Anastasios Dosis

The effects of redistributive taxation in credit markets with adverse selection

Keywords: Credit Market, Adverse Selection, Taxation, Redistribution, Welfare JEL: D82, D86, H82, H25

This paper studies the effects of redistributive taxation in credit markets with adverse selection and shows that there exists a range of taxes that creates Pareto improvement relative to the (zero-tax) market allocation by increasing aggregate investment. For sufficiently high taxes, an increase in the safe interest rate can be accompanied by an increase in investment.

Introduction

It is well known that adverse selection causes inefficiencies in markets that frequently justify public policy. For instance, loan government-backed guarantee programmes are frequently implemented to facilitate access to credit for small enterprises and start-ups. These programmes encourage banks to lend 5 to entrepreneurs with no collateral or other pledgeable assets by guaranteeing (partial) loan repayment even if an entrepreneur is unable to meet her obligations. The rationale underlying such schemes is that potential credit market $ I am grateful to Motty Perry and Herakles Polemarchakis for their support and guidance. I also thank Theo Diasakos, Peter Hammond and Phil Reny for insightful comments that improved the paper and seminar participants at various theory seminars at the University of Warwick for useful comments. All the remaining errors are mine.

Email address: dosis@essec.com (Anastasios Dosis $ ) frictions confine entrepreneurs with good ideas to enter the marketplace. 1 This paper studies the effectiveness of a simple tax-subsidy scheme that resembles a loan government-backed guarantee programme to boost investment and improve welfare in credit markets with adverse selection.

The market consists of a continuum of entrepreneurs with projects that succeed or fail. A project (or, equivalently, an entrepreneur) can be either high risk or low risk: low-risk projects yield a higher expected return than high-risk projects for the same amount of investment, although high-risk projects yield a higher ex post return in the case of success. The market also consists of competitive banks that inelastically raise funds at an exogenously given safe interest rate and offer loan contracts that specify the level of the loan and the payments of an entrepreneur to the bank in every possible contingency. I examine the effect of a simple budget-balanced, tax-subsidy scheme on equilibrium investment and welfare. The tax-subsidy system is similar to that analysed in [START_REF] Wilson | A model of insurance markets with incomplete information[END_REF], [START_REF] Dahlby | Adverse selection and Pareto improvements through compulsory insurance[END_REF] and Crocker and Snow (1985a,b) in the stylised insurance market of [START_REF] Rothschild | Equilibrium in competitive insurance markets: An essay on the economics of imperfect information[END_REF], and, more recently, in [START_REF] Ghatak | Entrepreneurial talent, occupational choice, and trickle up policies[END_REF] and [START_REF] Scheuer | Adverse selection in credit markets and regressive profit taxation[END_REF] in a credit market. 2 Every entrepreneur pays a specific tax if she succeeds; this tax is redistributed as a lump-sum subsidy, which can be pledged as collateral if an entrepreneur fails. I argue that an alternative interpretation of the tax-subsidy scheme is that of an entirely budget-balanced, loan government-backed guarantee programme. I establish that taxes can lead to Pareto improvement relative to the zero-tax allocation by increasing aggregate investment.

Regarding the literature, related papers are [START_REF] Innes | Investment and government intervention in credit markets when there is asymmetric information[END_REF] and [START_REF] Martin | Adverse Selection, Credit, and Efficiency: The Case of the Missing Market[END_REF], which study different types of policies in models similar to the model studied in the present paper. [START_REF] Innes | Investment and government intervention in credit markets when there is asymmetric information[END_REF] shows how the government can increase welfare by offering subsidised debt contracts. [START_REF] Martin | Adverse Selection, Credit, and Efficiency: The Case of the Missing Market[END_REF] shows that the government can attain Pareto efficiency by establishing a new market in which entrepreneurs can borrow without conditioning their loans. Unlike the present paper, these authors do not consider the effect of taxes on aggregate investment or the combination of interest rate changes and taxation on investment and welfare.

The remainder of the paper is organised as follows. In Section 2, I describe the economy and the tax system; in Section 3, I study the effect of taxation. In Section 4, I provide policy implications.

The economy

Entrepreneurs and banks

A continuum of entrepreneurs of mass one are each endowed with a project.

There are two possible projects: high-risk and low-risk, i = H, L and a set of measures λ of entrepreneurs is endowed with low-risk projects.3 By investing

x in the project, an entrepreneur can realise z i f (x) with probability π i or zero with probability 1 -π i , where

z i > 0 for every i, f (0) = 0, f (x) > 0, f (x) < 0, lim x→0 f (x) = ∞, lim x→∞ f (x) = 0, and π L > π H . 4 Uncertainty is purely idiosyncratic. I further assume that z H > z L and π H z H ≤ π L z L
Notably, when the two projects have the same expected return, the high-risk project is a mean-preserving spread of the low-risk project; when the expected return of the low-risk project is strictly higher than that of the high-risk project, the low-risk project second-order stochastically dominates the high-risk project.

Although this assumption is very common in the credit rationing literature, none of the results rely on it.5 Let

π p = λπ L + (1 -λ)π H
denote the population's "average probability of success". I assume that only the individual state is observable by outsiders and verifiable by a court of law. This assumption rules out equity as a feasible loan contract. Equivalently, it rules out linear or non-linear taxes (see below for more details). Last, I assume that entrepreneurs have no wealth, are risk neutral and do not discount the future.

50

There are at least two profit-maximising banks in the economy that inelastically raise deposits at a (net) risk-free interest rate equal to r. Entrepreneurs apply for a loan contract (x, c) ∈ R 2 + to banks, where x denotes the amount of the loan (henceforth, the loan) and c denotes the transfer from the entrepreneur to the bank if the project fails (henceforth, the collateral). I assume that en-55 trepreneurs are protected by limited liability. Following an application, banks compete in the interest rate they charge, denoted by ρ. The market takes the form of a signalling game, as is extensively analysed in Dosis (2019).

The tax system

Let t denote the net specific tax (tax minus subsidy) an entrepreneur pays if her project succeeds and T denote the subsidy she receives. The tax system is ex post budget balanced, which means that the government simply redistributes wealth. Moreover, the tax system is non-discriminatory (or anonymous) in the sense that every type pays the same specific tax and receives the same lump-sum subsidy regardless of her contract choice. This assumption fits well in environments in which the government is unable to observe the entrepreneurs' contract choices. Suppose that the tax-subsidy scheme is given by (t, T ); following the discussion above, this situation satisfies the following condition:

T = π p 1 -π p t
Because T is uniquely identified for every t, it suffices to solely specify t. 6An alternative, perhaps interesting, interpretation of the tax system is to consider it as a budget-balanced loan government-backed guarantee programme.

According to this interpretation, entrepreneurs voluntarily decide to participate in a scheme in which the government guarantees part of the losses of a loan undertaken if the entrepreneur is unable to fulfil her obligations. In return, an entrepreneur pays a fixed fee, which is equivalent to the specific tax specified above. Loan government-backed guarantee programmes constitute one of the most widespread public policies to encourage entrepreneurship. The objective of these programmes is to encourage banks to lend to small firms that might lack collateral or other pledgeable assets. Variations in loan government-backed guarantee programmes are implemented in the US, the UK, France, Germany and many other countries. The basic principles of loan government-backed guarantee programmes are similar in all countries: the government undertakes any losses that cannot be met by borrowers; borrowers pay an arrangement fee plus a small premium over the market rate. The main discrepancy between the policy studied in this paper and the loan government-backed guarantee programmes that are implemented in practice is that the policy studied in this paper is entirely budget balanced whilst loan government-backed guarantee programmes are mainly publicly funded.

Equilibria 80

Symmetric information

It is perhaps more convenient to study the equilibria of the game by defining allocations. An allocation is a pair of contracts, ((x i , ρ i , c i )) i , one for each type of entrepreneur.

Under symmetric information, competition in the banking sector ensures that entrepreneurs pay actuarially fair interest rates and, therefore, banks earn zero profits in equilibrium. It is only straightforward that in the unique equilibrium under symmetric information, the equilibrium allocation is given by

((x * L , ρ * L , 0), (x * H , ρ * H , 0))
, where for every i, π i ρ * i = x * i , and

f (x * i ) = 1 + r π i z i (1)
The equilibrium (expected) payoff of type i is

U * i = π i z i f (x * i ) -x * i (1 + r) (2)
Consider now a strictly positive tax. Evidently, because the tax is specific, it does not distort the equilibrium levels of investment. The equilibrium payoff of type i as a function of the tax is

U * i (t) = π i z i f (x * i ) -x * i (1 + r) + (1 -π i ) π p 1 -π p -π i t (3)
Given that π H < π p < π H , the payoff of the high-risk type is strictly in-85 creasing in t, while the payoff of the low-risk type is strictly decreasing in t; the high-risk is simply cross-subsidised by the low-risk type through the tax-subsidy scheme.

Asymmetric information

As shown in [START_REF] Dosis | Signalling, productivity and investment[END_REF], the equilibrium allocation is the least-cost separating (LCS) allocation. As is well known, in the LCS allocation, high-risk types face no distortion relative to the symmetric information equilibrium; lowrisk types' loans are distorted such that they are no longer desired by high-risk types. The low-risk type's level of investment xL in the LCS allocation is the [low-risk type's] payoff-maximising solution to the following equation:

z H f (x * H ) - x * H (1 + r) π H = z H f (x) - x(1 + r) π L , (4)
which represents the binding incentive constraint of the high-risk type. Do-90 sis (2019) shows that this equation has two solutions, and the solution that maximises the payoff of the low-risk type is such that xL < x * H : in the LCS allocation, the low-risk type is restricted by the incentive constraint and unable to raise as much capital as she would raise under symmetric information.

