Hélène Gomes

Coralie Kersulec

Luc Doyen

Fabian Blanchard

Abdoul Ahad Cissé

Nicolas Sanz

Abdoul Ahad Cissé

The major roles of climate warming and ecological competition in the small-scale coastal fishery in French Guiana

Keywords: Marine biodiversity, Multi-species, Multi-fleet fishery, Models of Intermediate Complexity (MICE), Climate change, Exclusion principle 1

Marine ecosystems, biodiversity, and fisheries are under strain worldwide due to global changes including climate warming and demographic pressure. To address this issue, many scientists and stakeholders advocate the use of an ecosystem approach for fisheries that integrates the numerous ecological and economic complexities at play rather than focusing on the management of individual target species. However, the operationalization of such an ecosystem approach remains challenging, especially from a bio-economic standpoint. Here, to address this issue, we propose a model of intermediate complexity (MICE) relying on multi-species, multi-fleet, and resourcebased dynamics. Climate change effects are incorporated through an envelope model for the biological growth of fish species as a function of sea surface temperature. The model is calibrated for the small-scale fishery in French Guiana using a time series of fish landings and fishing effort from 2006 to 2018. From the calibrated model, a predictive fishing effort projection and RCP climate scenarios derived from IPCC, we explore the ecosystem dynamics and the fishery production at the horizon 2100. Our results demonstrate the long-term detrimental impact of both climate change and ecological competition on fish biodiversity. The prognosis is particularly catastrophic under the most pessimistic climate scenario, with a potential collapse of both biomass targeted species and fishing activity by 2100.

Introduction

Global changes are exerting significant pressure on marine ecosystems, their biodiversity, and the ecosystem services they provide [START_REF] Butchart | Global Biodiversity: Indicators of Recent Declines[END_REF][START_REF] Österblom | Where and how to prioritize fishery reform[END_REF]. In particular, the rapid development of marine and coastal fisheries since the 1950s in order to ensure food and economic security for human populations increased the number of overfished marine stocks by about 20% worldwide between 1975 and 2015 [START_REF]The State of World Fisheries and Aquaculture 2018-Meeting the sustainable development goals[END_REF]. Climate change introduces new risks, uncertainties, and vulnerabilities and amplifies those already present by altering primary production and fish distribution thus potentially affecting yields [START_REF] Barange | Impacts of climate change on fisheries and aquaculture: synthesis of current knowledge, adaptation and mitigation options. Food and Agriculture Organization of the United Nations[END_REF][START_REF] Sumaila | Climate change impacts on the biophysics and economics of world fisheries[END_REF].

Under these circumstances, designing management tools and public policies that ensure the long-term bio-economic sustainability of marine fisheries has become a pressing challenge. To address this challenge, many scientists and experts advocate the use of ecosystem-based fishery management (EBFM) [START_REF] Fisheries | Ecosystem-Based Fisheries Management Policy[END_REF]. The EBFM approach aims to integrate the ecological and socio-economic complexities of fisheries rather than focusing on individual target species [START_REF] Cochrane | Reconciling sustainability, economic efficiency and equity in fisheries: the one that got away?[END_REF][START_REF] Sinclair | Responsible fisheries in the marine ecosystem[END_REF]. However, the question of how to operationalize EBFM in terms of models, scenarios, quantitative methods, and indicators remains a matter of debate [START_REF] Doyen | Ecoviability for ecosystem-based fisheries management[END_REF][START_REF] Fulton | Ecosystems say good management pays off[END_REF][START_REF] Link | Keeping Humans in the Ecosystem[END_REF][START_REF] Pitcher | An evaluation of progress in implementing ecosystem-based management of fisheries in 33 countries[END_REF][START_REF] Plagányi | Models for an ecosystem approach to fisheries[END_REF][START_REF] Plagányi | Multispecies fisheries management and conservation: tactical applications using models of intermediate complexity[END_REF][START_REF] Sanchirico | An empirical approach to ecosystembased fishery management[END_REF]. The general purpose of this article is to contribute to the operationalization of EBFM.

Of the various ecological and socio-economic complexities underlying EBFM, multispecies dynamics play a particularly important role. Ecopath with Ecosim [START_REF] Christensen | Ecopath with Ecosim: methods, capabilities and limitations[END_REF] and whole-of-ecosystem (or end-to-end) models, such as Atlantis [START_REF] Fulton | Lessons in modelling and management of marine ecosystems: the Atlantis experience[END_REF] can provide important insights and numerical tools to simulate these dynamics based on trophic or ecological competition mechanisms. However, whole-ecosystem models have been criticized for their dependence on exhaustive data [START_REF] Plagányi | Models for an ecosystem approach to fisheries[END_REF] (although Fulton et al. apply a whole-ecosystem model in a data-poor context and suggest that it may be useful in systems that are only slightly fished [START_REF] Fulton | Ecosystems say good management pays off[END_REF]), while Ecopath is constrained by its assumption of equilibrium and mass balance. Models of intermediate complexity (MICE) [START_REF] Plagányi | Multispecies fisheries management and conservation: tactical applications using models of intermediate complexity[END_REF] represent a methodological alternative to these approaches for EBFM. MICE are context and question-driven and aim to limit complexity by focusing only on the components needed to address the management question under consideration. Although they can integrate complex marine ecosystem dynamics with global change, the economic and social processes underlying marine capture fisheries, and their interactions with marine ecosystem services and human well-being, MICE remain simple enough to allow for easy adaptation and facilitate communication between disciplines. MICE maintain the relative simplicity of models currently supporting fisheries management, can be calibrated through standard statistical methods, while also accounting for broader ecosystem considerations within the scope of certain well-defined management objectives. In particular, important bio-economic factors such as multi-fleet dimensions, technical interactions, and joint production in mixed fisheries can be incorporated into MICE (see Doyen et al. [START_REF] Doyen | Ecoviability for ecosystem-based fisheries management[END_REF] and Tromeur & Doyen [START_REF] Tromeur | Optimal Harvesting Policies Threaten Biodiversity in Mixed Fisheries[END_REF]).

Species competition is an issue of fundamental importance in ecology. In that regard, Tilman [START_REF] Tilman | Invasions of equilibria: tests of resource competition using two species of algae[END_REF] has developed a mechanistic model that predicts the outcome of species competition based on the resource requirements of the competing species. He suggests that the species with the lowest resource requirement at equilibrium will displace all other species. This result is known as the 'exclusion principle' [START_REF] Doyen | Mathematics for Scenarios of Biodiversity and Ecosystem Services[END_REF]. Examples of species competition and exclusion principle in fisheries can be found in Daan [START_REF] Daan | A review of replacement of depleted stocks by other species and the mechanisms underlying such replacement [sardine, anchovy, pilchard, herring, blue whiting, mackerel, cod[END_REF] and Botsford [START_REF] Botsford | The management of fisheries and marine ecosystems[END_REF].

