Capello Manuela
email: manuela.capello@ird.fr

Rault Jonathan

Deneubourg Jean-Louis

Dagorn Laurent

Manuela Capello

Schooling in habitats with aggregative sites: the case of tropical tuna and floating objects

Keywords: Animal groups, heterogeneous habitats, aggregations, associative behavior, schooling, tropical tuna

Many marine and terrestrial species live in groups, whose sizes and dynamics can vary depending on the type and strength of their social interactions. Typical examples of such groups in vertebrates are schools of fish or flocks of bird. Natural habitats can encompass a wide range of spatial heterogeneities, which can also shape the structure of animal groups, depending on the interplay between the attraction/repulsion of environmental cues and social interactions. A key issue in modern applied ecology and conservation is the need to understand the relationship between these ethological and ecological scales in order to account for the social behaviour of animals in their natural environments. Here, we introduce a modeling approach which studies animal groups within heterogeneous habitats constituted by a set of aggregative sites. The model properties are investigated considering the case study of tropical tuna schools and their associative behavior with floating objects, a question of global concern, given the thousands of floating objects deployed by industrial tropical tuna fisheries worldwide. The effects of increasing numbers of aggregative sites (floating objects) on tuna schools are studied. This study offers a general modeling framework to study social species in their habitats, accounting for both ethological and ecological drivers of animal group dynamics.

Highlights

► We develop a model to assess the impacts of human-induced habitat modifications on social animals. ► The model accounts for the interplay of increasing numbers of habitat heterogeneities on animal groups. ► The model properties are investigated considering the case study of tropical tuna schools. ► This study offers a general modeling framework to study social species in their habitats. ► This approach can accounts for both ethological and ecological drivers of animal groups dynamics.

1

Introduction

Animal groups can follow different levels of organization, from aggregations of insects to schools of fish and flocks of birds [START_REF] Costa | The other insect societies[END_REF][START_REF] Krause | Living in groups[END_REF]. Generally, living in groups provides various advantages to animals, like higher reproductive rates [START_REF] Allee | Animal Aggregations, A Study in General Sociology[END_REF], a reduction in predation due to both the dilution/confusion effect [START_REF] Turner | Attack Abatement : A Model for Group Protection by Combined Avoidance and Dilution[END_REF]) and the "many-eyes" effect [START_REF] Pulliam | On the advantages of flocking[END_REF][START_REF] Roberts | Why individual vigilance declines as group size increases[END_REF], increased foraging success [START_REF] Galef | Social influences on foraging in vertebrates: Causal mechanisms and adaptive functions[END_REF], stress reduction in unfavorable situations [START_REF] Allen | Cohesive social behaviour shortens the stress response: The effects of conspecifics on the stress response in lake sturgeon Acipenser fulvescens[END_REF] or access to mutualistic endosymbiotic microbes [START_REF] Lombardo | Access to mutualistic endosymbiotic microbes: An underappreciated benefit of group living[END_REF]. Conversely, the presence of many individuals within the same group can also be deleterious, by facilitating detection by predators [START_REF] Ioannou | Grouping and Predation[END_REF], promoting disease or parasite transmissions [START_REF] Patterson | Parasite infection and host group size: A metaanalytical review[END_REF] and leading to increased competition for food [START_REF] Rubenstein | On Predation, Competition, and the Advantages of Group Living[END_REF]. Accordingly, the size of animal groups are often considered a result of trade-offs between these factors [START_REF] Ioannou | Grouping and Predation[END_REF][START_REF] Krause | Living in groups[END_REF][START_REF] Rubenstein | On Predation, Competition, and the Advantages of Group Living[END_REF].

At a larger scale, groups of animals share a given habitat with their congeners and the other species [START_REF] Goodale | Chapter 3 -Moving Mixed-Species Groups in Different Taxa[END_REF]. Any natural habitat presents a certain degree of spatial heterogeneity, e.g., an uneven spatial distribution of resources, variable environmental conditions and/or spatial cues, which can affect their local structure and attractiveness [START_REF] Levin | The problem of pattern and scale in ecology[END_REF][START_REF] Vinatier | Factors and mechanisms explaining spatial heterogeneity: A review of methods for insect populations[END_REF]. This local habitat structure can have multiple impacts on animal groups, by increasing their tendencies to disperse or gather together, depending on the local properties of the habitats and their functional interest [START_REF] Hart | Habitat heterogeneity and social factors drive behavioral plasticity in giraffe herd-size dynamics[END_REF][START_REF] Maeno | Aggregation site choice by gregarious nymphs of the desert locust, schistocerca gregaria, in the Sahara desert of mauritania[END_REF][START_REF] Rahmani | Flocking in complex environments-Attention trade-offs in collective information processing[END_REF][START_REF] Schmidt | Random and Aggregative Settlement in Some Sessile Marine Invertebrates[END_REF]. However, while the effects of habitat heterogeneities on the diversity of animal species have been widely studied [START_REF] Tews | Animal species diversity driven by habitat heterogeneity/diversity: The importance of keystone structures[END_REF], little is known regarding their effects on the structure and dynamics of animal groups [START_REF] Rahmani | Flocking in complex environments-Attention trade-offs in collective information processing[END_REF]).

An aggregation is defined as a gathering of individuals leading to a local density greater than that of neighboring regions [START_REF] Camazine | Self-Organization in Biological Systems[END_REF]. This phenomenon, referred to as associative behavior, is present as much in bacteria or other unicellular organisms as in arthropods or vertebrates [START_REF] Parrish | Complexity, pattern, and evolutionary trade-offs in animal aggregation[END_REF]. Aggregations can either be explained exclusively through the local attractiveness of an environment or to social interactions [START_REF] Camazine | Self-Organization in Biological Systems[END_REF]. The former results from the sum of individual responses to an external stimulus, whereas the latter is based on individual responses but also on interactions between individuals. These two mechanisms leading to animal aggregations are not mutually exclusive: very often, social interactions are influenced by surrounding environmental cues. Aggregations of social animals can then be defined as a gathering of individuals in the same place who interact with each other via the perception of stimuli of varying nature from other individuals (e.g., sounds, vocalisms or visual cues) and/or by local modifications of the environment (e.g., chemical marking, garbage, or trail creation).

Several terrestrial and marine species simultaneously manifest such aggregative behavior and collective group dynamics [START_REF] Camazine | Self-Organization in Biological Systems[END_REF][START_REF] Parrish | Complexity, pattern, and evolutionary trade-offs in animal aggregation[END_REF]. A typical example of such behavior is shown by starlings, which can form large congregations on trees and collective flocking behavior [START_REF] Cavagna | Scale-free correlations in bird flocks[END_REF][START_REF] Lyon | Habitat Selection by Roosting Blackbirds and Starlings: Management Implications[END_REF].

The same behavior is also found in several fish species and more particularly in tropical tunas, which can form large schools of several thousand individuals and also aggregate around floating objects found at the sea surface [START_REF] Fréon | Review of fish associative behaviour: Toward a generalisation of the meeting point hypothesis[END_REF].

Tuna fisheries provide global yields of about 7 millions tonnes and feature among the world's most important fisheries (FAO, 2020). Tropical tunas (yellowfin tuna -Thunnus albacares, bigeye tuna -Thunnus obesus and skipjack tuna -Katsuwomus pelamis) contribute to more than 90% of the major global tuna catches [START_REF] Issf | Status of the world fisheries for tuna[END_REF]. Skipjack tuna, with a catch exceeding 3 millions tonnes in 2018, being the third highest marine species in terms of total yield, following only Peruvian anchoveta (Engraulis ringens) and Alaska pollock (Gadus chalcogrammus) (FAO, 2020). Tuna captured around floating objects account for approximately half of the global tuna catch [START_REF] Dagorn | Is it good or bad to fish with FADs? What are the real impacts of the use of drifting FADs on pelagic marine ecosystems?[END_REF]. The recent introduction of thousands of artificial floating objects in the open ocean (termed Fish Aggregating Devices or FADs) by industrial fisheries, has resulted in numerous questions on their impacts on the size of tuna schools [START_REF] Sempo | Impact of increasing deployment of artificial floating objects on the spatial distribution of social fish species[END_REF], as well as their potential risk of forming an ecological trap [START_REF] Dagorn | Is it good or bad to fish with FADs? What are the real impacts of the use of drifting FADs on pelagic marine ecosystems?[END_REF][START_REF] Hallier | Drifting fish aggregation devices could act as an ecological trap for tropical tuna species[END_REF][START_REF] Marsac | Drifting FADs used in tuna fisheries: an ecological trap[END_REF]. These ecological impacts brought on by the large-scale exploitation of FADs across all oceans require the development of quantitative tools to study the effects of increasing FAD numbers on tuna schools and, more globally, on the populations of pelagic fish species that associate with them.

A wide variety of movement rules have been proposed to explain the formation and dynamics of animal groups [START_REF] Ballerini | Interaction ruling animal collective behavior depends on topological rather than metric distance: evidence from a field study[END_REF][START_REF] Bialek | Statistical mechanics for natural flocks of birds[END_REF][START_REF] Herbert-Read | Understanding how animal groups achieve coordinated movement[END_REF][START_REF] Vicsek | Collective motion[END_REF]. In particular, several models of fish schools have been developed in the past [START_REF] Lopez | From behavioural analyses to models of collective motion in fish schools[END_REF]. Alternatively, ecologically-relevant parameters, such as the amount of habitat heterogeneities, and the consequent associative behavior of animals forming aggregations induced by these heterogeneities, have so far been neglected when modeling animal group dynamics. Only a small number of recent studies have modeled flocking behavior in complex environments considering repulsive environmental cues and their consequences on the group-level coordination [START_REF] Rahmani | Flocking in complex environments-Attention trade-offs in collective information processing[END_REF]. Conversely, ecological models tend to neglect the behavioral drivers which can affect species abundance and distribution [START_REF] Geary | A guide to ecosystem models and their environmental applications[END_REF]. The main reason for this theoretical partitioning between ethological and ecological models can be related to the different spatial scales that are considered, ranging between a few centimeters/meters in ethology to several hundreds, or even thousands of kilometers in ecology.

Accounting for both ethological and ecological drivers is key to assess the effects of humaninduced habitat modifications on social species [START_REF] Dirzo | Defaunation in the Anthropocene[END_REF][START_REF] Hoffmann | The impact of conservation on the status of the world's vertebrates[END_REF].

Here, we introduce a new modeling framework to investigate the interplay between the tendency of animals to live in groups (i.e., forming schools, flocks or other self-organized forms of groups) and the presence of aggregative sites in their environment (i.e., attraction/retention sites). In so doing, we demonstrate the importance of such ecological parameters on the behavior of social species in natural environments. Using tropical tuna schools and their associative behavior around floating objects as a case study, we consider the interplay between the formation of tuna aggregations induced by the local environmental properties of their habitat and their schooling dynamics.