The following proposition characterises the effect of taxation on the LCS 95 allocation.

Proposition 1. For a sufficiently low t, the equilibrium allocation is given by

((x L (t), ρL (t), π p 1 -π p t), (x * H , ρH (t), cH (t))),
where

π H ρH (t) + (1 -π H )c H (t) = x * H (1 + r) π L ρL (t) + (1 -π L ) π p 1 -π p t = xL (t)(1 + r) z H f (x L (t))- xL (t)(1 + r) π L = z H f (x * H )- x * H (1 + r) π H + (1 -π H ) π H - (1 -π L ) π L π p 1 -π p t (5) and cH (t) ≤ π p 1 -π p t
The low-risk type uses the entire subsidy as collateral, although this does not necessarily imply that her payoff is higher after taxation than before taxation.

All Proposition 1 states is that in a specified interval of taxes, the low-risk type strictly prefers using the subsidy as collateral to borrow more rather than consuming it. By implicitly differentiating (5) with respect to t, one obtains the following:

dx L dt = (1-π H ) π H -(1-π L ) π L π p 1-π p t z H f (x L (t)) -(1+r) π L
which is strictly positive. Therefore, investment is strictly increasing in the tax because the subsidy relaxes the high-risk type's incentive constraint and allows the low-risk type to borrow more. The payoff of the low-risk type in the equilibrium allocation as a function of the tax is written, for notational convenience, as

ŪL (t) = π L z L f (x L (t)) -x L (t)(1 + r) + (1 -π L ) π p 1 -π p -π L t (6)
Given that the production function is strictly concave, ŪL (t) is also strictly concave in t; this is the first part proven in Proposition 2. The question of interest then boils down to whether ŪL (t) has an interior maximum. Proposition 2 states that there is indeed a threshold in the average probability of success π p L min , such that, for any π p ≥ π p L min , U L (t) has an interior maximum. The strict concavity of ŪL (t) implies that there is a closed interval of taxes that increase the payoff of the low-risk type after taxation. Proposition 2 formalises the discussion above. Taxation entails two countervailing effects for low-risk types. The negative effect is a consequence of cross-subsidisation; the positive effect is due to the relaxation of the incentive constraint of high-risk types that allows low-risk types to approach their symmetric information investment level. When the share of low-risk types is sufficiently high, the latter effect dominates and, consequently, low-risk types benefit from the tax system.

One interesting question is to examine the effect of interest rate changes on investment and welfare for a given tax. One can find the impact of an interest rate change on investment by implicitly differentiating (5)

dx L (t) dr = xL (t)/π L -x * H /π H z H f (x L (t)) -(1 + r)/π L , (7)
Because the low-risk type might invest more than the high-risk type-contrary to the separating equilibrium under zero tax-an increase in the interest rate might be accompanied by an increase in the investment of the low-risk type.

Because xL (t) is strictly increasing in t, this phenomenon is more prevalent for high taxes. This result is formally stated below.

Proposition 3. Suppose that xL (t) > π L x * H /π H ; then, an increase in the interest rate will cause an increase in investment by low-risk types. If the increase in investment by low-risk types offsets the decrease in investment by high-risk types, then an increase in the interest rate will cause an increase in aggregate investment.

Consider now the impact of an interest rate change on the payoff of the low-risk type. For a given tax, differentiating (6) with respect to r, one obtains

d ŪL (t)/dr = (π L z L f (x L (t)) -(1 + r))dx L (t)/dr Indirect effect -xL (t) Direct effect , (8)
The direct effect is negative for every tax; the indirect effect is positive if xL (t) > π L x * H /π H and negative otherwise, as explained above. Nonetheless, because xL (t) is strictly increasing in t, it is rather unclear whether the positive indirect effect can ever offset the negative direct effect.

Concluding remarks

At least two policy implications emerge from the analysis. First, taxes create Pareto improvement if and only if the share of high-quality projects in the market is relatively high. If one accepts that during booms, high-quality projects outnumber low-quality projects, an implication of the model is that Pareto improvement might be possible only during booms. During busts, the government might be unable to increase welfare, and hence, it might be optimal to decrease taxes. Second, Pareto improvement is feasible only if entrepreneurs can pledge government subsidies as collateral. An implication of this finding is that when collateral is scarce, the government can stimulate the economy by redistributing wealth.

Proof of Proposition 1. To specify the LCS allocation for pair of contracts for a sufficiently small t, one needs to solve the following recursive programme: max

(x,ρ,c)∈R 3 + π H (z H f (x) -ρ -t) + (1 -π H )(T -c) s.t. π H ρ + (1 -π H )c ≥ x(1 + r) ρ ≤ z H f (x) -t c ≤ T
which has a solution (x * , ρH (t), cH (t)) as defined in Eq. ( 1), and, max

(x,ρ,c)∈R 3 + π L (z L f (x) -ρ -t) + (1 -π L )(T -c) s.t. π L ρ + (1 -π L )c ≥ x(1 + r) π H (z H f (x * ) -ρH -t) + (1 -π H )(T -cH ) ≥ π H (z H f (x) -ρ -t) + (1 -π H )(T -c) ρ ≤ z L f (x) -t c ≤ T
The first and the second constraints are each binding at the optimum; combining these two constraints, one obtains

z H f (x) - x(1 + r) π L -z H f (x * ) - x * (1 + r) π H - 1 -π H π H - 1 -π L π L c = 0 (9) Given that z H f (x)-x(1+r) π L is strictly increasing in [0, x * L ] and 1-π H π H -1-π L π L c ≥
0 for every c ≥ 0, the smallest solution of Eq. ( 9) is strictly increasing in c.

The payoff of the low-risk type is

U L (x, ρ, c) = π L z L f (x) - x(1 + r) π L + π p -π L 1 -π p t
which is strictly increasing in x ∈ [0, x * ]; hence, at the optimum c = T .

Proof of Proposition 2. Because f (x) is continuous and the first and second derivatives exist and are continuous for any x > 0, xL (t) is also continuous and 145 differentiable in t ∈ [0, t], and ŪL (t) is also continuous and differentiable in [0, t],

then:

Ū L (t) = z L f (x L (t)) - 1 + r π L × x L (t) + 1 -π L π L π p 1 -π p -1 = z L f (x L (t)) -1+r π L z H f (x L (t)) -1+r π L × (1 -π H ) π H - (1 -π L ) π L π p 1 -π p t + 1 -π L π L
π p 1 -π p -1 (10) I show that there exists π p L min , such that U L ( tLopt ) = 0, for some tLopt > 0, for every π p ∈ [π p L min , π L ]. Eq. ( 10) can be re-written as

Ū L (t) = (1 -α(t)) 1 -π L π L + α(t) 1 -π H π H π p 1 -π p -1 where α(t) = z L f (x L (t)) -1+r π L z H f (x L (t)) -1+r π L Note that Ū L (0) = z L f (x L (0)) - 1 + r π L × x L (0) + 1 -π L π L π p 1 -π p -1
where the first term is strictly positive and the second term is strictly negative, given the maintained assumptions. Therefore, there exists π p L min such that Ū L (0) > 0 for π p ∈ [π p L min , π L ]. Moreover,

Ū L (t * ) = 1 -π L π L
π p 1 -π p -1 < 0 for every π p ∈ [π H , π L ). By applying the intermediate value theorem for π p ∈ [π p L min , π L ), there exists tLopt > 0 such that Ū L ( tLopt ) = 0, which, given that Ū L (t) > 0 for every t ∈ [0, tLopt ) and U L (t) < 0 for every t ∈ [ tLopt , t * ],

150 corresponds to a global maximum in [0, t * ). Therefore, for π p ∈ [π p L min , π L ], there exists tLopt > 0 that maximises the payoff of the low-risk type.

Proposition 2 .

 2 ŪL (t) is concave in t, and every π p ∈ [π p L min , π L ] attains a unique interior maximum.

For simplicity, I refer to an entrepreneur with a low-risk (high-risk) project as a "low-risk" ("high-risk") type.

Inada's conditions are sufficient to guarantee interior solutions and, hence, considerably simplify the analysis but are not necessary for any of the results.

The assumption of mean-preserving spreads was first imposed in the seminal work of[START_REF] Stiglitz | Credit rationing in markets with imperfect information[END_REF].

Evidently, the tax system specified above is unrealistic in many respects. Most notably, in reality, entrepreneurs do not pay specific taxes, i.e., regardless of their income, but likely linear or non-linear taxes. Note, however, that given that the only observable and contractible variable is the individual state (i.e., success or failure), the government faces the constraints that banks face; given that equity is not feasible, taxes that condition payments on earned profits are not feasible, either.

