Baptiste Le Bourg

Emmanuelle Cam

Age determination and lifespan of marine animal species

Keywords:

Ectotherms: species whose internal temperature is dependent on the ambient temperature.

Endotherms: species whose internal temperature is fixed and regulated by the organism.

Fish: paraphyletic group of fin and gill-bearing aquatic vertebrates. The term is used for convenience and refers usually to the teleosts taxa, but some authors may also include other taxa (e.g. elasmobranchs).

Iteroparity: a reproductive strategy with several reproductive events during life, these events possibly occurring in successive years.

Life-history strategies: strategies selected by natural selection during evolution allowing species to develop, live, and propagate (e.g. species with a short lifespan and many offspring, like mice, vs long-lived species with a few offspring, like elephants).

Life-history traits: traits moulding life-history strategies (e.g. body size, age at maturity, duration of development, number of offspring, lifespan).

Marine species: aquatic species living in seas and oceans, as opposed to freshwater species living in rivers, ponds, lakes and so on.

Record lifespan: longest duration of life of individuals observed in a species. In most marine species, this age can reflect the age at capture and not the maximal lifespan, i.e. the lifespan of the last survivors.

Introduction

Lifespan of species does not evolve independently of other life-history traits such as fecundity, gestation time, parental care, but also body size, predatory pressure and so on. In terrestrial mammals, there is a continuum with, on one end, short-lived species (e.g. mice) with a small body size maturing quickly after a short gestation time and giving birth at short intervals to many offspring. On the other end of the continuum, there are large species (e.g. humans) with a long lifespan, a long gestation time and parental care, and giving birth to a few offspring during successive years [START_REF] Stearns | The influence of size and phylogeny on patterns of covariation among lifehistory traits in the mammals[END_REF]. The predatory pressure is linked to body size, mice being at a higher risk than, say, elephants. For the time being, it seems that the longest-lived terrestrial mammal is Homo sapiens with a 122 years recorded lifespan [START_REF] Jeune | Biographical notes on the longest living humans[END_REF].

Marine animals include mammals, crustaceans, so-called fish (i.e. non-tetrapod craniates with gills and fins), molluscs, urchins, sea stars, sea turtles, and so on (marine birds are not within the scope of this article). When one compares the lifespan of marine animals to that of the longestlived terrestrial mammal, modesty is in order, because many species outlive it, not by decades, but by centuries. These long lifespans often intrigue people, like the roses in D'Alembert's Dream [START_REF] Diderot | OEuvres complètes de Diderot. Assézat Tourneux[END_REF] saying that "in the memory of a rose no one had ever seen a gardener die".

How to explain the disparate lifespans of marine and other aquatic animals? Short life spans are not an issue, because they can be linked to ecological conditions prohibiting long lives. For instance, Notobranchius furzeri fish live in African ponds that dry every year. When it comes to happen, fish die and desiccation-resistant eggs survive in diapause in the mud, waiting for months for better times, i.e. for the rainy season. Because of such conditions that shaped life-history traits, N. furzeri live for less than 3 months in the laboratory [START_REF] Cellerino | Life extension in the short-lived fish Notobranchius furzeri[END_REF]. A more extreme example is the coral reef fish Eviota sigillata whose adults are seemingly subjected to a high extrinsic mortality and live only for four weeks (larval stage: three weeks, [START_REF] Depczynski | Shortest recorded vertebrate lifespan found in a coral reef fish[END_REF]). Thus, while explaining short lifespans is not always an issue, the challenge could be to explain record lifespans of some marine animals.

As for other species, the lifespan depends on other life-history traits but, contrary to mammals, it can also depend on environmental conditions such as temperature, because most marine animals are ectotherms. Another difference with mammals is that fish can grow for many years, with a lower growth rate at older ages, but some species do not grow during their entire life [START_REF] Woodhead | Feral fishes[END_REF]. The fecundity of fish also increases with age [START_REF] Reznick | The evolution of senescence in fish[END_REF], which is opposite to mammals. Table 1 lists recorded or inferred record lifespans, from shortest to longest lifespans, of various long-lived marine animals. However, determining lifespans of marine species is not easy because they live underwater in the wild, and it can be needed to rely on indirect methods (see below), because capturing and re-capturing animals living underwater is difficult. It is thus not surprising that it has been stated that a given species can live for, say, one century, even if there are no robust data to support this conclusion. For instance, it is commonly said that green sea turtles Chelonia mydas can live for 80 years, but not a single article has been published in support of this statement: these claims are not reported in Growth rates [START_REF] Pearse | Antarctic sea star[END_REF] Orange roughy Hoplostethus atlanticus 149 ± 12 (SD) Radiometric analysis [START_REF] Fenton | Age determination of orange roughy, Hoplostethus atlanticus (Pisces: Trachichthyidae) using 210 P b : 226 Ra disequilibria[END_REF] Red sea urchin Strongylocentrotus franciscanus

> 200

Radiocarbon analysis [START_REF] Ebert | Red sea urchins (Strongylocentrotus franciscanus) can live over 100 years: confirmation with A-bomb 14carbon[END_REF] Tube worm Lamellibrachia sp.

170-250

Staining of growing tube worms and growth rates [START_REF] Bergquist | Longevity record for deep-sea invertebrate[END_REF] Bowhead whale Balaena mysticetus 211 ± 35 (SEM) Aspartic acid racemisation in the eye lens [START_REF] George | Age and growth estimates of bowhead whales (Balaena mysticetus) via aspartic acid racemization[END_REF] Greenland shark Somniosus microcephalus 392 ± 120 (95.4% probability range)

Radiocarbon analysis and growth rates [START_REF] Nielsen | Eye lens radiocarbon reveals centuries of longevity in the Greenland shark (Somniosus microcephalus)[END_REF] Bivalve clam Arctica islandica > 507 Growth bands count on shells [START_REF] Butler | Variability of marine climate on the North Icelandic Shelf in a 1357-year proxy archive based on growth increments in the bivalve Arctica islandica[END_REF] deep-sea sponge Monorhaphis chuni 11,000 ± 3,000 Stable isotopes [START_REF] Jochum | Siliceous deep-sea sponge Monorhaphis chuni: a potential paleoclimate archive in ancient animals[END_REF] Table 1. Some record lifespans, from shortest to longest, of some marine animals. Shortlived species are not reported. These records should not be considered as definitive, as they can reflect the age at capture and not the real lifespan. Abbreviations: SD: standard-deviation, SEM: standard-error of the mean.

Measuring lifespans in marine organisms

Most studies estimating the age of marine animals are done for fisheries stock management purpose. Indeed, poor age estimation (usually underestimation) may result in wrong estimation of growth and natural mortality rates, leading to risk of overexploitation of populations and their eventual collapse [START_REF] Campana | Accuracy, precision and quality control in age determination, including a review of the use and abuse of age validation methods[END_REF]. Consequently, it is critical to use accurate methods to estimate the age of marine animals.

Growth bands count

Growth bands count is one of the most commonly used ageing method for marine animals.

Alternation of growth bands, formed regularly from diurnal to annual time scales, can be observed on various hard tissues in various animal taxa. In some of these tissues, annual growth bands may appear as an alternation of opaque and translucent bands of different widths. Opaque bands appear as dark when observed with transmitted light but as bright when observed with reflected light or naked eye. They are wide and highlight a period of fast growth [START_REF] Fowler | Age in years from otoliths of adult tropical fish[END_REF][START_REF] Aldanondo | Validation of the first annual increment deposition in the otoliths of European anchovy in the Bay of Biscay based on otolith microstructure analysis[END_REF]. By contrast, translucent bands appear as bright when observed with transmitted light but as dark when observed with reflected light or naked eye. They are narrow and highlight a period of slow growth [START_REF] Fowler | Age in years from otoliths of adult tropical fish[END_REF][START_REF] Aldanondo | Validation of the first annual increment deposition in the otoliths of European anchovy in the Bay of Biscay based on otolith microstructure analysis[END_REF].

Opaque and translucent bands are also frequently associated with summer and winter temperatures respectively [START_REF] Fowler | Age in years from otoliths of adult tropical fish[END_REF][START_REF] Aldanondo | Validation of the first annual increment deposition in the otoliths of European anchovy in the Bay of Biscay based on otolith microstructure analysis[END_REF][START_REF] Mesa | Age and growth of brown meagre Sciaena umbra (Sciaenidae) in the Adriatic Sea[END_REF][START_REF] Wakefield | Timing of growth zone formations in otoliths of the snapper, Chrysophrys auratus, in subtropical and temperate waters differ and growth follows a parabolic relationship with latitude[END_REF], although variations of this pattern may appear in some cases [START_REF] Wakefield | Timing of growth zone formations in otoliths of the snapper, Chrysophrys auratus, in subtropical and temperate waters differ and growth follows a parabolic relationship with latitude[END_REF][START_REF] Jones | Sclerochronology: reading the record of the molluscan shell[END_REF][START_REF] Jones | Marking time with bivalve shells: oxygen isotopes and season of annual increment formation[END_REF]. As a result, direct estimation of age is possible by counting alternations of growth bands.