The principal novelty of this modeling approach relies on the fact that it borders between ethology and ecology, accounting for both behavioral drivers (such as the tendency of tuna to form schools) and ecological drivers (heterogeneous environments formed by attractive sites).

Materials and methods

Model definition

Due to tropical tunas being social species which live in schools [START_REF] Fréon | Review of fish associative behaviour: Toward a generalisation of the meeting point hypothesis[END_REF], the model accounts for a set of tuna school units within an array of FADs. These school units 𝑁 𝑃 are considered to be constituted by individuals showing the same associative behavior with FADs, i.e., of the same species and size category [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 FADs 𝑃 represent a set of aggregative sites present in the local tuna environment, that can attract/retain them in their vicinity, thus favoring the formation of aggregations of schools, corresponding to multiple schools localized near the FAD [START_REF] Fréon | Review of fish associative behaviour: Toward a generalisation of the meeting point hypothesis[END_REF]. Each tuna school can be in one of two states, either free-swimming (not associated with any of the FADs, i.e., a free-swimming school, referred to as free school for simplicity in the remainder of the text) or associated to one of the FADs. Both free schools and FAD aggregations can 𝑃 be constituted by one or more school units, due to the interplay between fission, fusion and association processes. The resulting association dynamics can be summarized according to the following rules (Figure 1):

A.

C.

Free schools have a probability to join a FAD, which is independent of their size. For 𝜇 each free school, the overall probability of associating with any of the FADs is .

𝑃 𝑃𝜇

D.

Multiple school units forming a FAD-aggregation can leave a FAD at the same time, leading to a free school of size . Namely, for a FAD aggregation of size (i.e., 𝑙 > 1 𝑠 composed of school units), a school of size can depart from the FAD with probability 𝑠 𝑙 , leading to a FAD aggregation of size and a free school of size 𝛾 𝑙 𝑠 𝑠 -𝑙 𝑙.

𝐹 𝑙 + 𝑁 ∑ 𝑙 = 𝑠 + 1 (𝜂 𝑠 𝑙 + 𝜂 𝑙 -𝑠 𝑙 ) 𝑋 𝑙 -(1 -𝛿 𝑠,1 ) 𝑋 𝑠 𝑠 -1 ∑ 𝑙 = 1 𝜂 𝑙 𝑠 + -𝜓𝑋 𝑠 𝑁 -𝑠 ∑ 𝑙 = 1 (1 + 𝛿 𝑠,𝑙 )𝑋 𝑙 + 𝜓 𝑠 -1 ∑ 𝑙 = 1 (1 + 𝛿 𝑠 -𝑙,𝑙 ) 2 𝑋 𝑙 𝑋 𝑠 -𝑙 (Eq.2)
with conservation of total number of FADs and the total number of schools :

(𝑃) (𝑁) 𝑁 ∑ 𝑠 = 0 𝐹 𝑠 = 𝑃; 𝑁 ∑ 𝑠 = 1 𝑠 (𝐹 𝑠 + 𝑋 𝑠 ) = 𝑁.
(Eq.3)

In In this study, the following definition of FAD-departure probabilities was considered:

𝛾 𝑙 𝑠 𝛾 𝑙 𝑠 = 𝑠 𝜃 𝐵(𝑙 -1;𝑠 -1,𝛽 𝑎𝑔𝑔 ) (Eq.4)
where represents the probability of departure, per unit time, for an individual school unit 𝜃 and is the binomial probability mass function:

𝐵(𝑙 -1;𝑠 -1,𝛽 𝑎𝑔𝑔 ) 𝐵(𝑙 -1;𝑠 -1,𝛽 𝑎𝑔𝑔 ) = ( 𝑠 -1 𝑙 -1 ) 𝛽 𝑎𝑔𝑔 𝑙 -1 (1 -𝛽 𝑎𝑔𝑔 ) 𝑠 -𝑙 (Eq.5)
where the term is the binomial coefficient. (Eq.5) represents the probability for ( 𝑠 -1 𝑙 -1 ) school units (with the forming the remaining of the FAD aggregation) to join the 𝑙 -1 𝑠 -1 departing school (leading to a free school of size ). The constant corresponds to the 𝑙 𝛽 𝑎𝑔𝑔 binomial probability of success, namely the probability for a FAD-associated school unit to follow the departing school. For a FAD aggregation of size , Eq.( 4) implies that each 𝑠 associated school unit has a probability of departure equal to , namely, 𝜃 (1 + (𝑠 -1) 𝛽 𝑎𝑔𝑔 ) a school being part of large FAD aggregations has higher probabilities to leave the FAD. The average size of the school leaving the FAD is . In the limit , for each 1 + (𝑠 -1)𝛽 𝑎𝑔𝑔 𝛽 𝑎𝑔𝑔 →0 time step, only individual school units ( ) can leave the FAD. Oppositely, for , 𝑠 = 1 𝛽 𝑎𝑔𝑔 →1

the whole aggregation departs from the FAD, resulting in associated schools behaving as a single unit.

In the same way, the following probability was considered for a school of size to split 𝜂 𝑙 𝑠 𝑙 from a larger school of size :

𝑠 𝜂 𝑙 𝑠 = 𝑠 𝜙 𝐵(𝑙 -1;𝑠 -1,𝛽 𝑠𝑐ℎ𝑜𝑜𝑙 ) (Eq.6)
where represents the fission probability, per unit time, for an individual school unit (i.e., 𝜙 the probability that a single school unit splits from the school) and is

𝐵(𝑙 -1;𝑠 -1,𝛽 𝑠𝑐ℎ𝑜𝑜𝑙 )
the binomial probability mass function that follows the same definition as in Eq.( 5) above. In this case, the constant corresponds to the binomial probability for another school 𝛽 𝑠𝑐ℎ𝑜𝑜𝑙 unit to follow the school that split. In the limit , only individual school units can 𝛽 𝑠𝑐ℎ𝑜𝑜𝑙 →0 split. Conversely, for , free schools split, in average, into two sub-schools of the 𝛽 𝑠𝑐ℎ𝑜𝑜𝑙 →0.5 same size.

Model configuration

The sets of model parameters that were studied are summarized in Table 1. The probabilities of departure/arrival from/to a FAD ( and ) were fixed to 0.1 days -1 and 0.01 𝜃 𝜇

days -1 respectively. The choice of the probabilities and respectively affect the residence 𝜃 𝜇 times (the time schools spend associated with a FAD) and the absence times (the time spent between two FAD association, in the free state) which can be measured through electronic tagging [START_REF] Capello | A methodological framework to estimate the site fidelity of tagged animals using passive acoustic telemetry[END_REF]. For a non-social model defined in an array of 10 FADs, these parameters imply average residence times and absence times of 10 days. Here, the choice of the model parameters and aimed at ensuring average residence and absence times of 𝜃 𝜇 the same order of magnitude of those observed in past electronic tagging studies [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] 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][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] Tolotti | Association dynamics of tuna and purse seine bycatch species with drifting fish aggregating devices (FADs) in the tropical eastern Atlantic Ocean[END_REF].

These parameters were kept fixed, in order to study the model sensitivity to other parameters, whose ranges of values are unknown. For this purpose, a range of parameter values were tested for both the social interaction parameter at the FAD ( and the 𝛽 𝑎𝑔𝑔 ) school fission and fusion probabilities and ), resulting in five main model configurations (𝜙 𝜓 (Table 2). The effects of social interactions at the FADs were studied considering three different values of : 𝛽 𝑎𝑔𝑔 -resulting in individual school units departing from FADs independently of 𝛽 𝑎𝑔𝑔 = 0 , each other (Non-social (NS)).

resulting, in average, in half of the aggregation leaving the FADs 𝛽 𝑎𝑔𝑔 = 0.5, simultaneously (Social (S)).

resulting in the collective departure of the full aggregation from the FADs 𝛽 𝑎𝑔𝑔 = 1, (Highly Social (HS)).

Because the NS model considers independent school units, the effects of the schooling dynamics were considered for the social models only. First, only the effect of school fission was studied, leading to models S+f and HS+f (Table 2). Secondly, both the fission and fusion parameters were considered, leading to models S+ff and HS+ff, see Table 2. In the schoolfission process, the parameter was kept fixed at 0.5, considering that the most likely 𝛽 𝑠𝑐ℎ𝑜𝑜𝑙 fission process corresponded to a breakup of a school into two sub-schools of the same size.

Finally, the model properties were studied for increasing numbers of tuna school units and FADs (Table 1).

Numerical resolution of the model

The mean-field equilibrium solutions of the model defined through Eqs.(1-2) and Table 2 were numerically derived using the Euler method. Initial conditions were set considering all tuna schools in the free state ( for any ) and all free schools corresponding to a 𝐹 𝑠 (0) = 0, 𝑠 school unit ( ). The Euler method was applied considering a time step 𝑋 1 (0) = 𝑁 ∆𝑡 = 0.01 days over a total of 50,000 time steps to ensure equilibrium (Supplementary Figures S1 andS2).

Model properties

A set of metrics was defined to characterize tuna free schools and FAD aggregations. Two metrics were estimated to characterize free schools: i. The total number of free schools ( ), defined as . 𝑁𝐹𝑆 𝑁𝐹𝑆(𝑡) = ∑ 𝑠 𝑋 𝑠 (𝑡) ii. The mean size of free schools ( )

𝐹𝑆 𝑠𝑖𝑧𝑒 (𝑡) = ∑ 𝑠 𝑠 𝑋 𝑠 (𝑡) ∑ 𝑠 𝑋 𝑠 (𝑡)
Similarly, two metrics were estimated to characterize FAD aggregations: i. The mean size of a FAD aggregation ( ), defined for the FADs occupied by at least one 𝑚 school,

.

𝑚(𝑡) = ∑ 𝑁 𝑠 = 1 𝑠 𝐹 𝑠 (𝑡) ∑ 𝑁 𝑠 = 1 𝐹 𝑠 (𝑡)
ii. The fraction of FADs occupied by at least one school unit ( ), defined as 𝑓1 𝑓1(𝑡) = .