Acknowledgements

Formatting of funding sources Funding 155


Morgane Travers-Trolet

Franck Coppin

Pierre Cresson

Philippe Cugier

Ricardo Oliveros-Ramos

Philippe Verley

Emergence of negative trophic level-size relationships from a size-based, individual-based multispecies fish model

Keywords: individual-based model, food web, fish community

Modeling the mechanisms underlying trophic interactions between individuals allows the food web structure to emerge from local interactions, which constitutes a prerequisite for assessing how marine ecosystems respond to various anthropogenic pressures. Using a multispecies spatially explicit individual-based model, the emergence of trophic patterns was explored in the eastern English Channel ecosystem, where pelagic-benthic trophic coupling was recently studied empirically. The OSMOSE model was applied to this ecosystem by explicitly representing the life cycle of 13 fish species and one squid group, forced by pelagic and benthic prey fields that are variable over time and space. A matrix defining

Introduction

Trophic ecology has been investigated empirically for decades in marine ecosystems to better understand key properties of ecosystems, including energy flows in ecosystems, the resilience and adaptation of ecosystems to large-scale pressures and the relationship between biodiversity and ecosystem functioning [START_REF] Belgrano | Aquatic Food Webs: An Ecosystem Approach[END_REF]. The current need to establish an integrated management framework fosters the development of a multitrophic approach, where all interspecific interactions are addressed [START_REF] Seibold | The Necessity of Multitrophic Approaches in Community Ecology[END_REF]. Initially addressed through stomach content analysis, trophic ecology is now based on various tools, including intrinsic tracers, such as stable isotope ratios and fatty acids [START_REF] Ramos | Trace me if you can: the use of intrinsic biogeochemical markers in marine top predators[END_REF]. Combining "old" and "modern" techniques is now viewed as the most powerful approach [START_REF] Cresson | Contrasting perception of fish trophic level from stomach content and stable isotope analyses: A Mediterranean artificial reef experience[END_REF] providing both a detailed vision of prey actually consumed and a general picture of trophic fluxes and food web topology. In parallel with these field studies based on biological sampling and chemical analysis, theoretical work has focused either on predator-prey interactions (e.g., Lotka-Volterra) or on network complexity and stability [START_REF] Belgrano | Aquatic Food Webs: An Ecosystem Approach[END_REF]. The development of holistic models allowed the coupling of theoretical and empirical approaches by conceptualizing the food web structure of a particular ecosystem based on data and simulating its dynamics. Typically, Ecopath models [START_REF] Christensen | ECOPATH II -a software for balancing steady-state ecosystem models and calculating network characteristics[END_REF] aim at balancing the food web structure of an ecosystem of interest based on observed diets and produce network indicators such as the recycling index, average path length and total system throughput [START_REF] Heymans | Global Patterns in Ecological Indicators of Marine Food Webs: A Modelling Approach[END_REF] but also information about species trophic positions and functions and their impacts on other functional groups.

Partly to increase their realism and partly to answer a wider range of scientific questions, the complexity of ecosystem models has been increasing by integrating temporal (e.g., Ecopath with Ecosim) and spatial heterogeneity (e.g., Ecospace [START_REF] Pauly | Ecopath, Ecosim, and Ecospace as tools for evaluating ecosystem impact of fisheries[END_REF], Atlantis [START_REF] Fulton | Lessons in modelling and management of marine ecosystems: the Atlantis experience[END_REF]) and by considering age or size structure within a trophic node defined to represent a species or functional group. Such models are currently mostly used to explore ecosystem responses to anthropogenic or environmental pressure, and their potential for theoretical trophic ecology is most likely underused. Trophic information from field studies is required to parameterize links between compartments, at least to identify them and sometimes to set their intensity (i.e., percentage of a prey in the diet of the predator) [START_REF] Pethybridge | Improving Marine Ecosystem Models with Biochemical Tracers[END_REF]. However, this information is at best used at the species level and is often averaged over several species to inform functional group trophic habits. Trophic variability exists among individuals and can be linked to ontogenetic changes, individual variability and composition of the local trophic environment (spatiotemporal heterogeneity) (e.g., [START_REF] Stehlik | Diet of winter flounder in a New Jersey estuary: Ontogenetic change and spatial variation[END_REF]. Instead of reducing this variability to parameterize ecosystem models, in this study, we aim to use a complex modeling approach to explore the individual trophic variability of marine fish. To do so, we used the multispecies individual-based model OSMOSE (Shin andCury, 2004, 2001;[START_REF] Travers | Two-way coupling versus one-way forcing of plankton and fish models to predict ecosystem changes in the Benguela[END_REF], where fish individuals constitute the structural unit of the model. Individual-based models (IBMs) allow for representing individuals that adapt to their local environment (leading to variability among individuals) and that interact mechanistically with each other and with their environment (both abiotic and biotic, i.e., composed of other individuals).

Interactions between these adaptive individuals lead to the emergence of population-level properties (e.g., resilience, spatiotemporal variations of abundance), which are more than the sum of individual properties [START_REF] Grimm | Individual-based Modeling and Ecology[END_REF]. Applied to trophic ecology, this means that the trophic structure of an ecosystem emerges from local predation interactions between fish individuals (being both prey and predator).

We applied the OSMOSE modeling framework to the eastern English Channel (EEC), where several empirical trophic studies have been recently conducted. The English Channel is an epicontinental sea located between the United Kingdom and France and is subject to environmental forcing (mega tidal regime and strong influence of rivers) and various human pressures, such as fisheries, aggregate extraction, maritime traffic, and wind farms [START_REF] Carpentier | Atlas des Habitats des Ressources Marines de la Manche Orientale -CHARM II, Channel Habitat Atlas for marine Resource Management -CHARM II[END_REF]. The structure and spatiotemporal variation of the fish community has been studied [START_REF] Vaz | Eastern English Channel fish assemblages: measuring the structuring effect of habitats on distinct sub-communities[END_REF], and the trophic links structuring this ecosystem have been recently investigated as well. [START_REF] Cachera | Implications of morphological and functional traits for trophic relationships within fish communities and marine trophic network architecture[END_REF] studied the trophic organization of the fish communities through digestive tract contents and geomorphometric measurements to link it to morphological and functional trait variation across and within species. [START_REF] Kopp | Reorganization of a marine trophic network along an inshore-offshore gradient due to stronger pelagic-benthic coupling in coastal areas[END_REF] investigated the strength of the pelagic-benthic coupling along an inshore-offshore gradient via stable isotope ratios. [START_REF] Giraldo | Depth gradient in the resource use of a fish community from a semi-enclosed sea[END_REF] coupled both approaches to make conclusions regarding the resource use of fish along the depth gradient. These studies showed that bentho-pelagic coupling is strong in the EEC, with benthic sources being important for both benthic and pelagic fish and with a decreasing intensity of the bentho-pelagic coupling as depth increases. In addition to these empirical studies, a holistic model has been applied to the EEC to explore the effects of fisheries management options on the flatfish and demersal fish species [START_REF] Girardin | Ecosystem and fishers' behaviour modelling : two crucial and interacting approaches to support ecosystem based fisheries management in the eastern English Channel[END_REF]. The calibration process of this Atlantis model allowed us to gain better insight into ecosystem functioning and to identify the main drivers of the system, including the importance of nutrient input through rivers and the competition interactions between demersal species [START_REF] Girardin | Identification of the main processes underlying ecosystem functioning in the Eastern English Channel, with a focus on flatfish species, as revealed through the application of the Atlantis end-to-end model[END_REF]. While the EEC trophic structure has been investigated through several methods, some of its variability remains unexplained and is assumed to be related to intraspecies and seasonal variations. To address the finer dynamics of the predation process and how it can shape observed patterns at different levels of organization, OSMOSE was applied to the EEC ecosystem to explore the trophic variability of fish individuals.

Materials and methods

The individual-based OSMOSE (Object-oriented Simulator of Marine eCOsystems Exploitation, Shin andCury, 2004, 2001;Travers et al., 2009, www.osmose-model.org) is a spatial model representing the whole life cycle of several fish species from eggs and larvae up to juveniles and adults. This multispecies model is size-structured and based on opportunistic predation that depends only on spatiotemporal cooccurrence and body size ratios between a predator and its prey. Because of this opportunism, neither the a priori food web structure nor the diet matrix are set, but they emerge from local trophic interactions. This model has been applied to a variety of ecosystems, such as upwellings (e.g., [START_REF] Marzloff | Trophic structure of the Peruvian marine ecosystem in 2000-2006: Insights on the effects of management scenarios for the hake fishery using the IBM trophic model Osmose[END_REF][START_REF] Travers-Trolet | An end-to-end coupled model ROMS-N2P2Z2D2-OSMOSE of the southern Benguela foodweb: parameterisation, calibration and pattern-oriented validation[END_REF][START_REF] Oliveros-Ramos | A sequential approach to calibrate ecosystem models with multiple time series data[END_REF], estuaries (e.g., [START_REF] Brochier | A multi-agent ecosystem model for studying changes in a tropical estuarine fish assemblage within a marine protected area[END_REF], semi-enclosed seas [START_REF] Fu | Exploring climate and fishing impacts in an ecosystem model of the Strait of Georgia[END_REF] and shelf seas (e.g., [START_REF] Grüss | Evaluation of the trophic structure of the West Florida Shelf in the 2000s using the ecosystem model OSMOSE[END_REF][START_REF] Halouani | Modelling food web structure using an end-to-end approach in the coastal ecosystem of the Gulf of Gabes (Tunisia)[END_REF]. The main structure and equations of the model are presented below, before focusing on its application to the EEC. An extended description of the OSMOSE model following the ODD protocol (Overview, Design concepts, and Details) proposed by [START_REF] Grimm | The ODD protocol: a review and first update[END_REF] and a description of the R packages dedicated to the model calibration are also available at https://documentation.osmose-model.org/osmose.html.

Model structure and processes represented in OSMOSE

The individual element of the OSMOSE model is a super-individual of identical fish [START_REF] Scheffer | Super-individuals a simple solution for modelling large populations on an individual basis[END_REF], i.e., of the same size, same trophic level (TL), same location and belonging to the same species. During each two week time step, the abundance (also called worth) and biomass of each super-individual changes according to the different modeled processes, described below (Figure 1). Only the main features and equations are recalled in this paragraph, and more complete details can be found in [START_REF] Shin | Using an individual-based model of fish assemblages to study the response of size spectra to changes in fishing[END_REF], 2001), Travers et al. (2009[START_REF] Travers-Trolet | An end-to-end coupled model ROMS-N2P2Z2D2-OSMOSE of the southern Benguela foodweb: parameterisation, calibration and pattern-oriented validation[END_REF].