Various tissues may be studied in order to estimate the age of marine animals with growth band counts (Fig. 1). For teleosts, age was previously estimated by counting annuli on scales but this method underestimates the age of old individuals [START_REF] Beamish | The forgotten requirement for age validation in fisheries biology[END_REF][START_REF] Baudoin | Comparison of otolith and scale readings for age and growth estimation of common dentex Dentex dentex[END_REF]. From now on, age is usually estimated by counting growth increments in otoliths (Fig. 1a). Otoliths are present in various vertebrate taxa, but have been mainly studied in teleosts (e.g. [START_REF] Mesa | Age and growth of brown meagre Sciaena umbra (Sciaenidae) in the Adriatic Sea[END_REF][START_REF] Kadison | Age, growth, and reproductive patterns of the great barracuda, Sphyraena barracuda, from the Florida Keys[END_REF][START_REF] Yershov | New data on the longevity of coastal cod Gadus morhua Linnaeus, 1758 in the White Sea[END_REF]). Otoliths are calcified structures in the inner ears of teleosts and play a role in equilibration. They continue to grow as teleosts age [START_REF] Fowler | Validation of annual growth increments in the otoliths of two species of damselfish from the southern Great Barrier Reef[END_REF][START_REF] Campana | Otoliths, increments, and elements: keys to a comprehensive understanding of fish populations?[END_REF] and are not resorbed even under conditions of high stress [START_REF] Campana | Feeding periodicity and the production of daily growth increments in otoliths of steelhead trout (Salmo gairdneri) and starry flounder (Platichthys stellatus)[END_REF][START_REF] Campana | Calcium deposition and otolith check formation during periods of stress in coho salmon, Oncorhynchus kisutch[END_REF]. As a result, otoliths are considered as one of the best tools to estimate age of teleosts [START_REF] Campana | Otoliths, increments, and elements: keys to a comprehensive understanding of fish populations?[END_REF]. Analysis of sectioned otoliths appears to produce the highest and most accurate estimation of age by improving the readability of growth bands [START_REF] Baudoin | Comparison of otolith and scale readings for age and growth estimation of common dentex Dentex dentex[END_REF]. Statoliths (Fig. 1b) are a structure similar to otoliths present in various invertebrate taxa, and annual or daily growth increments in these structures can be used to estimate the age of box jellyfish [START_REF] Ueno | Fine growth rings found in statolith of a cubomedusa Carybdea rastoni[END_REF][START_REF] Gordon | Growth and age determination of the tropical Australian cubozoan Chiropsalmus sp[END_REF], gastropods [START_REF] Barroso | The gastropod statolith: a tool for determining the age of Nassarius reticulatus[END_REF][START_REF] Richardson | Age and growth of the naticid gastropod Polinices pulchellus (Gastropoda: Naticidae) based on length frequency analysis[END_REF][START_REF] Hollyman | Statoliths of the whelk Buccinum undatum: a novel age determination tool[END_REF] and cephalopods [START_REF] Jackson | Age, growth, and maturation of Lolliguncula brevis (Cephalopoda: Loliginidae) in the northwestern Gulf of Mexico with a comparison of length-frequency versus statolith age analysis[END_REF][START_REF] Bettencourt | Age studies based on daily growth increments in statoliths and growth lamellae in cuttlebone of culture Sepia officinalis[END_REF][START_REF] Liu | Determination of squid age using upper beak rostrum sections: technique improvement and comparison with the statolith[END_REF]. In elasmobranchs (sharks and rays), growth bands are usually counted on sectioned vertebrae (e.g. [START_REF] Skomal | Age and growth of the blue shark (Prionace glauca) in the North Atlantic Ocean[END_REF][START_REF] Piercy | Age and growth of the scalloped hammerhead shark, Sphyrna lewini, in the north-west Atlantic Ocean and Gulf of Mexico[END_REF][START_REF] Porcu | Life-history traits of the commercial blonde ray, Raja brachyura, from the central-western Mediterranean Sea[END_REF], Fig. 1c). In squaliforme sharks, because annual growth bands are poorly visible on the vertebrae [START_REF] Clarke | Age estimation of the exploited deepwater shark Centrophorus squamosus from the continental slopes of the Rockall Trough and Porcupine Bank[END_REF][START_REF] Braccini | Comparison of deterministic growth models fitted to length-at-age data of the piked spurdog (Squalus megalops) in southeastern Australia[END_REF][START_REF] Cotton | Age, growth and reproduction of a common deep-water shark, shortspine spurdog (Squalus cf. mitsukurii), from Hawaiian waters[END_REF], dorsal spines are used to estimate age, either by counting growth bands on the enameled surface [START_REF] Braccini | Comparison of deterministic growth models fitted to length-at-age data of the piked spurdog (Squalus megalops) in southeastern Australia[END_REF][START_REF] Cotton | Age, growth and reproduction of a common deep-water shark, shortspine spurdog (Squalus cf. mitsukurii), from Hawaiian waters[END_REF] or in the sectioned spine [START_REF] Clarke | Age estimation of the exploited deepwater shark Centrophorus squamosus from the continental slopes of the Rockall Trough and Porcupine Bank[END_REF][START_REF] Braccini | Comparison of deterministic growth models fitted to length-at-age data of the piked spurdog (Squalus megalops) in southeastern Australia[END_REF]. In holocephalans (chimaeras), a relative taxon of elasmobranchs, dorsal spines have no enameled surface and thus sectioned dorsal spines are used to estimate age [START_REF] Calis | Preliminary age and growth estimates of the rabbitfish, Chimaera monstrosa, with implications for future resource management[END_REF]. In bivalves, age is estimated by counting annual growth increments in internal shells (Fig. 1d), which are less affected by environmental disturbances than external shells [START_REF] Jones | Sclerochronology: reading the record of the molluscan shell[END_REF]. Other hard tissues displaying growth rings and being used or having the potential to be used for age estimation include jaws in errand polychaete [START_REF] Britayev | Age determination of Polynoidae polychaetes based on growth lines on the jaws[END_REF][START_REF] Plyuscheva | Population ecology of two simpatric polychaetes, Lepidonotus squamatus and Harmothoe imbricata (Polychaeta, Polynoidae), in the White Sea[END_REF], cephalopod beaks [START_REF] Liu | Determination of squid age using upper beak rostrum sections: technique improvement and comparison with the statolith[END_REF][START_REF] Perales-Raya | Age estimation obtained from analysis of octopus (Octopus vulgaris Cuvier,1797) beaks: improvements and comparisons[END_REF], fin spines in billfish (Istiophoridae and Xiphiidae; [START_REF] Kopf | Age estimation of billfishes (Kajikia spp.) using fin spine cross-sections: the need for an international code of practice[END_REF][START_REF] Shimose | Age determination and growth estimation from otolith micro-increments and fin spine sections of blue marlin (Makaira nigricans) in the western North Pacific[END_REF] and teeth from odontocete whales [START_REF] Stewart | Bomb radiocarbon dating calibrates beluga (Delphinapterus leucas) age estimates[END_REF].

However, using growth bands has several limitations and validation is still needed [START_REF] Campana | Accuracy, precision and quality control in age determination, including a review of the use and abuse of age validation methods[END_REF]. In old individuals, the increasing narrowness of growth bands at the edge of the studied structure [START_REF] Mesa | Age and growth of brown meagre Sciaena umbra (Sciaenidae) in the Adriatic Sea[END_REF][START_REF] Francis | Age under-estimation in New Zealand porbeagle sharks (Lamna nasus): is there an upper limit to ages that can be determined from shark vertebrae?[END_REF][START_REF] Henry | The annual macroscopic growth pattern of the northern quahog [=hard clam, Mercenaria mercenaria (L.)], in Narragansett Bay, Rhode Island[END_REF][START_REF] Brooks | Age estimation and lead-radium dating of Antarctic toothfish (Dissostichus mawsoni) in the Ross Sea[END_REF] reduces their visibility, leading to underestimation of age [START_REF] Bettencourt | Age studies based on daily growth increments in statoliths and growth lamellae in cuttlebone of culture Sepia officinalis[END_REF][START_REF] Francis | Age under-estimation in New Zealand porbeagle sharks (Lamna nasus): is there an upper limit to ages that can be determined from shark vertebrae?[END_REF][START_REF] Harry | Evidence for systemic age underestimation in shark and ray ageing studies[END_REF]. The increasing narrowness of growth bands is the result of a reduction of somatic growth rates with age.