Results

Globally, the free-swimming school metrics (Figure 2) show larger school sizes and larger numbers of free schools for increasing population sizes, but very different trends relative to the number of FADs, depending on the model configuration. The average number of free schools follows a decreasing trend with the number of FADs for the non-social model (

). Similar trends are found for the social models with fission (S+f and 𝑁𝐹𝑆 = 𝜃𝑁/(𝑃𝜇 + 𝜃) HS+f). Conversely, in the case of model S+ff, the number of free schools shows a nonmonotonic trend, first increasing with the number of FADs, then reaching a maximum and then decreasing. Finally, for model HS+ff; the number of free schools is higher for smaller FAD numbers, then decreases monotonically with the number of FADs and is globally smaller than the other models. The average size of free schools is, by construction, equal to 1 for model NS. Larger (𝐹𝑆 𝑠𝑖𝑧𝑒 ) average school sizes are found for all social models, with different trends relative to the number of FADs, depending on the model configuration. Remarkably, increasing free school sizes are found for increasing FAD numbers for both highly-social models HS+f and HS+ff, with the HS model with fusion and fission producing the larger school sizes. Alternatively, the social model with fission (S+f) shows a non-monotonic trend, with average school sizes first increasing with the number of FADs, then attaining a maximum and finally decreasing.

Finally, when a fusion term is added to this model (S+ff) decreasing school sizes are found for increasing numbers of FADs. The average size of FAD aggregations ( , Figure 3) show global increasing trends for larger 𝑚 population sizes. The social models, both with fission and fission+fusion (S+f and S+ff) show decreasing trends of FAD aggregation sizes for larger number of FADs, as found for the nonsocial model, but relatively smaller aggregation sizes for small number of FADs. Conversely, both highly-social models (HS+f and HS+ff) demonstrate an opposite trend, with average aggregation sizes increasing for increasing numbers of FADs.

The fraction of FADs occupied by at least one school unit ( , Figure 3) shows a general 𝑓1

decrease with the number of FADs and is larger for larger populations. However, model S+ff show a non-monotonic trend, with f1 having a clear maximum for larger population sizes.

Moreover, the highly-social models with fission and fission+fusion (HS+f and HS+ff) demonstrate the highest and lowest sensitivity of f1 relative to the number of FADs respectively, while the size of the population appears less important. Finally, the fraction of associated schools ( , Figure 4) increases with the number of 𝐹 𝑎 /𝑁 FADs for all models. However, differences between social models and the non-social model exist. Increasing trends of , independent of the population size, are found for the non-𝐹 𝑎 /𝑁 social model (NS), whereas, for all social models, larger populations imply smaller fractions . This effect is amplified in the highly social models (HS+f and HS+ff). 𝐹 𝑎 /𝑁 Figures S3 and S5 show the equilibrium distribution of and , respectively. The 𝐹 𝑠 𝑋 𝑠 distribution of appears to be zero-inflated for the social models, particularly for the 𝐹 𝑠 highly social configurations (Figure S3-4). The trends of in semi-logarithmic and 𝑋 𝑠 logarithmic scale (Figures S6 andS7, respectively) demonstrate that the distribution of school sizes follows an exponential decay. The mean-to-variance relations of (Figure S8) 𝐹 𝑠 are equidispersed for the NS model and for social models with small population sizes or large numbers of FADs. Reversely, for social models with large population sizes/small numbers of FADs the distributions of show an overdispersion, with different trends 𝐹 𝑠 relative to the number of FADs, depending on the model (Figure S8). Similarly, overdispersed free-school size distributions ( characterize social models with large 𝑋 𝑠 ) population sizes (Figure S9). Finally, Figures S10 andS11 provide, for all model parameters, the free-school and FAD aggregation metrics divided by the total population size . (𝑁)

4.Discussion

This paper introduces a modeling approach to study the effects of habitat heterogeneities (here consisting of aggregative sites termed FADs) on groups of animals that display a schooling/shoaling behavior (tropical tunas in this case).

From the ethological to the ecological scale

The field of collective animal behavior has flourished in recent decades, deciphering the effects of local interactions between animals on their movements and behavior through self-organization [START_REF] Camazine | Self-Organization in Biological Systems[END_REF][START_REF] Krause | Living in groups[END_REF][START_REF] Parrish | Complexity, pattern, and evolutionary trade-offs in animal aggregation[END_REF][START_REF] Sumpter | The principles of collective animal behaviour[END_REF]. From a theoretical point of view, a variety of models were developed to explain the structure of the fish schools [START_REF] Lopez | From behavioural analyses to models of collective motion in fish schools[END_REF] and more generally, groups of animals [START_REF] Cavagna | Scale-free correlations in bird flocks[END_REF][START_REF] Sumpter | The principles of collective animal behaviour[END_REF][START_REF] Vicsek | Collective motion[END_REF].

Very often, ecological applications of these models remain absent [START_REF] Gordon | The Ecology of Collective Behavior[END_REF]. One of the reasons that can explain the disciplinary compartmentalization of such models could be attributed to the relatively small spatial scales that are considered. If interactions of few body-lengths can account for the formation of animal groups, accounting for the group responses to their habitats requires a shift to larger scales.

The present model accounts for the group dynamics of social animals (fission and fusion of tropical tunas in this case) at scales comparable to the spatial extent of their local habitat, which include numbers of spatial heterogeneities and other schools. For tropical tuna that display an associative behavior with floating objects in the open ocean, these scales can extend up to several tens (or even hundreds) of kilometers. In this respect, while this study still accounts for ethological processes related to social interactions such as collective departure from FADs, school fission and fusion, it also allows for the consideration of a series of ecological drivers, i.e., variable numbers of aggregative sites, that can also affect the groups' dynamics.

Previous studies conducted in the field of social ecology also considered the behavior of gregarious animals located into heterogeneous environments [START_REF] Ame | Cockroach aggregation based on strain odour recognition[END_REF][START_REF] Camazine | Self-Organization in Biological Systems[END_REF][START_REF] Halloy | Social integration of robots into groups of cockroaches to control self-organized choices[END_REF]. Because these studies focused essentially on social insects or arthropods, that do not form groups beyond of the aggregative locations, they cannot be directly transposed to social animals such as tunas, that display grouping behaviour both at and away from of the aggregation sites (forming aggregations and schools respectively). This study builds upon these modeling approaches and those developed for tropical tuna [START_REF] Capello | Population assessment of tropical tuna based on their associative behavior around floating objects[END_REF][START_REF] Robert | The aggregation of tuna around floating objects: What could be the underlying social mechanisms[END_REF][START_REF] Sempo | Impact of increasing deployment of artificial floating objects on the spatial distribution of social fish species[END_REF], explicitly adding a schooling component.

Model structure

Three main model parameters set the associative dynamics of tuna schools around spatial heterogeneities (FADs in this case): (i) the probability for a school to associate with a FAD (𝜇 ), (ii) the probability that a school initiates a departure from a FAD ( ) and (iii) the 𝜃 proportion of the aggregation leaving ( ). Moreover, three parameters determine the 𝛽 𝑎𝑔𝑔 free school fission/fusion dynamics: (i) the probability that a school unit splits from a larger school ( ) (ii) the proportion of school units that split (

) and (iii) the probability that 𝜙 𝛽 𝑠𝑐ℎ𝑜𝑜𝑙 two schools merge together ( ). 𝜓

The collective departure of multiple schools from a FAD (or from a school, for the fission events), follow a "starter" and "follower" rule. As such, the probability of initiating a departure is considered constant for every school unit (parameters and , respectively).

𝜃 𝜙

The proportion of followers is simply expressed through a binomial law (that depends on the parameters and , respectively). This dynamics implies that, every time the 𝛽 𝑎𝑔𝑔 𝛽 𝑠𝑐ℎ𝑜𝑜𝑙 collective departure parameters ( and ) are non-zero, the individual probability of 𝛽 𝑎𝑔𝑔 𝛽 𝑠𝑐ℎ𝑜𝑜𝑙 leaving the FAD (or the school) increases with the aggregation (school) size. Conversely, the probabilities of associating with a FAD and to merge with another school ( and , 𝜇 𝜓 respectively) are considered constant and are thus independent of the school size.

Alternative rules of association and school fusion could be studied, depending on the biological models of interest, with probabilities and that depend on the school or the 𝜇 𝜓 aggregation sizes. Similarly, more complex collective departure rules than the binomial laws, like sigmoidal functions presenting a characteristic threshold, could be studied, but would imply a larger number of parameters. The model studied herein aimed at considering a relatively simple dynamics, yet accounting for possible social interactions.

In the model, all FADs are considered equivalent to each other. The equivalence between a spatialized model and the current approach holds when the tuna diffusion coefficient is large relative to the scale of the FAD array and the spatial distribution of the free schools is homogeneous. For large and dense FAD arrays, where these conditions do not hold anymore, the model still accounts for the behavior of tuna schools at a local scale (i.e., the FAD of association and its neighboring FADs), where tuna have an equal probability of reaching all FADs of a given array through a random walk. This local scale can range from some few tens to a few hundred kilometers, depending on the FAD density and type of FAD array [START_REF] Capello | Population assessment of tropical tuna based on their associative behavior around floating objects[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]. Recent studies demonstrated that the time between two associations can be explained in terms of random walk movements between FADs [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], indicating that this hypothesis is the most parsimonious and plausible for tuna. Further modeling studies fitting the movement dynamics of tuna in a FAD array from field data using more realistic types of random walks (e.g. correlated random walks), should quantify the spatial scale of validity of the model for variable FAD densities.

This study investigates the dynamics of tuna in an array of FADs considering a set of school units as the basic model components. These school units account for the innate schooling behavior of tuna: it is very unlikely to find an individual tuna alone in the open ocean and generally tuna reach and depart from FADs in schools. This behavior is particularly evident for small size categories (40-60 cm fork length), that show a strong associative behavior with FADs and constitute the major proportion of the tuna found in FAD aggregations [START_REF] Fonteneau | Global spatio-temporal patterns in tropical tuna purse seine fisheries on drifting fish aggregating devices ( DFADs ): Taking a historical perspective to inform current challenges[END_REF][START_REF] Ménard | Exploitation of small tunas by a purse-seine fishery with fish aggregating devices and their feeding ecology in an eastern tropical Atlantic ecosystem[END_REF]. In the present model, all school units are equivalent and no intrinsic variability of their size is considered: the school units should be considered as the minimum size of a tuna school (e.g., 1 tonne, resulting in roughly 400 individuals with an average weight of 2.5 Kg), all other school sizes being composite schools built of these elementary units [START_REF] Gerlotto | The three-dimensional morphology and internal structure of clupeid schools as observed using vertical scanning multibeam sonar[END_REF]. It is plausible that a continuum spectrum of sizes of tuna schools exist. School size distributions of tuna school units could be added to the model, fitting the available data, i.e., from purse-seine catches of free tuna schools for a given species and size.

Model parametrization for tropical tuna

The model introduced in this study presents a continuum set of solutions, from the least social to the most aggregative, with very different properties depending on the choice of parameters. Five main sets of model parameters were studied for tropical tuna, that aimed at investigating the sensitivity of the model's properties to variable degrees of collective tuna departures from the FADs ( ), as well as variable tuna school fission/fusion 𝛽 𝑎𝑔𝑔 dynamics ( and ).