Climate is another crucial component of EBFM as the effects of climate change on marine resource dynamics are of key importance (Stock et al. [START_REF] Stock | On the use of IPCC-class models to assess the impact of climate on Living Marine Resources[END_REF], de Lange [START_REF] De Lange | Fishery forced to close as shrimp stocks collapse[END_REF], and Lopes et al. [START_REF] Lopes | Climate change can reduce shrimp catches in equatorial Brazil[END_REF]). Climate change has been shown to have a major impact on ecological processes such as population distribution and population dynamics [START_REF] Parmesan | Ecological and Evolutionary Responses to Recent Climate Change[END_REF][START_REF] Thomas | Extinction risk from climate change[END_REF]. As reproductive success and maturation are temperature-sensitive, climate-related temperature changes have a time-shifted effect on fisheries (depending on growth time to harvest size). This shift is thus tied to the growth rate of the fished species. The best way of integrating this effect in a population dynamics model has been the subject of much debate [START_REF] Cheung | Dynamic bioclimate envelope model to predict climate-induced changes in distribution of marine fishes and invertebrates[END_REF][START_REF] Zhao | Integrated modeling predicts shifts in waterbird population dynamics under climate change[END_REF]. For example, Garza-Gil et al. [START_REF] Garza-Gil | Evaluating the economic effects of climate change on the European sardine fishery[END_REF] incorporate sea surface temperature into several mathematical functions of the natural growth dynamic of sardine biomass as part of a bio-economic model of a European sardine fishery. They then determine the most plausible growth dynamic through statistical testing and calculate projections for future biomass and profits under several climate scenarios. Caballero-Alfonso et al. [START_REF] Alfonso | The role of climatic variability on the short-term fluctuations of octopus captures at the Canary Islands[END_REF] use statistical methods (e.g., Pearson's correlation coefficient, Monte Carlo analysis) to validate a linear relationship between octopus catch and SST in the Canary Islands, highlighting the influence of climate on this fishery. More broadly, Lehodey et al. [START_REF] Lehodey | Climate Variability, Fish, and Fisheries[END_REF] review the current understanding of the impacts of climate variability on fish populations and fisheries, while Brander [START_REF] Brander | Global fish production and climate change[END_REF] and Cheung et al. [START_REF] Cheung | Projecting global marine biodiversity impacts under climate change scenarios[END_REF] argue that, due in large part to their effect on sea temperature, climate change and global warming may be the strongest drivers of stock dynamics and harvest levels in the future. Diop et al. [START_REF] Diop | Maximum Economic Yield Fishery Management in the Face of Global Warming[END_REF] and Lagarde et al. [START_REF] Lagarde | How Does MMEY Mitigate the Bioeconomic Effects of Climate Change for Mixed Fisheries[END_REF] highlight the bio-economic advantages of fishing strategies that account for climate change. Furthermore, tropical fisheries are facing a particularly challenging situation, since biodiversity is projected to decrease with climate warming in tropical ecosystems [START_REF] Cheung | Projecting global marine biodiversity impacts under climate change scenarios[END_REF][START_REF] Cheung | Large benefits to marine fisheries of meeting the 1.5°C global warming target[END_REF].

The specific goal of this paper is to account for driving ecological processes in a fished ecosystem on a medium-to long-term time scale in the perspective of EBFM. Particular attention is paid to the impacts of climate change, competition between fish species, and the fishing efforts of different fleets. This goal also aligns closely with the objectives of the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES) with respect to scenarios of marine biodiversity and ecosystem services [START_REF] Ferrier | The methodological assessment report on scenarios and models of biodiversity and ecosystem services[END_REF]. To this end, we propose a multi-species, multi-fleet dynamic MICE that integrates climate change through an envelope model for species growth as a function of sea surface temperature. The model takes into account both ecological and technological complexities, incorporating biology through resource-based stock dynamics and fishing technology through a joint fishing production function. The model is calibrated for the tropical small-scale fishery in French Guiana using time series of fish landings and fishing effort from 2006 to 2018. From the calibrated model, along with RCP climate scenarios derived from the Intergovernmental Panel on Climate Change (IPCC), as well as a predictive fishing intensity at the horizon 2100, we explore possible long-term ecosystem Figure 1: Map of French Guiana with, in red, legal landing points of the coastal fishery. and fishery trajectories. The IPCC has adopted four climate scenarios, known as Representative Concentration Pathways, based on different greenhouse gas concentration trajectories [START_REF] Pörtner | Special Report on the Ocean and Cryosphere in a Changing Climate. Rationale Reference[END_REF]. Here, we focus on the two extreme scenarios, namely RCP 2.6 and RCP 8.5.

The paper is structured as follows: Section 3 introduces the case study and describes the coastal fishery in French Guiana; Section 4 details the model and scenarios used; Section 5 presents the results, including the scenario trajectories, and a comparitive analysis of scenarios. Finally, Section 6 contains a discussion of the results.

Case study

French Guiana is located in South America, between Suriname and Brazil. Its coastline measures 350 km, and its exclusive economic zone (EEZ) has an area of 130,000 km2, including 50,000 km2 of continental shelf. The coastal fishery in French Guiana is a small-scale fishery, operating in a 16 km offshore zone with depths ranging from 0 to 20 m. In 2010, there were 14 legal landing points distributed all along the territory's coast, with fishing areas concentrated around these points due to the fishing boats' short range [32] (Figure 1).

As of 2018, the fishery is exploited by 153 boats, mostly built of wood (although some are made of aluminium and plastic) and generally less than 12 meters long. Drift nets are the most commonly used equipment across all of the fleets, though some fixed nets are used as well. There are four categories of boats, illustrated in Figure 2, which are known locally as "pirogues" (hereafter denoted as P), "canots créoles" (CC), "canots créoles améliorés" (CCA) and "tapouilles" (T). These four categories differ in size and operate in different ways, as detailed in Table 1.

Over the last two decades, this coastal fishery in French Guiana has been landing approximately 2,000 tons per year. The fishery is non-selective and exploits more than 30 fish species. The most harvested species is the acoupa weakfish (Cynoscion acoupa), followed by the green weakfish (Cynoscion virescens) and the crucifix catfish (Sciades proops), representing an estimated 42%, 18%, and 11%, respectively, of total landings between 2006 and 2018. The French Guiana coastal fishery is particularly important for the territory as it provides employment and contributes to food security.

In the 2010s, the stocks exploited by this small-scale fishery to meet food demand were evaluated as underfished [START_REF] Cissé | A bioeconomic model for the ecosystem-based management of the coastal fishery in French Guiana[END_REF][START_REF] Cissé | Ecoviability for smallscale fisheries in the context of food security constraints[END_REF]. However, the INSEE (French National Institute of Statistics and Economic Studies) estimates that the Guianese population will double over the next three decades [START_REF] Demougeot | La population guyanaise à l'horizon 2050 : vers un doublement de la population?[END_REF], thus increasing future pressure on the coastal ecosystem and fish stocks. Since 2006, observers from the IFREMER Fisheries Information System have been tracking fishing effort (in days at sea) on a daily basis. They also collected daily fishing landing data from almost all of the landing points between 2006 and 2016, and from two-thirds of the landing points from 2017 onwards. 1 Observed sea surface temperature data (SST) are extracted from the NOAA Earth System Research Laboratory website 2 . As the coastal fleets operate at a maximum depth of 20 meters, sea temperature can be considered to be homogeneous throughout the water column. Temperature data are extracted at a resolution of 60km x 60km. Five points in total are examined (their geographic coordinates are given in Appendix A.1)), and the SST used in the model is obtained by computing the mean SST value of each point.

In this study, we focus on the period from 2006 to 2018 and on the three species most heavily exploited by the coastal fishery in French Guiana, representing about 71% of the total landings over this period: the acoupa weakfish (AW) and green weakfish (GW), both of which are predators, and the crucifix catfish (CrC), which is at a lower trophic level. We also focus on the three main categories of boats, namely tapouilles (T), canots créoles (CC), and canots créoles améliorés (CCA), and leave aside pirogues (P), as they represent only 0.3% of total landings. As detailed in Section 4 in the Subsection 4.3, we use catch data for these three species and for the three categories of boats as well as effort data for the three categories of boats to calibrate the model.