Overestimation of age may also occur when counting growth bands [START_REF] Greely | Age and growth of Electrona antarctica (Pisces: Myctophidae), the dominant mesopelagic fish of the Southern Ocean[END_REF][START_REF] Andrews | Lead-radium dating of Pacific cod (Gadus macrocephalus) -validation of the young-fish scenario[END_REF][START_REF] Kastelle | Age validation of Pacific cod (Gadus macrocephalus) using high-resolution stable oxygen isotope ( δ 18 O) chronologies in otoliths[END_REF] as non-annual growth bands may appear [START_REF] Brooks | Age estimation and lead-radium dating of Antarctic toothfish (Dissostichus mawsoni) in the Ross Sea[END_REF][START_REF] Kastelle | Age validation of Pacific cod (Gadus macrocephalus) using high-resolution stable oxygen isotope ( δ 18 O) chronologies in otoliths[END_REF][START_REF] Uriarte | Validation of age determination using otoliths of the European anchovy (Engraulis encrasicolus L.) in the Bay of Biscay[END_REF]. It may be due to environmental factors that may alter the pattern of growth bands such as salinity [START_REF] Narvaez | Growth bands are an unreliable indicator of sea urchin age: Evidence from the laboratory and the literature[END_REF] and food availability [START_REF] Henry | The annual macroscopic growth pattern of the northern quahog [=hard clam, Mercenaria mercenaria (L.)], in Narragansett Bay, Rhode Island[END_REF][START_REF] Narvaez | Growth bands are an unreliable indicator of sea urchin age: Evidence from the laboratory and the literature[END_REF]. For example, slow growth translucent bands were previously known to be formed only during winter in internal shells of hard clams Mercenaria mercenaria in Rhode Island [START_REF] Jones | Sclerochronological records of temperature and growth from shells of Mercenaria mercenaria from Narragansett Bay, Rhode Island[END_REF] but reduction of phytoplankton availability in summer led to the formation of slow growth translucent bands also in summer, meaning that a pattern of four bands instead of two became yearly for this species in this region.

Furthermore, the compression of growth bands in older individuals reduces the visibility of the fall opaque band at the edge of the shell [START_REF] Henry | The annual macroscopic growth pattern of the northern quahog [=hard clam, Mercenaria mercenaria (L.)], in Narragansett Bay, Rhode Island[END_REF]. The pattern of growth bands may also not be yearly in hard tissues of some taxa [START_REF] Greely | Age and growth of Electrona antarctica (Pisces: Myctophidae), the dominant mesopelagic fish of the Southern Ocean[END_REF][START_REF] Narvaez | Growth bands are an unreliable indicator of sea urchin age: Evidence from the laboratory and the literature[END_REF][START_REF] Fisher | Life in the slow lane: growth and longevity of cold-seep vestimentiferans[END_REF][START_REF] Russel | Natural growth lines in echinoid ossicles are not reliable indicators of age: a test using Strongylocentrotus droebachiensis[END_REF] making them invalid for age estimation. Moulting has also hampered direct estimation of crustacean age. As a result, the possibilities to directly estimate age of crustaceans using growth bands has begun to be investigated only recently in gastric mill and eyestalks (Fig. 1e) with contrasting results [START_REF] Kilada | Direct determination of age in shrimps, crabs, and lobsters[END_REF][START_REF] Sheridan | Investigating the effect of molting on gastric mill structure in Norway lobster (Nephrops norvegicus) and its potential as a direct ageing tool[END_REF][START_REF] Kilada | Age determination in crustaceans: a review[END_REF][START_REF] Kilada | Validation of band counts in eyestalks for the determination of age of Antarctic krill, Euphausia superba[END_REF].

Analysing chemistry of hard tissues

Calcified structures also incorporate environmental elements during their formations but are usually metabolically inert once formed. As a result, compounds present in growth bands are preserved over time and variations of chemical composition occur from the core to the edge of the chemical structures [START_REF] Jones | Marking time with bivalve shells: oxygen isotopes and season of annual increment formation[END_REF]. These variations may be a tool for estimating age of marine animals but are mainly used to validate age estimation obtained by band counting [START_REF] Campana | Accuracy, precision and quality control in age determination, including a review of the use and abuse of age validation methods[END_REF] as these methods are more expensive than growth band counting.

Stable isotope ratios of oxygen ( 18 O: 16 O, denoted δ 18 O) in calcified structures are negatively linked to seawater temperature [START_REF] Epstein | Carbonate-water isotopic temperature scale[END_REF][START_REF] Epstein | Revised carbonate-water isotopic temperature scale[END_REF]. Consequently, cyclical variations of δ 18 O occur in calcified structures along seasons, with maximum δ 18 O during winter and minimum δ 18 O during summer.

Thus, the number of δ 18 O cycles from the core to the edge of calcified structures may indicate the age of the organism. This method has been used either for age determination [START_REF] Gurney | Determining age and growth of abalone using stable oxygen isotopes: a tool for fisheries management[END_REF][START_REF] Naylor | Validated estimation of growth and age in the New Zealand abalone Haliotis iris using stable oxygen isotopes[END_REF] or for validation of other methods [START_REF] Hollyman | Statoliths of the whelk Buccinum undatum: a novel age determination tool[END_REF][START_REF] Kastelle | Age validation of Pacific cod (Gadus macrocephalus) using high-resolution stable oxygen isotope ( δ 18 O) chronologies in otoliths[END_REF].

Another well-known methodology is bomb radiocarbon. Atmospheric nuclear testings in the late 1950s led to an sharp increase of 14 C levels in the atmosphere and in the marine dissolved organic carbon. Indeed, the levels of 14 C in the environment are also integrated in the successive growth layers of calcified tissues of growing individuals [START_REF] Francis | Age under-estimation in New Zealand porbeagle sharks (Lamna nasus): is there an upper limit to ages that can be determined from shark vertebrae?[END_REF][START_REF] Leaf | The feasibility of bomb radiocarbon analysis to support an age-at-length relationship for red abalone, Haliotis rufescens Swainson in Northern California[END_REF][START_REF] Hamaday | Vertebral bomb radiocarbon suggests extreme longevity in white sharks[END_REF][START_REF] Andrews | Bomb radiocarbon and the Hawaiian archipelago: coral, otoliths and seawater[END_REF], and in particular, in the core of the calcified tissues, i.e. the birth mark. The integration of environmental 14 C levels in organisms resulted in the appearance of a temporal profile of 14 C levels in environment and species that reflects the pre and post-bomb testing 14 C levels in the environment [START_REF] Andrews | Bomb radiocarbon and the Hawaiian archipelago: coral, otoliths and seawater[END_REF][START_REF] Kalish | Pre-and post-bomb radiocarbon in fish otoliths[END_REF][START_REF] Baker | Use of bomb radiocarbon to validate otolith section ages of red snapper Lutjanus campechanus from the northern Gulf of Mexico[END_REF][START_REF] Kerr | Radiocarbon in otoliths of yelloweye rockfish (Sebastes ruberrimus): a reference time series for the coastal waters of southeast Alaska[END_REF] (Fig. 2). As a result, 14 C levels in the core of calcified tissues reflect 14 C levels in the environment at the birth of individuals and thus can be used to estimate the age of animals [START_REF] Andrews | Bomb radiocarbon and lead-radium disequilibria in otoliths of bocaccio rockfish (Sebastes paucispinis): a determination of age and longevity for a difficult-to-age fish[END_REF][START_REF] Roark | Radiocarbon-based ages and growth rates of bamboo corals from the Gulf of Alaska[END_REF] or, more frequently, to validate [START_REF] Stewart | Bomb radiocarbon dating calibrates beluga (Delphinapterus leucas) age estimates[END_REF][START_REF] Baker | Use of bomb radiocarbon to validate otolith section ages of red snapper Lutjanus campechanus from the northern Gulf of Mexico[END_REF][START_REF] Kerr | Radiocarbon in otoliths of yelloweye rockfish (Sebastes ruberrimus): a reference time series for the coastal waters of southeast Alaska[END_REF][START_REF] Campana | Bomb dating and age determination of large pelagic sharks[END_REF][START_REF] Neilson | A validated description of age and growth of western Atlantic bluefin tuna (Thunnus thynnus)[END_REF] or adjust [START_REF] Francis | Age under-estimation in New Zealand porbeagle sharks (Lamna nasus): is there an upper limit to ages that can be determined from shark vertebrae?[END_REF][START_REF] Hamaday | Vertebral bomb radiocarbon suggests extreme longevity in white sharks[END_REF] the year of birth determined with sclerochronology by comparing 14 C levels in studied organisms with a reference chronology of known-age animals (Fig. 2). The main drawbacks for this technique are that it is dependent on a time-specific event and that there are regional variations of 14 C levels and trends [START_REF] Mahadevan | An analysis of bomb radiocarbon trends in the Pacific[END_REF][START_REF] Scource | The marine radiocarbon bomb pulse across the temperate North Atlantic: a compilation of ∆ 14 C time histories from Arctica islandica growth increments[END_REF].

The radiometric method consists in comparing the abundance of a radioactive isotope with its daughter product [START_REF] Smith | The use of Pb-210/Ra-226 and Th-228/Ra-228 disequilibria in the ageing of otoliths of marine fish[END_REF]. For ageing marine animals, the use of this method is limited to teleost otoliths as an assumption to this methodology is that the carbonate acts as a closed system. this method is more suited to estimate the age of short-lived teleosts. However, it has only been used once [START_REF] Campana | Radiochemical determination of longevity in flyingfish Hirundichthys affinis using Th-228/Ra-228[END_REF] since its first documentary reference [START_REF] Smith | The use of Pb-210/Ra-226 and Th-228/Ra-228 disequilibria in the ageing of otoliths of marine fish[END_REF].

