zones of the sample on which we could set different acquisition parameters. This procedure of selection of analysis area was necessary because we must not forget that LIBS is a destructive technique. Therefore, we could not analyze the same area several times. As a consequence, two successive zones each having a size of 20 mm long and 2 mm wide were analyzed following the protocol already used for other work [START_REF] Cáceres | Megapixel multi-elemental imaging by Laser-Induced Breakdown Spectroscopy, a technology with considerable potential for paleoclimate studies[END_REF]. A spatial resolution of 20 µm and a spectral range from 245.85 to 334.03 nm were considered for these acquisitions generating two hyperspectral datasets defined each by 1000 pixels x 100 pixels x 2048 wavelengths. The laser pulse energy and the detection gate were adjusted for these two sub-zones in order to control the saturation level. Indeed, our aim was to obtain no saturated lines on the first zone of the sample (gate: 1 µs; energy: 1.2 mJ) and saturation of Si emission lines on the second zone (gate: 5 µs; energy: 1.2 mJ). All the other acquisition parameters such as the delay and detector gain was kept constant.

RESULTS AND DISCUSSION

Before tackling the problem of correcting saturation in the spectra, it is important to understand how this is necessary to manage it, at the risk of giving a completely biased vision of the analyzed sample.

For this purpose, we will use the first dataset of simulated spectra. Figure 2a thus presents the results of a first principal component analysis applied to the raw data (i.e. without saturated signals). Unsurprisingly, we note first of all that there are three significant eigenvalues in the scree plot that correspond to three spectral contributions. More specifically, the first three principal components respectively extract the spectra of the three pure elements Ag, Al and As. This is quite logical since there is no correlation between these elements in the considered dataset. The scores images then perfectly reproduce the distributions of the three elements given in SI Figure 1S. In a natural way, the fourth principal component extracts the noise variance. From the raw data, we then simulate a first level of saturation by clipping all emissions above 30, knowing that the maximum emission observed on the initial spectra is around 43. SI Figure 2S gives the location of the saturated signals at the spatial and spectral levels. 5047 spectra thus present saturations, i.e. 8% of all the spectra. We notice that saturations are present in areas where silver is the most concentrated with a percentage higher than 80%. From a spectral point of view, it is the most intense line of silver which is naturally saturated. Figure 2b shows again the PCA results on these new saturated data. The consequences are not long in coming since a fourth significant component is already detected in the eigenvalues scree plot. Of course, this is not normal because we know that only three elements are present. Compared to the initial results (in Figure 2a), both the first principal component and the first scores map are no different. Nevertheless, there is a small decrease in the expressed variance from 21.42 to 20.44%. As far as the second and third scores maps are concerned, they are quite comparable to those observed from the non-saturated dataset. On the other hand, the corresponding principal components show small artifacts in the spectral region of the saturated Ag band (highlighted by red boxes in the corresponding figure). Finally, the fourth principal component specifically reflects the saturation phenomenon observed on silver for an expressed variance of 0.08%. We see many structures in the corresponding scores map but we know that they do not reflect any analytical reality. We observe even more the typical W-shaped artifact in this principal component. This shape can be explained quite well. Indeed, when saturations are potentially present at a given wavelength, principal components have to express the variance precisely at this wavelength for the unsaturated spectra in the dataset but other ones also have to express variances specifically localized on the feet of this same peak. In other words, a clipped band at a certain wavelength of a given spectrum is no longer homothetic to an unsaturated band of another spectrum. So if we do not have any prior information about this dataset, we see that even a limited saturation level can induce the extraction of erroneous information at the spatial and spectral levels about the sample being explored. It is then interesting to amplify the saturation effect by considering this time a saturation level equal to 20. Under these new conditions, 10119 spectra are saturated, i.e. 16% of all the spectra. Once again, saturations are present in areas where Ag is the most concentrated, but this time for values higher than 50% (SI Figure 3S). We are also starting to see saturated spectra for pure Al pixels. Figure 2c show PCA results of this new dataset. Four significant contributions are still observed, but with an even greater influence of artifacts on all components. We notice thus on the first principal component which should be specific to Ag that contributions from Al and As are now easily observed. We note here that the presence of saturations can also create spurious correlations. The second and third components have even greater expressed variances and ever more pronounced 'W-shapes'. While the scores maps are relatively little changed under these new conditions for the first three principal components, this is not at all the case for the fourth one. This high-contrast, low-noise scores image could indeed lead us to believe that real chemical compounds are present, which is of course not the case. In a final step, the saturation is further increased by considering this time a level equal to 10. This situation is extreme since 27870 spectra are now saturated, i.e. 44% of the dataset. What is more, the saturated pixel location map shows that this percentage is even underestimated since almost all of the areas that should contain the three elements are almost all saturated, the unsaturated areas being mainly the background (SI Figure 4S). At the same time, we observe that almost all emission lines show saturation over the entire spectral range. PCA results of this new dataset is given in Figure 2d. Under these conditions where saturation is omnipresent, six significant contributions are now detected. The first principal components are more and more perturbed. They are now undeniably different from pure spectra extracted on unsaturated spectra. As examples, the first principal component contains distinct contributions from all three elements and the following ones, which contain more and more artifacts, have equally increasing explained variances. Two new principal components 5 and 6 are also extracted in these conditions with quite singular scores maps. The presence of these additional principal components is explained by the fact that the variance of all the saturated peaks must of course be explained, but also that they are not necessarily saturated at the same time in all the spectra of the dataset. Generally speaking, we can say that the more spectral variables containing saturations, the more parasitic principal components and biased scores maps are extracted. From this first experiment, it is obvious that we cannot directly process saturated spectra with multivariate tools at the risk of making very hazardous exploration of unknown and complex samples for which we have no a priori. Based on this observation, we know that we must now absolutely manage these saturations. Thus, if we wanted to implement a row-or a column-wise strategy that is simple to set up in order to eliminate these saturations, we would quickly observe too many deleted pixels or a particularly small explored spectral domain. It is in this sense that the proposed imputation strategy makes sense by first considering saturated signals as missing values and then applying the MICE approach to make statistical estimates of the latter, i.e. retrieve lost spectral information and consequently a full data matrix. Imputation was therefore applied to the previous datasets by considering the three levels of saturation. In order to appreciate the quality of the data reconstruction, we simply reapplied PCA on these three new datasets. Figure 3 shows the results concerning the intermediate saturation level equal to 20. The results for the other levels are presented in the supplementary material (SI Figure 5S). By comparing these new extractions with those obtained on unsaturated data, we observe rather spectacular results. First of all, we recover the three significant components on the eigenvalues scree plot, which is consistent with the initial results. Moreover, principal components and corresponding scores maps are also very comparable to the initial ones.