At the beginning of the time step, super-individuals are distributed over a 2-dimensional grid. The spatial distribution of fish is driven at the larger scale by presence/absence maps provided as input for each species and possibly for different ages and/or seasons according to available knowledge. When the input distribution map remains the same between two consecutive time steps, super-individuals can move to adjacent cells following a random walk pattern (foraging), while always remaining within the limits of their presence map.

After movement, all processes involving local interactions occur: explicit predation on other superindividuals and on plankton and/or benthic invertebrate groups, mortality from this explicit predation, starvation mortality, fishing mortality and mortality from other sources such as top predators. In the real world, such processes are concurrent and concomitant. To approximate real continuous time, the mortality algorithm introduces (i) a subdivision of the time step (here set to 10), (ii) random shuffling of super-individuals and mortality processes within every time step and (iii) asynchronous updating of the state variables (i.e., super-individual biomass is updated as the model goes through the processes) [START_REF] Caron-Lormier | Asynchronous and synchronous updating in individual-based models[END_REF]. The predation process first assesses the food requirement for each superindividual, based on the maximum ingestion rate r of the predator i. This value is then compared to the amount of suitable food available locally, i.e., in the cell of the predator, defined by the suitability of prey size compared to predator size, the biomass B j of each prey available and an accessibility coefficient a i,j representing vertical overlap and/or morphological constraints between the prey j and the predator i.

Depending on the available biomass of prey, a predator can thus eat an amount of food varying between 0 (no prey of suitable size available) and its maximum ingestion rate. The predated biomass PB i,j of a prey j by a predator i is expressed as follows:

( ∑ )
(Equation 1)

The predation pressure is applied to all prey, proportional to their relative contribution to the total amount of edible food (i.e., no preference). Predation mortality is then applied to the preyed superindividual by reducing its abundance and biomass according to the realized predation pressure, possibly leading the super-individual to disappear if abundance falls below 1. According to the amount of food eaten compared to its maximum ingestion, the predation efficiency ξ is computed for each superindividual i. If ξ i falls below the threshold corresponding to maintenance requirement ξ crit , the starvation mortality rate M ξ is positive and increases linearly with predation efficiency reduction (Equation 2).

(Equation 2)

The different mortality rates (starvation M ξ , fishing F and other sources M oth ) are applied similarly to decrease the abundance of a super-individual i following the survival formula (Equation 3).

with { } (Equation 3)

The fishing mortality rate is species-specific, but can vary temporally and/or spatially according to available knowledge. For the fishing process, knife-edge selectivity was used, affecting only recruited fish i.e., fish older than the species age at recruitment. Finally, mortality from other sources is also considered by taking into account predation by organisms nonexplicitly represented in the model (e.g., other fish, birds, mammals) as well as diseases and senescence. A particularly high mortality term is applied to the first stages (eggs) to represent the bottleneck of survival due to nonfertilization of eggs, starvation of first-feeding larvae, advection, sinking and predation by nonexplicitly modeled organisms.

Because very little quantification exists on these processes, the larval mortality rates are calibrated (see section 2.4).

After this loop of interaction processes, growth can occur if the predation was successful enough, i.e., if the biomass eaten is higher than maintenance requirements. The length increment depends on the predation efficiency and averaged length increment (∆L) at the super-individual's age derived from the von Bertalanffy growth curve (Equation 4). The weight W of an individual increases simultaneously with its length through an allometric relationship.

{ ( ) (Equation 4)

Finally, the time step ends with the reproduction process, where new super-individuals of eggs are produced, depending on the spawning stock biomass (computed from a sex ratio of 1:1 and from the biomass B of all fish older than age at maturity A mat ), the species relative fecundity φ and the seasonality of spawning s t (Equation 5).

∑ (Equation 5)

Application to the eastern English Channel

The EEC ecosystem is modeled with OSMOSE through the explicit consideration of 14 species, which constitute 80% of the international landings from this area (ICES area 7d, excluding invertebrates) and more than two-thirds of the fish biomass sampled during the scientific bottom trawl Channel Ground Fish Survey (CGFS, Coppin and Travers-Trolet 1989). This set of species is composed of mackerel 1) and undergo an additional mortality of 1.05 year -1 and 0.55 year -1 , respectively (values derived from an Ecopath model applied to North Sea, [START_REF] Mackinson | An ecosystem model of the North Sea to support an ecosystem approach to fisheries management: description and parameterisation[END_REF]. Reproductive seasonality of each species is reported in Appendix C, while the fishing mortality rate is considered constant over the seasons for all species except for squids (fishing closure from May to mid-July) and horse mackerel (increased fishing mortality rate from October to December).

Forcing prey fields: planktonic and benthic groups

During the predation process, super-individuals can feed both on other explicitly modeled fish and on low trophic level (LTL) sources. LTL groups are integrated in OSMOSE through the forcing of biomass prey fields. Plankton prey fields come from the ECO-MARS3D biogeochemical model applied to the English Channel (Le [START_REF] Goff | A coupled biophysical model for the distribution of the great scallop Pecten maximus in the English Channel[END_REF][START_REF] Vanhoutte-Brunier | Modelling the Karenia mikimotoi bloom that occurred in the western English Channel during summer 2003[END_REF] with a grid of 2 km horizontal resolution and 10 vertical layers. The nutrients and plankton dynamics simulated with this model have been validated with data from monitoring stations and correctly reproduce the interannual variability observed in the English Channel (Le [START_REF] Goff | A coupled biophysical model for the distribution of the great scallop Pecten maximus in the English Channel[END_REF]. The biomasses of two phytoplankton groups (grossly representing dinoflagellates and diatoms) as well as microzooplankton and mesozooplankton groups have been integrated vertically and over the 2-week time step of OSMOSE to be used as forcing prey fields. Furthermore, as the current application aims at simulating the EEC ecosystem at a stable state, plankton climatology was created by averaging data bimonthly from the 2000-2006 period (Appendix D). Six additional LTL groups were added to complement the LTL food source available to fish: a macrozooplankton group (representing both holoplankton and meroplankton mostly composed of benthic invertebrate larvae) and five benthic groups of different sizes (Table 2). As available information on the spatial distribution of these groups was not sufficient, they were considered to be homogeneously distributed.

The grid used in OSMOSE has no vertical dimension; therefore, accessibility coefficients were used to represent vertical overlap both among super-individuals and between super-individuals and LTL groups in the computation of prey biomass available for predators. According to their ecology, each stage of each species and each LTL group was associated with a vertical layer: "pelagic" for plankton, buoyant eggs, larvae and small pelagic fish, "benthic" for benthic groups and species living on the seabed such as flatfish, and "demersal" for individuals living near the sea bed and having access to both pelagic and benthic prey (such as gadoids). The accessibility parameters are presented in Table 3.

Calibration

The model was calibrated using the calibrar R package with the AHR-ES algorithm (Oliveros- Ramos and Shin, 2016), an automatic evolutionary algorithm developed for calibrating stochastic models such as OSMOSE. This algorithm explores a range of values for unknown parameters and uses likelihood objective functions to select the optimal values for the catches and biomass to be comprised within ranges of observed values when available. Landings per species have been extracted from the ICES Fisheries Statistics official database (ICES, 2011a) for the ICES area 7d (corresponding to the EEC) over the period 2000-2009. Total stock biomass estimates are directly available from stock assessment reports for sole and plaice (ICES, 2011b), while for whiting, cod, mackerel and herring, total stock biomass estimates were derived from stock assessments covering a wider area [START_REF] Ices | Report of the Working Group on Widely Distributed Stocks (WGWIDE)[END_REF](ICES, , 2011b) ) and were therefore scaled to the EEC proportional to the relative landings in this area. In OSMOSE, species biomass is computed as the sum over the entire area of the biomass of all super-individuals older than 6 months, averaged annually. Simulated landings come from the fished individuals (equation 3) over the entire area, integrated at the annual time-scale. The calibration was performed in 3 phases, following recommendations by Oliveros- [START_REF] Oliveros-Ramos | A sequential approach to calibrate ecosystem models with multiple time series data[END_REF] based on model dependency of the parameters and availability of initial estimates. First, the 10 LTL accessibility coefficients were adjusted for 200 generations; then, the 14 larval mortality rates were added to the set of parameters to adjust for 200 other generations. Finally, 12 additional mortalities (including fishing mortalities) were added to the third phase, where 300 generations were run with a total of 36 parameters to estimate. The first two phases allow optimization of the calibration convergence, while the third phase includes all the parameters and lasts longer to ensure that an optimal solution is reached.

Scenarios and exploration of simulated trophic patterns

Once the model is calibrated, it is run for 120 years, with the first 100 years corresponding to the spin-up time during which the system stabilizes and is no longer driven by the model initialization. The results presented thereafter, corresponding to the average state of the EEC ecosystem in the period 2000-2009, are computed from averaging the last 20 simulated years to smooth any interannual variability.

Furthermore, OSMOSE is a stochastic model, and 50 replicates were run using the same input parameters.