𝜙 𝜓

The values of the parameters and were fixed. Electronic tagging data, providing the time 𝜇 𝜃 that tuna aggregations spent both at and away from FADs (termed residence and absence times), can be used to infer the model's probabilities of association and departure [START_REF] Capello | A methodological framework to estimate the site fidelity of tagged animals using passive acoustic telemetry[END_REF][START_REF] Capello | Population assessment of tropical tuna based on their associative behavior around floating objects[END_REF]. Field studies also demonstrated that the associative behavior of tuna can be species and size-specific [START_REF] Robert | Size-dependent behavior of tuna in an array 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]. The choice of considering constant stems from previous electronic tagging studies, which demonstrated 𝜇 that the time that tagged individuals spent between two FAD associations follows exponential survival curves [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][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] Tolotti | Association dynamics of tuna and purse seine bycatch species with drifting fish aggregating devices (FADs) in the tropical eastern Atlantic Ocean[END_REF] and random walk types of movements [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]. Because the equilibrium solutions of the model depend on the ratio / and to 𝜇 𝜃 reduce the number of free parameters, the values of and were considered constant and 𝜇 𝜃 fixed to plausible values (average association/absence time of 10 days in an array of 10 FADs for the non-social model). For social models, the residence times also depend on the parameter (Eq.( 4)). In addition, the number of FADs ( ) indirectly affects the residence 𝛽 𝑎𝑔𝑔 𝑃 times for social models, since the aggregation's sizes depend on and larger aggregation 𝑃 sizes imply higher probabilities of departure for . Therefore, fitting the trends of 𝛽 𝑎𝑔𝑔 ≠ 0 residence times as a function of the number of FADs will be necessary to select the best model parameters. Further applications of the model would also require that the parameters were fitted to the field data for each tuna species and size category.

For the parameter choices of the social models, two main scenarios were studied, where on average, half (

) and the entire ( ) tuna aggregation collectively leave the 𝛽 𝑎𝑔𝑔 = 0.5

𝛽 𝑎𝑔𝑔 = 1
FAD during a departure event, resulting in the social (S) and highly-social (HS) model respectively. Obviously, intermediate cases could occur in nature. Unfortunately, the current state of knowledge and the current field data available from echosounder buoys (Baidai et al., 2020) do not allow for the assessment of this parameter for tropical tuna and more generally, for all marine species that display the same associative behavior. New field data, using sonars for instance [START_REF] Brehmer | Towards an Autonomous Pelagic Observatory: Experiences from Monitoring Fish Communities around Drifting FADs[END_REF], which provide accurate information on the temporal evolution of the associated biomass beneath the FAD, could allow for the assessment of this parameter. Furthermore, as knowledge on the fission and fusion dynamics of tuna schools is limited, the and parameters were set equal to the 𝜓 𝜙 probability of association . Faster fission dynamics ( ) would result in the non-social 𝜇 𝜙 ≫ 𝜇 model. Similarly, the limit , would make the fusion of schools negligible with respect 𝜓 ≪ 𝜇 to the FAD association dynamics.

Model properties and implications for tropical tuna

The free school metrics show a variety of trends that depend on the model configuration.

Interestingly, three social model configurations (S+f, HS+f and HS+ff) indicate that the presence of FADs leads to the formation of larger free schools. These trends are in agreement with the meeting point hypothesis [START_REF] Fréon | Review of fish associative behaviour: Toward a generalisation of the meeting point hypothesis[END_REF], which explains the natural associative behavior of tuna as means of meeting their congeners and forming larger schools. For model S+f, there is an optimal number of FADs that maximizes the school size.

For the highly-social models HS+f and HS+ff, the school size is an increasing monotonic function of the number of FADs, with no maximum. Conversely, the social model S+ff shows an inverse trend, with decreasing school sizes for increasing numbers of FADs. One of the potential negative impacts of increasing numbers of FADs is school fragmentation [START_REF] Dagorn | Is it good or bad to fish with FADs? What are the real impacts of the use of drifting FADs on pelagic marine ecosystems?[END_REF][START_REF] Sempo | Impact of increasing deployment of artificial floating objects on the spatial distribution of social fish species[END_REF]. This study suggests that this scenario strongly depends on the type of schooling and association dynamics in play. Interestingly, all these scenarios come from the same model structure. This continuous set of model solutions could mimic the behavioral plasticity of animals, that can adapt their dynamics to respond to a variable environment. These model's variants could also be considered as multi-species variants of the same associative behavior.

More globally, the analysis of the model's properties leads to a series of metrics with nonmonotonic trends that are not completely intuitive. In the case of the size of free schools mentioned above, for the S+f model, the non-monotonic trend of FS_size (Figure 2) can be explained by the propensity of FADs to aggregate multiple schools for small FAD numbers (and thus promote the departure of larger schools for ) and their tendency to 𝛽 𝑎𝑔𝑔 ≠ 0 disperse schools over different FADs (with one or few schools each), in the limit of large FAD numbers. This dispersive effect, which explains a reduction of the size of free schools (school fragmentation) for increasing number of FADs, is not apparent for the HS+f model. In this model, the higher aggregative capacity of FADs for counterbalances the 𝛽 𝑎𝑔𝑔 = 1 fragmentation of schools due to increasing numbers of FADs for the range of model parameters tested. On the other hand, in the presence of a fusion term, increasing FAD numbers also contribute to the reduction the number of free schools and thus their fusion rates. This effect can explain the monotonic decreasing trend of the size of free schools for increasing numbers of FADs for model S+ff. Reversely, for model HS+ff, the higher aggregative capacity of FADs for counterbalances this effect, similar to model HS+f. 𝛽 𝑎𝑔𝑔 = 1 Another example of non-monotonic trend is found for the number of free schools recorded for the S+ff model, which first increases with the number of FADs, then reaches a maximum and finally decreases. Generally, the number of free schools depends on the total associated population (which decrease with the number of FADs for all models, Figure 5) and the competition between the fission and fusion terms. For , if a single school of size 𝛽 𝑎𝑔𝑔 = 0.5 associates to a FAD, it has a non-null probability to depart into multiple schools, thus 𝑠 > 1 increasing the number of free schools. Therefore, the presence of FADs can first increase the number of free schools for this model configuration. On the other hand, in the limit of large FAD numbers, the decreasing free population and the presence of smaller FAD aggregations/school sizes prevail and thus cause a decreasing number of free schools.

The fraction of FADs occupied by tuna in a FAD array can be derived using both fisheriesdependent [START_REF] Sempo | Impact of increasing deployment of artificial floating objects on the spatial distribution of social fish species[END_REF] and independent data (Baidai et al., 2020). This is facilitated through the large-scale collection of data derived from echosounder buoys attached to FADs [START_REF] Moreno | Fish aggregating devices (FADs) as scientific platforms[END_REF] as well as of catch data. Similarly, purse-seine catch data can provide insight into the size of FAD aggregations and free schools. Assessing their trends for increasing numbers of FADs will be essential to parametrize the model. However, to date, the information on the total number of floating objects at fine spatial and temporal scales is still considered sensitive data and is only partially available to scientists though specific agreements with their national fleets. Moving towards the complete availability of data on all FADs present in the ocean at a local scale is key to parametrize the model and thus provide science-based advices on the impacts of increasing numbers of FADs. This study outlines an increasing trend in the fraction of associated schools with increasing FAD numbers, across all model configurations. Assessing which model best fits tuna behavior will be key to quantitatively evaluating the increase in vulnerability of tuna populations to the purse seine fishery induced by increasing numbers of FADs. Finally, the model parametrization could benefit future technological improvements in the acoustic discrimination of tuna species [START_REF] Moreno | Towards acoustic discrimination of tropical tuna associated with Fish Aggregating Devices[END_REF] and in the biomass estimates obtained from echosounder buoys (Baidai et al., 2020), which could allow for the evaluation of the dynamics of a FAD aggregation independently of catch data.

Conclusion and Perspectives

The availability of new technologies to study wild animals in their natural environment at multiple spatial scales continues to increase [START_REF] Hughey | Challenges and solutions for studying collective animal behaviour in the wild[END_REF]. In the case of tropical tuna and FADs, a variety of technologies can be used to characterize the associative behavior of tuna and the aggregation dynamics [START_REF] Brehmer | Towards an Autonomous Pelagic Observatory: Experiences from Monitoring Fish Communities around Drifting FADs[END_REF][START_REF] Moreno | Fish aggregating devices (FADs) as scientific platforms[END_REF]. These multiple data sources could be used to parametrize the models developed here. For tropical tuna, combining different data sources from electronic tagging, acoustic data and fisheries-dependent data could allow for estimations of the model parameters. This fieldbased model could be used as a FAD-operating model to predict trends in several fisheriesrelated metrics for variable tuna populations/FAD numbers, as well as to predict the impacts of increasing numbers of FADs on the ecology of these species. It could also be used to test the reliability and robustness of novel indicators of abundance developed for tuna [START_REF] Capello | Population assessment of tropical tuna based on their associative behavior around floating objects[END_REF][START_REF] Santiago | TOWARDS A TROPICAL TUNA BUOY-DERIVED ABUNDANCE INDEX ( TT-BAI )[END_REF]. More generally, this modeling approach could be applied to the study of social species living in groups in their natural environment, and allow for the evaluation of the impacts of habitat modifications due to anthropogenic activities and global change. In environments which are highly modified by humans, models such as the one summarized in this article, based on understanding the processes involved in the dynamics of animal groups in their habitats, will be increasingly necessary as management and prediction tools [START_REF] Evans | Modelling ecological systems in a changing world[END_REF]. 2). 2).

Figure 1 :

 1 Figure 1: Schematic view of the model. (A-C) Free-schools dynamics. (A) Fission: a free school of size can split into smaller schools of size and with probability . (B) Fusion: two 𝑠 > 1 𝑙 𝑠 -𝑙 (𝜂 𝑙 𝑠 + 𝜂 𝑠 -𝑙 𝑠 ) free schools can merge with probability independent of their size. (C) Association: any free school 𝜓 have probability to associate with a FAD, regardless of its size. (D) Associated-schools dynamics: for μ a FAD association of size , a school of size can depart (forming a free school) with probability .

𝛽

  relative number of associated schools over the full FAD array (𝐹 𝑎 (𝑡)/𝑁 = 1 𝑁 was estimated. For each combination of model parameters, each metric was ∑ 𝑁 𝑠 = 1 𝑠 𝐹 𝑠 (𝑡)) calculated at equilibrium (stationary states:).

Figure 2 .

 2 Figure 2. Free-swimming school metrics. Number of free-swimming schools (NFS) and average size of the free schools (

Figure 3 .

