Andres Castillo-Castellanos

Anne Sergent

Maurice Rossi

Rayleigh- Bénard Convection

CONFINED REGIMES IN RAYLEIGH-BÉNARD CONVECTION USING REDUCED DIMENSIONALITY MODELS

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

We consider Rayleigh-Bénard convection inside slim rectangular cells of transversal aspect ratio Γ. Previous works [1,2] show a change of regime as the depth becomes comparable to the size of thermal plumes, going from an unconfined regime, to a plume-controlled regime and to a confined regime (III). For the latter, we developed a reduced model, which improves the Hele-Shaw approximation by taking into account inertial corrections along the lines of [3]. This model is shown to be in good agreement with 3D DNS results, for instance we compared global quantities such as the Reynolds and Nusselt numbers, as well as the various boundary layer thicknesses. We take advantage of the lower computational cost of the model to perform a parametric study for different (Ra, Pr) in the range 1/256 < Γ < 1/32. In the parameter space Ra -Γ, we identify inside the confined regime reported by [1,2] a transition to a new regime denoted by IV (see figure 1) with larger scaling exponents for the Nusselt and Reynolds numbers. This transition is related to changes in flow structures as well as in the relative thicknesses of thermal and viscous boundary layers.

Figure 1 :

 1 Figure 1: Reduced model for Pr = 4.38. Fig. (a,b) Snapshot of the field for Γ = 1/256. (a) inside the confined regime (III) for Ra/Ra * = 3 • 10 -2 , where Ra/Ra * is a confinement parameter defined in [2]. (b) inside the new regime (IV) for Ra/Ra * = 2 • 10 -4 . (c) compensated Reynolds number as a function of Ra/Ra * .


domain: sde spi

text:
Ugur Soysal
email: ugur.soysal@u-pec.fr

Evelyne Géhin

Frédéric Marty

Emmanuelle Algré

Charles Motzkus

DEPOSITION CHARACTERISTICS OF BIOAEROSOLS BY INERTIAL IMPACTION

Keywords: Bioaerosols, deposition characteristics, Real-time detection, Microbalance, Microelectromechanical systems (MEMS)

Deposition characteristics of bioaerosols by inertial impaction

INTRODUCTION

Over the last decades, exposure to airborne biological particles such as pollen, viruses, bacteria, and fungal spores has been one of the main concerns due to their adverse health effects on human being. Nowadays, clear evidence for bioaerosols exposure-related health issues have been widely recognized and the exposures have been associated with contagious infectious diseases, acute toxic effects, allergies, and cancer [START_REF] Douwes | Bioaerosol health effects and exposure assessment: progress and prospects[END_REF] [START_REF] Fiegel | Airborne infectious disease and the suppression of pulmonary bioaerosols[END_REF] [START_REF] Bush | The role and abatement of fungal allergens in allergic diseases[END_REF] [START_REF] Lindsley | Measurements of airborne influenza virus in aerosol particles from human coughs[END_REF]. However, lack of quantitative bioaerosol exposure assessment methods leads difficulties to define exposure limits. For accurate quantitative characterization of the particles, bioaerosol sampling methods should be accompanied by a real-time detection method that would enable rapid mass concentration measurements.

Collection of the reliable and representative amount of bioaerosols has been realized by traditional aerosol sampling methods, including gravitational sedimentation, inertial impaction, centrifugation, electrostatic precipitation, and filtration. The latter, detection techniques such as polymerase chain reaction (PCR) [START_REF] Pyankov | Using a bioaerosol personal sampler in combination with real-time PCR analysis for rapid detection of airborne viruses[END_REF], enzyme-linked immunosorbent assay (ELISA) [START_REF] Speight | Enzyme-linked immunosorbent assay for the detection of airborne microorganisms used in biotechnology[END_REF], traditional colony counting [START_REF] Han | Bacterial population and chemicals in bioaerosols from indoor environment: Sludge dewatering houses in nine municipal wastewater treatment plants[END_REF], optics or spectroscopy (e.g. Fluorescence, Raman) [START_REF] Jonsson | Bioaerosol Detection Technologies[END_REF] have been used for qualitative and quantitative analysis of the collected bioaerosols. Most of the efforts have been recently given to real-time fluorescence-based optical systems either using microfluidic approaches [START_REF] Choi | Integrated micro-optofluidic platform for real-time detection of airborne microorganisms[END_REF] or integrating it with a sampling method [START_REF] Choi | A new method for the real-time quantification of airborne biological particles using a coupled inertial aerosol system with in situ fluorescence imaging[END_REF]. Although some of the proposed systems achieved real-time detection, none of them have demonstrated a miniature, integrable, low-cost, and real-time mass concentration measurement system. As discussed earlier, the integration of silicon-based high-performance inertial MEMS mass sensors to a micro sampling method can pave the way for the reliable real-time mass concentration measurements of airborne particles [START_REF] Soysal | Aerosol mass concentration measurements: Recent advancements of real-time nano/micro systems[END_REF]. But, small active surface area (1 mm 2 ) of MEMS should be applicable to the size and shape of the deposition patterns. There have been only a few studies discussing the underlying mechanism for the deposit shapes, but it hasn't been achieved a consensus. Usually, the halo-shaped, ring-shaped or only primary deposits (underneath the nozzle) have been observed in the impaction studies. This study presents a lab-made multiple nozzle bio-impactor based on classical impactor design criteria and investigates the deposition characteristics by impaction on smooth silicon and nanostructured silicon surfaces.

ELABORATION OF A LAB-MADE BIO-IMPACTOR

A single stage multiple nozzle inertial bio-impactor has been designed and elaborated. The bioimpactor consists of a probe connection where the impactor have attached to the homogenization sphere to extract particles from the controlled ambient, nozzle plate where 10 round nozzles each of 500 µm diameter located circularly, micro impaction chamber where is partially vacuumed during the operation and exhibit a 500 µm separation between the nozzles and silicon/black silicon samples which are located on the impaction plate. This lab-made single-stage impactor exhibits the calculated cut-off diameter of 0.39 µm and experimental cut-off diameter of ~ 0.8 µm while Reynolds (Re) number has been kept below 3000 that maintains a laminar flow. The operating flow rate is 10 LPM, therefore each nozzle delivers 1 LPM to each sample. Thereby, 10 nozzles are meant to be aligned with 10 individual silicon/nanostructured silicon samples. On the other hand, the major issue in inertial impactors is the bouncing particles off the impaction plate. To overcome this issue, silicon surface has been nanostructured thanks to microfabrication methods which are adaptable to development of MEMS mass sensors unlike the common practices such as using of sticky materials like oil/grease.

Following that, various sizes of monodispersed (σ g < 1.2) particles are generated between 0.9 µm to 4 µm mean median aerodynamic diameter (MMAD) of fluorescence test particles by using vibrating orifice aerosol generator (VOAG), Aspergillus niger spores with MMAD of (3.04 ± 0.05)μm by dry generation, Staphylococcus epidermidis, and Pseudomonas fluorescens with MMAD of (0.70 ± 0.02)µm, and (0.66 ± 0.01)μm, respectively by Collison nebulizer method. These particles have been impacted on silicon (smooth surface) and nanostructured silicon (black silicon) as impaction plates of the bio-impactor.

RESULTS AND CONCLUSION

Although the properties of the biological and non-biological test particles used in this study are different, their deposition characteristics show similarities and the deposition patterns correlated with the size of each type of particles. The results show that the halo-shaped, ring-shaped or only primary deposits (underneath the nozzle) have been observed. A halo type pattern consists of a primary deposit in the center that is surrounded by a secondary deposit. A ring-shaped pattern forms a particle-free area underneath the nozzles, thus the deposit encloses this area.

This study shows that the collection efficiency of the primary impaction zone is the particle of sizedependent due to the bounce effect. In the case of smooth silicon impaction surface, the local collection efficiency at the primary impaction zone was estimated as low as three times as that of the global efficiency for the sub-µm particles. This local collection efficiency at the primary impaction zone has been found to be less than 1% for the impaction of particles of MMAD>1µm size.

In the present study, the black silicon surface has been used as an impaction plate to overcome the bounce effect by its surface properties. It has not significantly changed the deposition characteristics of subµm particles. However, preliminary experiments have shown that the black silicon enables to reduce the bounce effect of particles of MMAD>1µm size and provide a confined circular deposition spot by breaking these particles into fragments. This study suggests that nanostructured inertial MEMS mass sensors can be favorable for the detection of micron size particles.


Juliette Calvez

Victoire Neirynck

Anne-Geneviève Marcelin

AUTHOR. Dr Aude Jary
email: aude.jary@aphp.fr

Extending vaccination periods against Human Papillomavirus: lessons from the SARS-COV-2 pandemic

Keywords: Human papillomavirus, HPV vaccine, COVID-19 pandemic, France, vaccination catch-up

Unprecedent shutdowns during COVID-19 pandemic led to considerable disruptions of routine immunization programs, including HPV vaccination program. For instance, in France, at least 200,000 young women lost the possibility to be vaccinated against HPV during this period. Major efforts should be done to facilitate and promote access to HPV vaccination, with the possibility of catch-up vaccination up to a later age.