Following the pattern-oriented modeling approach (POM, [START_REF] Grimm | Pattern-Oriented Modeling of Agent-Based Complex Systems: Lessons from Ecology[END_REF], the model's ability to reproduce independent patterns is explored by comparing simulated output with data neither used during the parameterization nor during the calibration. As the OSMOSE model is based on opportunistic predation, validation patterns could include emerging features linked to the predation process, such as realized diets and associated TLs or food web structures. Here, we used independent data of TLs calculated from nitrogen stable isotope ratios (SI) measured on the same species in the same ecosystem [START_REF] Cresson | Underestimation of chemical contamination in marine fish muscle tissue can be reduced by considering variable wet:dry weight ratios[END_REF][START_REF] Cresson | Individual isotopic ratio and trophic levels of fish species in the Eastern English Channel[END_REF][START_REF] Jennings | Trophic levels of marine consumers from nitrogen stable isotope analysis: estimation and uncertainty[END_REF][START_REF] Kopp | Reorganization of a marine trophic network along an inshore-offshore gradient due to stronger pelagic-benthic coupling in coastal areas[END_REF][START_REF] Mialet | Bilan des essais et optimisation du suivi mutualisé « réseaux trophiques et contaminants » sur les campagnes halieutiques DCF 2014-2015[END_REF]. TL calculations are based on the premise that the nitrogen isotopic ratio (δ 15 N hereafter) is gradually enriched at each TL, a phenomenon called trophic enrichment. TL is thus considered as the isotopic difference between the species of interest and a trophic baseline, i.e., a proxy of the ultimate organic matter source at the base of the food web, divided by the trophic enrichment factor (TEF). The queen scallop Aequipecten opercularis was used as a trophic baseline due to the trophic importance of benthic production and because the use of a primary consumer (i.e., at TL = 2) allows smoothing of the small scale isotopic fluctuations of primary production that are not integrated in fish isotopic ratios. Two methods are used, where TEF is either considered the same at all levels of the food web (e.g., in [START_REF] Kopp | Reorganization of a marine trophic network along an inshore-offshore gradient due to stronger pelagic-benthic coupling in coastal areas[END_REF]Cresson 2017;2018;[START_REF] Mialet | Bilan des essais et optimisation du suivi mutualisé « réseaux trophiques et contaminants » sur les campagnes halieutiques DCF 2014-2015[END_REF] or decreases with increasing δ 15 N of the diet [START_REF] Jennings | Trophic levels of marine consumers from nitrogen stable isotope analysis: estimation and uncertainty[END_REF]. Details about the method can be found in dedicated literature [START_REF] Hussey | Rescaling the trophic structure of marine food webs[END_REF], but sensitivity analyses demonstrated that for intermediate-TL species such as the ones considered in the present study, calculated TLs are rather similar regardless of the method (Jennings and van der Molen, 2015; P. Cresson unpubl. results).

In OSMOSE, each super-individual has a proper TL, which depends on its feeding history. The TL computation of a super-individual i is based on the classical formula in which the TL of a predator equals 1 plus the average TL of the prey weighted by their relative ingested biomass (Equation 6): 6)

∑ (Equation
where TL i,t is the trophic level of i at time t and DC j,i,t is the proportion of prey j in the diet of predator i at time t. While the TL of explicitly modeled individuals is dynamic, the TL of the LTL groups is fixed and has been set to 1 for phytoplankton and derived from TL estimates based on stable isotope studies in the same area [START_REF] Kopp | Reorganization of a marine trophic network along an inshore-offshore gradient due to stronger pelagic-benthic coupling in coastal areas[END_REF] for the other groups (Table 2). The TL of very small benthos is set to 3 to represent the omnivory of this group (partly composed of meiofauna). The TL of newly spawned eggs within OSMOSE is arbitrarily set to 3 to be close to the TL of the first-feeding larvae. Finally, we assume that an individual that has not fed keeps its previous TL.

After comparison of simulated TLs with data, model exploration is performed by analyzing the variation of diet composition and TL with size for all species. Diet composition is computed using the following predefined size classes for predators: [0; 5[,[5;10[,[10;15[,[15;20[,[20;25[,[25;30[,[30;40[,[40;50[,[50;60[,[60;70[,[70;90[,[90;110[ and [110;130[. From

Results

The evolutionary algorithm used for calibrating the model converged to an acceptable configuration where all median values of simulated biomass distribution are within the range of observed values (Figure 3). Median values of simulated catches are within the range of observations for half of the species (lesser spotted dogfish, whiting, cod, mackerel, sardine and squids), while for red mullet, horse mackerel and herring, catches are underestimated as only 42%, 42% and 18% of the 50 simulated replicates are within the range of the observations, respectively. Simulated catches of pouting, sole and plaice are smaller than the observations (median values corresponding to 73%, 57% and 80% of the minimal observed values, respectively), even if the biomass of the flatfish species corresponds to the total stock biomass estimates through the stock assessment (ICES 2011). For the other assessed species (whiting, cod, mackerel and herring), simulated biomass also displays a good fit to biomass estimated over the period of 2000-2009. The optimized values of accessibility parameters show high variability across the LTL groups, from approximately 10 -4 for dinoflagellates to approximately 0.4 for mesozooplankton and very large benthos (Table 2), two important prey groups for the fish community.

A comparison of simulation outputs with published TLs from empirical SI analysis is performed as a validation process. Figure 4 displays the trophic spectra of the modelled species, i.e., for each species, the distribution of the individual TL weighted by the individual biomass. In the simulations, the width of the trophic spectrum (i.e., the difference between the maximal and minimal individual TLs) varies according to species from 1.6 levels for red mullet up to 3.9 levels for herring. More importantly, the way biomass is distributed along TLs also varies: for some species, biomass distribution is concentrated around a particular TL (e.g., approximately 3.9 for red mullet, pouting, poor cod, dragonet, sole), while for other species, biomass is spread over a wide range of TLs (e.g., whiting, cod, sardine, squids). The biomass concentration of approximately 3.9 for benthic fish species is linked to the dominant proportion of very small benthos and small benthos (TL=3 and TL=2.9, respectively, Table 2) in the diet of these species (Figure 5). Plaice individuals of intermediate length (15-50 cm) also largely rely on these prey groups, explaining the concentration of biomass around TL=3.8 in the trophic spectrum (Figure 4). The biomass around TL=4.5 is explained by the presence of very large benthos (TL=3.6) in the diet of larger plaice individuals. The wide trophic spectra of lesser spotted dogfish, whiting and cod are explained by the diversity of prey composing their diets (Figure 5).

Simulated trophic spectra were in good agreement with the range of TLs estimated from stable isotope measurements for most species. For red mullet, poor cod, and plaice, simulated TLs were similar to SIderived TLs, which were, moreover, coherent between empirical studies. For lesser spotted dogfish, pouting, whiting, sole, horse mackerel and mackerel, empirical data display high variability across studies, but this variability is generally well encompassed by the model. However, empirical TL estimates show that the maximal TL observed for sole can be higher than that simulated, while mackerel can have a minimal SI-derived TL smaller than that simulated. It is worth noting that for mackerel, the model simulates two TL modes, approximately 3.6 and 4.3, corresponding respectively to young individuals feeding only on mesozooplankton (TL=2.6, Table 2) and larger individuals feeding on small squids and small fish, mostly young sardine and horse mackerel (Figure 5). Similarly, empirical estimates of mackerel TL show low values of approximately 3.5 in [START_REF] Cresson | Underestimation of chemical contamination in marine fish muscle tissue can be reduced by considering variable wet:dry weight ratios[END_REF] and [START_REF] Jennings | Trophic levels of marine consumers from nitrogen stable isotope analysis: estimation and uncertainty[END_REF], with fish being between 16.9 and 41 cm long (Table 4), while TL values are higher than 4 in the three other studies but for similar fish lengths (18 to 34 cm, Table 4). If we assume that TL estimated from stable isotopes are representative of the trophic position of the bulk of a species, then the EEC-OSMOSE model tends to slightly overestimate the TL of cod, dragonet and squids and to underestimate the TL for herring. The SI-derived TL of sardine corresponds to the bulk of the simulated biomass, but the model also simulates sardine individuals at a TL between 2 and 3 (feeding on diatoms and mesozooplankton, Figure 5).

To further explore the drivers of individual variability among species TL distribution, the evolution of the mean TL with size is presented in Figure 6. While mean TL generally increases with size for most species, this is not the case for red mullet, poor cod, dragonet, and sole and for pouting and plaice to a lesser extent (respectively, from 10 to 35 cm and from 20 to 50 cm), for which the mean TL decreases with size.

These species are characterized by a benthic diet, with the proportion of very small benthos (TL=3)

decreasing with size and the proportion of medium benthos (TL=2.2) increasing as fish grow larger, which explains the decreasing TL with size for these species. The evolution of mean TL with size is not linear, and most species display a strong change of TL at smaller size, while mean TL varies less with size for larger individuals. Tipping points can be identified and linked to ontogenetic changes in the diets of species. For instance, sardine and herring fish longer than 20 cm no longer feed on diatoms (Figure 5), explaining the abrupt TL increase at this size. Other ecological features can be observed, such as the marked shift from a plankton-feeding larval stage (roughly for fish smaller than 5 to 10 cm on Figure 6) to a benthic feeding juvenile stage for all benthic and demersal species. Finally, other TL breakpoints linked to diet shifts exist for larger fish: the occurrence of very large benthos for lesser spotted dogfish larger than 30 cm, pouting larger than 35 cm, whiting larger than 15 cm, cod larger than 20 cm and plaice larger than 50 cm, and the disappearance of mesozooplankton for horse mackerel and mackerel larger than 20 cm. To supplement the patterns observed over the entire area between TL and size, the spatial distribution of the TL-size relationship is mapped (Figure 7). The negative relationship between TL and size is confirmed in every grid cell for red mullet, dragonet and sole. This pattern appears robust (R² > 0.3) in the Dover Strait (Northeast), in the north of the Central English Channel (Northwest) and in the Bay of Seine (South). For poor cod, another species showing a decreasing TL-size relationship at the global scale, the spatial distribution of the slope is less informative (R²<0.3) but shows both positive and negative relationships (the latter occurring also in the Dover Strait and north of the Central English Channel). For plaice and pouting, the relationship is positive in most cell grids and is probably driven by the strong difference of TL between fish of intermediate size and larger fish. Robust positive relationships between TL and size also occur for pouting, herring, sardine and squids.