 3 Figure 3. FAD aggregation metrics. Average number of school units associated with the FADs that are occupied by at least one school

Figure 4 .

 4 Figure 4. Relative number of associated schools. Ratio between the number of FAD-associated school units and the total number of school units, as a function of the number of FADs (abscissa) for different population sizes (colors). Each column represents a model configuration : Non-social (NS); Social with fission (S+f); Highly Social with fission (HS+f); Social with fission and fusion (S+ff); Highly Social with fission and fusion (HS+ff).

Figure S3 :

 S3 Figure S3 : Equilibrium distribution of the number of FAD aggregations of size 𝑠 (𝐹 𝑠 ). Rows correspond to different population sizes (from top to bottom: N=10, 40, 100) and columns correspond to different numbers of FADs (from left to right: P=1, 2, 10, 50, 100). Each color indicates one of the five model configurations considered (see Table2).

Figure S4 :

 S4 Figure S4 :The same as FigureS3in semi-logarithmic scale.

Figure S5 :

 S5 Figure S5 : Equilibrium distribution of the number of free schools of size 𝑠 (X 𝑠 ). Rows correspond to different population sizes (from top to bottom: N=10, 40, 100) and columns correspond to different numbers of FADs (from left to right: P=1, 2, 10, 50, 100). Each color indicates one of the five model configurations considered (see Table2).

Figure S6 :

 S6 Figure S6 :The same as FigureS5in semi-logarithmic scale.

Table 1 :

 1 Model parameters.

	PARAMETER DESCRIPTION

Table 2 . Summary of the five model configurations. Non

 2 The other parameters are the same for all models, 𝛽 𝑎𝑔𝑔 = 1.0 𝜙 =

	-social (NS,	, 𝛽 𝑎𝑔𝑔 = 0 𝜙 = 𝜓 0; = 0); Social

𝜓

see Table

1

.

Acknowledgements

This study was supported by the MANFAD project and the CIGOEF ANR project.

𝐹 𝑠 (0)

814

), for the five model configurations (see Table 2), with = ∀ 𝑠; 𝑋 1 (0) = 𝑁; 𝑋 𝑠 > 1 (0) = 0


Baidai Yannick
email: yannick.baidai@ird.fr

Dagorn Laurent

Amandè Monin

Gaertner Daniel

Capello Manuela

Proud Roland

Yannick Baidai

Tuna aggregation dynamics at Drifting Fish Aggregating Devices: a view through the eyes of commercial echosounder buoys

Keywords: absence times, associative behaviour, colonization times, Drifting Fish Aggregating Devices (DFADs), echosounder buoys, residence times, tropical tunas

This study addresses novel questions on the dynamics of tuna aggregations around floating objects, using echosounder buoys data collected throughout the drifts of newly deployed Drifting Fish Aggregating Devices (DFADs) in the Atlantic Ocean (AO) and Indian Ocean (IO). Time series of presence/absence of tunas were obtained by supervised classification of acoustic data. To avoid biases related to the variability in individual DFAD soak times, a new approach was developed to estimate the average colonization time of new DFADs by tuna aggregations. We showed that tunas colonize DFADs after an average of 16 days in the AO, and 40 days in the IO. Moreover, the analysis indicated that the time span during which tuna aggregations occupy DFADs is driven by a time-independent process with short-and long-term residence modes. On average, DFADs were continuously occupied by tuna aggregations for 6 and 9 days in the IO and AO, respectively. The time between two consecutive aggregations at the same DFAD averaged 9 days in the IO and 5 days in the AO. Throughout their soak time after being colonized, DFADs remained occupied for a larger proportion of time in the AO (63%) than in the IO (45%).

Introduction

Substantial development in the tropical tuna purse-seine fishery has occurred over recent decades and it now accounts for the majority of the world's tropical tuna catch [START_REF] Issf | Status of the world fisheries for tuna 2013 -October 2019[END_REF].

The increasing trend in catches has been accompanied by regular technological developments of vessels and fishing tools [START_REF] Gaertner | The European Union Research Project, Efficiency of Tuna Purse-Seiners and Effective Effort (ESTHER): Scientific report of project[END_REF][START_REF] Fonteneau | A worldwide review of purse seine fisheries on FADs[END_REF][START_REF] Torres-Irineo | Changes in fishing power and fishing strategies driven by new technologies: The case of tropical tuna purse seiners in the eastern Atlantic Ocean[END_REF]. Since the early 1990s, these developments have included the deployment of artificial floating objects, known as drifting Fish Aggregating Devices (DFADs) used to increase fishery efficiency. This fishing mode exploits the behavioural trait of the target tuna species, skipjack tuna (Katsuwonus pelamis), yellowfin tuna (Thunnus albacares), and bigeye tuna (Thunnus obesus), to naturally aggregate around floating objects (see [START_REF] Fréon | Review of fish associative behaviour toward a generalisation 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][START_REF] Castro | A general theory on fish aggregation to floating objects: An alternative to the meeting point hypothesis[END_REF]. Thousands of DFADs specifically designed to attract tunas, are deployed by purse seine fleets in all of the world's oceans to enhance their catches. Initial estimates put the number of DFADs operated annually across the three major oceans in the range of 50,000 and 100,000 [START_REF] Baske | Estimating the use of drifting Fish Aggregation Devices (FADs) around the globe[END_REF][START_REF] Scott | The use of FADs in Tuna Fisheries[END_REF][START_REF] Gershman | Estimating the use of FADS Around the World, The Pew Charitable Trusts[END_REF]. Furthermore, the scale at which this fishing gear is used has quadrupled in less than a decade, in both the Atlantic and Indian oceans [START_REF] Fonteneau | Managing tropical tuna purse seine fisheries through limiting the number of drifting fish aggregating devices in the Atlantic: food for thought[END_REF][START_REF] Maufroy | Massive increase in the use of drifting Fish Aggregating Devices (dFADs) by tropical tuna purse seine fisheries in the Atlantic and Indian oceans[END_REF]. Over the past 30 years, this fishing mode has been significantly improved through the sequential introduction of new technologies (radio, GPS and echosounder buoys), with the latter now providing skippers and fleet managers with detailed information on the location and biomass associated with DFADs [START_REF] Lopez | Evolution and current state of the technology of echo-sounder buoys used by Spanish tropical tuna purse seiners in the Atlantic, Indian and Pacific Oceans[END_REF]. In recent years, more than half of the world's purse seine catch of tropical tunas has come from DFAD fishing [START_REF] Dagorn | Is it good or bad to fish with FADs? What are the real impacts of the use of drifting FADs on pelagic marine ecosystems?[END_REF][START_REF] Fonteneau | Global spatio-temporal patterns in tropical tuna purse seine fisheries on drifting fish aggregating devices (DFADs): Taking a historical perspective to inform current challenges[END_REF].

The mechanisms underlying the associative behaviour of tropical tunas with floating objects remain poorly understood, despite the proposal of numerous hypotheses (see [START_REF] Fréon | Review of fish associative behaviour toward a generalisation 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][START_REF] Castro | A general theory on fish aggregation to floating objects: An alternative to the meeting point hypothesis[END_REF]. As a consequence of the massive increase in the use of DFADs in the recent years, improving knowledge on the associative behaviour of tropical tunas with floating objects has become a key research priority. Primary areas of concern include the concomitant changes in catchability of tunas at floating objects as well as the understanding of the impact of DFADs on their ecology and that of other associated fauna. To date, most research efforts have focused on describing the associative dynamics of individual fish, primarily through electronic tagging studies, at both coastal anchored FADs (e.g. [START_REF] Holland | Horizontal and vertical movements of yellowfin and bigeye tuna associated with fish aggregating devices[END_REF][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]Dagorn et al., 2007a;[START_REF] Mitsunaga | Association of early juvenile yellowfin tuna Thunnus albacares with a network of payaos in the Philippines[END_REF][START_REF] Robert | Intra-individual 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], and drifting FADs (e.g. [START_REF] Schaefer | Simultaneous behavior of skipjack (Katsuwonus pelamis), bigeye (Thunnus obsesus), and yellowfin (T. albacares) tunas, within large multi-species aggregations associated with drifting fish aggregating devices (FADs) in the equatorial eastern Pacific Ocean[END_REF][START_REF] Matsumoto | Behavior of skipjack tuna (Katsuwonus pelamis) associated with a drifting FAD monitored with ultrasonic transmitters in the equatorial central Pacific Ocean[END_REF][START_REF] Matsumoto | Comparison of the behavior of skipjack (Katsuwonus pelamis), yellowfin (Thunnus albacares) and bigeye (T. obesus) tuna associated with drifting FADs in the equatorial central Pacific Ocean[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]. In contrast, behavioural patterns of FAD-associated aggregations (i.e. entire tuna schools under a DFAD) have received considerably less research attention. When investigated, studies were primarily focused on the spatial or temporal characterization of aggregations at fine timescales, using acoustic equipment on board research vessels [START_REF] Josse | In situ acoustic target strength measurements of tuna associated with a fish aggregating device[END_REF][START_REF] Doray | Acoustic characterisation of pelagic fish aggregations around moored fish aggregating devices in Martinique (Lesser Antilles)[END_REF]Moreno et al., 2007a;[START_REF] Trygonis | Spatiotemporal distribution of fish schools around drifting fish aggregating devices[END_REF]. The instrumentation of DFADs with satellite-linked echosounder buoys began in the late 2000's. Since then, their use has become widespread in many fleets. Currently, almost all deployed DFADs are equipped with these devices which provide remote and near real-time information on the DFAD location and aggregated biomass [START_REF] Lopez | Evolution and current state of the technology of echo-sounder buoys used by Spanish tropical tuna purse seiners in the Atlantic, Indian and Pacific Oceans[END_REF][START_REF] Moreno | Towards acoustic discrimination of tropical tuna associated with Fish Aggregating Devices[END_REF]. Echosounder buoys generate a considerable stream of data that can be used to characterize DFAD aggregations [START_REF] Lopez | A model based on data from echosounder buoys to estimate biomass of fish species associated with fish aggregating devices[END_REF]Orue et al., 2019a;Baidai et al., 2020).

The availability of such data, which is continuously being collected, represents an unprecedented opportunity to observe fish aggregations associated with floating objects over long time scales. To date, only one study has provided characteristics of tuna aggregations at DFADs over the scale of weeks and months, using data from fisher's echosounder buoys [START_REF] Orue | Aggregation process of drifting fish aggregating devices (DFADs) in the Western Indian Ocean: Who arrives first, tuna or non-tuna species?[END_REF]. This work aims to characterize how tunas occupy DFADs, in order to improve the understanding of their aggregation dynamics around these objects. Using data from commercial echosounder buoys attached to DFADs deployed in the Western Indian Ocean and Eastern Atlantic Ocean, we assessed several parameters related to the association of tuna aggregations with DFADs. These include the elapsed time between deployment of a new DFAD and its colonization by tunas; the average duration of association of tuna aggregations with DFADs and the length of time that DFADs remains vacant between consecutive tuna aggregations.