Model and scenarios

The model we developed for the fishery is in line with models of intermediate complexity (MICE ; [START_REF] Doyen | Ecoviability for ecosystem-based fisheries management[END_REF][START_REF] Plagányi | Multispecies fisheries management and conservation: tactical applications using models of intermediate complexity[END_REF]). As represented in the conceptual model displayed in Figure 3, the model relies on a multi-stock and multi-fleet discrete time dynamics, accounting for climate impact through sea surface temperature (SST). Multi-species dynamics are largely drawn from the resource-based model [START_REF] Tilman | Invasions of equilibria: tests of resource competition using two species of algae[END_REF]. Uncertainties are captured by the two climate scenarios. The model is calibrated through a least squares regression of fishery catch data.

Multi-stock, multi-fleet dynamics

Fished species are denoted by i = 1, . . . , N while fleets are denoted by f = 1, . . . , F . As under the resource-based model [START_REF] Tilman | Invasions of equilibria: tests of resource competition using two species of algae[END_REF], it is assumed that N fished species compete for a common resource (e.g. shrimps and fishes in the case study), denoted by res, and that no direct trophic interactions occur between these fished species; in other words, there 1 Using data on fish landings for a given effort as well as comprehensive data on fishing effort, IFRE-MER observers are able to extrapolate landings for all boats and landing points on a quarterly basis using the rule of three. During this period, the fishermen made no technical adaptations and installed no new equipment that would have increased fishing power. Therefore, we can assume that the efficiency of the French Guiana fishery remains constant over time.

2 https://www.esrl.noaa.gov/ are no predator/prey mechanism between the fished species3 . The growth of each species is also assumed to depend on SST, denoted by θ. Thus, for every species, at each time step t, the biomass B i (t + 1) depends on the biomass B i (t), the state of the resource B res (t), the temperature θ(t) (with a time lag), and harvesting H i (t), as follows:

B i (t + 1) = B i (t) 1 -M i + G i (t) -H i (t). (1)
with

G i (t) = g i a res,i B res (t)γ i θ(t -τ i ) (2)
In equation ( 1), M i stands for the mortality rate of fish stock i. In the equation (2), representing the resource consumption by fish species i, parameter g i stands for the growth efficiency of i and a res,i is the consumption rate of the predator i on the resource, res (in line with Ecosim formulation [START_REF] Walters | Structuring dynamic models of exploited ecosystems from trophic mass-balance assessments[END_REF]). The term γ i (θ(t -τ i )), based on the species' thermal envelopes together with a time delay τ i , is specified below in equation ( 6). This formula captures climate impact on species growth (see Ainsworth et al. [START_REF] Ainsworth | Potential impacts of climate change on Northeast Pacific marine foodwebs and fisheries[END_REF] and Thompson et al. [START_REF] Thompson | Lagged effects of ocean climate change on fulmar population dynamics[END_REF] regarding time delays).

Catches H i (t) of the fish species i at time t are derived from the harvests H i,f (t) of the different fleets f :

H i (t) = F f =1 H i,f (t). (3)
Catches H i,f (t) of stock i by fleet f at time t are based on the Schaefer production function:

H i,f (t) = q i,f E f (t)B i (t), (4)
where the variable E f (t) represents the fishing effort of fleet f (time spent at sea in the example), and q i,f measures the catchability of stock i by fleet f , that is, the probability that a biomass unit of stock i will be caught by a boat from fleet f during one unit of fishing effort.

The dynamics of the resource stock B res (t) depends on the consumption of this resource by the different fish species, according to the following equation [START_REF] Brock | Optimal Ecosystem Management when Species Compete for Limiting Resources[END_REF][START_REF] Lara | Sustainable Management of Natural Resources: Mathematical Models and Methods[END_REF]:

B res (t + 1) = B res (t) 1 - N i=1 a res,i B i (t) + I(t), (5)
where I(t) corresponds to the external input (source) for this resource. The impact of climate on the resource is not directly taken into account, but temperature affects the consumption of the resource by its predators.

Climate impact

The bioclimatic envelope, also known as environmental niche, is the set of physical and biological conditions suitable for a given species [START_REF] Cheung | Dynamic bioclimate envelope model to predict climate-induced changes in distribution of marine fishes and invertebrates[END_REF][START_REF] Cheung | Projecting global marine biodiversity impacts under climate change scenarios[END_REF]. Bioclimatic envelope models calculate species' preference profiles by linking environmental data with maps of relative abundance of the species on a defined size grid. Candela et al. [START_REF] Candela | Species distribution modeling in the cloud[END_REF] use this type of model to create a Half-Degree Species Environmental Envelope table containing ranges of suitable and preferred temperatures. From this temperature table, we define the biological efficiency for each species i, denoted by γ i (θ), such that efficiency equals 1 when the temperature matches the preferred temperature of the species, while it approaches zero when the temperature is far from this preferred level. The Figure 4 represents the biological efficiency for species i as a function of temperature.In more mathematical terms, the biological efficiency of species i depends on the preferred temperature θ i,opt as follows:

γ i (θ) = exp (θ -θ i,opt ) 2 κ 2 i , (6)
where the constant κ i is defined by:

κ i = θ i,10 -θ i,opt ln(0.1) 1 2 . ( 7
)
Figure 4: Biological efficiency for species i depending on temperature levels θ i,10 , θ i,opt and θ i,90 .

In equation ( 7), the detrimental temperature θ i,10 is the temperature at which biological efficiency equals 10%:

γ i (θ i,10 ) = 10%.
The reference temperatures (θ i,opt , θ i,10 and θ i,90 ) for each species, obtained from the Aquamaps website, are listed in Appendix A.2.

Calibration method

The model for the French Guiana case study was calibrated using data and time series from the IFREMER Fisheries Information System on a quarterly basis, from the first quarter of 2006 to the last quarter of 2017. The parameters estimated in the calibration are the mortality rate M i of each species i, the catchability q i,f of each species relative to each fleet f , the terms of interaction a i,res between the species and the resource, the growth efficiency g i of each species, the initial biomass B i (t 0 ) of each species, at time t 0 = 2006, and the time lag τ i for each species. The calibration is performed by applying the least squares method to fishery catch data. This method consists of minimizing the mean square error between the quarterly observed catches H data i,f and the catches H i,f simulated by the model, as follows:

min M i ;q i,f ;a res,i ;g i ;B i (t 0 );τ i t 1 -1 t=t 0 N i=1 F f =1 (H data i,f (t) -H i,f (t)) 2 , (8)
with t 1 -1 is the last period of data namely the last quarter of 2017.

The nonlinear optimization problem was solved numerically using the scientific software SCILAB. We made particular use of the "optim ga" routine, which relies on an evolutionary (or genetic) algorithm. A genetic algorithm is a search heuristic that mimics the process of natural evolution. This heuristic is routinely used to generate solutions to nonlinear optimization problems. Genetic algorithms belong to a larger class of evolutionary algorithms that use techniques inspired by natural evolution, such as inheritance, mutation, selection, and crossover. In our case, the genetic algorithm performed better than the usual optimization and calibration algorithms. This type of numerical method has already been used for bio-economic purposes in Mardle and Pascoe (2000) [START_REF] Mardle | Use of evolutionary methods for bioeconomic optimization models: an application to fisheries[END_REF], for instance, and for the small-scale fisheries in French Guiana in particular [START_REF] Cissé | A bioeconomic model for the ecosystem-based management of the coastal fishery in French Guiana[END_REF]. The calibration is carried out using both historical fishing catches and effort as inputs; effort data are used as model inputs though equation (4).