Discussion

Ability of the model to capture EEC ecosystem dynamics

In this study, we were able to adapt the 2D OSMOSE model using a vertical overlap matrix and apply it to the EEC shallow ecosystem characterized by strong bentho-pelagic coupling. After parameterizing the model, the semiautomatic calibration method produced an overall good fit of the model to the 2000-2009 average state of the EEC ecosystem, with biomass of all species and catch values of half of the species being within the range of the observed values. The discrepancies observed for some species between modeled and observed catches and biomasses can be explained by several factors. First, a constant fishing mortality is applied in OSMOSE to individuals older than the age at recruitment (i.e., similar to broken-stick selectivity with age), while in reality due to the different fleet selectivity and variable catchability-at-age, the fishing pressure endured by fish varies with age/length [START_REF] Quinn | Quantitative Fish Dynamics[END_REF]. Nonetheless, it is worth noting that the total mortality varies with age within OSMOSE, notably due to explicit predation mortality, which tends to decrease with size. Second, the biomass target values come from single-stock assessments, i.e., correspond to model outputs with specific hypotheses and thus should be taken as estimates with associated uncertainty rather than exact values [START_REF] Brooks | When "data" are not data: the pitfalls of post hoc analyses that use stock assessment model output[END_REF]. Similarly, target catch values come from declared landings completed by estimates of discards when available. Even if the EEC is considered a data-rich ecosystem, some uncertainties persist when estimating discards and total catches [START_REF] Enever | Discarding in the English Channel, Western approaches, Celtic and Irish seas (ICES subarea VII)[END_REF][START_REF] Pauly | Catch reconstructions reveal that global marine fisheries catches are higher than reported and declining[END_REF]. Furthermore, the hypothesis made to allocate the biomass of widely distributed stock to the ICES 7.d area based on the landings ratio does not take into account the spatial variability of fishing effort and assumes a homogeneous distribution of fish, again contributing to the uncertainty around biomass target values. Third, the calibration process was limited to the optimization of 36 unknown parameters, therefore constraining the space of simulated output reachable during the calibration.

Despite these limits, the model was able to reproduce species biomasses and most species catches, but also other features independent of the data used for parameterization and calibration. For most species, the simulated TLs are in good accordance with TL estimates derived from SI data, both in terms of average values and variability within species. However, EEC-OSMOSE underestimates sardine and herring mean TLs compared to SI estimates. The exploration of simulated TL and diet composition versus size shows that the smaller size classes have a diet mostly composed of diatoms and mesozooplankton (resulting in small TL values), while the larger individuals rely on mesozooplankton, explaining their higher TL. One hypothesis for the difference observed between the data and the model is that empirical data underestimate the importance of phytoplankton food source. This could be explained by the absence of very small individuals (smaller than 5 cm for herring, smaller than 7.7 cm for sardine, Table 4) in the sample, and/or by the sampling season (autumn) corresponding to higher zooplankton food available compared to phytoplankton. Another hypothesis is the biased simulation of diet shift from phytoplankton to zooplankton prey at larger size than observed for herring and sardine. Both species are known to consume these two types of prey, with seasonally variable intensity [START_REF] Costalago | Ontogenetic and seasonal changes in the feeding habits and trophic levels of two small pelagic fish species[END_REF], but the ontogenetic shift in their diet has been reported at an earlier larval stage (e.g., [START_REF] Denis | Feeding strategy of Downs herring larvae (Clupea harengus L.) in the English Channel and North Sea[END_REF]. These results suggest that the minimum and maximum predation size ratios set for herring and sardine may be revised, possibly by setting different ratios according to individual ontogenetic development (e.g., [START_REF] Travers-Trolet | An end-to-end coupled model ROMS-N2P2Z2D2-OSMOSE of the southern Benguela foodweb: parameterisation, calibration and pattern-oriented validation[END_REF]. Moreover, due to the model structure and lack of suitable stable isotope data, the mesozooplankton group has a fixed TL that prevents simulation of the spatiotemporal variability of the TL of the zooplankton community available to fish. It should nevertheless be remembered that fish stable isotope ratios (and the derived TL values) can be seen as emergent properties, resulting from their diet but also from a large set of environmental or physiological parameters (e.g., [START_REF] Boecklen | On the use of stable isotopes in trophic ecology[END_REF]. Among these, large spatial and temporal variations of phytoplankton isotopic ratios [START_REF] Magozzi | Using ocean models to predict spatial and temporal variation in marine carbon isotopes[END_REF] at the basis of the food web and/or fish migrations between zones where primary production exhibits different isotopic ratios may drive changes in fish isotopic ratios that are hard to capture and that may blur TL calculation.

The overestimation of the trophic position of cod in the model comes with an overestimation of the proportion of fish in the diet. The model simulates the proportion of fish biomass in cod diets as between 50% and 80% according to size classes, while fish represent nearly one quarter or less of the prey found in stomach content analysis (crustaceans being the main prey for juveniles and adults, [START_REF] Cachera | Implications of morphological and functional traits for trophic relationships within fish communities and marine trophic network architecture[END_REF][START_REF] Pinnegar | DAPSTOM -An Integrated Database & Portal for Fish Stomach Records[END_REF][START_REF] Mialet | Bilan des essais et optimisation du suivi mutualisé « réseaux trophiques et contaminants » sur les campagnes halieutiques DCF 2014-2015[END_REF]. This bias is due to the relatively simple accessibility matrix set for representing the proportion of prey biomass available to a predator according to their vertical distributions. For this matrix, cod is considered to be demersal, i.e., to have full access to other demersal individuals and to have access to half of the pelagic biomass and half of the benthos biomass.

To better represent the feeding behavior of cod, accessibility coefficients should be revised, for instance by increasing accessibility to benthic prey and reducing accessibility to pelagic and demersal individuals.

For this study, the accessibility matrix was introduced to mimic vertical overlap between predators and prey as required to model both benthic and pelagic communities with an opportunistic size-based predation, but its parameterization was kept as simple as possible. For their coupled size-spectrum model, [START_REF] Blanchard | How does abundance scale with body size in coupled size-structured food webs?[END_REF] considered that all predators spent half of their time feeding on benthic invertebrates and the other half feeding on pelagic organisms. Future developments on how to better set these accessibility parameters could involve consideration of the spatial variability of trophic interactions (e.g., depth-driven variability in bentho-pelagic coupling; [START_REF] Giraldo | Depth gradient in the resource use of a fish community from a semi-enclosed sea[END_REF] or use morphological attributes (trait-based approach) of the different species (e.g., orientation of the mouth).

Relationship between size and TL

When considering TL with regard to size for the different species modeled, two main patterns emerge from the simulations. The most frequent pattern is an increase of TL as size increases, which is often more pronounced for the smaller size classes. This positive relationship can display some breakpoints linked to diet composition shifts, as illustrated by planktivorous fish species at 20 cm. The second pattern is observed for only four benthic species (red mullet, poor cod, dragonet and sole) and corresponds to a decrease of TL with increasing size. For the small individuals of these four benthic species (smaller than 5-10 cm), the initial increase in TL is explained by the pelagic and planktivorous mode of the larvae before settlement on the sea bottom, modeled through change of the accessibility predation coefficient (Table 3).

In aquatic ecology, the assumption that larger individuals have a higher TL is often admitted, as predation is constrained by body size through gape limitation. Such a relationship has been explored and confirmed across species in various ecosystems by confronting the mean or maximum size of species with their mean δ 15 N (e.g., [START_REF] France | Mapping trophic continua of benthic foodwebs: body size-δ 15 N relationships[END_REF][START_REF] Romanuk | Trophic level scales positively with body size in fishes[END_REF]. However, other studies have reported an absence of correlation between species mean length and their trophic position (e.g., [START_REF] Layman | Body Size and Trophic Position in a Diverse Tropical Food Web[END_REF]. [START_REF] Jennings | Weak cross-species relationships between body size and trophic level belie powerful size-based trophic structuring in fish communities[END_REF] also documented a weak cross-species relationship between the maximum size of fish species and their mean δ 15 N value but a strong relationship at the community level, i.e., using the individual length of fish and pooling the data together within size classes. The ontogenetic increase of TL with increasing size has also been confirmed for benthic fish species by [START_REF] Badalamenti | Size-related trophodynamic changes in three target fish species recovering from intensive trawling[END_REF]. Investigating the North Sea trophic structure, Jennings et al. (2002a) found a significant positive relationship between fish length and δ 15 N for 16 species over 31. More interestingly, this relationship was found to be negative for herring and plaice whose TL decreases as their length increases. In addition, the pattern observed may be positive in one environment but negative in another [START_REF] Jennings | Trophic levels of marine consumers from nitrogen stable isotope analysis: estimation and uncertainty[END_REF]. The results obtained in the present study thus demonstrate that the variability may appear at even a lower spatial scale, confirming the call for a better understanding of the effect of environmental gradients on trophic functioning [START_REF] Ings | Review: Ecological Networks: Beyond Food Webs[END_REF]. Based on stable isotope data in the EEC, [START_REF] Kopp | Does the positive body-size-trophic level relationship hold at the species level? Presented at the Colloque « Vulnérabilité des écosystèmes côtiers au changement global et aux évènements extrêmes[END_REF] confirmed this decreasing trend of TL with size for plaice but also for skates and even for whiting in some particular habitats (located in the central Bay of Seine and part of the Dover Strait). In half of the region × species combinations they studied, [START_REF] Jennings | Trophic levels of marine consumers from nitrogen stable isotope analysis: estimation and uncertainty[END_REF] observed no relationship between mass and TL, and the positive relationships mostly occurred for piscivore species. As they have to capture mobile prey, gape size is a key factor driving feeding abilities in these species. In benthic systems, feeding mechanisms could be more based on opportunistic predation of carrion and living organisms. In this context, prey size may not be as important in driving the feeding mechanism as for pelagic systems.