Other methods outside of the sclerochronology discipline

Lipofuscin are fluorescent aggregates made of oxidised proteins and lipids that are no more degraded by cell metabolism and thus continuously accumulate within lysosomal residual bodies.

Consequently, in areas of the brain where neurons persist throughout life, lipofuscin is accumulated with age in various taxa, notably crustaceans [START_REF] Sheehy | Widespread occurrence of fluorescent morphological lipofuscin in the crustacean brain[END_REF]. The correlation between lipofuscin content and age of crustaceans [START_REF] Sheehy | New perspectives on the growth and longevity of the European lobster (Homarus gammarus)[END_REF][START_REF] Sheehy | Potential of morphological lipofuscin age-pigment as an index of crustacean age[END_REF] led lipofuscin quantification to be a common tool to estimate the age of crustaceans [START_REF] Kilada | Age determination in crustaceans: a review[END_REF]. Lipofuscin quantification can be done by using successive histological sections of the brain where lipofuscin is quantified as an area fraction (e.g. [START_REF] Bluhm | Age determination in the Antarctic shrimp Notocrangon antarcticus Crustacea: Decapoda), using the autofluorescent pigment lipofuscin[END_REF][START_REF] Bluhm | The autofluorescent age pigment lipofuscin: key to age, growth and productivity of the Antarctic amphipod Waldeckia obesa (Chevreux, 1905)[END_REF]) or percent volume fraction (e.g. [START_REF] Sheehy | New perspectives on the growth and longevity of the European lobster (Homarus gammarus)[END_REF][START_REF] Sheehy | Potential of morphological lipofuscin age-pigment as an index of crustacean age[END_REF]). Lipofuscin content can also be determined using spectrophotometry and is expressed as a concentration relative to protein content (e.g. µg.mg -1 protein, e.g. [START_REF] Ju | Use of extractable lipofuscin for age determination of blue crab Callinectes sapidus[END_REF][START_REF] Bosley | Use of extractable lipofuscin to estimate age structure of ghost shrimp populations in west coast estuaries of the USA[END_REF]). Age determination can thus be done by using the relationship between lipofuscin content and age in individuals of known age (e.g. [START_REF] Sheehy | New perspectives on the growth and longevity of the European lobster (Homarus gammarus)[END_REF][START_REF] Sheehy | Potential of morphological lipofuscin age-pigment as an index of crustacean age[END_REF]), or by separating age groups derived from lipofuscin content frequency histograms (e.g. [START_REF] Bluhm | Age determination in the Antarctic shrimp Notocrangon antarcticus Crustacea: Decapoda), using the autofluorescent pigment lipofuscin[END_REF][START_REF] Bluhm | The autofluorescent age pigment lipofuscin: key to age, growth and productivity of the Antarctic amphipod Waldeckia obesa (Chevreux, 1905)[END_REF][START_REF] Bosley | Use of extractable lipofuscin to estimate age structure of ghost shrimp populations in west coast estuaries of the USA[END_REF]).

Limited knowledge on growth rates of an organism may allow a preliminary estimation of lifespan. However, these lifespans are highly likely to be inaccurate or imprecise. For example, the antarctic sea star Odontaster validus was estimated to live between 50 and 100 years but these ages were estimated assuming that the growth rate of O. validus with age is linear [START_REF] Pearse | Antarctic sea star[END_REF]. However, animals grow until a maximum size and then continue to live. Actually, growth of animals usually follows the von Bertalanffy's [START_REF] Bertalanffy | Untersuchungen über die Gesetzlichkeit des Wachstums. I. Allgemeine Grundlagen der Theorie; mathematische und physiologische Gesetzlichkeiten des Wachstums bei Wassertieren[END_REF] growth model, where growth rates decrease with age as length is approaching an asymptote. Knowledge on variations of growth rates during life and several given parameters (e.g. size at birth) allow to generate growth models. These growth models then help to estimate the age of animals according to their size, and longevity is estimated according to the age estimated for the largest organism (e.g. [START_REF] Ebert | Red sea urchins (Strongylocentrotus franciscanus) can live over 100 years: confirmation with A-bomb 14carbon[END_REF][START_REF] Bergquist | Longevity record for deep-sea invertebrate[END_REF][START_REF] Nielsen | Eye lens radiocarbon reveals centuries of longevity in the Greenland shark (Somniosus microcephalus)[END_REF]).

Attempting to explain long lifespans of some species

Some long-lived marine animals can live strikingly longer than terrestrial ones. While the maximal recorded lifespan of humans is 122 years, clams can live at least for 5 centuries and sharks for ca 400 years and, at a first sight, such lifespans are astounding. Yet, some mechanisms explaining lifespan of terrestrial species may be applied to marine animals too.

Longevity and life-history strategies

Longevity is an integral part of life history strategies. Species reproducing in a single season, as mice do [START_REF] Phelan | Natural selection, dietary restriction, and extended longevity[END_REF], are not expected to live long simply because a long life is not necessary to make the species thrive. These species are well able to quickly take advantage of plentiful food to reproduce heavily: they are called opportunistic species [START_REF] Demetrius | Of mice and men. When it comes to studying ageing and the means to slow it down, mice are not just small humans[END_REF]. This life-history strategy is also present in the marine environment. Opportunistic species include animals such as small pelagic teleosts (i.e. anchovies and sardines), with a small size, a fast maturation, a rather short lifespan (from 1.5 to 15 years, [START_REF] Greely | Age and growth of Electrona antarctica (Pisces: Myctophidae), the dominant mesopelagic fish of the Southern Ocean[END_REF][START_REF] King | Marine fish life history strategies: applications to fishery management[END_REF]), and strong abundance fluctuations over time. One can thus understand why the stock of these species (e.g. the numerous anchovies) can recover if overfished [START_REF] Adams | Life history patterns in marine fishes and their consequences for fisheries management[END_REF]. However, some of these opportunistic species still have a lifespan (e.g. 13 years in Pacific sardines and 15 years in herrings) that may be considered as long in, say, dogs, and a challenge is to explain why "short-lived" fish can live so long. Another example of opportunistic species are planktonic cladocerans which have population maxima during periods of favourable conditions but are practically absent from the water column for the rest of the year. Indeed, their life cycle is characterised by fast maturation and a period of asexual reproduction followed by a period of sexual reproduction, resulting in the seasonal abundance fluctuations for this group [START_REF] Atienza | Life history and population dynamics of the marine cladoceran Penilia avirostris (Branchiopoda: Cladocera) in the Catalan Sea (NW Mediterranean)[END_REF][START_REF] Miyashita | Life cycle and reproductive traits of marine podonids (Cladocera, Onychopoda) in a coastal subtropical area[END_REF].

By contrast, species unable to quickly reproduce and thrive even if resources are plentiful are called equilibrium species [START_REF] Demetrius | Of mice and men. When it comes to studying ageing and the means to slow it down, mice are not just small humans[END_REF], such as for instance humans that can only have one offspring every two years at a maximum and need parental care for ca 15 years. This pattern is not only observed in terrestrial species but also in marine ones. Marine species with low fecundity reproduce repeatedly during life, and the offspring need time to reach maturity. This is the case for whales or sharks. For instance, short-finned pilot whales have their first calf at 8-10 years of age, after a ca 16 months gestation, sucking lasting for ca 5 years and up to 15 years for the last calf [START_REF] Bernard | The pilot whales, Globicephala sp[END_REF]. Such a life-history strategy requires living long for whales being able to survive and the species to thrive.

However, a main difference between the so-called fish and mammals is that, even if marine biologists make use of the term "parental investment" in fish [START_REF] Winemiller | Patterns of variation in life history among South American fishes in seasonal environments[END_REF], this investment is rudimentary when compared to parental care in mammals. In the best of the cases, parents will simply protect larvae from predators, like the male lingcod Ophiodion elongatus does [START_REF] O'connell | Submersible observations on lingcod, Ophiodon elongatus, nesting below 30 m off Sitka, Alaska[END_REF]. As a result, while elasmobranchs are still considered as equilibrium species because of low fecundity, large eggs and important parental investment (e.g. gestation), long-living teleosts may instead be considered as "periodic strategists" [START_REF] King | Marine fish life history strategies: applications to fishery management[END_REF]. Periodic strategists are "slow-growing, long-lived demersal species (with) a lower degree of variability in abundance" and the authors stressed that lifespans greater than 20 years ensure "a relatively long reproductive cycle, which minimises the risk that periods of unfavourable environmental conditions will result in the loss of a stock". However, teleosts, like most other marine taxa, actually display a great fecundity by releasing large numbers of eggs in the water column. It is a little bit surprising that long-lived animals can display a great fecundity, by contrast to terrestrial mammals, but one should not forget that one million of eggs of an oviparous marine organism does not mean one million of new adults, because of a high predatory pressure on eggs and juveniles for instance. Fish often grow throughout life and their fecundity increases with age [START_REF] Reznick | The evolution of senescence in fish[END_REF], but the increased number of eggs produced by older fish could result in only a few more adult fish than at younger ages. Yet, laying as many eggs as possible may be the only available lifehistory strategy when eggs are simply dispersed in water, and thus offered to predators. Therefore, the increased fecundity with age could explain why many fish live long: without a long lifespan, these fish could not reproduce and these species would be extinct.