Material and methods

Echosounder Data

The echosounder data used in this study were collected using M3I buoys 1 attached to DFADs from the French tropical tuna purse seiner fleet operating in the Western Indian Ocean and Eastern Atlantic Ocean, from 2016 to 2018. The M3I buoy is equipped with a GPS positioning device and an echosounder powered by solar panels, operating at a frequency of 50 kHz, with a power of 500 W, and a beam angle of 36°. The data output of the buoy is simplified acoustic information, designed for easy visual interpretation by fishers. The M3I buoy samples the water column in 3-meter layers covering a total depth of 150 m (50 layers, with the first two corresponding to the transducer near-field). An acoustic sample consists of 50 ordered categorical scores (ranging from 0 to 7), resulting from the automatic conversion of the acoustic backscatter signal recorded per 3-meter layer, with an inbuilt algorithm. In the default-operating mode, 12 samples collected at about 2 hour intervals, are transmitted daily via satellite by the buoy.

Data cleaning process

The raw data provided by the echosounder buoys were cleaned using the following protocol (see [START_REF] Baidai | Towards the derivation of fisheries-independent abundance indices for tropical tunas: Progress in the echosounders buoys data analysis[END_REF] for details on the procedure):

(1) Duplicated rows, inconsistent positions, data recorded on land, at shallow positions (depth less than 150 meter), or under low voltage conditions (poor reliability of acoustic data collected below 11.5V) were omitted from the database.

(2) A rule-based algorithm, which uses buoy speed and its variations as main classifiers, was applied to discriminate acoustic data recorded when the buoy is on board a vessel from those actually recorded when the buoy is deployed at sea.

Classification of tuna presence/absence

The presence or absence of tuna at a DFAD was assessed from acoustic data collected by echosounder buoys, following the methodology described in Baidai et al., (2020). This approach involves preliminary processing of the acoustic data, followed by a classification using random forest algorithms applied separately to each ocean. The learning datasets were constructed by cross-referencing the acoustic data with the activities of fishers at DFADs (namely sets with associated tuna catches, DFAD deployments and DFAD visits) recorded in logbooks and by on-board observers. A detailed description of the classification procedure can be found in Supplementary Material S1. The minimum catch value representing tuna presence in the learning dataset was 1 ton. Thus, in this work, the term "tuna aggregation" refers to a fish aggregation whose tuna biomass is at least equal to this value.

An additional post-processing step was applied to improve the predictions made by the classification algorithm during the course of DFAD trajectories. Prediction results with short durations (i.e. an isolated event of presence or absence lasting a single day) were considered unlikely, attributed rather to misclassification, and corrected using the previous or following day's predicted values. This step allowed for the correction of 9 and 7% of the initial predictions made by the classification model, in the Atlantic Ocean (AO) and the Indian Ocean (IO) respectively.

Newly deployed DFADs

Only referencing the logbook and observer databases with the echosounder buoy database, using the unique identification code of the buoy and the deployment date. To ensure that the subset correctly identified newly deployed DFADs (and not potentially misreported reinforcement activities), records for which fishing sets were reported during the week following the deployment were removed from the dataset. An additional cleaning step was applied to the dataset in order to omit data with inconsistent positions between the location of the DFAD deployment recorded in the logbook or observer database, and the actual position recorded by the buoy (0.3% and 0.8% of the dataset in Atlantic and Indian Oceans respectively). The cleaned dataset of newly deployed DFADs included 9118 trajectories with 498,276 presence/absence data points for the IO and 285 trajectories with 18,102 presence/absence data points for the AO (Figure 1).

Soak time and colonization time

Soak time was defined as the number of days between the deployment of a DFAD equipped with a buoy and the first reported operation on it (i.e., either a fishing set or the retrieval of the buoy). Tuna colonization time refers to the number of days between the deployment of a DFAD and the first day when a tuna aggregation is detected by the echosounder buoy (Figure 2). The term "colonized DFAD" thus refers to a DFAD that has aggregated tuna at least once (for longer than one day).

Due to fishing and buoy retrievals, the number of buoys at sea available for the analysis declined for increasing soak times. This can induce bias in the estimate of tuna colonization times obtained from simple averages (Figure 3). Specifically, the lower the number of DFADs with long soak times, the lower the chances of observing long colonization times, which leads to an underestimate of colonization times from simple arithmetic averages. To overcome this bias, colonization times were estimated from daily colonization rates, considering the daily fraction r i of colonized DFADs relative to the total available DFADs, for each day i after deployment, see (Eq.1):

𝑟 𝑖 = 𝑁 𝑐𝑜𝑙𝑜𝑛𝑖𝑧𝑒𝑑 𝑖 𝑁 𝑐𝑜𝑙𝑜𝑛𝑖𝑧𝑒𝑑 𝑖 + 𝑁 𝑢𝑛𝑐𝑜𝑙𝑜𝑛𝑖𝑧𝑒𝑑 𝑖 (Eq.1)
Where, Ncolonizedi indicates the number of DFADs colonized during day i after deployment and Nuncolonizedi denote not-yet-colonized DFADs on day i after deployment. The denominator of (Eq.1) corresponds to the total number of DFADs available for colonization on day i, namely, the total number of DFADs in the water that at day i-1 after deployment were not yet colonized.

Mann-Whitney U tests, were used to compare daily colonization rates between the IO and the AO. The unbiased mean colonization time (𝑇 𝑐𝑜𝑙 ) (in days) was then estimated as the inverse value of the average of daily colonization rates (𝑟̅ ):

𝑇 𝑐𝑜𝑙 = 1 𝑟 ̅ (Eq.2)
where 𝑟̅ denotes the average daily colonization rate:

𝑟̅ = 1 𝐷 ∑ 𝑟 𝑖 𝐷 𝑖=1 (Eq.3)
where D represents the total number of days during which the daily colonization rates ri were calculated. When numbers of available DFADs were too low (i.e., the denominator in (Eq.1)), the daily colonization rate becomes less reliable. A preliminary sensitivity analysis, included in the Supplementary Material S1 (Figure S1.2), showed that D corresponds to the number of days after deployment when at least 30 DFADs remained available for colonization.

Aggregation stability

The continuous residence time (CRT) is commonly used to represent the amount of time spent by acoustically-tagged individual tunas around a FAD without a day scale (>24h) absence [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] Capello | A methodological framework to estimate the site fidelity of tagged animals using passive acoustic telemetry[END_REF]. Alternatively, the continuous absence time (CAT) refers to the time interval between two consecutive associations for an individual tuna [START_REF] Robert | Size-dependent behavior of tuna in an array 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]. In this work, the concepts of CRT and CAT were adapted and applied to DFAD aggregations rather than to individual fish. Accordingly, the aggregation's continuous residence time at a floating object (FOB-aCRT) was considered as the time span within which a tuna aggregation was continuously detected at a DFAD without a day scale (>24h) absence. Similarly, the continuous absence time of aggregation at a floating object (FOB-aCAT) was defined as the period between two consecutive detections of tuna aggregations at the same DFAD. Values occurring directly before an operation on the DFAD (fishing event or retrieval of the buoy) were excluded from the analysis as they were artificially truncated. Finally, the overall proportion of time that a tuna aggregation remained at a colonized DFAD (named DFAD occupancy rate), expressed as the ratio of the sum of all FOB-aCRTs against its soak time after the colonization period, was assessed and compared between oceans using Mann-Whitney U tests.

Survival analyses of FOB-aCRT and FOB-aCAT

Survival analyses (e.g. [START_REF] Capello | A methodological framework to estimate the site fidelity of tagged animals using passive acoustic telemetry[END_REF] were used to characterize the distribution of FOB-aCATs and FOB-aCRTs. Survival curves were constructed using the fraction of FOB-aCATs and FOB-aCRTs shorter than a given time, and compared between oceans using the logrank statistical test [START_REF] Harrington | A class of rank test procedures for censored survival data[END_REF], implemented in the "survival" package in R [START_REF] Therneau | A Package for Survival Analysis in S. Version 2[END_REF].

Survival curves were also fitted using three models: (i) single exponential, (ii) double exponential and (iii) power law (Supplementary Material S1: Table S1.3), by adapting the methodology of [START_REF] Robert | Intra-individual behavioral variability displayed by tuna at fish aggregating devices (FADs)[END_REF] to the DFAD aggregation metrics. Exponential models assume association dynamics (presence or absence of an aggregation at a DFAD) to be independent of time. Double exponential models imply the existence of two distinct time-scales occurring within aggregation presence or absence at a DFAD. Power law models indicates a time-dependent probability of presence and absence of tuna aggregations, meaning the longer the time a DFAD is occupied or vacant, the smaller the probability that a change in state will occur. Models were discarded if one or more parameters were not significant (p > 0.05 based on the t-statistics). The best-fitting models were chosen based on the Akaike Information Criterion (AIC) and q-q plots.

Results

Daily colonization rates and colonization times

No significant difference was found between DFAD soak times from the AO and the For colonized DFADs, the time before the echosounder buoy detected the first aggregation of tunas averaged 13.17 days (SD 12.37 days) in the AO and 20.22 days (SD 20.83 days) in the IO. Stable trends in daily colonization rates were observed in both oceans (see Figure 3). The average daily colonization rates were significantly higher (Mann-Whitney U test, p < 0.001) in the AO (𝑟̅ = 0.062, SD 0.037) than in the IO (𝑟̅ = 0.025, SD 0.011). Calculating the unbiased average colonization times following Eqs. (1-3) resulted in colonization times that were 2.5 times shorter in the AO (Tcol = 16.10 days, SD 9.66 dayssee Table 1) than in the IO (Tcol = 40.46 days, SD 17.31 dayssee Table 2).

Aggregation continuous residence (FOB-aCRT) and absence times (FOB-aCAT)

A total of 15,415 FOB-aCRTs and 13,328 FOB-aCATs events were recorded during the course of the trajectories of newly deployed DFADs in the IO. In the AO, 723 FOB-aCATs and 779 FOB-aCRTs were recorded. Distributions of FOB-aCATs and FOB-aCRTs in both oceans are

shown in Figure 4. The average duration of tuna aggregations was 8.96 days (SD 11.52) around DFADs in the AO and 6.20 days (SD 6.86) in the IO. It should be noted that very long continuous residence times of tuna aggregations under the same DFAD were also observed in both oceans (96 and 109 days, in the AO and IO respectively). The average time that DFADs remained vacant between two consecutive tuna aggregations (FOB-aCAT), was 5.38 days (SD 6.01 days), with a maximum duration of 86 days in the AO, and at 8.84 days (SD 10.93 days), with a maximum of 119 days in the IO (Table 1 andTable 2).