While based on opportunistic size-based predation, OSMOSE was unexpectedly able to reproduce decreasing trends of TL with size for some benthic species. In EEC-OSMOSE, the benthic species demonstrating a clear declining TL trend with size are not the same as the benthic species found to display this pattern empirically. However, it is worth noting that the empirical negative relationship found for plaice between 9 and 48 cm (Jennings et al. 2002a) is partly present in the model if we focus on intermediate-sized individuals, i.e., before the introduction of very large benthos in the diet (at about 50 cm).

Being able to reproduce the negative TL-size relationship using such a model allows for drawing two nonexclusive hypotheses of its origin. First, the spatial distribution of fish individuals changes with age (Appendix B), which may result in different prey compositions being available locally, including the case where only prey with lower TLs are available in the area inhabited by larger fish individuals. The spatial distribution of the TL-size relationship confirms this spatial heterogeneity for some species. Thus, the absence of squid eggs in the Dover Strait and the North Central Channel is linked to the strong TL-size negative relationship observed in these areas, where the benthic fish diet is only composed of benthic invertebrates. For mackerel, the absence of juveniles in the Bay of Seine explains the spatial heterogeneity of the signal and suggests that a negative TL-size relationship could be observed empirically if focus was placed on the adults of this region. In the current model, spatially homogeneous benthic prey fields were used because insufficient knowledge of benthos dynamics was available at this scale. The simulated trophic spatial variability would probably be higher if a more realistic benthic community was included in the model.

The second hypothesis underlying the simulated pattern is that, conversely to what is largely admitted for the pelagic prey, the trophic structure of the benthic prey is not linked to the size structure of the benthic invertebrate community. In the diet of the simulated benthic fish, the increasing proportion of medium benthos with a small TL compared to the proportion of small benthos with a higher TL leads mathematically to a TL decreasing with size at the predator level. This pattern is linked to the predation hypothesis underlying the model and reflects the actual opportunistic pattern of the benthic fish species that consume the most available resources [START_REF] Van Denderen | Global patterns in marine predatory fish[END_REF]. The selection of species used to set the TL of the benthic groups could have an impact on the overall TL-size relationships of fish.

However, they were selected because of their abundance in the area, therefore they were considered suitable to represent the main prey available for fish. Only a few studies have investigated the relationship between size and trophic position for marine benthic invertebrates. Jennings et al. (2002b) demonstrated that for benthic invertebrates, the relationship between size and TL reflected intraspecific patterns (i.e., individual growth) and not interspecific patterns (i.e., no evidence for a relationship between maximum body size and TL across species). Similarly, [START_REF] Dinmore | Predicting abundance-body mass relationships in benthic infaunal communities[END_REF] observed a negative relationship between TL and body mass, demonstrating that body dimension may not be a major driver of predation in benthic systems. In their coupled size-based model, [START_REF] Blanchard | How does abundance scale with body size in coupled size-structured food webs?[END_REF] confirmed that benthic invertebrates share a common size-unstructured resource and therefore are not strongly trophically size-structured. In other words, two benthic invertebrates of different sizes can exhibit the same TL as their diet would be the same. An ontogenetic diet change in the predator could thus result in an inconclusive or decreasing length-TL pattern.

Variability of TL across sources

The current study benefited from the existence of several stable-isotope analyses performed in the EEC.

Here, we used the available TL estimates at the individual level and explored the intraspecies variability of SI-derived TLs, which increased both with the number of fish individuals sampled and with the width of body sizes sampled (Table 4). The high variability of TLs within a species was confirmed by the model, where individuals can have different TLs depending on their size (involving different size ranges of available prey), their spatial location (local encounters with different prey) and the feeding history of their prey (leading to different TLs of the prey). While the intraspecific TL variability from stable isotopes was required to validate the emergent patterns of the model, the comparison of TL values between different SI studies was also informative. Indeed, the agreement observed between the five studies (e.g., plaice) increases the reliability of these estimates, both in terms of value and width of distribution. For sardine, the very similar TL distribution observed between two studies counterbalances the low number of individuals sampled (10 in each study) and therefore improves the reliability of these data. While the five empirical studies provided similar estimates of species mean TLs and variability for some species, they can lead to different estimates of the TL for other species (e.g., the lesser spotted dogfish mean TL goes from 3.5 to 4.8; the whiting mean TL ranges from 4 to 5.1). Discrepancies between the empirical studies (and with the model) can be due to differences in sampling dates and therefore temporal variation of diet and integration dynamics (seasonal and/or interannual, e.g., [START_REF] Schafer | Comparisons between the influence of habitat type, season and body size on the dietary compositions of fish species in nearshore marine waters[END_REF], the spatial location of sampling and its effect on diet [START_REF] Kopp | Reorganization of a marine trophic network along an inshore-offshore gradient due to stronger pelagic-benthic coupling in coastal areas[END_REF][START_REF] Giraldo | Depth gradient in the resource use of a fish community from a semi-enclosed sea[END_REF], the variability of the trophic baseline used [START_REF] Magozzi | Using ocean models to predict spatial and temporal variation in marine carbon isotopes[END_REF] or hypothesis regarding TEF [START_REF] Hussey | Rescaling the trophic structure of marine food webs[END_REF]. These intraspecific variations are nonetheless classically observed (e.g., [START_REF] Jennings | Trophic levels of marine consumers from nitrogen stable isotope analysis: estimation and uncertainty[END_REF].

Isotopic data allowed validation of the model, but other trophic data sources could have been used to provide a complementary vision. Comparison with stomach content data allowed for a better understanding of the discrepancies regarding the cod TL; the TL overestimation is linked to the overestimation of fish in the cod diet composition. Both isotopic and stomach content data sources are now considered complementary (e.g., [START_REF] Cresson | Contrasting perception of fish trophic level from stomach content and stable isotope analyses: A Mediterranean artificial reef experience[END_REF][START_REF] Giraldo | Depth gradient in the resource use of a fish community from a semi-enclosed sea[END_REF], the latter one informing a snapshot diet with identified prey, while the former integrates trophic fluxes over months and allows us to quantify the fluxes between predators and a pool of prey of similar isotopic signatures. The ecosystem model can now be added to the list of available tools to explore trophic function and individual variability of TLs and could be used in a similar way to explore individual variability across seasons and/or space (i.e., at different depths).

Conclusion

Using a multispecies IBM constrained by size-based opportunistic predation, we were able to reproduce the average trophic structure of the EEC over 2000-2009, including benthic and pelagic communities.

Due to the individual variability in terms of size, spatial location and feeding history, the model simulations displayed patterns that were observed in empirical studies but were unexpected from a sizebased predation approach. Here, the IBM framework has been shown to be effective in investigating among-individual trophic variability and for understanding the plausible drivers of the negative TL-size relationship observed empirically for some species. The uncoupling of the trophic structure and size structure of benthic invertebrates appeared to be the key to this pattern, but future studies should further explore this potential link and identify morphological aspects to better represent the predation of fish on benthic invertebrates. The availability of TL estimates from stable isotopes has been a key to validating the model and encouraging strong collaborations between modelers and field/laboratory scientists. Indeed, while trophic data are often used to parameterize or validate ecosystem models [START_REF] Pethybridge | Improving Marine Ecosystem Models with Biochemical Tracers[END_REF], complex models -and particularly IBMs -appear useful to inform on the trophic functioning of an ecosystem and to explore different hypotheses regarding the causes of observed patterns. As the trophic patterns simulated with OSMOSE have been validated for the EEC, the model will now be available to explore the ecosystem impacts of different scenarios, including management measures and climate change. The flexibility of the food web structure emerging from local interactions in OSMOSE appears promising when aimed at exploring the cumulative impacts of different pressures.

Acknowledgments

This study was partly funded by the European Community's Seventh Framework Programme 4.

  all super-individuals pertaining to a size-class, the biomasses of the different prey eaten (including other super-individuals and LTL groups) are grouped by species over the entire area. To explore the relationship between TL and size, super-individuals are grouped by centimeters and the TL distribution within each size group is computed (min, first quartile, median, third quartile, max). The TL-size relationship is then explored spatially by fitting a linear model in each cell with more than 10 super-individuals. The resulting slope values are then mapped for each species, with indication of the quality of the fit using R² values.

(

  FP7/2007e2013) under Grant Agreement No. 266445 for the project VECTORS of Change in Oceans and Seas Marine Life, Impact on Economic Sectors (VECTORS), by the French project EMIBIOS (FRB, contract no. APP-SCEN-2010-II), and by the French government and the region Hauts-de-France under the framework of the project CPER 2014-2020 MARCO. The authors acknowledge the Pôle de Calcul et de Données Marines (PCDM, http://www.ifremer.fr/pcdm) for providing DATARMOR storage and computational resources.