Temperature and metabolism of ectotherm species

Fish and other marine animals, except mammals, are ectotherms and, as for any ectotherm species, their lifespan is expected to be longer at lower temperatures [START_REF] Munch | Latitudinal variation in lifespan within species is explained by the metabolic theory of ecology[END_REF]. However, experimentally testing this hypothesis can only be done with very short-lived species for obvious reasons. For instance, mean lifespans of the freshwater fish Cynolebias belotti are 14 months at 25

°C and 19 months at 20 °C: transfer at 8 months of age from 20 °C to 15 °C increases lifespan to 23 months, while the reverse change has nearly no effect (15 months; [START_REF] Liu | Mid-life temperature-transfer effects on life-span of annual fish[END_REF]).

Because temperature is lower in deep sea than near the surface, it has been hypothesised that deeper-dwelling fish live long, but as deep sea also means higher pressure, lower light, oxygen, and food levels than near the surface (references in [START_REF] Cailliet | Age determination and validation studies of marine fishes: do deep-dwellers live longer?[END_REF]), it is rather difficult to tease apart these factors. In any case, the evidence showing that deep-sea fish live longer is fragile: in a review on deep-dwelling fish, Cailliet et al. [START_REF] Cailliet | Age determination and validation studies of marine fishes: do deep-dwellers live longer?[END_REF] concluded that metabolic rate was lower with increasing depth, and that because of a lower oxygen pressure, oxidative stress could be lower, all of this possibly explaining long lives but, as stressed by the authors "our findings are at best correlative".

Another review on bivalves showed that depth only explains 4% or the variance of lifespan (Fig. S4 in [START_REF] Moss | Lifespan, growth rate, and body size across latitude in marine Bivalvia, with implications for Phanerozoic evolution[END_REF], and see also [110]), bivalves living longer at higher depths, but there is a caveat in the fact that most of depths were in the 0-100 m range.

Nevertheless, it remains that a low temperature could explain partly why fish and other ectotherm marine species can live so long. For instance, sampled Salmo trutta trouts are older at higher latitudes in Norway where water temperature decreases [START_REF] Jonsson | Longevity, body size, and growth in anadromous brown trout (Salmo trutta)[END_REF]. Bivalves of various species have been shown to live longer at higher latitudes, and thus in increasingly cold waters, even if this is not always observed (Fig. S2 in [START_REF] Moss | Lifespan, growth rate, and body size across latitude in marine Bivalvia, with implications for Phanerozoic evolution[END_REF]). This results not only from temperature decrease per se, because predation is more important in the tropics and metabolism could be lower at higher latitudes because of a reduced food supply during winter [START_REF] Moss | Lifespan, growth rate, and body size across latitude in marine Bivalvia, with implications for Phanerozoic evolution[END_REF]. If food supply is lower at high latitudes, starvation could occur. It has been argued that species unable to emigrate in the event of starvation have to wait at the same place for better times and thus that food restriction can make them living longer (e.g. nematodes, mice), while larger and less predated species (e.g. elephants, humans) do not need to live longer because they can emigrate to discover new food sources [START_REF] Bourg | The somatotropic axis may not modulate ageing and longevity in humans[END_REF].

Because bivalves cannot emigrate, one could make the hypothesis that food restriction would increase their lifespan: such a hypothesis could be tested with short-lived bivalves. By contrast, whales or sharks could try to discover new food sources and thus food restriction could have no effect on lifespan: anyway, it is simply impossible to test this hypothesis by recording lifespan of food-restricted whales or sharks.

Therefore, it seems possible to explain why ectotherm marine species can live long. Their metabolism is highly dependent on their environment, not only regarding temperature, but also food supply, and it is not surprising that a long lifespan, for instance in some bivalve species, has been selected. Because bivalves can hardly move away, populations could become extinct and possibly the whole species, too, if they were unable to sustain a low food supply: like spiders on their web, Arctica islandica clams have to wait for food coming to them and, as spiders [START_REF] Austad | Life extension by dietary restriction in the bowl and doily spider, Frontinella pyramitela[END_REF], living longer can be a strategy to wait for better times. Combined with a low temperature under the surface, and thus a longer life with lower temperature as in other ectotherms, this could make they can live long.

However, this would not be observed if life would be ended at an early age because of a severe predatory pressure.

A low predatory pressure…except from fishery

Overfishing is an issue, particularly for slow-growing long-lived species. Fisheries predate preferably large subjects, while marine predators usually prefer prey smaller than their own size, because gape limitation prohibits ingesting too large individuals (see e.g. [START_REF] Schmitt | Gape-limitation, foraging tactics and prey size selectivity of two microcarnivorous species of fish[END_REF]). Indeed, as large subjects need an extended time to grow, catching them means catching the most prolific ones, which can make soon a species becoming endangered, at risk not to recover even after years or decades [START_REF] Musick | Ecology and conservation of long-lived marine animals[END_REF][START_REF] Barnett | Old-growth fishes become scarce under fishing[END_REF], and these consequences are similar to those of hunting adult African elephants, even if does not result in extinction [START_REF] Pape | Overfishing causes frequent fish population collapses but rare extinctions[END_REF]. Predating large subjects could select for animals investing their resources in reproduction at an earlier age at the expense of their size [START_REF] Dieckmann | The dawn of Darwinian fishery management[END_REF].

Therefore, the main predator of marine species is the fisherman and not the marine predators.

It has been estimated that "among nonhuman predators across all oceans, 50 % of exploitation rates were less than 1 % of annual adult biomass. In contrast, fisheries exploited more than 10 % of adult biomass in 62 % of cases. Overall, the median fishing rate (0.14) was 14.1 times the take (0.01) by marine predators" [START_REF] Darimont | The unique ecology of human predators[END_REF]. Therefore, in the absence of fishing, it can be assumed that the predatory pressure is low and sustainable. Oceans are immense, and for many species they are a threedimensional world allowing more escape than for mice in sight of a cat, for instance. This may explain why even the highly predated sardines during the sardine run in South Africa [START_REF] Van Der Lingen | Overview of the KwaZulu-Natal sardine run[END_REF] can sustain such an annual toll in a few days, and this every year from ancient times.

For slow-growing species, a long lifespan is mandatory; thus, if protected from predators, because they can escape or hide in the ground like clams do, individuals of these species can indeed live long. The clam A. islandica is buried in sands and is hardly visible, waiting for carbon particles and, as stressed by Morton [START_REF] Morton | The biology and functional morphology of Arctica islandica (Bivalvia: Arcticidae): A gerontophilic living fossil[END_REF], "the lifestyle of A. islandica is characterised by slow, deliberate, near undetectable, movements possibly to avoid detection". Therefore, if the predatory pressure is low, there is no selective pressure for a reduced lifespan combined with a higher fecundity at younger ages (see [START_REF] Bourg | Evolutionary theories of aging can explain why we age[END_REF]) and longer lifespan can evolve, as in opossums living on an island free from predators for millenaries [START_REF] Austad | Retarded senescence in an insular population of Virginia opossums (Didelphis virginiana)[END_REF]. This could be particularly the case for the clam A. islandica that can live for 5 centuries [START_REF] Butler | Variability of marine climate on the North Icelandic Shelf in a 1357-year proxy archive based on growth increments in the bivalve Arctica islandica[END_REF].

However, it may happen that a mere accident has dire consequences and kill most animals.

For instance, A. islandica clams were subjected to a mass extinction in Iceland after a storm.

Innumerable clams were "swept from their natural sandy habitat at depth of more than 9 m, up onto the hard bottom in shallower water (7-9 m)" and thus, "lying exposed, unable to escape, they were easy prey for fish as wolffish… and invertebrate predators" [START_REF] Thórarindsóttir | Mass mortality of ocean quahog, Arctica islandica, on hard substratum in Lonafjordur, north-eastern Iceland after a storm[END_REF]. One year after the storm, only empty shells and no living clam were seen on the ground.

Marine ectotherms and mammals

-13 -Therefore, taking into account a lower metabolism at lower temperatures in ectotherms, a low predation rate, a fecundity often increasing with age, and iteroparity, it seems possible to (partly?) explain why marine species can live so long. However, it remains that marine ectotherms can live much longer than marine mammals. Table 1 shows that Greenland shark Somniosus microcephalus can live for 4 centuries while the whales Eubalaena glacialis live only for several decades and Balaena mysticetus up to 200 years. Thus, in the best case, mammals live for only half the lifespan of large Greenland sharks: it could be linked to the fact that sharks are ectotherms and not endotherms like whales.

The 211-year lifespan of the bowhead whale B. mysticetus is however not exceptional, given that this whale is the largest living mammal and that larger mammals usually live longer [START_REF] Stearns | The influence of size and phylogeny on patterns of covariation among lifehistory traits in the mammals[END_REF].

