René Sandretto Mars

René Sandretto
email: sandretto@gate.cnrs.fr

François Perroux, a precursor of the current analyses of power

Keywords: JEL classification: B19 -History of Economic thought since 1925 B4 -Economic Methodology B5 Current Heterodox approaches Asymmetry, power, domination, influence, coercion

Despite its important contributions to economic thought, namely in the field of spatial economics and economics of development, François Perroux, one of the most important French economists of the 20st century, remains today poorly appreciated and frequently unrecognized. This paper tends to show how unfair is this deficit of recognition. We underline Perroux's illuminating views on asymmetry, domination and power which can be considered as a prefiguration and -to some extent -as a generalization of works made in this field half a century later, for example the American realist and neo-realist approaches of power (namely the concepts of hard and soft power) or by Susan Strange (with her concept of structural power).

Introduction

Unquestionably, François Perroux is one of the most original European economists of the 20st century. His innovations are many, ranging from spatial economics in which he analyzed the economics of location, the forces of agglomeration and dispersion [START_REF] Perroux | Les Macrodécisions[END_REF], to the analysis of economic development, including an interesting attempt to develop an alternative approach of the general equilibrium, based on recognition of the active role of agents [START_REF] Perroux | Unités actives et mathématiques nouvelles: révision de la théorie de l'équilibre économique général[END_REF]1976). However, among the various topics to which he made decisive contributions, the most insightful one is his "domination effect" and his analysis of power. Despite its numerous enlightening contributions to economic thought, nowadays the work of François Perroux is not really appreciated to its true value.

This paper aims at underlining Perroux's illuminating views on asymmetry, domination and power that one can consider as a prefiguration and -to some extent -as an extension of works made in this field half a century later.

When, in 1948, François Perroux wrote his famous article "Esquisse d'une théorie de l'économie dominante" [START_REF] Perroux | Esquisse d'une théorie de l'économie dominante[END_REF](Perroux, , 1950)), he was obviously influenced by the economic and political context of the times. In 1945, the United States had become the dominant economy in the world, and it seemed destined to remain so for many years to come [START_REF] Perroux | Leadership économique des États-Unis et analyse moderne des échanges extérieurs[END_REF]. A superficial reading of this seminal article might lead one to believe that Perroux had restricted himself to constructing a theoretical architecture, based on this single concrete example. But Perroux's range of interest was considerably broader.

In the present as in the past, an analysis of the effect of domination on international relations tightly conditions our knowledge of current affairs. After the Second World War, lopsided power relations induced trade imbalances and generated an irreversible orientation of trade and financial flows that was apparently incompatible with the creation of a new international economic multilateralism. At the same time, the chronic shortage in international liquidities raised formidable threats to the viability of the Bretton Woods arrangement. Creditors seemed perpetually to remain creditors; debtors became more and more indebted.

The domination effect and the concept of the internationally dominant economy offer particularly penetrating views of the new world that was being built on the threshold of the second half of the twentieth century. The scope of Perroux's analysis, however, is of a completely different nature.

It is much larger and more ambitious.

In this paper, I want to stress the potentially operational character of Perroux's concepts of asymmetry, domination (and dominance), and power. All of his theoretical concepts were based on attentive observation of the facts, especially those bearing on the future. His entire body of work bore witness to the imperative upon which he unremittingly insisted: a symbiosis between the "theoretician's discourse" and the "observer's discourse" (section 2). Then I describe more thoroughly the relations between structures and power (section 3) and the difference introduced in Perroux's later publications between domination and dominance (section 4).

The most interesting aspect of Perroux's thinking is that the domination effect represents a common denominator and a key to interpreting a multiplicity of apparently heterogeneous phenomena (section 5). This concept is probably what confers upon Perroux's work its overarching character and its pioneering feature (section 6). The components of power relations called asymmetries, inequalities, and irreversibilities therefore constitute central themes and structural elements. They are the main building blocks of a possible reconstruction of the general equilibrium along with a new way to look at human beings and society (section 7).

The Concept of Power and the Domination Effect

Starting with Max Weber, Perroux defines power as "the probability that an agent within a social relation will be in a situation to make his own will effective, in spite of resistances (…) The essence of power, sought after, used, expected, or predicted, is an asymmetric relationship that stems from unequal actions and reactions" (Perroux, 1973: 30). This asymmetry of influence, which he calls the domination effect, can exist between various units: individuals, firms, social groups, nations, and others.

It is useful at the outset to quote Perroux's own definition: "To consider just two economic units, we would say that A exercises a domination effect over B, when, in the absence of any particular intention, A exerts a certain influence on B without the inverse being true or true to the same degree. A dissymmetry or irreversibility of principle or degree is constitutive of this effect" (1948: 248). As an imperfect form of reciprocity and interdependence, the domination effect is therefore not necessarily the expression of a desire for power. It may also be the consequence of an existing situation -the result of differences in size and disparities in structure.

According to F. Perroux, the domination effect has three essential components. The first is the relative sizes of the units, including factor components, assets, respective contributions to supply and demand, information at their disposal, and so on. The second is bargaining power -the units' respective abilities to negotiate conditions and exchange rates, or even to set the rules of the game. Third, a unit's domination effect results from its belonging to an active zone, the position that it occupies in that zone, and the nature of the activity that it exercises. Of the three above components, this last is the least intuitive. It is, however, fundamental. The implication is that the strength or domination of one unit is not reduced exclusively to its individual features, but results from synergies and externalities -from the connection between the unit and its "environment."