Inter-ocean comparisons of FOB-aCAT and FOB-aCRT survival curves indicated significant differences in the associative dynamics of tuna aggregations (logrank test, p < 0.001 for both FOB-aCAT and FOB-aCRT ocean-comparisons -Figure 5).

In the IO double exponential models were the best fitting for survival curves of both FOB-aCATs and FOB-aCRT. Short-term residences represented 94% of the FOB-aCRTs with a mean duration of 4.58 days, while long-term residences represented 6% with a mean duration of 20.18 days. Short-term absences lasted an average of 4.43 days (representing 66% of FOB-aCATs), while long-term absences had a mean duration of 15.45 days (34% of FOB-aCATs).

In the AO, a double exponential model was the best fit for the survival curve of FOB-aCRTs with averages of 3.75 days (62% of FOB-aCRTs) and 15.70 days (38% of FOB-aCRTs) for short and long-term residence times, respectively. Conversely, a single exponential model was the best fit for absence times of tuna aggregations at DFADs with a mean duration of 4.30 days (see Table 3 and Figure 6).

DFAD occupancy rate

Significant differences in the proportion of time that colonized DFADs were occupied by tuna were observed between the two oceans (Mann-Whitney U tests p < 0.001). After colonizing DFADs, in the AO tuna aggregations were detected for an average of 63.27% (SD 19.86%) of the soak time (Figure 7A), while in the IO, this figure was 45.45% (SD 21.73%) (Figure 7B).

Discussion

This work aimed at characterizing the dynamics of the tuna aggregation processes around DFADs, using acoustic data collected by commercial echosounder buoys on newly deployed DFADs in the IO and AO. To date, very few studies have designed scientific protocols to quantify the time that pelagic species take to colonize newly deployed DFADs. The only previous documented observations in the Atlantic Ocean come from [START_REF] Bard | Les épaves artificielles comme auxiliaires de la pêche thonière en océan Atlantique : quel avenir ?[END_REF], who reported rapid colonization by tunas, ranging from 1 hour to 6 days, through the monitoring of a dozen newly deployed DFADs and detecting tuna presence by visual observations, on-board echosounders, or by fishing sets. Their estimates are significantly shorter than ours for the same ocean (average of 16 days); however, interpretation of these discrepancies is complicated by the large differences in methods and the time when the studies were conducted. The Bard et al.

study was performed before the development of the FAD-fishery, when tropical tuna stocks were only moderately exploited. Furthermore, their observation protocol could not identify whether observed individuals only visited or remained associated with the DFAD. Ocean and suggested that tunas begin to aggregate approximately 13 days after deployment. At three times longer, the findings of the current study (an average of about 40 days in the IO)

appear to be more aligned with the knowledge of purse seine skippers (Moreno et al., 2007b).

The discrepancy between these acoustic studies may be related to (i) differences in methodological approaches applied in the conversion of acoustic data into indicators of presence or absence of tuna, (ii) the method used in the current study to estimate colonization times, which avoids possible underestimation biases linked to the large variability in DFAD soak times, or (iii) from the differences in the specificities of the buoy models used in each study. Since their introduction into the fishery, echosounder buoys have evolved rapidly, through continuous technological innovations in both hardware and software [START_REF] Lopez | Evolution and current state of the technology of echo-sounder buoys used by Spanish tropical tuna purse seiners in the Atlantic, Indian and Pacific Oceans[END_REF]. Thus, the intrinsic performance of buoys for detecting tuna aggregations may differ by model and/or manufacturer. Hardware and software differences in the design of buoys may lead to variable thresholds for the detection of aggregations, which could ultimately result in biases in the detection of small aggregations for some models. Such disparities highlight the critical need for a detailed assessment of the reliability of outputs from the different models of buoys and the accuracy of the data processing methods they use to estimate fish abundance. This is especially important when considering the growing use of echosounder buoy data for scientific purposes [START_REF] Moreno | Fish aggregating devices (FADs) as scientific platforms[END_REF].

Until now, most scientific knowledge on the behaviour of tunas around floating objects stems from observations of individuals, using electronic tags, with the majority of studies focused on anchored FADs (e.g. [START_REF] Holland | Horizontal and vertical movements of yellowfin and bigeye tuna associated with fish aggregating devices[END_REF][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]Dagorn et al., 2007a;[START_REF] Mitsunaga | Association of early juvenile yellowfin tuna Thunnus albacares with a network of payaos in the Philippines[END_REF][START_REF] Robert | Intra-individual 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]. By exploiting the potentially massive data source that echosounder buoys on DFADs represent, this work introduces two novel metrics (FOB-aCAT and FOB-aCRT), providing descriptive elements of DFAD use by entire tuna aggregations. It is particularly interesting to note that, in both oceans, the time taken for tunas to colonize new DFADs was significantly longer than durations between consecutive tuna aggregations (average FOB-aCATs: 9 and 6 days in AO and IO respectively). This result is consistent with previous assertions regarding the role of non-tuna species in the tuna colonization process. Several authors have suggested that the colonization of FADs is a sequential process starting with the arrival of non-tuna species, which may play a key role in the attraction or retention processes of tunas [START_REF] Deudero | Fish communities associated with FADs[END_REF][START_REF] Castro | A general theory on fish aggregation to floating objects: An alternative to the meeting point hypothesis[END_REF][START_REF] Nelson | Marine fish assemblages associated with fish aggregating devices (FADs): Effects of fish removal, FAD size, fouling communities, and prior recruits[END_REF]Moreno et al., 2007b;[START_REF] Taquet | Behavior of dolphinfish (Coryphaena hippurus) around drifting FADs as observed from automated acoustic receivers[END_REF][START_REF] Macusi | Local Ecological Knowledge (LEK) on fish behavior around anchored FADs: the case of tuna purse seine and ringnet fishers from Southern Philippines[END_REF]. The duration of the settlement stage of these pioneer communities could be one of the major factors driving the colonization time of tunas at a new DFAD. As such, colonization time may be viewed as a unique type FOB-aCAT with an extended duration due to the requisite maturation phase of the DFAD. Further studies on interspecific relationships would be of major benefit for improving our understanding of the role played by non-tuna species in the aggregative processes of tunas with DFADs.

A review of the main findings from electronic tagging studies on the associative behaviour of tunas under DFADs reveals that the continuous residence time of individual tuna (CRT) is subject to a degree of variability related to the species or the oceanic region under consideration (see Table 4). Off the coast of Guinea in the Atlantic Ocean, [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] estimated average CRT values of 9 and 19 days, for skipjack and yellowfin tuna respectively. For bigeye tuna the reported CRTs were up to 25 days, which is longer than observations from other oceans. Shorter CRTs (about 1 day on average) were observed for the same three species by Dagorn et al., (2007b) in the Western Indian Ocean. However, these results are likely to be underestimated due to artificial truncation of the observation experiments. [START_REF] Govinden | Behaviour of tuna associated with Drifting Fish Aggregating Devices (FADs) in the Mozambique Channel, IOTC-2010-WPTT-25[END_REF] reported residence times ranging from 4 to 10 days (median values) depending on the tuna species, at DFADs monitored in the Mozambique Channel. In Eastern Pacific Ocean, studies carried out by [START_REF] Matsumoto | Behavior of skipjack tuna (Katsuwonus pelamis) associated with a drifting FAD monitored with ultrasonic transmitters in the equatorial central Pacific Ocean[END_REF] and [START_REF] Matsumoto | Comparison of the behavior of skipjack (Katsuwonus pelamis), yellowfin (Thunnus albacares) and bigeye (T. obesus) tuna associated with drifting FADs in the equatorial central Pacific Ocean[END_REF], both indicated that individual tunas remain associated with DFADs for less than 7 days. Despite this variability, tuna CRTs reported by this limited number of tagging studies appear to be lower or equal to the average FOB-aCRTs obtained in this work (9 and 6 days in the AO and the IO, respectively), especially for skipjack tuna which is the dominant species in DFAD-associated catches [START_REF] Dagorn | Is it good or bad to fish with FADs? What are the real impacts of the use of drifting FADs on pelagic marine ecosystems?[END_REF].

Survival analyses of the FOB-aCRTs indicated the coexistence of two distinct modes of DFAD association by tuna aggregations: a dominant mode consisting of short durations, and a longer residence mode. Nearly all of the FOB-aCRTs measured in the IO belonged to the short-term residence mode, whereas the two modes occurred in more similar proportions in the AO. There are several possible explanations for the occurrence of these different modes and their interocean variation. Individually, bigeye and yellowfin tuna generally exhibit longer residence times than skipjack tuna, as indicated by the tagging studies mentioned above. Long-term residence modes may therefore reflect aggregations with a large proportion of the two former species. Furthermore, this study was conducted at a broad spatial and temporal scale. As such, it is possible that the observed differences in modes could be a result of behavioural patterns of tuna that are driven by local environmental differences (such as prey or conspecific abundance, or densities of floating objects) between seasons or oceanic regions. The long-term residence mode could also be indicative of the occurrence of turnover processes of schools at the same DFADs as reported by [START_REF] Weng | Fine-scale vertical and horizontal movements of juvenile yellowfin tuna (Thunnus albacares) associated with a subsurface fish aggregating device (FAD) off South-western Taiwan[END_REF]. Further spatially constrained analyses combined with electronic tagging studies, conducted on DFADs equipped with echosounder buoys, will be crucial to relate the individual and the collective dynamics of tuna around DFADs.

The associative behaviour of the tuna population implies that, at any given time, the overall abundance in an area is the sum of the abundance of two permanently interacting components:

the associated and the free-swimming (or unassociated) populations. At present, the underlying reasons driving the association or departure of tunas from floating objects remain unclear.