Indeed, bowhead whales live only twice as long as humans, a species with a small body size when compared to the up to 100 tonnes whales. However, it is a caveat that the 122-years lifespan of the recordwoman Jeanne Calment has been observed among several billions of people, while sharply less bowhead whales can be observed, with a lower chance to observe exceptional individuals. The other massive blue and fin whales (Balaenoptera musculus and Balaenoptera physalus, indicated respectively just below the bowhead whales point on Fig. 3) do not display an extraordinary lifespan. Therefore, the long lifespan of marine mammals is far from being exceptional when compared to other mammals, even if they are long-lived, and does not depart from the general trend linking the log of body mass and the log of maximal lifespan in mammals (Fig. 3): explaining the lifespan of marine mammals is not an issue but explaining why only rather large marine mammals exist is surely an issue. The marine otter Lontra felina, which weighs ca 4 kg and whose lifespan is unknown (and thus not shown on Fig. 3), is probably the smallest marine mammal [START_REF] Valqui | The marine otter Lontra felina (Molina, 1782): A review of its present status and implications for future conservation[END_REF].

By contrast, lifespans of marine ectotherms can be impressive and are not so easy to explain: more studies are necessary to ascertain and explain the variation of lifespan among marine species. Picture from [START_REF] Richardson | Age and growth of the naticid gastropod Polinices pulchellus (Gastropoda: Naticidae) based on length frequency analysis and statolith growth rings[END_REF]. c) Sagittally sectioned vertebrae from a 4 year-old shark (Spyrna lewini).

Figure 1 .

 1 Figure 1. Examples of tissues displaying growth bands and being used to estimate the age of marine animals. a) sectioned otolith from a 23 year-old teleost (Dentex dentex) . Annual growth bands are indicated by white dots. Picture from [126]. b) Statolith from a gastropod (Polinices pulchellus) with larval ring (LR), settlement ring (SR), and two years growth rings (1 st and 2 nd ).

Figure 2 .

 2 Figure2. Temporal evolution of14 C levels (∆ 14 C) recorded in coral layers from Kure Atoll (Northwestern Hawaiian Islands,[START_REF] Andrews | Bomb radiocarbon and the Hawaiian archipelago: coral, otoliths and seawater[END_REF]), in otolith cores from Lutjanus campechanus from the northern Gulf of Mexico[START_REF] Baker | Use of bomb radiocarbon to validate otolith section ages of red snapper Lutjanus campechanus from the northern Gulf of Mexico[END_REF], Chrysophrys auratus from New Zealand[START_REF] Kalish | Pre-and post-bomb radiocarbon in fish otoliths[END_REF] and Sebastes ruberrimus from southeast Alaska[START_REF] Kerr | Radiocarbon in otoliths of yelloweye rockfish (Sebastes ruberrimus): a reference time series for the coastal waters of southeast Alaska[END_REF] and in the atmosphere of the northern hemisphere (zone 2,[START_REF] Hua | Atmospheric radiocarbon for the period 1950-2010[END_REF]).

Figure 3 .

 3 Figure 3. Relationship between body mass and maximal lifespan in mammal species (log scales). Drawn from the database AnAge (http://genomics.senescence.info/species/, [131]. Each point is for a species and marine mammals are shown with black squares.

Table

  . In the absence of a direct lifespan record, reported lifespans in Table1should be only considered as estimates, whose precision is dependent on the method used for estimation.

		-4 -
	Species	Record lifespan (years)	Measuring method	Reference
	North Atlantic right	≥ 65	Sighting	[8]
	whale Eubalaena
	glacialis
	European lobster	72 ± 9	Age pigment	[9]
	Homarus gamarrus		accumulation
	Antarctic sea star	> 100
	Odontaster validus

Table 1

 1 shows that various methods are used to determine age and lifespan. In the laboratory, recording birth and death date allows knowing lifespans of model species, e.g. flies or mice, which is not possible in most of the cases for marine animals not kept in the laboratory. Therefore, it is needed to implement other, indirect, methods to determine the age or lifespan of samples. The

	methodologies used to estimate age or lifespan of marine animals are more or less taxa or tissue-
	specific. For example, measurement of lead 210 and radium 226 ratio and quantification of
	lipofuscin are limited to teleost otoliths and crustacean brains respectively. By contrast, growth
	band counts and growth models are used in various taxa.
	Most of the ageing methods are part of the discipline of sclerochronology, i.e. the study of
	physical and chemical variations in hard tissues in animals.

  The most commonly used pair of radioactive isotopes are radium 226 ( 226 Ra) and lead 210 ( 210 Pb).Radium is a naturally occurring radioactive element. Its isotopes are highly soluble in water in comparison of their parent and daughter radio-isotopes and efficiently absorbed by tissues as a proxy of calcium. As a result, radium is integrated in calcified tissues. In particular, teleost otoliths integrate226 Ra and discriminate against its daughter radio-isotope 210 Pb. Consequently, the subsequent decay of 226 Ra into 210 Pb, which is itself retained by the otoliths, occurs at predictable rates according to the half-life of the two isotopes. As a result, the ratio of210 Pb ov e r 226 Ra ( 210 Pb/ 226 Ra) increases consistently and thus can be used as an independent chronometer to estimate the otolith's, and thus the teleost's, age. It is possible to determine 210 Pb/ 226 Ra in both the whole otolith or the core of the otolith. However, analysing 210 Pb/ 226 Ra in the whole otolith requires to take into account the growth of the otolith[START_REF] Fenton | Age determination of orange roughy, Hoplostethus atlanticus (Pisces: Trachichthyidae) using 210 P b : 226 Ra disequilibria[END_REF]. Indeed, as the otolith grows, it continuously integrates radium that subsequently decays, leading to variation of 210 Pb/ 226 Ra from the core to the edge of the otolith. By contrast, 210 Pb/ 226 Ra in the core provides more accurate ages[START_REF] Smith | The use of Pb-210/Ra-226 and Th-228/Ra-228 disequilibria in the ageing of otoliths of marine fish[END_REF] and improvement of technology made it possible to work on small amounts of samples. 210 Pb/ 226 Ra has been used either to assess the age of teleosts of age up to 100 years or as a validation tool for growth zones count (e.g.[START_REF] Fenton | Age determination of orange roughy, Hoplostethus atlanticus (Pisces: Trachichthyidae) using 210 P b : 226 Ra disequilibria[END_REF][START_REF] Brooks | Age estimation and lead-radium dating of Antarctic toothfish (Dissostichus mawsoni) in the Ross Sea[END_REF][START_REF] Andrews | Bomb radiocarbon and the Hawaiian archipelago: coral, otoliths and seawater[END_REF][START_REF] Andrews | Lead/radium dating provides a framework for coordinating age estimation of Patagonian toothfish (Dissostichus eleginoides) between fishing areas[END_REF][START_REF] Andrews | Lead-radium dating of orange roughy (Hoplostethus atlanticus): validation of a centenarian life span[END_REF]. Another pair of isotopes that can used to estimate teleost age is thorium 228 ( 228 Th) and radium 228 ( 228 Ra). However, as the age limit with this dating method is 10 years[START_REF] Smith | The use of Pb-210/Ra-226 and Th-228/Ra-228 disequilibria in the ageing of otoliths of marine fish[END_REF],

Picture from [START_REF] Piercy | Age and growth of the scalloped hammerhead shark, Sphyrna lewini, in the north-west Atlantic Ocean and Gulf of Mexico[END_REF]. d) Sectioned shell from a bivalve (Arctica islandica) with each black bar showing one year of growth. Picture from [START_REF] Wanamaker | Very long-lived mollusks confirm 17th century ad tephra-based radiocarbon reservoir ages for north icelandic shelf waters[END_REF]. e) Sectioned eyestalk of a 4 year-old crustacean (Euphausia superba). Annual growth bands are indicated by green dots. Green and white arrows respectively indicate the epicuticle and endocuticle layers. Picture modified from [START_REF] Kilada | Validation of band counts in eyestalks for the determination of age of Antarctic krill, Euphausia superba[END_REF]. Reprinted with permission.


Théo Hannotte

Louis Thomas

Mélanie Lavancier

Sergey Mitryukovskiy

Jean-François Lampin

Romain Peretti
email: romain.peretti@univ-lille.fr

Towards broadband THz spectroscopy and analysis of subwavelength size biological samples

Keywords: Terahertz, Biophotonics, time domain spectroscopy, vibrational spectroscopy

The Terahertz (THz) technology has now reached a level of maturation, which allows its uses beyond its core domains of application (telecom and imaging for security or healthcare). Vibrational spectroscopy in the THz range is employed in various fields and is specifically promising in (µ)biology. Indeed, the probed vibrational states extend over several nanometers and give a signature of the sample 3D structure at the nanoscale. This is particularly salient for macromolecules (proteins, DNA and RNA strands etc.) since, on one hand, their 3D structure is very difficult to probe in physiological condition with other techniques, and on the other hand, this structure determines their function and is consequently of utmost importance for the living. A major hurdle still arises when applying THz spectroscopy on biological or macromolecular samples. The samples are generally smaller than the THz wavelength, which requires concentrating the THz field in the sample. Solutions aimed at tackling this challenge by using µ/nano technology of THz field concentration and a proper data analysis will be presented.