These good results can be explained by the fact that the multivariate regressions used in the MICE approach predict missing values rather well. By way of illustration, Figure 4 shows the emission predicted by the imputation model as a function of known values at the wavelength 323.96 nm from non-saturated data, this silver emission line being the most often saturated for a saturation level equal to 20. Looking specifically at the results concerning the most saturated dataset (SI Figure S5, saturation level equal 10), some readers might say that despite the three significant contributions detected on the scree plot, it is possible to observe information related to a fourth component at both spectral and spatial levels. This would be quite commendable but we must not lose sight of the fact that these contributions are very close to the noise level. Moreover, these results were obtained from a dataset for which almost all the spectra were saturated, which could not be more challenging.

In this second part, we propose to explore a lung biopsy sample. This sample is particularly interesting because the analyzed area of lung presents a certain diversity of materials since we have naturally biological tissues but also mineral phases and metal particles localized in specific sub-areas. In these conditions, we quickly understand that it is almost impossible to find acquisition conditions allowing us to avoid saturation over the entire surface analyzed. In a way, one always make a bet before such an analysis because the considered spectroscopy is destructive and it is not possible to return to this sample area with new acquisition parameters. Location of the spectra containing saturations on the surface of this sample is shown in SI Figure 6S. Although only 1014 spectra out of the 43089 in total are saturated (i.e. 2.35%), this phenomenon is finally observable almost everywhere, mainly on two well-localized areas (denoted A and B in this figure) but also in the form of single pixels scattered over almost the entire surface of the sample. Additionally, Figure 6S shows that saturations are observed for almost all emission bands in the considered spectral range. Figure 5a andb shows PCA results on raw spectral data and spectra corrected with imputation respectively. Differences are noticed very quickly if we look at the contributions of each principal component in these two conditions two by two. So even though the first principal component is quite comparable in both cases with the main spectral contributions observed for Mg and Si but also smaller ones for Al and Fe, the associated scores maps are very different. Indeed, there is an overestimation of this first contribution for raw data on zones A and B of the sample but also widely around zone B. For its part, the first scores map associated with the corrected data mainly locates this contribution on the periphery of zones A and B or on specific pixels scattered outside these zones. Another way to observe these differences is to compare the histograms of positive scores for this first component in the two conditions (SI Figure 7S). The saturation effect thus limits the range of scores values that should be observed and profoundly changes the structure of the distribution and therefore the visual perception one might have of it. For the second component, we are in much the same situation as before. We therefore have very comparable second principal components on the raw and imputed data. The Mg contribution is now anticorrelated to the Si, Fe and Al ones. On the other hand, once again there are differences on the scores maps for this component in the two conditions.

Negative scores (blue color scale) are thus distributed more homogeneously in areas A and B when the spectral data are imputed. It is from the third principal components that we observe the largest spectral differences between the two conditions. Thus for raw data, typical W-shaped artifacts are observed (in red in Figure 5) around the Mg contribution with correlations or anticorrelations with other elements.