IMPACT OF COVID-19 PANDEMIC ON HPV VACCINATION WORLWIDE

Human papillomavirus (HPV) vaccines have been used in the prevention of cervical cancer for female patients since 2006. More recently, however, the usage of these vaccines has been extended to the prevention of gender-neutral malignancies -including anal, oral, and head and neck cancers -for both male and female patients. In November 2020, the Cervical Cancer Elimination Initiative was launched by the World Health Organization (WHO) with an ambitious goal to eliminate cervical cancer as a public health problem [START_REF]Global strategy to eliminate cervical cancer as a public health problem: are we on track? eClinicalMedicine[END_REF] and to achieve a reduction of the cancer cervical incidence to fewer than 4/100 000 women-years worldwide by 2030 [START_REF]Global strategy to eliminate cervical cancer as a public health problem: are we on track? eClinicalMedicine[END_REF]. To accomplish this goal, the initiative is focusing on getting 90% of girls fully vaccinated against HPV by age 15. In 2019, only 15% of women and 4% of men have been fully vaccinated worldwide [START_REF] Bruni | HPV vaccination introduction worldwide and WHO and UNICEF estimates of national HPV immunization coverage 2010-2019[END_REF].

The COVID-19 Pandemic caused unprecedented shut downs of global activity that extended equally into the health care space. Government instituted measures to manage the spread of the COVID-19 virus had collateral effects on standard medical activity. These effects came from two main sources: physical and mental exhaustion of the healthcare workforce including a degradation of hospital infrastructure; and, a growing backlog of healthcare procedures. For instance, the inability or fear of high-risk patients to consult a doctor was disrupting chronic disease management and delaying some critical cancer care procedures [START_REF] Arsenault | COVID-19 and resilience of healthcare systems in ten countries[END_REF]. Furthermore, significant decreases in the administration of regular immunizations have been seen internationally during and after the SARS-CoV-2 virus pandemic. The WHO has stated that routine immunization programs have been substantially disrupted in at least 68 countries, affecting more than 80 million children worldwide, especially in poor countries [START_REF]COVID-19 disrupts routine vaccination efforts, warn Gavi[END_REF]. In addition, due to school closings, apathy in seeking medical attention, and the redirection of time, resources, and money to COVID-19 measures within healthcare infrastructures, this disruption has strongly harmed teenage immunizations. In light of these developments, the WHO released recommendations urging governments to routinely assess the need for largescale catch-up vaccination programs and urging countries to prioritize immunization [START_REF]Guiding principles for immunization activities during the COVID-19 pandemic: interim guidance[END_REF].

During the COVID-19 pandemic, HPV vaccination programs had considerable disruptions, like other regular vaccines, which led to a significant proportion of teenagers missing a chance to get vaccinated [START_REF] Daniels | Impact of reduced human papillomavirus vaccination coverage rates due to COVID-19 in the United States: A model based analysis[END_REF]. In April 2020, there was a 75% drop in HPV vaccination coverage compared to previous years, according to a modeling study looking at the effects of the first wave of COVID-19 measures in the USA [START_REF] Daniels | Impact of reduced human papillomavirus vaccination coverage rates due to COVID-19 in the United States: A model based analysis[END_REF]. Based on its finding, the study warned there would be a significant rise in HPV-related diseases if there were not significant public health interventions made. According to the model, 48,682 to 110,192 additional cases of CIN2/3; and 2,882 to 6,487 additional cases of cervical cancer would occur over the next 100 years [START_REF] Daniels | Impact of reduced human papillomavirus vaccination coverage rates due to COVID-19 in the United States: A model based analysis[END_REF]. In Europe, a similar pattern was reported in Switzerland and Greece for the year 2020 with 14.8% and 4.8% reductions of HPV vaccine administration in each country, respectively, compared to 2019 [START_REF] Gountas | Impact of the COVID-19 Pandemic on HPV Vaccinations in Switzerland and Greece: Road to Recovery[END_REF]. In Switzerland, the effect has been reversed in 2021 as the dose deficit decreased by 46.6% compared to 2020 while in Greece, the dose deficit in 2021 increased by 156.2% compared to 2020.

IMPACT OF COVID-19 PANDEMIC ON HPV VACCINATION IN FRANCE

In France, consultations with general practitioners fell 40% and consultations with specialists fell by 50% during the pandemic compared to pre-pandemic levels, even when accounting for the surge of tele-consultations [START_REF] Echos | Hors coronavirus, le renoncement aux soins prend des proportions très inquiétantes[END_REF]. Concurrently, cancer centers had to postpone monitoring consultations and medical operations considered to be non-urgent. In addition to these short-term effects, containment (and progressive de-confinement) measures, compounded by the economic recession, will undoubtedly affect mental health (e.g., anxiety, depression) and physical health (e.g., weight gain, unbalanced nutrition).

As a result of these events, there was a shortfall of 377,000 undelivered doses of HPV vaccine in France between mid-March 2020 and mid-April 2021 [START_REF]Covid-19 : usage des médicaments de ville en France[END_REF]. This shortfall was not made up during the remainder of 2021; on the contrary, it worsened to 407,072 undelivered doses when considering mid-March 2020 to the end of 2021 [START_REF]Rapport charges et produits -Propositions de l'Assurance Maladie pour[END_REF]. There was no evidence that this backlog was being cleared even by early 2022.Two approaches can be used to estimate the number of unvaccinated girls. One approach, the EPI-PHARE study, compares against the natural vaccination trend observed in recent years 2018 and 2019 to estimate the number of unvaccinated girls in France using assumptions for 2020 (Figure 1). During the lockdown (weeks 12 to 19), the study showed an unprecedented fall of HPV-vaccine prescription compared to the expected trend [START_REF]Covid-19 : usage des médicaments de ville en France[END_REF]. As the recommended vaccination schedules up to the age of 15 years includes two injections, it can be stated that at least 200,000 young women have lost the chance to be fully vaccinated against HPV solely because of COVID-19 and in a more pessimistic hypothesis this number could rise to 500,000. These COVID-19 effects add to an already alarming situation of none-vaccination driven by mis/none-information about HPV infection, HPV-related diseases and HPV vaccination leading to concerns about side effects or the efficacy of the HPV vaccine [START_REF]contre les infections à papillomavirus humain des filles âgées de 15 à 18 ans et déterminants de vaccination[END_REF]. Thus, the historically very low vaccine coverage in France after 2010 decade (i.e. only 13.2% with a complete regimen at age 16 for young women born in 1999 [START_REF]contre les infections à papillomavirus humain des filles âgées de 15 à 18 ans et déterminants de vaccination[END_REF]) translates into a very large number, up to 2 million, of young women aged 20 to 26 who are not protected against several HPV-induced cancers. This is particularly concerning because France already demonstrates a prevalence of HPV infection nearly twice as high compared to other countries included in the Ferris et al 2020 study (29.2% vs 16.4%) [START_REF] Dg | Prevalence, incidence, and natural history of HPV infection in adult women ages 24 to 45 participating in a vaccine trial[END_REF]. In France, the circulation of the virus is also reflected in the highest incidence of precancerous cervical lesions in the population of women aged 25-44 years in France [START_REF] Hamers | Population-based organized cervical cancer screening pilot program in France[END_REF]. Additionally, France's vaccination coverage is compounded by glaring social inequalities; vaccination coverage is 4 times higher among financially well-off people compared to economically disadvantaged populations [START_REF]contre les infections à papillomavirus humain des filles âgées de 15 à 18 ans et déterminants de vaccination[END_REF].

HOW TO IMPROVE HPV-VACCINE COVERAGE IN FRANCE?

Current studies show that starting HPV vaccination at a younger age is associated with greater effectiveness in preventing genital warts, high-grade precancerous cervical lesions and cervical cancer [START_REF] Lei | HPV Vaccination and the Risk of Invasive Cervical Cancer[END_REF] and current recommendations in several countries recommended catch-up vaccination through age 26. Additionally, the WHO also recommends two doses with a 6month interval for women older than 21 years to improve access to the vaccine and coverage among women [START_REF]WHO updates recommendations on HPV vaccination schedule[END_REF]. Among Swedish girls and women aged 10 to 30 years old, quadrivalent vaccination was associated with a 63% global reduction of cervical cancer incidence, with an 88% reduction in women vaccinated before 17 years old. In women vaccinated after 17 years old, a decrease of 53% of the incidence was still observed showing a benefit to catch-up vaccination in older women [START_REF] Lei | HPV Vaccination and the Risk of Invasive Cervical Cancer[END_REF]. Thus, even though effectiveness of HPV vaccination for prevention of HPV-lesions decreases with the age of the first vaccination, there is evidence that a catch up in older population is of benefit. The latest HPV-vaccination schedule from the WHO also recommends a one or two-dose schedule for young girls and women aged from 9 to 20 years as another option to improve coverage worldwide [START_REF]WHO updates recommendations on HPV vaccination schedule[END_REF]. The WHO estimates that a single dose strategy could prevent 60 million cervical cancer cases and 45 million deaths worldwide over the next 100 years [START_REF]WHO updates recommendations on HPV vaccination schedule[END_REF].