Nevertheless, an improved understanding of the interactions between the two population components can be achieved through the study of the relationships between the association metrics assessed at the scale of the individual (i.e. CAT and CRT) and at the scale of aggregations (FOB-aCAT and FOB-aCRT). [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] suggested that high FAD densities tend to reduce the time that tuna spend in an un-associated state (CAT). While these findings may need to be interpreted with caution as they stem from observations at anchored FADs, this could suggest that the underlying trend may occurs irrespective of the FAD type. Logically, higher FAD densities would increase the probability of an individual encountering and associating with a FAD, hence reducing the time individual tuna spend in a free-swimming state (CAT). Similarly, FAD vacancy (FOB-aCATs) should be related to the abundance of the un-associated tuna population. Long FOB-aCATs would result when the unassociated population is small, either due to a low overall tuna population or a large density of FADs drawing them in to aggregate. Following this reasoning, the longer FOB-aCAT and colonization time observed in the IO may thus be indicative of a smaller size of the tuna population and/or higher densities of DFADs in this ocean than in the AO. Furthermore, the double exponential curve for FOB-aCATs observed in the IO, could be a result of regions/periods where at least one of these two factors differ. Previous work by [START_REF] Capello | Population assessment of tropical tuna based on their associative behavior around floating objects[END_REF] demonstrated that indicators of abundance for tropical tuna populations could be derived from their individual associative dynamics (CRT and CAT). Combining our current understanding of the individual associative behaviour of tunas with the metrics describing tuna aggregation dynamics provided by this work could aid in developing new methods for obtaining direct abundance estimates of tuna populations. Such methods will depend upon the availability of estimates of the total number of DFADs at sea (more specifically the total number of floating objects). Currently, obtaining these statistics is a challenge in all oceans despite the recent data reporting requirements for DFAD activities by Tuna Regional Fisheries Management Organisations (t-RFMOs).

Conclusion

Using data from the echosounder buoys of French purse seiner fleets, this study characterized key parameters of tuna aggregations at DFADs: colonization times, aggregation lifetimes and time span between aggregations. In both oceans, lifespan of tuna aggregations at DFAD followed a time-independent process with two modes. This suggests that the species composition and/or the local conditions (e.g. prey, conspecifics or density of floating objects) could play key roles in aggregation dynamics. However, opposing trends also existed between the two oceans, with shorter residence time of aggregations and longer periods of DFAD vacancy in the IO than in the AO. Further spatially restricted analyses assessing these behavioural metrics at smaller spatial and temporal scales could help in understanding the dynamics of aggregations at a local scale, as well as the role played by various environmental factors. The integration of these new findings into population assessment models which account for the associative behaviour of tunas present an opportunity for the development of alternative abundance indices (independent from catch and effort data) for tropical tunas and the construction of reliable scenarios on the impacts that DFADs have on tuna populations.

Figure 1 :

 1 Figure 1: Presence/absence of tuna aggregations along the course of the trajectories of newly deployed DFADS monitored in Western Indian Ocean and Eastern Atlantic Ocean from 2016 to 2018. Orange dots indicate days when tuna aggregations were present, white dots represent days with no tuna aggregations.

Figure 2 :

 2 Figure 2: Schematic representation of the timeline of tuna aggregation dynamics at a DFAD.The term "end of trajectory" denotes here the first operation carried out on FADs likely to affect the aggregation (e.g. either a fishing set or the retrieval of the buoy).

Figure 3 :

 3 Figure 3 : Daily colonization rates (bars) and percentage of equipped DFADs available (solid lines) over time in the Atlantic Ocean (Panel A) and the Indian Ocean (Panel B). Red dashed lines indicate the number of days after deployment at which 30 DFADs were still available.

Figure 4 :

 4 Figure 4: Distribution of FOB-aCATs (left) and FOB-aCRTs (right) in the Atlantic Ocean (top) and Indian Ocean (bottom). FOB-aCRT and FOB-aCAT denote the aggregation's continuous residence time at a floating object and the continuous absence time of aggregation at a floating object, respectively.

Figure 5 :

 5 Figure 5: Survival curves of FOB-aCRTs (Panel A) and FOB-aCATs (Panel B) recorded on trajectories of newly deployed DFADs in Atlantic Ocean (black dots) and Indian Ocean (white dots). The y-axis is on a logarithmic scale. FOB-aCRT and FOB-aCAT denote the aggregation's continuous residence time at a floating object and the continuous absence time of aggregation at a floating object, respectively.

Figure 6 :

 6 Figure 6: Survival curves of FOB-aCAT (left) and FOB-aCRT (right) the observed in Atlantic Ocean (top) and Indian Ocean (bottom) fitted with single exponential, double exponential and power law models. The red line indicates the best fit. FOB-aCRT and FOB-aCAT denote the aggregation's continuous residence time at a floating object and the continuous absence time of aggregation at a floating object, respectively.

Figure 7 :

 7 Figure 7: Distribution of the DFAD occupancy rates in the Atlantic Ocean (Panel A) and the Indian Ocean (Panel B).

Table 1 .

 1 Summary of tuna aggregation metrics measured in the Atlantic Ocean.

	Tables
		Min.	Max.	Median	Mean	Standard deviation
	DFAD Soak time (days)	1	305	44	63.28	65.08
	Daily colonization rate (days -1 )	0	0.15	0.06	0.06	0.04
	Tuna colonization time (days)	-	-	-	16.10	9.66
	FOB-aCAT (days)	2	86	4	5.38	6.01
	FOB-aCRT (days)	2	96	4	8.96	11.52
	Occupancy rate (%)	5.13	97.59	60.49	63.27	19.86

Table 2 .

 2 Summary of tuna aggregations metrics measured in the Indian Ocean.

		Min.	Max.	Median	Mean	Standard deviation
	DFAD Soak time (days)	1	363	43	54.24	45.52
	Daily colonization rate (days -1 )	0	0.07	0.02	0.02	0.01
	Tuna colonization time (days)	-	-	-	40.46	17.31
	FOB-aCAT (days)	2	119	5	8.84	10.93
	FOB-aCRT (days)	2	109	4	6.20	6.86
	Occupancy rate (%)	2.83	98.08	46.16	45.45	21.73

Table 3 :

 3 Summary of the model fits of the survival curves of aggregation continuous residence and absence times (FOB-aCRTs and FOB-aCATs) obtained in Atlantic and Indian Oceans. , Est = parameter estimate, Std. Error = standard error, t-value = value of t-statistic, Pr(> |t|) = pvalue at t-tests and AIC = Akaike Information Criterion. AIC values of the best-fitted models are highlighted in bold.

	Significance codes: *** = 0; ** = 0.001; * = 0.01; .= 0.05
	Ocean	Metric	Fitting law	Parameter	Estimate	Std. Error	t-value	Pr(>|t|)		AIC
			Single exponential	a	0.14	3.61E-03	38.35	6.92E-42	***	-217.80
		FOB-aCRT	Double exponential	a b p	0.27 0.06 0.62	8.51E-03 2.13E-03 1.89E-02	31.29 29.95 33.03	2.75E-36 2.58E-35 1.71E-37	*** *** ***	-416.09
	Atlantic		Power law	a b	2.29 11.73	7.19E-02 5.11E-01	31.87 22.94	3.87E-37 7.76E-30	*** ***	-389.71
	Ocean		Single exponential	a	0.23	5.03E-03	46.16	7.42E-31	***	-154.98
		FOB-aCAT	Double exponential	a b p	0.24 0.03 0.98	1.24E-02 6.18E-02 3.24E-02	19.59 0.43 30.26	1.20E-18 6.68E-01 4.86E-24	*** ***	-155.22
			Power law	a b	22.04 91.78	2.51E+01 1.08E+02	0.88 0.85	3.87E-01 4.03E-01		-153.74
			Single exponential	a	0.20	2.84E-03	69.54	3.63E-69	***	-404.29
		FOB-aCRT	Double exponential	a b p	0.22 0.05 0.94	8.71E-03 1.94E-02 3.37E-02	25.04 2.56 27.90	2.85E-37 1.27E-02 2.42E-40	*** * ***	-426.38
	Indian		Power law	a b	8.49 39.48	2.17E+00 1.10E+01	3.92 3.58	2.00E-04 6.24E-04	*** *	-415.36
	Ocean		Single exponential	a	0.14	2.12E-03	64.29	1.01E-80	***	-471.48
		FOB-aCAT	Double exponential	a b p	0.23 0.06 0.66	3.10E-03 1.11E-03 1.02E-02	72.73 58.30 64.71	1.98E-84 1.34E-75 9.41E-80	*** *** ***	-875.29
			Power law	a b	3.06 17.36	5.51E-02 4.04E-01	55.51 43.01	3.31E-74 4,41E-64	*** ***	-806.27

Table 4 :

 4 Summary of main findings from previous studies on continuous residence time of individual tunas at drifting FADs. (FL: fork length, YFT: Thunnus albacares, SKJ: Katsuwonus pelamis, BET: Thunnus obesus)

	Study	Location	Species	FL range (cm) CRT
			SKJ		Average at 0.91 days (maximum: 7.03 days)
	Dagorn et al., (2007b)	Western Indian Ocean	BET	Not provided	Average at 1.43 days (maximum: 3.06 days)
			YFT		Average at 1.04 days (maximum: 15.22 days)
			SKJ	47 -57	Median at 4.47 days (maximum: 18.33 days)
	Govinden et al., (2010)	Mozambique Chanel, (Western Indian Ocean)	BET	54 -56	Median at 3.89 days (maximum: 6.56 days)
			YFT	29 -60	Median at 9.98 days (maximum: 26.72 days)
	Matsumoto et al., (2014)	Equatorial central Pacific Ocean	SKJ	36 -65	Average at 2.3 days (maximum: 6.4 days)
			SKJ	34.5 -65.0	Average at 1.3 days
	Matsumoto et al., (2016)	Equatorial central Pacific Ocean	BET	33.5 -85.5	Average at 3.8 days (maximum: about 11 days)
			YFT	31.6 -93.5	Average at 4.1 days (maximum 14.5 days)
			SKJ	46 -60	Median at 1 day (maximum: 18 days)
	Scutt et al., (2019)	Western Central Pacific Ocean	BET	37 -90	Median at 10 days (maximum: 30 days)
			YFT	36 -98	Median at 2 days (maximum: 50 days)
			SKJ	39 -61	Average at 9.19 days (maximum value to 15 days)
	Tolotti et al., (2020)	Eastern Atlantic Ocean	BET	45 -61	Average at 25.31 days (maximum value to 55 days)
			YFT	34 -82	Average at 19.15 days (maximum value to 55 days)

Marine Instruments, Nigrán, Spain, www.marineinstruments.es

Acknowledgements

This project was co-funded by the ANR project BLUEMED (ANR-14-ACHN-0002), leadered by MC and the Ob7 -"Observatoire des Ecosystèmes Pélagiques Tropicaux exploités" from IRD/MARBEC. The authors are grateful to ORTHONGEL and its contracting parties (CFTO, SAPMER, SAUPIQUET) for providing the echosounder buoys data. The authors also thank all the skippers who gave time to share their experience and knowledge on the echosounder buoys.

The authors sincerely thank the contribution of the staff of the Ob7 on the databases of the echosounder buoys and observers' data.

Data availability statement

The data underlying this article were provided by Ob7 -"Observatoire des Ecosystèmes Pélagiques Tropicaux exploités" from IRD/MARBEC under data exchange agreement with fishing companies. Data will be shared on request to Ob7 with permission of the owners.

Supplementary Material

The following supplementary material is available at ICESJMS online version of the manuscript