Fishing and climate scenarios

From the calibrated model, we calculate projections from current period t 1 = 2018 until T = 2100 to explore potential changes in the fishery, in fish biodiversity, and in the marine ecosystem. Projections are made over a relatively long timeframe in order to better compare both climate scenarios, which in the short term differ only slightly in terms of predicted sea surface temperature 4 . We consider a predictive scenario for fishing activity, denoted by PS, and two contrasting climate scenarios, RCP 8.5 and 2.6, drawn from the latest IPCC report [START_REF] Pörtner | Special Report on the Ocean and Cryosphere in a Changing Climate. Rationale Reference[END_REF]. We still assume SST to be constant over the entire coast.

Predictive fishing scenario, denoted by PS: This scenario simulates fishing effort based on the assumption that the fishery and all of its fleets will maintain their current dynamics. Using a first-order approximation of current fishing-effort trends for the various fleets over the period 2006-2018, the PS runs as follows [START_REF] Doyen | Mathematics for Scenarios of Biodiversity and Ecosystem Services[END_REF]:

E f (t + 1) = E f (t)(1 + δ hist f ), t = t 0 , . . . , T. (9)
In equation ( 9), δ hist f stands for growth rate of fishing effort based on a regression over the historical data. For the case study, the growth rates δ hist f of each fleet are detailed in Appendix A.3. We acknowledge that these effort scenarios are somewhat simplified, as they do not rely on a fishing behavioral model [START_REF] Fulton | Human behaviour: the key source of uncertainty in fisheries management[END_REF] and do not fully account for potential adaptive relationships and redistributions of fleet effort with respect to the future state of stocks. Further discussion of the limitations of the fishing projection in that regard is provided in Section 6.4.

Climate scenario RCP 8.5: This climate scenario is a pessimistic projection proposed by the IPCC. This scenario assumes a mean increase of about 0.95°C in global SST in the near term (2031-2050) and of 2.58°C towards the end of the century (2081-2100) compared to the recent past (1986)(1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005).

Climate scenario RCP 2.6: This scenario relies on an optimistic IPCC projection in which global SST increases on average by about 0.64°C in the near term (2031-2050) and by about 0.73°C at the end of the century (2081-2100) compared to the recent past (1986)(1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005).

For each climatic scenario, the temperature θ(t + 1) at time t + 1 depends on the temperature at time t, θ(t), and the rise in temperature over a given time period (per quarter in the case study), denoted by ∆ ω,t f , where ω represents the scenario and t f the final time:

θ ω (t + 1) = θ ω (t) + ∆ ω,t f . ( 10
)
In Table 2, we report the quarterly rise in temperature as well as initial and midterm conditions, represented as θ ω (2005) and θ ω (2050) for the near term and for the end-of-century, respectively: Resource dynamics: To compute biomass projections for resource B res (t), we assume that the external input I(t) for this resource varies according to a uniform random distribution between its minimum (I low ) and maximum (I high ) calibration values as follows:

I(t) ∼ U(I low , I high ).
Moreover, this uniform distribution is assumed to be independently and identically distributed (i.i.d.).

Results

Calibration of the model

For this paper, we focused on N = 3 fish species (AW, GW, and CrC) and F = 3 fleets (CC, CCA, and T). The estimation of all parameters, including the mortality rate M i of each species i, the catchability q i,f of each species i relative to each fleet f , the terms of interaction a i,res between the species and the resource, the growth efficiency g i of each

(t) = i H i,f (t), the total catch H(t) = f H f (t)
, and the calibrated biomass B i (t) of each stock i. Figure 5 shows the historical and calibrated catch by fleet and by stock as well as the aggregated catch. We can see in the three cases (catch by fleet, catch by stock, and aggregated catch) that the historical values and the calibrated model values are close. Although the historical values show more variability than the estimated ones, the model outputs fit the historical outputs well, capturing major increasing and decreasing trends. The mean relative error in the catch for each fleet f , each species i, and the aggregated catch are computed through equation [START_REF] Cheung | Projecting global marine biodiversity impacts under climate change scenarios[END_REF]:

k = 1 t 1 -t 0 -1 t 1 -1 t=t 0 H data k (t) -H k (t) H k (t) , (11)
with k = f for catch by fleet, k = i for catch by species, and k = ∅ for the aggregated catch. Table 4 shows the results. From the mean relative errors k , 95% confidence intervals, denoted by CI, are computed through the equation:

CI k (t) = [1 -1.96 k , 1 + 1.96 k ]H data k (t). ( 12
)
Furthermore, Figure 6 compares historical and estimated catch by fleet and by species, as well as aggregated catch, throughout the 2006-2018 time series. The proximity of the crosses to the diagonal demonstrates the goodness of fit for the different catches.

A sensitivity analysis was also carried out to evaluate reliability and contribution to the outputs for each calibrated parameter. The method and results are detailed in Appendix A.4. Figure 11 shows limited variation in the aggregated catch, ranging from -10% to 10%. The parameters with the greatest impact were found to be catchability, mortality, growth efficiency, and the value of resource input I. As aggregated catch varies little, we can conclude that the model is stable and the parameters are reliable.

In Appendix A.5, goodness of fit is also assessed in terms of abundance using Catch Per Unit Effort (by fleet), denoted by CPUE, suggesting a satisfactory goodness-of-fit for every biomass. Figure 12 in particular confirms the quality of the calibration.

Projections and scenario outcomes

As explained in Section 4.4, we apply two contrasting climate scenarios for the horizon T = 2100 to the predictive scenario for fishing. The outcomes of the scenarios are measured in both catch and species biomass. Regarding species state, we assume that a species is extinct when its biomass falls below a viability threshold set at 1% of the initial state. RCP 2.6: In the optimistic RCP 2.6 scenario (Figure 7), we can observe that two species become extinct in the long run, namely the AW around year 2034 and the GW around year 2065, in contrast to the third species, CrC, whose biomass remains at high levels until 2100 (Figure 7c). The two species extinctions entail the collapse of AW and GW catch. Consequently, CrC accounts for all catch from 2065 onward (Figure 7b, second row). The growth of CrC fishing leads to a reduction in CrC biomass in the long run (Figure 7, third column). It should also be noted that harvesting by CCA and T increases during the projection period, whereas CC catch decreases (Figure 7b, first row). This is consistent with projected effort (Figure 7a), since the CC effort growth rate δ hist CC is negative, whereas the growth rates for the effort of other fleets (δ hist CCA and δ hist T ) are positive (Appendix A.3). The increase in CCA and T catch despite reduced CrC biomass can be explained by high growth in CCA and T fishing efforts. Finally, it can be seen that the development of CCA and T catch allows for a major increase in the overall harvest of the fishery over the period of the projection (Figure 7b right). RCP 8.5: In the pessimistic climate scenario RCP 8.5, displayed in Figure 8, we can observe a collapse of fish species and harvest in the long run. The collapse of species biomass highlights that an erosion of fish biodiversity may occur. Figure 8b shows extinction of all the three fish species in the long run: in year 2033 for the AW, 2053 for the GW, and 2063 for the CrC. Hence, the catch for each targeted stock as well as the aggregated catch also fall to 0 in the long run (Figure 8a). In this scenario, as captured by Figure 8b (right hand side), resource biomass begins to grow exponentially from 2050 onward because it is no longer consumed by the fish species AW,GW and CrC.