Figure 1 :

 1 Figure 1: Processes undertaken by a superindividual during a 2-week time step : 1) Movement of

Figure 2 :Figure 3 :

 23 Figure 2: Grid corresponding to the modeled EEC (0.6° x 0.6° cells) with indication of depth (from

Figure 4 :

 4 Figure 4: Modelled distribution of species biomass across TLs (trophic spectra, in grey), and comparison with published TLs for these species in the same

Figure 5 :

 5 Figure 5: Emerging diet composition across size classes for the 14 modelled species over the entire

Figure 6 :

 6 Figure 6: Modelled distribution of superindividuals' TL across 1-cm size classes for the simulated

Figure 7 :

 7 Figure 7: Spatial distribution of the direction of the TL-size relationship. In each cell with more than 10 superindividuals, a linear model has been applied

Table 1 :

 1 Input parameters of OSMOSE for the 14 fish species modelled explicitly. L ∞ , K, and t 0 are the parameters of the von Bertalanffy growth model, with a linear growth before the threshold age a th and a growth following the von Bertalanffy model after a th ; c is Fulton's condition factor and b the exponent of the L-W allometric relationship; L mat is length at maturity and φ is relative fecundity; a max is longevity; F is the annual fishing mortality rate and a rec is age of recruitment; M oth is an additional mortality rate (resulting from predation by other species of the ecosystem that are not explicitly modelled); M ξ max is the maximum starvation mortality rate, M L is the larval mortality rate applied to the first life stage; min and max size ratios define suitable prey size for a predator, ξ crit is the critical predation efficiency corresponding to maintenance requirements, max ingestion rate corresponds to the maximum amount of food edible per year relatively to the predator mass. Values reported in the table come from literature (references in Appendix 1) except from M oth , F and M L which come from calibration.

			GROWTH AND CONDITION		REPRODUCTION			SURVIVAL				PREDATION
	Species	L ∞	K	t 0	a th	c	b	L mat	φ	a max	F	a rec	M oth	M ξ max	M L	Min size ratio	Max size ratio	ξ crit	max ingesti on rate
		cm	y -1	y	y	g.cm -3		cm	eggs.g -1	y	y -1	y	y -1	y -1	month -1				g.g -1
	Lesser spotted dogfish	87.4	0.118	-1.09	0.5	0.00308	3.029	57	0.14	10	0.09	4	0.087	0.3	4.29	50	3	0.57	3.5
	Red mullet	53.3	0.18	-1.23	1	0.00716	3.178	16.7	500	11	0.194	0.4	0	0.3	13.01	125	10	0.57	3.5
	Pouting	37.6	0.46	-0.77	0.5	0.00657	3.202	23	620	4	0.106	1	0.12	0.3	6.69	50	3.5	0.57	3.5
	Whiting	40.2	0.63	-0.37	1	0.00621	3.103	20	797	20	0.122	1	0.405	0.3	17.03	30	1.5	0.57	3.5
	Poor cod	22.2	0.462	-0.679	0.5	0.0092	3.026	13	100	3	0	1	0.085	0.3	4.73	50	3.5	0.57	3.5
	Cod	103.9	0.19	-0.1	0.5	0.00835	3.053	56	800	25	0.219	1	0	0.3	21.95	50 / 20*	2.3 / 1.8*	0.57	3.5
	Dragonet	28.3	0.471	-0.443	0.5	0.0262	2.442	17.4	255	6	0	1	0.148	0.3	2.58	125	10	0.57	3.5
	Sole	37.3	0.35	-1.61	0.5	0.00391	3.264	29	482	20	0.187	1.5	0	0.3	7.4	125	10	0.57	3.5
	Plaice	71.7	0.23	-0.83	0.5	0.0103	3.017	27	255	15	0.44	1	0	0.3	13.52	125	5	0.57	3.5
	Horse mackerel	39.2	0.18	-1.515	1	0.0054	3.114	22	1655	15	0.052	0.5	0	0.3	3.52	100	2.5	0.57	3.5
	Mackerel	42	0.24	-2.07	1	0.00338	3.241	29	1070	17	0.142	0.5	0	0.3	7.94	100	2.5	0.57	3.5
	Herring	29.2	0.37	-0.67	0.5	0.00503	3.1	25	458	11	0.156	1.5	0.008	0.3	1.24	1000	5	0.57	2
	Sardine	24.6	0.79	-0.22	0.5	0.00594	3.077	15	2228	15	0.03	0.5	0.216	0.3	14.07	1000	5	0.57	3.5
	Squids	50	2	0.5	0.7	0.25	2.27	30	50	2	0.036	0.5	0.298	0.3	7.97	20	1.5	0.57	3.5
																*below and above 12cm respectively

Table 2 :

 2 Parameters of the low trophic level (LTL) groups used in OSMOSE as forcing prey field. Size range of plankton groups correspond to size class used in biogeochemical models, and size class of benthic invertebrates are arbitrarily set to represent a discretized size spectrum. Trophic levels are either set arbitrarily (identified by *) or derived from SI-derived estimates from[START_REF] Kopp | Reorganization of a marine trophic network along an inshore-offshore gradient due to stronger pelagic-benthic coupling in coastal areas[END_REF] with the corresponding species indicated. Accessibility coefficients are calibrated.

		LTL groups	Size range (cm)	Trophic level	Accessibility coefficient
		Dinoflagellates	0.0002 -0.002	1*	10	-3.98
	PELAGIC PREY	Diatoms Micro-zooplankton Meso-zooplankton	0.002 -0.02 0.002 -0.02 0.02 -0.2	1* 2* 2.6 (copepods)	10 10 10	-2.79 -0.97 -0.37
		Macro-zooplankton	0.2 -2	3.8 (Crangon crangon)	10	-1.56
		Very small benthos	0.02 -0.5	3*	10	-1.20
	BENTHIC PREY	Small benthos Medium benthos Large benthos	0.5 -1 1 -5 5 -10	2.9 (Nereis sp.) 2.2 (bivalves) 2.3 (Psammechinus miliaris)	10 10 10	-1.30 -1.87 -2.96
		Very large benthos	10 -15	3.6 (Maja brachydactyla)	10	-0.38

Table 3 :

 3 Accessibility coefficients between individuals depending on their vertical position, representing the proportion of prey biomass available to a predator. The vertical position of individuals depends on their stage and is indicated in the last column.Lesser spotted dogfish younger than 0.45 year, Red mullet, Dragonet, Plaice older than 3 months Sole older than 0.15 year Squids younger than 1.5 month Very small benthos, Small benthos, Medium-size benthos, Large benthos, Very large benthos

			Predator
			Pelagic	Demersal	Benthic
						Red mullet, Pouting, Whiting, Dragonet, Plaice younger than 3
						months
						Cod younger than 0.4 year
		Pelagic	1	0.5	0	Sole younger than 0.15 year
						Horse mackerel, Mackerel, Herring, Sardine
						Dinoflagellates, Diatoms, Microzooplankton, Mesozooplankton,
						Macrozooplankton
	Prey	Demersal	0.5	1	0	Lesser spotted dogfish older than 0.45 year, Pouting, Whiting older than 3 months Cod older than 0.4 year
						Squids older than 1.5 month
		Benthic	0	0.5	1

Table 4 :

 4 Size range and number of fish individuals (N) used to estimate species TL based on SI measurement in four empirical studies realized in the EEC. For[START_REF] Jennings | Nitrogen and carbon stable isotope variation in northeast Atlantic fishes and squids[END_REF], body size are estimated from body mass using allometric relationship[START_REF] Robinson | Length-weight relationships of 216 North Sea benthic invertebrates and fish[END_REF][START_REF] Mahé | Evidence of a relationship between weight and total length of marine fish in the North-eastern Atlantic Ocean: physiological, spatial and temporal variations[END_REF]. Squid length was estimated based on an unpublished relationship (ln(Length)= 2.86 + 0.44 ln(mass) calculated on individual length-mass measurement performed during CAMANOC survey in the English Channel (K.Mahé, Ifremer Halieutic Information System, pers. comm.)

		Kopp et al.,	Jennings and	Mialet et al.	Cresson et al.,	Cresson et al.,
		2015	Cogan, 2015	2017	2017	2018
	Lesser spotted	11-64 cm	17-63.7 cm	40-63 cm	42-67.9 cm	50.5-65 cm
	dogfish	N=36	N=53	N = 18	N=25	N=10
	Red mullet	7-32 cm N=63	N=0	20-25 cm n=5	N=0	15-19.6 cm N=10
	Pouting	9-27.5 cm N=24	7.9-33.9 cm N=37	n=0	12.9-32.9 cm N=50	11.9-22.7 cm N=19
	Whiting	7-41 cm N=39	12.5-32.7 cm N=28	21-38 cm N=30	14.6-35 cm N=80	6.8-36.4 cm N=16
	Poor cod	10.6-21.5 cm N=12	7.2-19.3 cm N=27	9-12 cm n=9	8.4-17.5 cm N=77	9.3-15.6 cm N=10
	Cod	35-73 cm N=33	36cm N=1	29-93 cm N=18	N=0	33.2-68.7 cm N=8
	Dragonet	9-23 cm N=18	5.8-24.5 cm N=83	N=0	N=0	12-18.7 cm N=15
	Sole	9-38 cm N=51	12.7-36.7 cm N=78	N=0	N=0	7.5-29.5 cm N=1
	Plaice	9-43 cm N=37	8.5-55.3 cm N=134	20-38 cm n=40	22.5-42.6 cm N=28	13.4-25 cm N=15
	Horse mackerel	8-39 cm N=54	19.6-21.4 cm N=7	10-13 cm N=7	11.4-31.5 cm N=148	4.3-20.4 cm N=23
	Mackerel	18-37 cm N=39	32cm N=1	30-34 cm N=6	16.9-41 cm N=158	24.3-28.9 cm N=10
	Herring	6.2-29 cm N=10	N=0	5-27 cm N=6	N=0	7-25.1 cm N=15
	Sardine	7.7-29 cm N=10	N=0	N=0	N=0	9.8-20.2 cm N=10
	Squids	N=0	11.5-16.8 cm N=4	N=0	N=0	9-31 cm N=17