Based on the findings around preventative and catch-up vaccinations, governments and healthcare professionals such as gynecologists and obstetricians, as well as general practitioners, must make major efforts to facilitate and promote access to HPV vaccination, with the possibility of catch-up vaccination up to a later age. This is the only solution if we are to make up for the missed vaccination resulting from the global COVID-19 crisis. If efforts of this kind are not made, we will undoubtedly see a resurgence of HPV-related cancers and other pathologies in the coming years. It's up to healthcare professionals and governments not to give in to fate. More specifically in France, a catch-up until 26 years old should be discussed as advised in a press release by several French academic, medical and professional institution involved in HPV-related cancers in 5 June 2023 [START_REF]Eradiquer les cancers dus aux papillomavirus (HPV), une bataille française qui reste à mener Appel des scientifiques et des patients pour une campagne d'envergure[END_REF].

Figure 1 :

 1 Figure 1: Number of HPV-vaccine prescriptions dispensed per 2 weeks in the first 47 weeks

Authors contributions. Conception and design of the study: JC, VN, AGM and AJ; drafting of significant portion of the manuscript or figures: JC, VN, AGM and AJ. All the authors red, corrected and approved the final version of the manuscript.

Transparency declarations. The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Ethics. Not applicable


Pérez Géraldine
email: geraldine.perez@ntymail.com

Dupaix Amael

Dagorn Laurent

Deneubourg Jean-Louis

Holland Kim

Beeharry Sunil

Capello Manuela

Géraldine Pérez

Correlated Random Walk of tuna in arrays of Fish Aggregating Devices: A field-based model from passive acoustic tagging

Keywords: Correlated Random Walk, Tropical tuna, Spatial model, Fish Aggregating Device, Acoustic tagging, Survival curve, Tuna motion, Residency

For centuries fishers have exploited the propensity for tuna to associate with floating objects, yet the reasons and mechanisms behind this behavior remain unclear. The number of man-made floating objects (FADs, Fish Aggregating Devices) undergone a dramatic increase in recent decades, with the development of industrial tuna purse seine fishing. However, current knowledge does not allow for the evaluation of the consequences of this increase on the ecology of tuna. Here, we developed a model of tuna movements in an array of FADs, using passive acoustic tagging data. The model was built using four behavioral rules: (1) when no FAD is perceived, tuna exhibit a random search behavior, (2) individuals can orient directly to a FAD when they perceive it (within a given orientation radius), (3) the associative dynamics of tuna follow a daily rhythm and (4) Continuous Residence Time (CRTstime spend at FAD by tuna) are independent from previous Continuous Absent Time (CATs-time between two consecutive CRTs). The model is based on only four parameters: swimming speed, path sinuosity, orientation distance and a loss term to account for natural and fishing mortality events. The model was calibrated on 70±10 cm yellowfin tuna (Thunnus albacares), acoustically tagged in two different networks of anchored FADs (Oahu, Hawaii, U.S.A. and Mauritius) with different FAD densities. Our results show that the model can reproduce the time tuna spent traveling between FADs (i.e., time away from the FADs), as well as the total time spent by the fish in the FAD array (total residence time) at both study sites. The parameter sets that best reproduce the experimental data correspond to a steering radius between 2 and 5 km, a sinuosity (correlated random walk parameter) between 0.9 and 0.995 and mortality rates between 1 and 3% per day. This model, thus parameterized, could be used in future studies to predict tuna movements in arrays of different FAD densities and thus provide scientific advice for their management. The same approach can be used for modeling the movements of marine and terrestrial animals detected near aggregation sites.

Introduction

With more than 5.3 million tonnes caught in 2019 (ISSF, 2021) tropical tuna constitutes one of the major harvested fish species. Currently, yellowfin tuna (Thunnus albacares), bigeye tuna (T. obesus) and skipjack (Katsuwonus pelamis) represent almost 95% of the global tuna catches (ISSF, 2021) .

Tropical tunas display an associative behavior with floating objects, forming large multi-specific aggregations around them. The reasons why tuna associate with floating objects are still unknown.

Two main hypotheses are widely accepted: [START_REF] Moreno | Fish behaviour from fishers' knowledge: the case study of tropical tuna around drifting fish aggregating devices (DFADs)[END_REF] the meeting-point hypothesis [START_REF] Dagorn | Tropical tuna associated with floating objects: a simulation study of the meeting point hypothesis[END_REF][START_REF] Fréon | Review of fish associative behaviour: Toward a generalisation of the meeting point hypothesis[END_REF] and (2) the indicator-log hypothesis [START_REF] Hall | The association of tunas with floating objects and dolphins in the Eastern Pacific ocean: VII. Some hypotheses on the mechanisms governing the association of tunas with floating objects and dolphins[END_REF]. The meeting-point hypothesis posits that floating objects act as meeting-points, where tuna gather to form bigger schools.

The indicator-log hypothesis posits that natural floating objects, such as logs, are more numerous in productive areas , as they concentrate in river months, estuaries and frontal structures. Following this hypothesis, tuna could use floating objects as indicators of productive areas.

Fishers have used this associative behavior to their advantage for centuries [START_REF] Dempster | Fish aggregation device (FAD) research: Gaps in current knowledge and future directions for ecological studies[END_REF]) and, more recently, have deployed human-made floating objects, called Fish Aggregating Device (FAD), to increase their catches. In the open ocean, drifting FADs are primarily used by industrial purse seine fleets, while, in coastal areas, anchored FADs are used by artisanal and semiindustrial fisheries (Dagorn et al. 2013b;[START_REF] Dempster | Fish aggregation device (FAD) research: Gaps in current knowledge and future directions for ecological studies[END_REF][START_REF] Scott | The use of FADs in tuna fisheries[END_REF] . About 37% of the tropical tuna catches (all fishing gears) are made by purse seiners on drifting FADs, ranging between 32% to 51% depending of the ocean (Dagorn et al. 2013b;[START_REF] Murua | The potential connectivity of waterhole networks and theeffectiveness of a protected area under various drought scenarios[END_REF] . The number of FADs has drastically increased in the three past decades, with more than 100,000 FADs deployed globally, each year [START_REF] Scott | The use of FADs in tuna fisheries[END_REF] , although precise numbers are difficult to obtain. This increase raised concerns over possible impacts on tuna populations, because FADs increase the vulnerability of tunas to capture but also because increasing the number of floating objects (Dagorn et al. 2013b) could affect their ecology. [START_REF] Marsac | Drifting FADs used in tuna fisheries: an ecological trap?[END_REF] , were the first to suggest that FADs could act as an ecological trap for tunas. Following the indicator-log hypothesis, FADs could mislead tuna if they are deployed or drift into biologically poor areas and if tuna do not differentiate between natural and man-made objects. Therefore, tuna could remain associated with FADs even if their surrounding environment is detrimental to their fitness [START_REF] Marsac | Drifting FADs used in tuna fisheries: an ecological trap?[END_REF]. However, current knowledge does not allow for the assessment of the effects of increasing FAD densities on tuna ecology, even when the environment (other than floating objects) remains constant.

Acoustic telemetry has been widely used to monitor tuna movements and behavior within FAD arrays.

With this technology, acoustically tagged fish (i.e., fish equipped by an acoustic tag ) can be either actively tracked or detected by a set of fixed acoustic receivers. In the former case, known as active tracking, the recorded path of the receiver, which is considered as a proxy of the animal path, generally corresponds to short periods of time (few days at most) [START_REF] Girard | FAD: Fish Aggregating Device or Fish Attracting Device? A new analysis of yellowfin tuna movements around floating objects[END_REF][START_REF] Girard | Homing abilities of dolphinfish (Coryphaena hippurus) displaced from fish aggregating devices (FADs) determined using ultrasonic telemetry[END_REF]). In the latter case, known as passive acoustic telemetry, a time series of acoustic detections is recorded within the array of receivers [START_REF] Dagorn | Behavior of yellowfin (Thunnus albacares) and bigeye (T. obesus) tuna in a network of fish aggregating devices (FADs)[END_REF][START_REF] Tolotti | Association dynamics of tuna and purse seine bycatch species with drifting fish aggregating devices (FADs) in the tropical eastern Atlantic Ocean[END_REF]. The acoustic receivers are generally placed in proximity of aggregation/attraction sites (FADs in this case), where it is more likely to detect the tagged individuals. Passive acoustic telemetry has the advantage to cover longer period of time (up to several months or even more than a year, depending on the tag battery life and the fish residency within the array). However, the time series of acoustic detections recorded at aggregation sites cannot be easily translated into movement rules.