Comparison between RCP 2.6 and RCP 8. of non extinct species among the three species taken into account) and the aggregated catch on a logarithmic scale for both climate scenarios under the PS.

With respect to species state, the largest difference between the two scenarios is predicted for the CrC, which is projected to go extinct under the pessimistic scenario while remaining viable until 2100 under the optimistic scenario. For the two other species, AW and GW, we can observe that the extinctions occur earlier in the pessimistic case than in the optimistic case. Thus, the collapse of fished species under RCP 8.5 is more severe than under RCP 2.6, suggesting a major loss of fish biodiversity under RCP 8.5 as compared to RCP 2.6.

The two extreme climate scenarios also predict vastly different outcomes for fishing production. In the pessimistic scenario, the species extinctions result in a complete collapse of landings and production; whereas, in the optimistic case, fishery production overall persists and even grows thanks to rising of CrC catch.

Analysis in terms of ecological competition and Tilman exclusion

As represented by equation ( 5) in Section 4.1, the fish species compete for a common resource entitled 'res'; this is a situation involving multi-species competition for a limiting factor. Tilman et al. [START_REF] Tilman | Niche tradeoffs, neutrality, and community structure: A stochastic theory of resource competition, invasion, and community assembly[END_REF][START_REF] Tilman | Invasions of equilibria: tests of resource competition using two species of algae[END_REF] investigated this type of ecosystem dynamic and proposed an 'exclusion principle' [START_REF] Lara | Sustainable Management of Natural Resources: Mathematical Models and Methods[END_REF] under which the stock with the lowest resource requirement at equilibrium, denoted by B * res,i , displaces all other stocks. In Table 5, we compute resource stock equilibrium in the long run for each stock i under the RCP 2.6 scenario and given PS fishing effort 5 . 5 We used the level of the resource stock at equilibrium in year 2085 to obtain B * res,i

B * res,i = Mi + F f =1 q i,f E f (t2085)
γi θ(t2085 -τi) giares,i , Table 5 shows that CrC is the species with the lowest resource requirement in 2085. This result is consistent with the trajectories predicted by the model and scenario (PS -RCP 2.6) and plotted in Figure 7c, where the CrC has the highest biomass in 2085 while the two other species are extinct. The finding confirms that the model results are consistent with what would be expected form the exclusion principle. However, it is important to note that this exclusion mechanism depends on sea surface temperature. SST, θ(t 2085 ) = 28.11°C, for this climate scenario in 2085 is indeed closer to θ CrC,opt (= 27, 9°C), the optimal temperature for the CrC, than to θ i,opt temperatures for either the AW (θ AW,opt = 25.94°C) or the GW (θ GW,opt = 27.59°C) (see Appendix A.2). In other words, SST in year 2085 favors CrC dynamics due to its higher biological efficiency γ(θ) at that temperature. Therefore, it is the interplay of climate and exclusion mechanisms that accounts for the extinctions of the AW and GW under climate scenario 2.6.

Different mechanisms may be in play in other parts of the marine environment of French Guiana. For example, Vallée et al. apply the Pecuchet method [START_REF] Pecuchet | Patterns and drivers of fish community assembly in a large marine ecosystem[END_REF] to the continental shelf of French Guiana at a depth of between 20 and 50 meters in order to study the relationship between species richness and functional diversity. Using this method, with t2085 corresponding to the value of the first quarter of the year 2085. The choice of the year 2085 is rather arbitrary. The idea is to consider a relatively distant year in which two species would already be extinct. they describe how the ecosystem is influenced by environmental filtering and competitive exclusion and show that, based on comparisons of functional and taxonomic fish diversity, environmental filtering is a more important driver than competitive exclusion in this region. High ecosystem productivity and the large surface area of the shelf -the two resource dimensions laid out under niche theory [START_REF] Vandermeer | Niche Theory[END_REF] -are the main factors explaining why competition is less important in this system. By contrast, in the coastal area relevant to our study of the coastal fishery, the fish community is more tolerant of large environmental variations, including high fluctuations in salinity from the estuaries. In other words, competition is the most important process in the coastal ecosystem, while environmental filtering is more important on the continental shelf. It would be interesting to investigate the taxonomic and functional diversity of the coastal fish community using the Pecuchet method [START_REF] Pecuchet | Patterns and drivers of fish community assembly in a large marine ecosystem[END_REF] in order to confirm this interpretation.

Interpretation of climate time lags

In this Subsection, we focus on species climate time lags (τ i ), which play a role in ecosystem dynamics (1) through the thermal envelope defined in equation ( 6). These time lag parameters are closely related to the 'resilience' parameter in FishBase 6 . This resilience value, denoted here as t * 2 i , is equal to the minimum time necessary to double the biomass of each species i, and thus indicates species' time to maturity and growth rate. In other words, a low t * 2 means fast growth and a low age at maturity. The 'resilience' values for the three species considered in our case study are reported in Table 6 and compared to time lags τ i . As reproductive success and maturation are temperature-sensitive processes, climate change has a time-shifted effect on fisheries, with the magnitude of the delay dependent on growth time to harvest size. This delay is thus tied to the growth rate. Here, t * 2,i and τ i represent different values, but are correlated. Accordingly, we can see that the parameters given by FishBase are consistent with the time lags τ i identified by the model, since they have the same ranking. In particular, the growth rate of the CrC is higher than that of the AW and GW, and age at maturity is lower for the CrC than for the AW and GW. Consequently, climate change affects the population state of the CrC almost immediately, while it has a delayed impact on the two weakfish species. These results suggest that our model captures the age-structured processes underlying species dynamics. In other words, it paves the way for age-structured models [START_REF] Quinn | Quantitative Fish Dynamics[END_REF].

Discussion

As shown in the previous section, through two model-based scenarios in line with MICE, this paper mainly contributes to the identification of long term harvesting and ecological leading processes for the coastal fishery in French Guiana. By doing this, it gives insights into the EBFM, in particular for tropical coastal fisheries. In this section, we discuss several points relating to the model and results of the paper, namely: the advantages of models of intermediate complexity (MICE) in subsection 6.1; the impact of environmental changes on ecosystem dynamics in subsection 6.2; recommendations for improving the sustainability of the coastal fishery in French Guiana in subsection 6.3; and finally the limitations of the model in subsection 6.4.

The advantages of models of intermediate complexity (MICE)

To operationalize the EBFM, many researchers advocate the use of whole-ecosystem or end-to-end models such as Atlantis [START_REF] Fulton | Human behaviour: the key source of uncertainty in fisheries management[END_REF]. Such models integrate many ecological complexities including trophic web dynamics, climate change together with the economic processes underlying marine fisheries. By contrast, models of intermediate complexity aim to limit complexity. MICEs instead focus only on the components and interactions necessary to address the main effects of the management question under consideration. Plagànyi et al. [START_REF] Plagányi | Multispecies fisheries management and conservation: tactical applications using models of intermediate complexity[END_REF] advocate using MICE for ecosystem modeling and present principles for their application. MICE help to explain the underlying ecological processes for a limited group of populations (typically <10) subject to fishing and anthropogenic pressure, and include at least one explicit representation of an ecological process. Our paper follows this approach toward MICE, as in Cissé et al. and Doyen et al. [START_REF] Cissé | A bioeconomic model for the ecosystem-based management of the coastal fishery in French Guiana[END_REF][START_REF] Doyen | Ecoviability for ecosystem-based fisheries management[END_REF], to develop a model integrating the dynamics of three fished stocks and a resource along with competition interactions, the impact of three fleets harvesting the fish species, and the impact of global warming.