INTRODUCTION

During the XVII century, the controversy between D'Alembert [START_REF] Le Rond D'alembert | Recherches sur la courbe que forme une corde tendue mise en vibration[END_REF], Euler [START_REF] Euler | De vibratione cordarum[END_REF] and Bernoulli [START_REF] Bernouilli | Reflexions et éclaircissemens sur les nouvelles vibrations des cordes exposées dans les mémoires de l'académie de 1747 et 1748[END_REF] shined the light towards the study of resonant vibrations of objects. This had consequences on a wide range of scales from vibrations of violin's strings to vibration of molecular bonds in infrared spectroscopy. The vibrations eigen frequencies serve as a signature for the size, the stiffness and the structure of a body. The size of a lot of biomolecules e.g. proteins and DNA or RNA strands lies roughly in the range from one to 10 nm, making them biochemical nano-objects with a relative symmetry deriving from the repetition of monomers. Consequently, the vibrations supported by these biomolecules lie in the broad THz range. E.g., collective motion of DNA base pairs along the DNA backbone [START_REF] Roggenbuck | Coherent broadband continuous-wave terahertz spectroscopy on solid-state samples[END_REF]. Additionally, since biological macromolecules(MMs) are polar, those vibrations couple to the EM-field. In other words, if spectroscopy in the midinfrared region probes vibrations associated to localized atom-atom stretches in molecules, THz frequency probes delocalized collective vibrational modes in long molecules like MMs. These resonances can serve as "fingerprint" signatures that reveal their internal structure and vibrational dynamics. There are both theoretical and experimental evidences supporting this perspective [START_REF] Chou | Low-frequency collective motion in biomacromolecules and its biological functions[END_REF][START_REF] Pereira | Terahertz and Mid Infrared Radiation: Generation, Detection and Applications[END_REF].

Performing THz spectroscopy was a challenge for decades. Indeed, using the historical Fourier transform infrared spectrometer needs good sources and detectors not available in the THz spectral range. However, spectroscopy in THz frequency range has shown an important development in the last decades. The invention of short pulse lasers and its development up to industrial performances as to progress of semiconductor materials and devices lead to time-domain spectroscopy (TDS). The setup comes from sub-picosocond electrical sampling demonstrated by G. Mourou's group [START_REF] Valdmanis | Subpicosecond electrical sampling[END_REF], that D.H. Auston improved to THz range using non-linear optics [START_REF] Auston | Picosecond photoconducting hertzian dipoles[END_REF] for THz emission and detection. Finally, Grischkowsky et al. [START_REF] Van Exter | Terahertz time-domain spectroscopy of water vapor[END_REF] introduced the photoconductive antennas as in most of nowadays commercial systems. It uses a benchtop short pulsed (<~100 fs) lasers illuminating a semiconductor at a λ (energy) above the energy band-gap to generates mobile carriers. Effectively, the semiconductor changes abruptly from being an insulator into being a conductor. This leads to a sudden electric current across a biased antenna patterned on the semiconductor and an emission of broadband THz pulse. This pulse goes through the sample and is recombined with a controlled delay together with the original laser pulse onto a photoconductive or electro-optical material acting as detector. This allows access not only to the amplitude but as well to the phases of the THz pulse. This coherent technique shows a very high signal to noise ratio and record a spectrum from 0.2 to 5 THz with a dynamic range of 100 Db in about ten minutes, in commercial apparatus.

Consequently, the use of THz spectroscopy has been proposed for a variety of medical and biological applications. In this proceeding, we will report on major development axes. One of the major issues to solve to enable THz spectroscopy of actual bio-samples is that a lot of them are very small compared to the THz wavelength. Therefore, it is mandatory to enable sub-wavelength confinement of the THz electromagnetic field. We will explain our approach to concentrate the THz field to enable THz spectroscopy of small samples.

BROADBAND TERAHERTZ CONCENTRATORS

Although the sensitivity of THz-TDS systems are very high, it is not enough to enable the spectroscopy of a single cell and even more a single virion or protein. To enable the performance of THz spectroscopy on subwavelength samples one needs to concentrate the electromagnetic field in a small volume compared to the wavelength. Such confinement has been a subject of interest in the THz community. To our knowledge, all the approaches exploit the relatively good response of metals in the THz range compared to the visible and infrared. This field enhancement can be achieve using scanning µscopy or integrated photonics.

Scanning THz near-field microscopy set-ups can be classified in two different kinds. The scattering Scanning Near-field Microscopy (s-SNOM) [START_REF] Chen | Modern scattering-type scanning near-field optical microscopy for advanced material research[END_REF][START_REF] George | Terahertz field confinement in nonlinear metamaterials and near-field imaging[END_REF], uses the oscillating tip of an Atomic Force µscope (AFM) to concentrate the incident light on its nm-sized apex enabling to probe the dielectric constant of a material at a resolution similar to the apex radius (today's record ~ 15 nm [START_REF] Maissen | Probes for ultrasensitive thz nanoscopy[END_REF]). It can be used as a nano-spectroscopy system [START_REF] Moon | Subsurface nanoimaging by broadband terahertz pulse near-field microscopy[END_REF], for instance in the recent report of the characterization of lactose [START_REF] Moon | Computed terahertz near-field mapping of molecular resonances of lactose stereo-isomer impurities with sub-attomole sensitivity[END_REF]. Although, in this case, due to a relatively low signal to noise ratio, the resolution is ~2 µm using complex experiments and very long integration time. The laser scanning THz emission or detection µscope (LSTEM or LSTDM) [START_REF] Ma Seo | Near field imaging of terahertz focusing onto rectangular apertures[END_REF] is a TDS system where the sample to probe is directly in contact with a THz non-linear optics detector or emitter. The laser gating this emitter or detector scans the surface of the sample. In this configuration, the spatial resolution is defined by the size of the laser spot on the surface of the non-linear crystal and is ~ 1 µm. Since this setup is built around a TDS setup, the near-field spectroscopy is included. Using this configuration the group of A. Markelz recently demonstrated THz near-field spectroscopy of µcrystal of MM, namely lysozyme, photoactive yellow protein and RNA [START_REF] Acbas | Optical measurements of long-range protein vibrations[END_REF][START_REF] Katherine A Niessen | Protein and rna dynamical fingerprinting[END_REF]. These results are clearly the most convincing in the frame of biosamples, however, the recording of a spectrum lasts 6 hours, according to the team.

THz integrated photonics achieved light matter interaction enhancement by confining light or EM radiation by two different ways, broadband or resonantly. A broadband concentrator only uses spatial confinement while resonant devices recycle the light in time, building a stronger field enhancement but on a smaller spectral range.

Most of the broadband approaches use a metallic waveguide such as a parallel plate metallic waveguide [START_REF] Laman | High-resolution waveguide thz spectroscopy of biological molecules[END_REF] because the lowest frequency mode (transverse EM) has no cut-off, is low-losses and low-dispersion. However, this is a 1D waveguide, and besides the drawback of only confining in 1D, using it with a beam induces dispersion and coupling losses. It enabled spectroscopic measurements of thin polycrystalline film of deoxycytidine. The group of E. R. Brown overcame this by setting the sample transversally to the beam. This allowed smaller sample size with a nanofluidic integration enabling the recording of a signature between 850 and 950 GHz of both DNA & RNA molecules in µL samples [START_REF] Zhang | Observation of terahertz absorption signatures in microliter dna solutions[END_REF]. Furthermore, we recently demonstrated that the combination of tapered antenna [START_REF] Shutler | Gap independent coupling into parallel plate terahertz waveguides using cylindrical horn antennas[END_REF] and a planar geometry [START_REF] Peretti | Broadband terahertz light-matter interaction enhancement for precise spectroscopy of thin films and micro-samples[END_REF] overcames the losses dispersion and enables a 2D-confinement. The design is presented in Figure 1: The device, that we named butterfly due to its shape, is designed to fulfil three requirements: (i) An accessible hollow part to insert an sample; (ii) the waveguide should be broadband, low losses and low dispersion (iii) THz-TDS beam should be easily injected & extracted in it. The thick-slot waveguide fulfils (i) & (ii) and the tapered antenna -(iii). We improved the first technology based on laser etching of copper plate to a more rigid and technology compatible material: silicon covered by gold [START_REF] Mitryukovskiy | Device for broadband THz spectroscopy of 1-nl-volume samples[END_REF][START_REF] Mitryukovskiy | Shining the light to terahertz spectroscopy of nl-volume biological samples[END_REF]. Thanks to this new technology [START_REF] Mitryukovskiy | Towards broadband THz spectroscopy and analysis of sub-wavelength-size biological samples[END_REF], we succeed in making 20-µm-wide, 300-µm-thick and 1-cm-long waveguide going from a factor 5 [START_REF] Peretti | Broadband terahertz light-matter interaction enhancement for precise spectroscopy of thin films and micro-samples[END_REF] in field enhancement to a factor 30 [START_REF] Mitryukovskiy | Device for broadband THz spectroscopy of 1-nl-volume samples[END_REF][START_REF] Mitryukovskiy | Shining the light to terahertz spectroscopy of nl-volume biological samples[END_REF]. Consequently, we were able to perform TDS spectroscopy of small amount of powder samples. The first example on α-Lactose is shown in Figure 2. Here one can see the two well established lactose peaks (e.g. [START_REF] Peretti | THz-TDS time-trace analysis for the extraction of material and metamaterial parameters[END_REF]). We continued our study with less usual samples. Amino-acids are the brick from which the proteins are built. We performed the spectroscopy of crystal powder and dried solution of glutamine [C5H10N2O3] as shown in Figure 3.