Previous passive acoustic telemetry studies conducted in anchored FAD arrays quantified the amount of time that tuna spend associated with these floating objects (residence times), as well as the time they spend traveling between two objects (absence times) [START_REF] Dagorn | Behavior of yellowfin (Thunnus albacares) and bigeye (T. obesus) tuna in a network of fish aggregating devices (FADs)[END_REF][START_REF] Govinden | Movement behaviour of skipjack (Katsuwonus pelamis) and yellowfin (Thunnus albacares) tuna at anchored fish aggregating devices (FADs) in the Maldives, investigated by acoustic telemetry[END_REF][START_REF] Robert | Intraindividual behavioral variability displayed by tuna at fish aggregating devices (FADs)[END_REF][START_REF] Rodriguez-Tress | Associative behavior of yellowfin Thunnus albacares, skipjack Katsuwonus pelamis, and bigeye tuna T. obesus at anchored fish aggregating devices (FADs) off the coast of Mauritius[END_REF] . These studies highlighted the variability of such durations according to both the size of the tagged individuals [START_REF] Robert | Intraindividual behavioral variability displayed by tuna at fish aggregating devices (FADs)[END_REF] as well as the species [START_REF] Rodriguez-Tress | Associative behavior of yellowfin Thunnus albacares, skipjack Katsuwonus pelamis, and bigeye tuna T. obesus at anchored fish aggregating devices (FADs) off the coast of Mauritius[END_REF] . Recently, [START_REF] Pérez | Effects of habitat modifications on the movement behavior of animals : the case study of Fish Aggregating Devices ( FADs ) and tropical tunas[END_REF] compared the residence and absence times recorded for individual tuna tagged within different FAD arrays, demonstrating that tuna spend less time traveling between FADs and more time in association as FAD density increases.

Passive and active acoustic telemetry studies have also shown a diel rhythm in the associative behavior of tunas, with close association occurring mostly during the daytime while regular excursions away from the FAD are undertaken at night [START_REF] Holland | Horizontal and vertical movements of yellowfin and bigeye tuna associated with fish aggregating devices[END_REF][START_REF] Marsac | Telemetry 'applied to behaviour analysis of yellowfin tuna (Thunnus albacares, Bonnaterre, 1788) movements in a network of fish aggregating devices[END_REF][START_REF] Dagorn | Modeling tuna behaviour near floating objects: From individuals to aggregations[END_REF][START_REF] Forget | Behaviour and vulnerability of target and non-target species at drifting fish aggregating devices (FADs) in the tropical tuna purse seine fishery determined by acoustic telemetry[END_REF][START_REF] Tolotti | Association dynamics of tuna and purse seine bycatch species with drifting fish aggregating devices (FADs) in the tropical eastern Atlantic Ocean[END_REF] . Furthermore, active tracking studies allowed the fine-scale movements of tagged individuals in arrays of FADs to be investigated. Using acoustic telemetry data from actively tracked yellowfin tuna in anchored FAD arrays in the Pacific and Indian oceans, [START_REF] Girard | FAD: Fish Aggregating Device or Fish Attracting Device? A new analysis of yellowfin tuna movements around floating objects[END_REF] found that tuna adopt a random search behavior until they perceive a FAD, then orient towards the device at distances ranging between 4 to 17 km.

Recently, [START_REF] Pérez | Effects of habitat modifications on the movement behavior of animals : the case study of Fish Aggregating Devices ( FADs ) and tropical tunas[END_REF] , used a simple random walk model to assess whether the observed trends in behavioural indices, obtained from passive acoustic tagging data across increasing FAD densities, could result from the random-search component in tuna behaviour suggested in previous experiments [START_REF] Girard | FAD: Fish Aggregating Device or Fish Attracting Device? A new analysis of yellowfin tuna movements around floating objects[END_REF] . While this simple model was able to explain the observed trends of shorter absence times for increasing FAD densities, it could not quantitatively predict their durations, since it did not account for the oriented movements [START_REF] Girard | FAD: Fish Aggregating Device or Fish Attracting Device? A new analysis of yellowfin tuna movements around floating objects[END_REF] or for the diel pattern in tuna behavior [START_REF] Marsac | Telemetry 'applied to behaviour analysis of yellowfin tuna (Thunnus albacares, Bonnaterre, 1788) movements in a network of fish aggregating devices[END_REF][START_REF] Forget | Behaviour and vulnerability of target and non-target species at drifting fish aggregating devices (FADs) in the tropical tuna purse seine fishery determined by acoustic telemetry[END_REF] . Correlated Random Walk (CRW) models are frequently used to reconstruct animal paths from active tracking data (e.g. [START_REF] Girard | FAD: Fish Aggregating Device or Fish Attracting Device? A new analysis of yellowfin tuna movements around floating objects[END_REF][START_REF] Patterson | Classifying movement behaviour in relation to environmental conditions using hidden Markov models[END_REF][START_REF] Mcclintock | A general discrete-time modeling framework for animal movement using multistate random walks[END_REF][START_REF] Cramer | Distinguishing residency behavior from random movements using passive acoustic telemetry[END_REF] , as well as to simulate their movements [START_REF] Byers | Correlated random walk equations of animal dispersal resolved by simulation[END_REF]Carita et al. 2012;[START_REF] Ahearn | A context-sensitive correlated random walk: a new simulation model for movement[END_REF][START_REF] Cramer | Distinguishing residency behavior from random movements using passive acoustic telemetry[END_REF]) . These models are used because, unlike a simple random walk, they account for the tendency of animals to go forward. A CRW model is thus a better choice than a simple random walk for animals with bilateral symmetry such as tuna. On the other hand, despite the large availability of passive acoustic telemetry data for tuna and their large temporal coverage, this data has not been used so far to construct this type of models, due to the discrete nature of the data (acoustic detections) recorded both in time and space.

The aim of this study was to develop a data-based model of tuna movements in an array of FADs, which can reproduce the motion of tuna from one FAD association to another detected through passive acoustic telemetry. Such model constitutes the first step to predict the effects of increasing FAD numbers on tuna behavior and ecology. The model was calibrated using passive acoustic telemetry data collected at two study sites (Mauritius, see Rodriguez-Tress et al. 2017, and Oahu, Hawaii, U.S.A., see [START_REF] Dagorn | Behavior of yellowfin (Thunnus albacares) and bigeye (T. obesus) tuna in a network of fish aggregating devices (FADs)[END_REF][START_REF] Robert | Intraindividual behavioral variability displayed by tuna at fish aggregating devices (FADs)[END_REF] with different FAD densities [START_REF] Pérez | Effects of habitat modifications on the movement behavior of animals : the case study of Fish Aggregating Devices ( FADs ) and tropical tunas[END_REF]) .

Materials & Methods

Field data

Passive acoustic telemetry data were used to characterize tuna movements in FAD arrays. This technology is based on the transmission of an acoustic signal between an acoustic transmitter (or tag) implanted in a tuna and acoustic receivers (or hydrophones) installed at specific study sites. The identification of the tagged fish is possible when the fish is located close to the receivers, within a given detection range. Passive acoustic tagging data were collected in two anchored FAD arrays, one around the island of Mauritius [START_REF] Rodriguez-Tress | Associative behavior of yellowfin Thunnus albacares, skipjack Katsuwonus pelamis, and bigeye tuna T. obesus at anchored fish aggregating devices (FADs) off the coast of Mauritius[END_REF] in the Western Indian Ocean, and the other around the island of Oahu [START_REF] Robert | Intraindividual behavioral variability displayed by tuna at fish aggregating devices (FADs)[END_REF] , within the Hawaiian archipelago in the Central Pacific Ocean (Fig. 1). These anchored FAD arrays differ in their inter-FAD distances, with the Mauritian array having shorter nearest and next-nearest neighboring distances than the Hawaiian array [START_REF] Pérez | Effects of habitat modifications on the movement behavior of animals : the case study of Fish Aggregating Devices ( FADs ) and tropical tunas[END_REF] . The Mauritian array consisted of 9 FADs with 7 equipped with acoustic receivers, and the Hawaiian array comprised 13 FADs, all of which were equipped with acoustic receivers (see [START_REF] Dagorn | Behavior of yellowfin (Thunnus albacares) and bigeye (T. obesus) tuna in a network of fish aggregating devices (FADs)[END_REF][START_REF] Rodriguez-Tress | Associative behavior of yellowfin Thunnus albacares, skipjack Katsuwonus pelamis, and bigeye tuna T. obesus at anchored fish aggregating devices (FADs) off the coast of Mauritius[END_REF] for specifications of acoustic receivers).