As emphasized in Section 5.1 on calibration results, our model accurately represents the complex multi-species, multi-fleet dynamics that we intend to manage through harvesting strategies. Our MICE contributes to EBFM in several ways: it provides important insights into the role of interspecies competition within the ecosystem, as described in Section 5.3; it captures the detrimental impact of global warming on catch, as detailed in Section 6.2; and, as the species modeled represent around 71% of the total landing, the MICE provides major insights into the sustainability of the coastal fishery in French Guiana.

Environmental changes as a major driver of ecosystem dynamics

As highlighted in the Subsection 5.2, RCP 2.6 entails better performances than RCP 8.5. Indeed, under RCP 2.6, in the long-run, one species remains viable, supporting the fishery, whereas the three species and the global fishing collapse under RCP 8.5. However, it can be noticed that the temporal ranking of species decline is the same for both climate scenario. This collapse in term of species biomass can be in large part explained by the fish species' thermal envelopes and preferred temperatures (θ i,opt ), which vary between species as detailed in Appendix A.2. Indeed, Table 8 shows that the CrC benefits more from high temperatures than do the other two species. In particular, the θ i,opt and θ i,90 temperature thresholds are both higher for the CrC. Furthermore, as quantified by θ i,opt in Table 8 of Appendix A.2, the ranking of the species in term of optimal temperature (i.e., θ AW,opt < θ GW,opt < θ CrC,opt ) matches the sequence of species declines: AW collapses first, followed by GW and then by CrC.

However, although preferred temperature θ i,opt may be the main driver of species extinctions, it is not the only one. The projected SST at the extinction dates, indicated in Appendix A.6, is lower than θ i,90 for the GW in the optimistic climate scenario and for the AW in both climate scenarios, whereas SST is higher than the θ i,90 for the GW and CrC in the pessimistic case. These observations can be explained by the available biomass of the resource. In the climate optimistic case, the biomass of the resource is low, whereas in the pessimistic case resource biomass is high, entailing high food availability for the species in the ecosystem and thus fostering species growth.

These findings illustrate that environmental changes, in this case climate warming, are a major driver of ecosystem dynamics and ecosystem services in the coastal area of the French Guiana. In this region, climate change has a negative impact on both biodiversity and the provisioning ecosystem service (seafood) underpinning fishing activities. This result is consistent with the conclusions of Cheung et al. [START_REF] Cheung | Large benefits to marine fisheries of meeting the 1.5°C global warming target[END_REF], who suggest that an increase in SST in the equatorial area significantly reduces maximum catch potential. In French Guiana, Diop et al. [START_REF] Diop | Maximum Economic Yield Fishery Management in the Face of Global Warming[END_REF] also highlight similar very detrimental impacts of climate warming on the shrimp fishery.

Policy recommendations for French Guiana fishery

The major challenges of this fishery are to meet sustainably the local food demand and to ensure economic security of the territory while preserving the coastal biodiversity. Our study globally emphasizes the interest to operationalize the EBFM to address the challenges, complexities and vulnerabilities of this small-scale fishery [START_REF] Link | Keeping Humans in the Ecosystem[END_REF].

In the 2010s, the small-scale fishery of French Guiana was evaluated as viable [START_REF] Cissé | Ecoviability for smallscale fisheries in the context of food security constraints[END_REF][START_REF] Cissé | A bioeconomic model for the ecosystem-based management of the coastal fishery in French Guiana[END_REF]. However, increasing demographic pressure raises concerns about the sustainability of this fishery, as the INSEE (French National Institute of Statistics and Economic Studies) estimates that the Guianese population will double over the next three decades [START_REF] Demougeot | La population guyanaise à l'horizon 2050 : vers un doublement de la population?[END_REF], placing great strain on marine and coastal resources. Other vulnerabilities for this coastal fishery, as for many other small-scale tropical fisheries, include insufficient data and the lack of effective policies to manage fishery access [START_REF] Garcia | Towards integrated assessment and advice in small-scale fisheries: principles and processes[END_REF]. The present study also points to major vulnerabilities relating to climate change. The results of the pessimistic climate scenario (RCP 8.5) indicate that the coastal fishery could be jeopardized by around 2070, while in the optimistic climatic scenario (RCP 2.6), the coastal fishery would be entirely dependent on one species (the crucifix catfish) from 2080 onward. It should be noted that in the latter scenario, crucifix catfish biomass begins to decrease in 2050, thus questioning the viability of this species after 2100. This highlights a major threat to the long-term viability of the French Guiana coastal fishery as a whole; said differently, the fishery's sustainability seems weak in the face of climate change. The implementation of aquaculture could be a pillar of the policy to address the challenges and vulnerabilities of this coastal fishery by supporting the local seafood production and mitigating the pressure on the coastal fishery. However, in order to have a sustainable aquaculture, the territory has to prepare itself now, by identifying species and areas compatible with aquaculture or training the futures generations for example. The present paper points out that climate change should be strongly integrated in the design of such economic marine activities to be viable.

Furthermore, our paper highlights the key role played by the resource consumed by the fishes species including small fishes and shrimps. In that sense, it is necessary to support the preservation of this resource for instance by limiting the shrimp fishery operating in French Guiana or increasing the minimal mesh size of the coastal fishery to reinforce the selectivity and preserve the small fishes. Moreover, as the resource depends of the state of the environment, it is necessary to preserve the coastal ecosystem as a whole. In that sense all the policies established by the Water Framework Directive have to be applied [START_REF] Communities | Directive 2000/60/EC of the European Parliament and of the Council of 23 October 2000 establishing a framework for Community action in the field of water policy[END_REF]. In particular, in French Guiana, the mangrove is a major resource's habitat and plays a key role of nursery for fish stocks. Thus, the study of its dynamic and policies protecting it in line with EBFM would improve the sustainability of the coastal fishery.

Moreover, our paper shows to what extent environmental change are visible with time lags. In that respect, the design of multi-year management plan could improve the sustainability of this fishery. Thus the management of the coastal fishery based on licenses currently allocated each year by the Fisheries Committee should be adapted. One way to establish multi-year management consists in of developing ecological-economic and EBFM policies based on multi-species Maximum Sustainable Yield (MMSY) [START_REF] Lagarde | How Does MMEY Mitigate the Bioeconomic Effects of Climate Change for Mixed Fisheries[END_REF][START_REF] Tromeur | Optimal Harvesting Policies Threaten Biodiversity in Mixed Fisheries[END_REF], eco-viability [START_REF] Briton | Providing Integrated Total Catch Advice for the Management of Mixed Fisheries with an Eco-viability Approach[END_REF][START_REF] Doyen | Ecoviability for ecosystem-based fisheries management[END_REF] or resilience management [START_REF] Grafton | Realizing resilience for decision-making[END_REF]. These last strategies potentially coping with several constraints (food demand, economic, ecologic, etc) and complex dynamic systems are clearly in line with the EBFM and the challenges of the Guianese coastal fishery. The merits of the different ecological-economic instruments that could be derived from such strategies, including limited numbers of licensed boats, catch quotas or subsidies to foster categories of fleet should be discussed with the local stakeholders.

Limitations of the model

The present paper is a step forward in our understanding of leading processes for the ecosystem and harvesting dynamics of the French Guiana coastal fishery and more globally tropical coastal fisheries. However, many future improvements are of course possible.