Figure 3: Spectrum of glutamine [C5H10N2O3] samples. Left -6.8 µg of powder (volume of about 5 nL), right -250 ng of dried solution (volume of dried solution of about 200 pL). We cut the spectrum at 2.5 THz for the dried solution because of the lower signal-to-noise ratio.

On the left figure, one can see four peaks, known for Glutamine molecular crystal, for the sample volume as small as 5 nL, and on the right -only the peak around 1.7 THz is distinguishable, due to losses consequent to scattering. This last spectrum was performed on a 200-pL-volume sample corresponding to a cuboid of about 20 µm by 100 µm by 100 µm. To our knowledge, this is the smallest sample from which a THz spectrum has been extracted. Still, this volume is much larger than the one of a single molecule and one needs to implement better confinement to go towards this goal.

THZ RESONATORS

By essence, resonators have a smaller bandwidth but show better concentration. In the THz range, resonators often take the form of metamaterials or metasurfaces coming from radar field and build-up periodic arrangement of sub-λ elements. Typical examples are the dipoles or the split-ring resonator (SRR) [START_REF] Hardy | Split-ring resonator for use in magnetic resonance from 200-2000 mhz[END_REF][START_REF] Hannotte | Terahertz radiation confinement using metallic resonators[END_REF], where the strong confinement (V<λ 3 ) of the electric field of the resonant mode inside the gap leads to strong field enhancement accordingly to Purcell law [START_REF] Purcell | Spontaneous emission probabilities at radio frequencies[END_REF]. These structures are very sensitive to any change in the dielectric constant inside the gap. Thus, sensing based on resonant metamaterials has been studied. THz SRRs enable the detection of extremely small amounts of chemicals [START_REF] Chang | A multi-functional plasmonic biosensor[END_REF][START_REF] Lee | Highly sensitive and selective sugar detection by terahertz nano-antennas[END_REF] and biological substances as spore bacteria and viruses [START_REF] Berrier | Selective detection of bacterial layers with terahertz plasmonic antennas[END_REF][START_REF] Park | Detection of microorganisms using terahertz metamaterials[END_REF]. Recently, the group of M. Tonouchi proposed to combine metasurfaces with µfluidic circuitry to set the analyte in a gap sizing ~ 2mm x (10 µm) 2 , together with LSTEM to select only a few meta-atoms [START_REF] Serita | Invited article: Terahertz microfluidic chips sensitivity-enhanced with a few arrays of meta-atoms[END_REF].

SRRs are metallic structures with inductive and capacitive area, thus exhibiting a LC resonance at a wavelength larger than the structure itself. The simplest example is a single metallic loop with a small gap, where the loop itself is the inductive part, and the gap is the capacitive part (see Figure 4). When excited at its resonant frequency, the magnetic field in a SRR is located in the inductive area, while the electric field is confined into the capacitive area. This makes the SRR an excellent tool to confine THz radiation in space (in the gap) and extends the light-matter-interaction time through the resonance.

For our application, we choose the design illustrated in Figure 4. This design has only one capacitive area, allowing for the sake of a better electric field confinement, and two inductive loops. At resonance, the current flows in the two inductive loops in opposite directions, so that the magnetic radiation cancels out in the far-field. This reduces the radiative losses of the device and therefore increases its quality factor. However, we do not want to completely cancel the radiation losses, seeing as they define how the resonator couples with the far-field excitation and measurement. Since we want to test the limit of the field confinement with those resonators, the width of the gap, which defines the final confinement volume, should be an adjustable variable of the design. We therefore use a tapered design that allows to decrease or increase the confinement volume while keeping a constant capacity and thus keeping a constant resonance frequency (see Figure 5). Right: the design we have chosen for our study, the magnetic field inside each loop is oriented in opposite direction.

Figure 5: Left: based on the parallel-plate capacitor model, the capacitance is kept constant by keeping the same ratio A/G. Right: variation of the SRR shape with the two independent parameters (size and gap width).

0. The resonators are made of gold on a 150-µm-thick quartz substrate, which has the advantage of being transparent in both the visible and the THz range. They are fabricated using electron beam lithography according to the following steps (illustrated in Figure 6):Cleaning of a bare quartz substrate using piranha solution to ensure a good hydroxylation of the surface and thus a good adhesion of the resist 1. Coating with a double positive resist layer (PMMA) 2. Deposition of 10 nm Ge layer by electron-beam evaporation to make the sample electrically conductive 3. Electron beam writing of the SRR shape 4. Ge removal using hydrogen peroxide and resist development 5. Deposition of 20 nm of titanium for the adhesion, 200 nm gold 6. Attack on the remaining resist to remove the unwanted and keep only the SRRs (Lift-off) Using a double resist layer leads to an undercut profile after the development (see Figure 7), resulting in a clean lift-off. As can be seen in the SEM images of the final result in Figure 8, we were able to obtain an excellent agreement with the desired shape and to reach large aspect ratio and very small gap size, down to 30 nm for a total metal thickness of 220 nm. The fabricated resonators are characterized with THz-TDS setup, by measuring the transmission of a broadband THz beam through an array of identical resonators. To get a good indication on the resonance frequency of a single resonator, the period of the array must be large enough so that the evanescent near-field of each resonator does not interact with its neighbors. A 50-µm period is large enough according to our simulation, and the array is dense enough to be easily detected with our TDS setup. Although the precise spectral response of a single resonator is not strictly identical to the one measured in an array due to far-field coupling between resonators [START_REF] Hale | Noninvasive near-field spectroscopy of single subwavelength complementary resonators[END_REF], it still allows us to measure the resonance frequency depending on the two parameters of our resonators (the size and the gap width). Using the frequency response of the quartz alone as a reference, we observe a clear resonance with a quality factor Q ~ 15, which is quite high considering the deliberately high radiation losses of our device. One can see from Figure 9 right that the tapered shape is very effective in keeping a constant resonance frequency for variable gap width. The spectral characteristics of an array of resonator is in perfect agreement with our expectations. In order to evaluate our resonator as a way to probe single macromolecule, the next step will be to characterize experimentally the spectral characteristics of a single resonator, and the electric field distribution with SNOM measurement.

CONCLUSION

In this proceeding, we briefly presented the methods we are developing to tackle the issue of small-size samples in Terahertz spectroscopy. First, we showed the use of the butterfly device, made of two tapered-antennas to interface a thickslot metal waveguide toward free space, to enable spectroscopic measurement of sub-nanoliter-volume samples. Then, we explained our strategy and technology to go even further in enabling measurements of samples inside the gap such as of a single split ring resonator.

Still, even when the described technology is mature it will not be enough to be directly useful for biology or biochemistry. First, it will be important to analyze properly the time-trace from the TDS similarly to what was done for free-space experiments such as the metasurface ones [START_REF] Peretti | Modeling and parameter retrieving in time domain spectroscopy of material and metamaterial[END_REF] for the butterfly. Second, life intrinsically needs water and we need to enable THz spectroscopy in aqueous environment [START_REF] Lavancier | Retrieving permittivity model parameters for polar liquids and multilayer systems through THz-TDS time-trace data analysis[END_REF] in our device to fulfill this requirement.

Figure 1 :

 1 Figure 1: Schematic of the 'butterfly' device showing the waveguide where the sample is to be inserted. The exponentially tapered antenna to couple with the incoming and outgoing THz field and the farfield of the antenna to show the potential of this coupling.

Figure 2 :

 2 Figure 2: Left -spectrum of a powder of α-Lactose monohydrate. The sample volume is ~ 15 nL corresponding to a mass of ~ 23 µg. Right -schematic view of the lactose molecule.

Figure 4 :

 4 Figure 4: Left: simplest example of SRR with its equivalent circuit, the resonance frequency is given by 𝜔 0 = 1/√𝐿𝐶.Right: the design we have chosen for our study, the magnetic field inside each loop is oriented in opposite direction.

Figure 6 :

 6 Figure 6: Step by step illustration of the fabrication process.

Figure 7 :

 7 Figure 7: SEM picture of the resist after development (step 4).

Figure 8 :

 8 Figure 8: SEM image of a SRR (left) and close up view on a 27 nm gap (right).

Figure 9 :

 9 Figure 9: Relative transmission of different arrays of SRR divided by the transmission of a bare quartz substrate, for different resonator sizes (left), and for different gap widths (right).

0,5 1,0 1,5 2,0 2,5 3,0 0,4 0,6 0,8 1,0 1,2 Transmission spectrum for several gap widths Normalized transmission Frequency (THz) 200nm 500nm 1000nm 1500nm 2000nm