In both arrays, FADs were moored in depths of between 1000 and 2500 m. The design of FADs was similar within the same array, but differed slightly between arrays. Since previous studies outlined species and size-dependent variability in the associative behavior of tuna at FADs [START_REF] Robert | Intraindividual behavioral variability displayed by tuna at fish aggregating devices (FADs)[END_REF][START_REF] Rodriguez-Tress | Associative behavior of yellowfin Thunnus albacares, skipjack Katsuwonus pelamis, and bigeye tuna T. obesus at anchored fish aggregating devices (FADs) off the coast of Mauritius[END_REF][START_REF] Pérez | Effects of habitat modifications on the movement behavior of animals : the case study of Fish Aggregating Devices ( FADs ) and tropical tunas[END_REF] , this study focused on a single species (yellowfin tuna) and size of ~70 cm fork length (fork length range: 60-80 cm), named YFT-70, which was common to both study sites. For the Mauritian array, due to the short duration of the experiment [START_REF] Rodriguez-Tress | Associative behavior of yellowfin Thunnus albacares, skipjack Katsuwonus pelamis, and bigeye tuna T. obesus at anchored fish aggregating devices (FADs) off the coast of Mauritius[END_REF] , the data recorded during the first 38 days was considered, resulting in the smallest observation time. For the Hawaiian array, where the experiment lasted more than one year, only the initial 120 days after tagging were considered because 95% of the time between the first and the last detection at a FAD lasted less than 120 days [START_REF] Robert | Intraindividual behavioral variability displayed by tuna at fish aggregating devices (FADs)[END_REF] . As a result, the field data consisted of 14 YFT-70 tagged in the Mauritian array and 56 YFT-70 individuals in the Hawaiian array (Table 1). Details on the tagging procedures can be found in [START_REF] Rodriguez-Tress | Associative behavior of yellowfin Thunnus albacares, skipjack Katsuwonus pelamis, and bigeye tuna T. obesus at anchored fish aggregating devices (FADs) off the coast of Mauritius[END_REF] for the Mauritian array and in [START_REF] Robert | Intraindividual behavioral variability displayed by tuna at fish aggregating devices (FADs)[END_REF] for the Hawaiian array.

Residence and absence times in the FAD array

Acoustic telemetry data were processed to obtain information on durations of presence at and absence from instrumented FADs displayed by tagged tuna, following the procedure described in Capello et al. (2015) . This procedure translates the discrete time series of acoustic detections into continuous bouts of time. It relies on the definition of a maximum blanking period (MBP), i.e., a maximum temporal separation between two subsequent acoustic detections at the same FAD (or receiver), where fish is still considered to be associated. The definition of a MBP not only allows to account for small data gaps related to detection issues and sonic collisions [START_REF] Forget | Behaviour and vulnerability of target and non-target species at drifting fish aggregating devices (FADs) in the tropical tuna purse seine fishery determined by acoustic telemetry[END_REF], but also for fish excursions out of the detection range of the receiver. In the case of tropical tuna, a MBP value of 24h was chosen, in order to account for the regular diel excursions that tuna perform out of the FAD at nighttime [START_REF] Holland | Horizontal and vertical movements of yellowfin and bigeye tuna associated with fish aggregating devices[END_REF][START_REF] Marsac | Telemetry 'applied to behaviour analysis of yellowfin tuna (Thunnus albacares, Bonnaterre, 1788) movements in a network of fish aggregating devices[END_REF][START_REF] Dagorn | Modeling tuna behaviour near floating objects: From individuals to aggregations[END_REF][START_REF] Forget | Behaviour and vulnerability of target and non-target species at drifting fish aggregating devices (FADs) in the tropical tuna purse seine fishery determined by acoustic telemetry[END_REF].

Following this procedure, the Continuous Residence Times (CRTs) [START_REF] Ohta | Periodic behavior and residence time of yellowfin and bigeye tuna associated with fish aggregating devices around Okinawa Islands, as identified with automated listening stations[END_REF][START_REF] Dagorn | Behavior of yellowfin (Thunnus albacares) and bigeye (T. obesus) tuna in a network of fish aggregating devices (FADs)[END_REF][START_REF] Capello | A methodological framework to estimate the site fidelity of tagged animals using passive acoustic telemetry[END_REF] , corresponded to continuous bouts of time spent at the same FAD without any day-scale absence (>24h). Conversely, the time spent away from FADs were defined as Continuous Absence Times (CAT) [START_REF] Govinden | Movement behaviour of skipjack (Katsuwonus pelamis) and yellowfin (Thunnus albacares) tuna at anchored fish aggregating devices (FADs) in the Maldives, investigated by acoustic telemetry[END_REF][START_REF] Capello | A methodological framework to estimate the site fidelity of tagged animals using passive acoustic telemetry[END_REF] . Absence times related to movements between two different FADs were referred to as CATdiff [START_REF] Pérez | Effects of habitat modifications on the movement behavior of animals : the case study of Fish Aggregating Devices ( FADs ) and tropical tunas[END_REF] . Finally, for each individual, the sum of all recorded CRTs and CATs corresponded to the Total Residence Time (TRT), namely the time between the first and the last detection recorded in the FAD array (Fig. 2).

Model

The model was built upon four behavioral rules, based on the current knowledge of the associative behavior of tuna at FADs (Fig. 3): (1) Tuna display a random search behavior between two FAD associations [START_REF] Girard | FAD: Fish Aggregating Device or Fish Attracting Device? A new analysis of yellowfin tuna movements around floating objects[END_REF][START_REF] Pérez | Effects of habitat modifications on the movement behavior of animals : the case study of Fish Aggregating Devices ( FADs ) and tropical tunas[END_REF]) , (2) at a certain distance from FADs tuna show oriented movements towards FADs [START_REF] Girard | FAD: Fish Aggregating Device or Fish Attracting Device? A new analysis of yellowfin tuna movements around floating objects[END_REF]) , (3) the tuna association dynamics follows a diel rhythm [START_REF] Holland | Horizontal and vertical movements of yellowfin and bigeye tuna associated with fish aggregating devices[END_REF][START_REF] Marsac | Telemetry 'applied to behaviour analysis of yellowfin tuna (Thunnus albacares, Bonnaterre, 1788) movements in a network of fish aggregating devices[END_REF][START_REF] Dagorn | Modeling tuna behaviour near floating objects: From individuals to aggregations[END_REF][START_REF] Forget | Behaviour and vulnerability of target and non-target species at drifting fish aggregating devices (FADs) in the tropical tuna purse seine fishery determined by acoustic telemetry[END_REF][START_REF] Tolotti | Association dynamics of tuna and purse seine bycatch species with drifting fish aggregating devices (FADs) in the tropical eastern Atlantic Ocean[END_REF][START_REF] Govinden | Behavior of skipjack ( Katsuwonus pelamis ), yellowfin ( Thunnus albacares ), and bigeye ( T. obsesus ) tunas associated with drifting fish aggregating devices (dFADs) in the Indian Ocean, assessed through acoustic telemetry[END_REF] , and (4) CRTs were independent from previous CATs [START_REF] Robert | Intraindividual behavioral variability displayed by tuna at fish aggregating devices (FADs)[END_REF] .

As tuna, like most animals, have a tendency to move forward, the random-search movements were simulated using a Correlated Random Walk model [START_REF] Kareiva | Analyzing Insect Movement as a Correlated Random Walk[END_REF][START_REF] James | Caribou movement as a correlated random walk[END_REF][START_REF] Codling | Random walk models in biology[END_REF][START_REF] Ahearn | A context-sensitive correlated random walk: a new simulation model for movement[END_REF]) . These models are based on a Markov process where consecutive changes in the animal's consecutive direction are correlated. For each time step Δt, the position of an individual at time t depends on its previous position at time t-Δt and the turning angle α, defining the change in direction relative to the previous time step. Turning angles were randomly sampled from a normal distribution defined in the range [-π; π], with zero mean and standard deviation σ following the method of [START_REF] Bovet | Spatial analysis of animals' movements using a correlated random walk model[END_REF], using the scipy.stats.truncnorm python function. Standard deviation σ = 0 correspond to straight trajectories whereas in the limit σ→∞ the model converges to a simple random walk. In the following, σ was expressed in terms of the coefficient of sinuosity (c) according to the relationship, σ=√(-2ln(c)) [START_REF] Bovet | Spatial analysis of animals' movements using a correlated random walk model[END_REF][START_REF] Benhamou | How to reliably estimate the tortuosity of an animal's path: Straightness, sinuosity, or fractal dimension[END_REF]) . The limit c→0 corresponds to a simple random walk (highest sinuosity) whereas increasing c decreases the sinuosity, with straight trajectories for c=1. A total of 9 coefficients of sinuosity were tested, ranging between 0.2 and 0.9999 (Table 2). Fig. 4 illustrates the distribution of turning angles and an example of a tuna trajectory for each coefficient of sinuosity tested. In order to account for the orientation behavior of tuna towards FADs, different values of the orientation radius were tested (Fig. 4, Table 2 and Supplementary Information 1). Each time a tuna enters within this radius, its path changes to a straight trajectory oriented towards the FAD location.

with c Є ]0,1] (Bovet &
If the tuna was located within the orientation radius of multiple FADs, a FAD was randomly selected between them using a uniform distribution. A total of six orientation radii were tested, ranging between 0 (no orientation) to 20 km, see Table 2. The diel rhythm in the associative behavior of tunas was accounted for by defining two behavioral modes ("daytime" and "nighttime") with a periodicity of 24 hours each. During the 12 hours of "daytime" tuna displayed an orientation behavior towards FADs (if located within the orientation radius). Conversely, during the 12 hours of "nighttime" tuna did not exhibit a long-range attraction to FADs (no oriented behavior within the orientation radius)

and therefore followed a simple CRW dynamic. In both "daytime" and "nighttime" behavioral modes a tuna was, however, considered to be associated with a FAD when it was located within 500 m of it.