The refinement of resource dynamics and the incorporation of trophic interactions between species constitute major potential ecological improvements. The resource variable includes shrimps and other fish species. It would be interesting to decompose this global aggregated resource stock into more detailed stocks. Following Cissé et al. [START_REF] Cissé | A bioeconomic model for the ecosystem-based management of the coastal fishery in French Guiana[END_REF] who suggest that trophic interactions between the main fished species have only a limited impact, we have chosen so far to exclude them from our model. However, a next step of the modeling work could be to account for these trophic interactions for the sake of a more realistic model.

Furthermore, the model in its current form does not allow for other species in the ecosystem to play a more important role in the fishery over the course of the projection period. As we assume that no technical adaptations will be made nor new equipment installed to increase fishing power, we can also assume that the exploitation of a given species will vary with its biomass, itself a function of the species' thermal affinity. Figure 13 in the Appendix A.7 shows biological efficiency for the 13 most-fished species in the coastal fishery in French Guiana, representing around 90% of the total landings. We can observe that the suitable temperature curves of the species included in the model (in red) are similar to those of the other species (in black), suggesting that the species not taken into account in the current model should also be strongly altered by climate warming over the projection period. In other words, these species are not good candidates to replace in term of future catches the three main species we focused on.

With regard to fishing activity, the predictive scenario PS is essentially illustrative. The model assumes that there is no adaptive relationship between future biomass and effort by the fleets of the coastal fishery, and that the fishery will maintain its current dynamics throughout the projection period. This paper is a first step towards a bioeconomic model exploring leading processes for ecosystems under fishing pressure. Going forward, it would be interesting to apply economic scenarios incorporating an adaptive relationship between future biomass and effort; such scenarios would be more accurate and better model the economic performance of the fishery.

Even if the model takes into account the uncertainty through the two climate scenarios, many other uncertainties including observation uncertainty, parameter uncertainty and model structural uncertainty are here neglected. Ongoing works expanding the model and the analysis by accounting for other uncertainties in the framework of 'decision under uncertainty' and 'resilience management' as in Doyen [START_REF] Doyen | Mathematics for Scenarios of Biodiversity and Ecosystem Services[END_REF] or Grafton et al. [START_REF] Grafton | Realizing resilience for decision-making[END_REF] should reinforce the relevance and reliability of the model and the scenarios. Furthermore, our choice of a long temporal horizon (T = 2100) is also open to adjustment. Such a lengthy timeframe clearly compounds the uncertainties underlying ecosystem and fishery dynamics. There may be a need to explicitly account for uncertainties in the model and scenarios through stochastic approaches, as in Doyen [START_REF] Doyen | Mathematics for Scenarios of Biodiversity and Ecosystem Services[END_REF].

Conclusion

This paper illustrates leading processes for the ecosystem and harvesting dynamics of the coastal fishery in French Guiana and for tropical small-scale fisheries in general. Our work contributes in particular to EBFM through two model-based scenarios. These two model-based scenarios combine IPCC climatic scenarios and a predictive fishing strategy with a MICE. Such MICE integrates resource-based multi-species and multifleet components, in which the fish species' growth function depends on climate through SST. The model is validated using time series data over the period 2006-2018.

The projections show alarming outcomes for the future of the fishery. Under the pessimistic climate scenario, the fishery outcome seems catastrophic, as both fish diversity and catch are severely altered. Under the optimistic scenario, the fishery seems to persist by specializing in one species (CrC). These results highlight the importance of limiting the rise in SST and thus the emissions of greenhouse gases. As our model incorporates climate change only in the form of increased SST, and does not consider other effects such as ocean acidification, changes in primary productivity, etc., the impact of climate change could be greater in reality.

Lastly, the paper identifies the exclusion principle as one of the leading biological processes affecting population dynamics in the fishery. Our results show that both the exclusion principle and environmental filtering as a result of climate change are major drivers of population dynamics. Finally the paper underlines the importance of adapting the fishery in order to improve its sustainability. To identify sustainable fishing management, a number of different integrated strategies, such as MMSY (Multi-species Maximum Sustainable Yield) [START_REF] Tromeur | Optimal Harvesting Policies Threaten Biodiversity in Mixed Fisheries[END_REF], MMEY (Multi-species Maximum Economic Yield) [START_REF] Poudel | Do Species Interaction and Stochasticity Matter to Optimal Management of Multispecies Fisheries[END_REF] or Eco-viability, should be applied to the model. Moreover, it may be helpful to expand the model to include other stocks of the marine ecosystem.

A Appendix

A.1 Geographic coordinates of the points used for the SST See Table 7.

A.4 Sensitivity analysis

A sensitivity analysis was carried out to evaluate reliability and contribution to the outputs for each calibrated parameter. To this end, additional simulations were run based on the PS, RCP 2.6, and RCP 8.5 scenarios. Due to the large number of parameters, we simplified the sensitivity analysis for each climate scenario by simultaneously perturbing all of the calibrated parameters of the same category. There were seven categories in total: trophic interactions, catchability, mortality rate, growth efficiency, initial biomass, time lag, and values of I. For each category of parameters, a level of noise ranging from -10% to +10% of the calibrated values was added. Relative differences in average catch per quarter H = 1

t f -t 1 t f t=t 1 F f =1 N i=1 H i,f (
t) were computed for each climate scenario.

Figure 11 displays the sensitivity results for both climate scenarios. These results show that the parameters with the greatest impact, in both cases, are catchability, mortality, growth efficiency, and values of I. With the exception of the time-lag parameter, the relative change in average catch appears to vary more or less linearly with the magnitude of the perturbations, with the absolute value of the slopes ranging from 0.008 to 0.97, indicating the bounds of the marginal effects of the parameters. Since the relative changes are smaller than the magnitude of the perturbations for these parameters, it appears that the effects of these parameters are small. We can see that the impact of the perturbations on trophic interactions, growth efficiency, initial biomass, and parameter I is similar for both climate scenarios: the red and blue lines practically coincide. For the perturbations of the time lag, the graph of the relative change in catch is stepped; time lag is an integer value, so the magnitude of the perturbation has an impact when its value is higher than 1. Finally, we can see that the time lag has a greater effect on relative change in average catch in the RCP 8.5 scenario than in the RCP 2.6 scenario. This is because the temperature increase ∆ ω,t f is higher under RCP 8.5 than under RCP 2.6.

A.5 Comparison of historical and estimated CPUE

As the efficiency of the fishing time of the French Guiana coastal fishery is assumed to be constant between 2006 and 2018, the catch per unit effort (CPUE) can be considered a proxy for abundance [START_REF] Lorance | CPUE abundance indices of the main target species of the French deep-water fishery in ICES Sub-areas V-VII[END_REF]. Since ours is a multi-species, multi-fleet model, we cannot calculate the CPUE for each species. However, we can compute the CPUE for each fleet and for the aggregated catch. Figure 12 compares historical CPUE with the estimated CPUE. The position of the crosses on the diagonal suggests a satisfactory goodness-of-fit for every biomass.

A.6 Sea surface temperatures at extinctions dates of each species for both climate scenario See Table 10. A.7 Biological efficiency for the 13 most-fished species in the coastal fishery in French Guiana.

See Figure 13

Figure 2 :

 2 Figure 2: Pictures of the different categories of boats of the coastal fishery in French Guiana.

Figure 3 :

 3 Figure 3: Conceptual model.

Figure 5 :

 5 Figure 5: Historical (dark blue points) and calibrated (black line) catch by fleet (first row), by stock (second row), and aggregated (last graph) with 95% confidence intervals (dotted black lines) from the first quarter of 2006 to the last quarter of 2017.