We observe on this occasion that the third and fourth principal components are extracted from raw data to express the saturation of pixels mainly located in the B zone of the sample. Even more specifically, we can see on the third principal component that the W-shaped artifact on Mg is positively correlated with another Ca contribution around 300 nm. This component thus just testifies to the simultaneous saturation of emission bands associated with the Mg and Ca elements on specific pixels according to the information given in SI Figure 6S. This example shows a very good example of spurious correlation created by the saturation phenomenon, which no longer exists once the data are corrected by imputation.

Finally, the imputation strategy allows the appearance of dispersed particles opposing the Si and Al elements for the third principal component and the Ti et Al elements for the fourth one. It is obvious that such potentially less biased observations of particles represent a precious help for clinicians to diagnose the causes of the patient's exposure. From a general point of view, it is very interesting to see how a small percentage of saturated spectra can have an influence on a multivariate exploration method as sensitive as principal component analysis. This experience shows again here the necessity not to neglect the saturation phenomenon by setting up an adapted correction method such as imputation prior any chemometric analysis. This last part of this work is dedicated to the analysis of the rock sample. As a reminder, two contiguous regions of the sample were analyzed considering two acquisition settings. In this way, we analyzed the sample by ensuring the absence of saturation for a first area but also its presence in the second one. Figure 8S shows the location of pixels containing saturations on the surface of the second sample area. It can be said that in this case saturation is omnipresent since it is observed on 32.5 percent of the analyzed surface. On the other hand, the same figure shows that this time these saturations are only found on the specific contribution of an element, namely silicon around 288 nm. Figure 6 presents the three principal component analysis calculated on the first sample area (i.e. with no saturation), on the raw data of the second sample area (i.e. with saturations) and on the imputed data (i.e. corrected ones) of the same area. By comparing the principal components two by two in Figures 6a and6b, we observe very quickly the impact of saturation since we find the typical W-shaped artifact around 288 nm for components 3 and 4. The situation is even more critical for the fifth principal component with completely different profiles between Figures 6a and6b. In fact, it is above all the saturation effect that is expressed here for the second area of the sample. Finally, by comparing the results on the imputed data in Figure 6c and the unsaturated data of the first sample area, we observe a perfect agreement between extracted profiles demonstrating the capacity of our approach to correct the saturated spectral data.

CONCLUSION

As we have seen in the work, it is crucial to consider the phenomenon of saturation present in the spectra. Through different datasets we have indeed shown that its presence quickly induces artifacts on spectral profiles but also on generated images when multivariate tools are used for their exploration. Make no mistake, even the presence of a limited percentage of saturated spectra in a given dataset can have an impact on the veracity of the chemometric results. It is obvious that it is absolutely necessary to avoid the presence of saturation in the acquired spectroscopic data whenever possible by modifying, for example, the sample preparation or the acquisition parameters. Unfortunately, there are many situations where this phenomenon is observed as in LIBS imaging and we have to find solutions to exploit these acquired data anyway. The usual column-or row-wise deletion is not a satisfactory solution because it can be accompanied by a large loss of spectral information in the dataset. As a consequence, we would have a partial or even biased view both at the spectral and spatial level of the sample. All the originality of our work was to consider the saturated signals as values that had not really been measured and by extension as missing values. The goal being to preserve all the spectral and spatial dimensions of the dataset, statistical imputation allowed us to retrieve complete data cubes consistent with the analytical

FIGURESFigure 1 .

 1 FIGURES

Figure 2 .

 2 Figure 2. Principal component analysis on a) raw data, b) on the saturated dataset with a 30 saturation level, c) with a 20 saturation level and, d) with a 10 saturation level.

Figure 3 .

 3 Figure 3. Principal component analysis on the imputed dataset with an initial saturation level equal to 20.

Figure 4 .

 4 Figure 4. Emission of a silver line predicted by the imputation model as a function of known values at the wavelength 323.96 nm from non-saturated data.

Figure 5 .

 5 Figure 5. a) Principal component analysis on raw spectral data of the lung biopsy. (b) Same analysis on spectra corrected with imputation.

Figure 6 .

 6 Figure 6. Three principal component analysis calculated on, a) the first sample area (i.e. with no saturation), b) the raw data of the second sample area (i.e. with saturations) and c) the imputed data (i.e. corrected ones) of the same area.

ACKNOWLEDGMENT

The authors would like to acknowledge the French ANR research program for their financial support. In addition, the authors are grateful to B. Busser, V. Bonneterre and G. Panczer for helpful discussions.

AUTHOR INFORMATION

Corresponding Author (*) Corresponding author: ludovic.duponchel@univ-lille.fr ORCID Alessandro Nardecchia: 0000-0003-3131-8436 Vincent Motto-Ros: 0000-0001-6063-5532 Ludovic Duponchel: 0000-0002-7206-4498

Author Contributions

The manuscript was written through contributions of all authors.

Notes

The authors declare no competing financial interest.