This value is in accordance with both the observations of tuna when they were associated with FADs (see [START_REF] Josse | Typology and behaviour of tuna aggregations around fish aggregating devices from acoustic surveys in French Polynesia[END_REF][START_REF] Moreno | Fish behaviour from fishers' knowledge: the case study of tropical tuna around drifting fish aggregating devices (DFADs)[END_REF] , and the detection range of acoustic tags used in telemetry studies around instrumented FADs (see [START_REF] Forget | Behaviour and vulnerability of target and non-target species at drifting fish aggregating devices (FADs) in the tropical tuna purse seine fishery determined by acoustic telemetry[END_REF] .

The model did not represent the association time of tuna at FADs (CRT), but these durations were needed to compare the model with the field data. Therefore, the CRTs recorded from field data were used as a model input. Each time a tuna reaches a FAD (i.e., it was located within 500 m of it), a CRT value was randomly sampled from the actual CRT data of the corresponding array and the simulated individuals do not move away from the FAD during the entire duration of the CRT. The CRTs recorded from field data in each array are shown in the Supplementary Information 2. Once this time has elapsed, individuals could leave the FAD in a random direction sampled from a uniform distribution between [-π; π]. To avoid immediate returns, during the 24 hours following the end of a CRT, fish was not affected by the association radius (Ro) of the FAD of departure. Similarly, returns due to tuna re-entering the detection range within 24 hours (which were already taken into account in the CRT duration) were neglected. For this purpose, each time a CATreturn of less than 24 hours was recorded after a CRT, this movement was discarded and the simulation time was reset to the end of the last CRT recorded (Fig. 3). This procedure ensured that CRT durations were consistent with field data. Since the CRTs recorded immediately after tagging were significantly longer than the other CRTs in the Hawaii field experiments and slightly longer in the Mauritius field data, (see Supplementary Information 2) they were not considered in the above procedure. Accordingly, the first CRT were also subtracted from the TRT to ensure data consistency.

Finally, a mortality rate (m) was considered to account for natural and fishing mortality events that may cause the interruption of the acoustic detections for some tagged individuals. For this purpose, a

Monte Carlo algorithm was applied where, for each individual and at each time step, a random number ε was sampled from a uniform distribution in the interval [0,1] and compared with the corresponding mortality rate using a Bernoulli test. A death was accepted for ε < m*T. The constant T depends on the time step Δt and on the temporal units of the mortality rate. Different mortality rates were tested, ranging between 0 and 5% per day (Table 2). For a mortality rate expressed in days -1 and Δt in seconds, T= Δt/(3600×24). The upper bound of 5% per day was estimated from survival analyses of field data (see Supplementary Information 3). TRTs values therefore depended on both the CRW dynamics (which affects the number of tuna associations, thus the time at which the last FAD detections occur) and the mortality rates (Fig. 2). A summary of all model parameters can be found in Table 2. All the simulations were performed using the Python 3 programming language (Python Software Foundation, version 3.8.5). For the Mauritian array, see Supplementary Information 2.

Comparison between simulated and field data

Since the model aimed at fitting the time that tuna spent between two FAD associations (CATdiff), the comparison between the model and the field data focused on this metric. However, the distribution of CATdiff also depends on the total time spent in the FAD array (i.e. longer CATdiff can only be observed for longer TRT). As such, the comparison between the model and the field data was performed for both metrics. For this purpose, CATdiff and TRT were obtained from the simulated data using the same procedures applied to the field data. The selection of model parameters which best fitted the field data was made using a survival analysis, by comparing the theoretical survival curves of the TRT and the CATdiff with those obtained from field data, through a bootstrap method. Experimental survival curves S(t) were constructed [START_REF] Capello | A methodological framework to estimate the site fidelity of tagged animals using passive acoustic telemetry[END_REF] , which represented the proportion of events (TRT or CATdiff) longer than a given duration t. For each set of parameters the survival curve of the field data was compared 1000 times with a sub-sample of the same size as the field data, i.e. 56 individuals for

Hawaii and 14 for Mauritius (Table 1), randomly sampled from the 1000 simulated individuals. For each of the bootstrap sample , survival curves obtained from the simulated and field data were The Cox proportional hazards regressions and logrank tests were performed using the R software (R Core Team 2018 version 3.4.4) with the function "coxph" in the "survival" package version 3.1-8 [START_REF] Therneau | Modeling Survival Data: Extending the Cox Model[END_REF] .

Results

A total of 648 sets of parameters were tested (Table 2), of which 7 appeared to best fit both the CATdiff and TRT recorded in the Mauritian and Hawaiian arrays considering a percentage of retained bootstrap tests ≥85% (Table 3 andSupplementary Information 5). That is, over the 1000 tests performed for each set of parameters, 7 sets were not statistically different from the field data in more than 85% of the tests performed on both survival curves (TRT and CATdiff) and FAD arrays (Mauritius and Hawaii). Fig. 5 and Fig. 6 present the CATdiff and TRT survival curves for each FAD array, for the two sets of parameters performing the best.

5%, see Table 3). The first row corresponds to the survival curves of CATdiff (A and B) and the second row to the TRT (C and D). The first column denotes the Hawaiian FAD array (A and C) and the second column the Mauritian array (B and D). The red line corresponds to the theoretical curve (exp(-mt)) representing the upper bound of TRT.

and 1% did not appear among the 7 best fits (Table 3). However, combinations of parameters exist with high percentages of retained bootstraps (83.5% for m=5%/day and 80.1% for m=1%/day, see Fig. 7, Supplementary Information 6 and 7). On the opposite, orientation radii of 2 and 5 km clearly stand out (Fig. 7 and Supplementary Information 7)), all the other values having a percentage of retained bootstraps below 55% (Fig. 7, Supplementary Information 6) and even below 20% for orientation radii of 15 and 20 km (Fig. 7, Supplementary Information 6). Finally, the coefficients of sinuosity (c) performing the best range from 0.9 to 0.995 (all with a percentage of retained bootstraps above 80%, Fig. 7, Supplementary Information 6 and 7). Coefficients of c=0.2, 0.999 and 0.9999

showed poorer results (percentage of retained bootstraps respectively 37.2%, 51.3% and 7%, see Fig. 7, Supplementary Information 6 and 7).

Discussion

The study of animal behavior made considerable progress in the last decades, thanks to the development of electronic tagging and camera trapping technologies [START_REF] Swann | Camera trapping for animal monitoring and management: a review of applications[END_REF][START_REF] Hughey | Challenges and solutions for studying collective animal behaviour in the wild[END_REF]. However, characterizing the movement of animals in their own environment still remains a challenging task, particularly in marine environments, where GPS technologies can rarely be used. Here, through the use a field-based modeling approach and passive acoustic telemetry data, we provide, for the first time, a method for describing the movement behavior of tunas in FAD arrays.

The model is built upon four main behavioral components, based on the state-of-the-art knowledge of the associative dynamics of tunas at FADs: random walk dynamics, orientation capabilities, diel behavior and a lack in correlation between the duration of consecutive CRTs and CATs. A relatively small number of parameters drive the model's properties: swimming speed, path sinuosity, orientation radius and mortality rate. Despite the model's structural simplicity and the reduced number of parameters, it was able to reproduce both of the investigated movement metrics (time between two FAD associations and total time spent in the array) in two different FAD arrays.

The four parameters tested can be related to the physiological capabilities and condition of tuna, as well as their environment (including the FADs, other tuna and non-tuna species present in the array).

The two swimming speeds tested (corresponding to the 0.7 and 1.4 m/s) stem from previous studies

showing that swimming speed typically range between 1 and 2 body lengths per second [START_REF] Girard | FAD: Fish Aggregating Device or Fish Attracting Device? A new analysis of yellowfin tuna movements around floating objects[END_REF]Dagorn et al. 2013b) . In contrast, despite previous evidences of a random walk behavior in tuna movements between FADs [START_REF] Girard | FAD: Fish Aggregating Device or Fish Attracting Device? A new analysis of yellowfin tuna movements around floating objects[END_REF][START_REF] Pérez | Effects of habitat modifications on the movement behavior of animals : the case study of Fish Aggregating Devices ( FADs ) and tropical tunas[END_REF] , no empirical studies have estimated the sinuosity of a tuna path in a FAD array. As a consequence, large ranges of sinuosity were considered. The results show that, while both speed values could be retained by the simulations, only a limited subset of sinuosity coefficients emerged. The majority of sinuosity coefficients that were retained indicated a rather skewed distribution of turning angles (Fig. 3, Table 3). Lower sinuosity coefficients were mostly found for the highest swimming speed (Table 3). This is to be expected considering that for a given average distance traveled during a correlated random walk, higher speeds imply lower sinuosity coefficients and vice-versa [START_REF] Hall | Amoeboid Movement as a Correlated Walk[END_REF][START_REF] Kareiva | Analyzing Insect Movement as a Correlated Random Walk[END_REF][START_REF] Marsh | The form and consequences of random walk movement models[END_REF] . Hence, the values of the sinuosity coefficient (c) retained are valid considering the chosen time step (Δt=100 s). It is likely that the tuna movement characteristics (speed and sinuosity) also depend on the fine-scale environmental characteristics within the FAD array, such as the type and distribution of prey, or the physiological conditions of the tuna itself. In future, the consideration of a range of swimming speeds and path sinuosity, as opposed to single values, could provide a more realistic picture of tuna movements. However, the range of values used in this study provides an initial set of movement characteristics that are compatible with field observations, thus contributing to the poorly understood dynamics of tuna in a FAD array.