Figure 6 :

 6 Figure 6: Comparison of historical and estimated catch in the 2006-2018 time series in terms of catch by fleet (first row), catch by species (second row), and aggregated catch (last graph).

5 :Figure 7 :

 57 Figure 7: Scenario PS for fishing under RCP 2.6: calibrated (black) and projected (blue) trajectories. The first row (a) shows fishing effort by fleet. The second row of (b) shows catch by fleet and the third row of (b) catch by stock, while aggregated catch is displayed at the end of these two rows; the last row (c) represents biomass. The line of black dashes represents the separation between the calibrated and projected trajectories.

Figure 8 :

 8 Figure 8: Scenario PS for fishing under RCP 8.5: calibrated (black) and projected (blue) trajectories. The first row of (a) shows catch by fleet and the second row of (a) catch by stock, while aggregated catch is displayed at the end of these two rows; the last row (b) represents biomass. The line of black dashes represents the separation between the calibrated and projected trajectories.

Figure 9 :

 9 Figure 9: Estimated number of non extinct species among the three species taken into account for RCP 8.5 (red) and RCP 2.6 (blue) under the PS fishing scenario.

Figure 10 :

 10 Figure 10: Aggregated catch on a logarithmic scale for RCP 8.5 (red) and RCP 2.6 (blue) under the PS fishing scenario.

Figure 11 :

 11 Figure 11: Relative change in average catch per quarter H for scenarios RCP 8.5 (red) and RCP 2.6 (blue) as a function of variations in input parameters by 1% increments from -10% to +10%. The baseline is the predictive scenario.

Figure 12 :

 12 Figure 12: Comparison between historical and estimated CPUE in the 2006-2018 time series for CC, CCA, T and aggregated catches.

Figure 13 :

 13 Figure 13: Biological efficiency for the 13 most-fished species in the coastal fishery in French Guiana. The species included in the model are represented by red curves, while the others are represented by black curves.

Table 1 :

 1 Characteristics of each fleet of the coastal fishery in French Guiana

	Characteristics Tapouilles (T) Canots Créoles	Canots Créoles	Pirogues (P)
						Améliorés	(CC)
						(CCA)
	Width			between 3 and	≈ 2 m	≈ 1.5 m	≈ 1 m
				4 m
	Number			≈ 4		3	2	1
	of	fishers
	boarded
	Duration	of	between 8 and	between 4 and	between 2 and	1
	trip (days)		12		8	3
	Engine			Inboard diesel	Outboard	outboard gaso-	outboard gaso-
				engine		gasoline	en-	line engine	line engine
						gine
	% of the total	6%		71.2%	22.5%	0.3%
	landing
	Cooling sys-	Interior	of	≈ 2 custom-	Repurposed	Repurposed
	tem			boat	parti-	built ice holds	refrigerator or	refrigerator or
				tioned off to		freezer	with	freezer	with
				serve as ice		ice inside	ice inside, or
				hold			no	cooling
							system at all

Table 2 :

 2 Quarterly rise in temperature and initial and mid-term conditions for the near term and the end-of-century, for each climatic scenario ω ∈ {RCP 8.5, RCP 2.6}.

	Parameters	RCP 8.5 RCP 2.6
	∆ ω,2050 ( * 10 3 ) (°C) 5.275	3.56
	∆ ω,2100 ( * 10 3 ) (°C) 8.15	0.45
	θ ω (2005) (°C)	27.41	27.41
	θ ω (2050) (°C)	28.36	28.05

Table 3 :

 3 Parameters obtained by the calibration initial biomass B i (t 0 ) of each species i in year t 0 = 2006, and the time lag τ i for each species, are given in Table3.The main outputs of the model include calibrated catch by species H i (t) as defined in equation (3), catch by fleet defined by H f

	Parameters	Acoupa Weak-	Green Weak-	Crucifix Cat-	Resource (Res)
		fish (AW)	fish (GW)	fish (CrC)
	a res,i ( * 10 6 )	2.5	7.6	6.8	/
	q i,CC ( * 10 6 ) (day -1 )	3.3	0.5	1.4	/
	q i,CCA ( * 10 6 ) (day -1 ) 7.3	0.5	1.1	/
	q i,T ( * 10 6 ) (day -1 )	13.2	2	1	/
	M i ( * 10)	0.8	1.4	1.4	/
	g i ( * 10)	1.5	0.6	0.6	/
	B i (2006) (tons)	14, 070	25, 055	12, 866	282, 625
	τ i (months)	12	48	0	/
	species, the

Table 4 :

 4 Mean relative errors on catches

	Parameters Mean relative errors k
	CC	0.173
	CCA	0.143
	T	0.278
	AW	0.179
	GW	0.310
	CrC	0.306
	Aggregated 0.149

Table 5 :

 5 Resource requirement in equilibrium, B

	B * res,i (2085)(ktons) 10,718	1,420	704

* res,i (t) (ktons), for each stock i in 2085

Parameter

Acoupa Weakfish (AW) Green Weakfish (GW) Crucifix Catfish (CrC)

Table 6 :

 6 Minimal time to double, t * 2,i , for each stock i

	Parameters Acoupa Weakfish (AW) Green Weakfish (GW) Crucifix Catfish (CrC)
	t * 2,i	1,4 to 4,4 years	4.5 to 14 years	less than 15 months
	τ i (months) 12	48	0

Table 7 :

 7 Geographic coordinates of each point Temperatures θ i,10 , θ i,opt , θ i,90 used for climate change modelling

	Point Latitude Longitude
	1	5.625	-53.625
	2	5.375	-52.875
	3	5.125	-52.375
	4	4.875	-52.125
	5	4.375	-51.625
	A.2 See

Table 8 Table 8 :

 88 Temperatures θ i,10 , θ i,opt , θ i,90 for each stock i

	Temperature (°C) Acoupa Weakfish (AW) Green Weakfish (GW) Crucifix Catfish (CrC)
	θ i,10	23.56 °C	26.9 °C	27.38	°C
	θ i,opt	25.94 °C	27.59 °C	27.9	°C
	θ i,90	28.32 °C	28.28 °C	28.42	°C
	A.3 Rate δ hist f	used for projected efforts
	See Table 9.

Table 9 :

 9 Rate δ hist

	f	for each fleet

Table 10 :

 10 Sea surface temperatures at extinctions dates of each species for both climate scenario Species RCP 2.6 RCP 8.5 AW t extinction = 2034; SST=27.83°C t extinction = 2033; SST=27.98°C GW t extinction = 2065; SST=28.08°C t extinction = 2053; SST=28.46 °C CrC / t extinction = 2063; SST=28.79°C

In the model proposed for the French Guiana fishery by Cissé et al.[START_REF] Cissé | A bioeconomic model for the ecosystem-based management of the coastal fishery in French Guiana[END_REF], trophic interactions turn out to have a weak influence. Here, we have simplified the model by ignoring trophic interactions between fishes in order to focus on the influence of the environment on population dynamics.

However we are aware that a longer timeframe introduces significant additional uncertainties to the model.

https://www.fishbase.se

This study, including data collection and analyzes, was funded by the IFREMER (Institut Français de Recherche pour l'Exploitation de la Mer; english: French Research Institute for Exploitation of the Sea). It also benefited from the CNRS research project entitled ENTROPIC (Ecological-ecoNomic resilience of TROPIcal coastal eCosystem).

1.

are extracted from the NOAA Earth System Research Laboratory website (https://www.esrl.noaa.