The mortality rate (which accounts for both natural and fishing mortality) is primarily influenced by risks associated with fishing activity, natural predation and disease. A previous study using conventional tags from the Hawaii Tuna Tagging Project (HTTP) showed a natural mortality rate of 0.36% per day and a fishing mortality of 0.67 % per day for yellowfin tuna larger than 56 cm [START_REF] Adam | Dynamics of bigeye (Thunnus obesus) and yellowfin (T. albacares) tuna in Hawaii's pelagic fisheries: Analysis of tagging data with a bulk transfer model incorporating size-specific attrition[END_REF] . As such, the global mortality rates estimated through our simulations appear to be higher than previous findings. This difference could be due to a specific mortality in each study site and period considered. Indeed, even if in both cases the Hawaiian archipelago was considered, these studies concern different islands and study periods, for which the fishing pressure might differ as well as the natural mortality.

Acoustic telemetry data do not allow for the direct estimation of mortality rate, but do provide information on the time at which an individual is no longer detected by receivers deployed on FADs.

Generally, a lack of acoustic detections indicates that tuna have either left the FAD array or died.

Movement dynamics of tuna can explain the first potential causes for a lack of detection. Within the model, the propensity of an individual to depart from the array is directly linked to the sinuosity of its path, its swimming speed and its orientation radius. For instance, large path sinuosity (resulting from small values of the sinuosity coefficient c) primarily leads to movements close to the FAD of departure and little or no detections at the other FADs. Conversely, small path sinuosity (form high values of the coefficient of sinuosity c) generally results in individuals rapidly leaving the array (Fig. 3 and Supplementary Information 1). In this way, the model provides direct information on the rate at which tuna are lost from FAD arrays. Fitting the model to the field data allows for differentiation between loss through randomness of movement and loss due to mortality (Table 2 andSupplementary Information 3). As such this field-based movement model could provide a new and alternative methodology for estimating the mortality rates of tuna in a FAD array.

In the model, the orientation radius represents the distance from which tunas are able to orient themselves towards FADs them, while on the field tuna could be able to perceive FADs before orienting themselves toward them. No data is available on the distance at which tunas perceive FADs, but tuna movements provide input on the distance at which tunas start to orient themselves toward FADs. Therefore, the FAD perception radius was not considered in this study. This distance naturally depends on the tuna's ability to perceive its surrounding environment, as well as on the physical characteristics of the area. Given the large distances from which tuna can orient themselves towards FADs, highlighted in previous studies [START_REF] Girard | FAD: Fish Aggregating Device or Fish Attracting Device? A new analysis of yellowfin tuna movements around floating objects[END_REF]) , as well as those found in this study, the use of visual cues as explanatory factors can be discarded. As sound can travel great distances underwater, the perception of acoustic stimuli could be a valid hypothesis for explaining the ability of tunas to orient towards FADs from such large distances. Environmental characteristics may impact the propagation of sounds between FADs and tunas and influence how strong these sound stimuli are.

The physical characteristics of the water mass are known to affect the propagation of sound waves [START_REF] Lee | Sound speed and attenuation measurements within a seagrass meadow from the water column into the seabed[END_REF][START_REF] Siddiqui | Effects of Water Column Variations on Sound Propagation and Underwater Acoustic Communications[END_REF] . Furthermore, the topology of the FAD array and its location relative to the coastline could also affect underwater sound propagation. As sounds may be produced by the FAD structures themselves, they can vary depending on the materials used and the design of each structure, which often differ among FAD arrays. Although FAD design has not been identified

as influencing the attractiveness of FADs [START_REF] Fréon | Review of fish associative behaviour: Toward a generalisation of the meeting point hypothesis[END_REF] , it may impact their detectability.

Tunas may also perceive the presence of a FAD through the emission of noise generated by the fish aggregation itself. In such a situation the intensity of the noise could be dependent on the quantity of fish present, but also on the types of species and their activities. Considering these multiple potential sources of environmental variability, the distance at which tuna are able to perceive FADs (orientation radius) is likely to vary both within and between FAD arrays. No single value of the orientation radius can exist, but rather a distribution of these distances with a subset of values for which the probability of being located in the environment is greatest. A general model that describes the movements of tuna in different FAD arrays with the same parameters, such as the one developed in this study, provides a subset of the most probable orientation distances. However, it is likely that a distribution of orientation distances could be more realistic and for a particular FAD, the orientation radius could have its own dynamics according to local environmental conditions.

A previous study by [START_REF] Girard | FAD: Fish Aggregating Device or Fish Attracting Device? A new analysis of yellowfin tuna movements around floating objects[END_REF] determined orientation radii between 4 and 17 km, with a mode around 10 km. This study was based on 14 yellowfin tuna (YFT) from 47 cm to 167 cm FL, that were acoustically tracked in different FAD arrays [START_REF] Holland | Horizontal and vertical movements of yellowfin and bigeye tuna associated with fish aggregating devices[END_REF][START_REF] Marsac | Telemetry 'applied to behaviour analysis of yellowfin tuna (Thunnus albacares, Bonnaterre, 1788) movements in a network of fish aggregating devices[END_REF][START_REF] Brill | Horizontal movments and depth distribution of large adult yellowfin tuna (Thunnus albacares) near the Hawaiian Islands, recorded using ultrasonic telemetry: implications for hte physiological ecology of pelagic fishes[END_REF][START_REF] Dagorn | Modeling tuna behaviour near floating objects: From individuals to aggregations[END_REF] and included the specie-size category considered in our simulations (YFT of ~70 cm). These 14 individuals were actively tracked over short durations, between 12 and 86 hours (due to the constraints of active tracking) rather than passively monitored as in our study. The radii found in our 7 sets of parameters (5 km and 2 km in one set) are similar to the lower range of the orientation distances (4-17 km) found by [START_REF] Girard | FAD: Fish Aggregating Device or Fish Attracting Device? A new analysis of yellowfin tuna movements around floating objects[END_REF] . The longer orientation distances identified in that study could be attributed to the inclusion of only long paths (more than 7 km away from the FADs) in their analysis. Furthermore, the authors considered that the longest orientation distances (e.g. > 15 km) could be the result of tuna patrolling along the coast, thus using some bathymetric information rather than signals from FADs. As such, the distances found by [START_REF] Girard | FAD: Fish Aggregating Device or Fish Attracting Device? A new analysis of yellowfin tuna movements around floating objects[END_REF] may represent maximum orientation distances, while the average could be shorter, and more similar to the values we found (2-5 km).

Finally, it is important to note that the two studies considered different datasets collected in different regions, and possible inter-FAD array variability in the orientation radius cannot be excluded. It is important to stress that the retention of the model parameters was very conservative: only those valid for both metrics (TRT and CATdiff) and FAD arrays were kept. In doing so, possible local variability in tuna behavior (for example, a different orientation radius depending on the study site) were excluded. This choice was made to obtaining the minimal, and most general model, that could reproduce the observations. Considering a threshold of 85% for the percentage of retained bootstraps provides 7 sets of parameter values over the 648 tested. These values (radius of orientation ranging between 2-5 km, coefficient of sinuosity between 0.9 and 0.995, mortality rates between 2 and 3%)

provide the main characteristics of tuna movements in FAD arrays. To avoid any scaling issue, the same data treatment was applied to both field and simulated data sets. Therefore, the model can be considered to correctly reproduce the tuna movements between FADs at the dayscale, i.e., the scale related to a maximum blanking period of 24h [START_REF] Capello | A methodological framework to estimate the site fidelity of tagged animals using passive acoustic telemetry[END_REF], which was used to process the acoustic data. Further studies, across a greater number of study sites, could provide insight into how these model parameters could vary between FAD arrays. Similarly, it would be of interest to consider how this model, fitted for YFT-70, is able to describe the behavior of other tuna species and sizes.

This model could also be used for other non-tuna species that associate with FADs and in particular vulnerable species such as the silky sharks (Carcharhinus falciformis).

As this model aimed to simulate tuna movements in FAD arrays, the time tuna spent associated with FADs (CRT) was not simulated and the experimental CRT distribution was used as an input of the model. Further model developments, which consider social interactions at FADs [START_REF] Robert | The aggregation of tuna around floating objects: What could be the underlying social mechanisms[END_REF][START_REF] Pérez | Effects of habitat modifications on the movement behavior of animals : the case study of Fish Aggregating Devices ( FADs ) and tropical tunas[END_REF], may allow the CRT durations within different FAD arrays to also be integrated into the model. This integration of CRTs into the model would involve adding social interactions between individuals and behavioral rules of social retention at the FAD that follow the meeting point hypothesis [START_REF] Dagorn | Tropical tuna associated with floating objects: a simulation study of the meeting point hypothesis[END_REF][START_REF] Fréon | Review of fish associative behaviour: Toward a generalisation of the meeting point hypothesis[END_REF], Robert el al. 2014).

Conclusion

Building on current knowledge of the associative behavior tuna at FADs from acoustic telemetry data, our model is the first to reproduce the movement behavior of tunas in a FAD array. A total of 7 sets of parameters (Table 3) were able to reproduce, with a high confidence, the movements of yellowfin tuna (fork length 70 cm) in two different FAD arrays, suggesting the model is robust. Future model improvements could consider distributions of speeds, sinuosity, detection radii and mortality rates (rather than fixed values) which may provide a better reflection of the variability induced by the local environment and the physiological conditions of the tuna themselves.

This model can be used on all species that display associative behavior with floating object. This includes species such as dolphinfish (Coryphaena hippurus) or the vulnerable silky shark (Carcharhinus falciformis). When combined with acoustic telemetry data, the model can provide an alternative method for determining the mortality rate of tuna and other associated species in a FAD array. Given the difficulty in assessing natural and fishing mortality for wild marine species, this novel approach could be of interest for the stock assessment community. Moreover, the model could be used to predict how increasing numbers of FADs affect the ecology of tunas ecology, both in terms of the time spent away from FADs and the total time spent in a FAD array. This study offers a new tool to provide science-based advice for the management of FAD fisheries, since the more time fish spend associated, the more vulnerable these individuals are to the fishery. Scenarios could be extended to drifting FADs in open ocean areas, as both anchored and drifting FADs alter the environment in a similar way [START_REF] Dagorn | Are drifting FADs essential for testing the ecological trap hypothesis[END_REF] . While acoustic telemetry experiments have successfully characterized residence times at drifting FADs [START_REF] Govinden | Behaviour of Tuna associated with Drifting Fish Aggregating Devices ( FADs ) in the Mozambique Channel[END_REF][START_REF] Forget | Behaviour and vulnerability of target and non-target species at drifting fish aggregating devices (FADs) in the tropical tuna purse seine fishery determined by acoustic telemetry[END_REF] , measuring in situ absence times of tunas within drifting FAD arrays is a major research challenge and these parameters are key for the development of robust FAD management plans by Tuna Regional Fisheries Management Organisations (RFMOs). Our model provides a method for estimate these parameters in the absence of data from acoustically tagged tuna in drifting FAD arrays.

Finally, the same approach can be used to study the movement behavior of other marine and terrestrial species that manifest an associative behavior with aggregating sites, and for which presence/absence data are recorded at these sites. For instance, our model could be used to study the movements of terrestrial animals who show associative behaviors with waterholes [START_REF] Zvidzai | Waterhole usepatterns at the wildlife/livestock interface in a semi-arid savanna ofsouthern Africa[END_REF]O'Farrill et al. 2014) detected through camera traps [START_REF] Swann | Camera trapping for animal monitoring and management: a review of applications[END_REF][START_REF] Hughey | Challenges and solutions for studying collective animal behaviour in the wild[END_REF]. More generally, this method could be used even without any associative behavior at specific sites, as long as the study site is equipped with regularly spaced and sufficiently numerous receivers where individuals can be identified.

Fig. 1 :

 1 Fig. 1: Anchored FAD arrays of Mauritius (left) and Oahu (right). Positions of the anchored FADs are represented by a black dot when equipped with an acoustic receiver, and by a black cross otherwise.

Fig. 2 :

 2 Fig. 2: Schematic diagram of behavioral sequences and Total Residence Time (TRT) definition. The tuna #1 presents a TRT ending at the end of the last Continuous Residence Time (CRT), recorded before the end of the experiment (indicated by a C-shape). The tuna #2 presents a TRT ending during a CRT because the experiment stopped, while the tuna was associated. CAT corresponds to Continuous Absence Times.

Fig. 3 :

 3 Fig. 3: Flow-Chart diagram illustrating the model algorithm. CRW denotes Correlated Random Walk, R0 corresponds to the orientation radius, dist corresponds to the distance between the tuna and

Fig. 4 :

 4 Fig. 4: Example of tuna path trajectories according to the coefficient of sinuosity (c; rows) and the orientation radius (Ro, columns) tested for the Hawaiian array. The first column shows the distribution of turning angles (α in radians) for each coefficient of sinuosity tested. The orientation radii are represented by red circles centered around each FAD and the case Ro=0 is not represented.

  compared using Cox proportional hazards regressions. The statistical significance of the model was assessed using the p-value from a logrank test, which tested the null hypothesis of identical hazards between the model and the field data. For each survival curve (TRT and CATdiff) and FAD array (Mauritius and Hawaii), the percentage of retained bootstrap tests was calculated, corresponding to the number of bootstrap tests showing p-values>0.05 over the 1000 tests performed. Finally, each set of parameters was assigned the lower percentage of retained bootstraps estimated over survival curves (TRT and CATdiff) and FAD arrays (Hawaii and Mauritius).

Fig. 5 .

 5 Fig. 5.: Comparison of survival curves obtained from field data(black) and from the 1000 bootstrap samples (gray) for a speed v=0.7 m s -1 , a mortality m=2%, a orientation radius Ro=5 km and a coefficient of sinuosity c=0.99 (with % retained bootstrap = 91.5%, see Table3). The first row

Fig. 7 :

 7 Fig. 7: Heatmap of the percentage of retained bootstraps that fit the field data for each set of model parameters. Rows corresponds to the tested speeds (v), columns denote the mortality rates (m). Tested values of the orientation radius (R0) are shown in the x-axis and tested coefficients of sinuosity (c) in the y-axis.

Table 1 :

 1 Number of yellowfin tuna of ~70 cm tagged (Ntuna), total number of CRTs (excluding the first CRT, NCRT) and total number of CATdiff (NCATdiff) recorded in the Mauritian and the Hawaiian array.

		Hawaii	Mauritius
	Ntuna	56	14
	NCRT	111	29
	NCATdiff	59	19

Table 2 :

 2 Model parameters that gives the 648 sets of parameters tested.

		Parameters	Values
			Tested parameters
	v	Speed (m/s)	0.7, 1.4
	m	Rate of mortality (%/day)	0, 1, 2, 3, 4, 5
	Ro Orientation radius (km)	0, 2, 5, 10, 15, 20
	c	Coefficient of sinuosity	0.2, 0.7, 0.9, 0.97, 0.99, 0.995, 0.997, 0,999, 0.9999
			Fixed parameters
	Δt Time step (s)	100
	N	No. of simulated individuals 1000
	T	Total duration (day)	38 (Mauritius), 120 (Hawaii)

Table 3 :

 3 Set of retained model parameters for which more that 85% of the bootstrap tests fit the field data. .

	v (m/s)	m (%/day)	Ro (km)	c	Retained Bootstraps (%)
	0.7	2	5	0.99	91.5
	1.4	2	2	0.97	90.7
	1.4	3	2	0.9	89.8
	0.7	2	5	0.995	89.7
	1.4	4	2	0.9	89.4
	1.4	2	2	0.9	87.5
	0.7	3	5	0.99	86.6

Acknowledgements

The authors would like to acknowledge the two anonymous reviewers for their extensive and constructive feedback.

Funding

This project was co-funded by the ANR project BLUEMED (ANR-14-ACHN-0002), "Observatoire des Ecosystèmes Pélagiques Tropicaux exploités" (Ob7) from IRD/MARBEC and by the International Pole-and-line Foundation (IPNLF).

Data Availibity Statement

Simulations were performed with the model FAT albaCoRaW v1.3. All scripts and data used in this study are available on GitHub (https://github.com/adupaix/FAT_albaCoRaW, doi: 10.5281/zenodo.5834056.).

 3). The first row corresponds to the survival curves of CATdiff (A and B)

and the second row to the TRT (C and D). The first column denotes the Hawaiian FAD array (A and C) and the second column the Mauritian array (B and D). The red line corresponds to the theoretical curve (exp(-mt)) representing the upper bound of TRT.

The complete results of the bootstrap test are available in Supplementary Information 6. Any speed values between the tested ones (0.7 and 1.4 m/s) will reflected the field behavior (Fig. 7 and Supplementary Information 7). In the same way, all values of the mortality rate can be retained. However, null mortalities (m=0), showed poorer bootstrap results (higher percentage of retained bootraps of 62.2%, see Fig. 7, Supplementary Information 6 and 7). Similarly, mortality rates of 5% Authors' contributions SB, KH and LD collected the raw data in the field. GP developed the model, with major contribution of AD and MC. GP analysed the data and wrote the paper with major contribution of MC, LD, JLD and AD. All authors read and approved the final manuscript.