Unintentional Domination

Independent of all desire to act on other decision-making centres, unit A exerts a dissymmetrical influence on them, for example, by increasing or decreasing its production or changing its prices.

The other units must adjust to A's decision by changing, in their turn, their level of activity and/or their prices, without these reactions affecting or influencing A to the same degree. This effect can be clearly observed when we examine, for example, how changes to the monetary or budgetary policy of the United States affect the circumstances of its partners. The domination effect may take the form of a cumulative sequence of asymmetrical influences in concentric rings. For instance, a restrictive monetary policy instituted in the United States to smother domestic inflationary pressures forces other industrialized countries to align themselves by raising their interest rates. Attempts at disconnection almost always prove to be impractical, except through rigorous control of the exchange rate (this is the first circle of asymmetry). The corresponding rise in international interest rates then induces a more strongly asymmetrical influence on developing countries, which are indebted at a floating rate, by increasing the service of their debt (this is the second circle of asymmetry).

An internationally dominant economy thus appears to be a "relatively autonomous" conjunctural centre of momentum, which, independent of any hegemonic intentions, influences the situations of its partners. In a world that is de facto more and more tightly interlinked, the interplay of irreversible and dissymmetrical influences develops both directly and indirectly along more or less complex chains (or sequences) of domination effects.

The market for Eurodollars is a cogent example. During the critical period of dislocation of the international currency system (late 1960s and early 1970s), the Eurodollar market undeniably served as a communication channel for an indirect domination effect. Unintentional at first, it relayed the influence of the American monetary market to other national monetary markets, complex relations between "structures" and "power". Two examples can illustrate these relations.

-Trade in raw materials. Industrialized countries and raw material producing countries have unequal capacity to influence trade and international markets. Indisputably, raw material producers would be less vulnerable and their negotiating power would be stronger if: (i) they were not so hyper-specialized (sometimes mono-specialized), as opposed to the diffused specialization of industrial countries. (ii) If industrialized countries were not so dangerous competitors in the export of raw materials. Contrary to a received idea, the most important exporters in raw materials (agricultural and mineral) are developed countries. (iii) If they were not sometimes forced to sell at any price, and were less dependent on markets in industrialized countries and on foreign firms. Transnational firms also intentionally structure relationships.

-Location strategy of transnational firms. In some particular industrial sectors, transnational groups sometimes apply what may be called a strategy of "specialization/diversification," in which each of their subsidiaries is made into an ultra-specialized plant. In this strategy, the transnational firm spreads the geographic distribution of its subsidiary plants in different countries for each stage of the production process. For example, one subsidiary of a car manufacturer will produce only brake pads, and this part will be manufactured simultaneously in Mexico, Brazil, and Asia. This particular strategy is obviously a case of intentional implementation of structural power relations. It leads, among other things, to a productive and spatial structure that generates domination effects between the firm's management and the government and social groups in the host country. It minimizes the effects on the firm of potential technical, political, or social incidents. It dissuades host countries from nationalizing foreign firms established on their soil, since each "plant" is viable only within the industrial group upon which it is totally dependent. It also protects the industrial group against the consequences of strikes, which are not internationally coordinated. On the other hand, this structure makes the group's threat or counterthreat of lock-out or closure credible to both unions and local governments, since a local production stoppage does not disrupt the group's activity [START_REF] Sandretto | Le commerce international[END_REF].

These two examples illustrate clearly that power relations do not 'fall from the sky', but that they may be structurally determined.

Domination and Dominance

In his later writings, Perroux has refined his analysis of the domination effect with the distinction between 'domination' and 'dominance' depending on the intensity and extent of asymmetrical relations [START_REF] Perroux | Unités actives et mathématiques nouvelles: révision de la théorie de l'équilibre économique général[END_REF]:

-Dominance is a degree of asymmetry that cannot be evaded over a given period, resulting from the asymmetry in the respective influences, which is such that Unit A exerts an influence on B, while B exerts an influence on A but not at the same degree.

-At the opposite, domination (strictly speaking) is corresponding to an intrinsic dissymmetry of principle (total irreversibility, always within a given period). In other words, domination would correspond to total dominance. Perroux also sometimes used the term domination to designate crystallized dominance in structures and institutions.

Analytically, dominance is more interesting than domination, as it has a greater range. As F. Perroux wrote in a personal correspondence with the author (in 1975), "Total dominance of A over B destroys (economically) duality," because it suppresses B's quality as an actor -its decision-making capacity, individuality, and integrity. This may be why Perroux abandoned the expression of domination (and "domination effect") for the more general one of "dominance" in his later writings.

The main problem resides in the difficulty of measuring the intensity and effectiveness of the dominance effect. Expressing it in the most general terms, Perroux characterized the search for the most useful result possible in the behaviour of two units, A and B, in a relationship of pure trade. This point is reached when A and B equalize the marginal return obtained and the marginal return ceded:

1 ceded return Marginal obtained return Marginal =
The impact of the dominance effect, according to Perroux, is evaluated by the external advantage of pure trade -by the proportion within which the respective performances of A and B may deviate from the above standard of optimality and equity. The breadth of the dominance effect may thus be quantified by the price supplement that A imposes on B above the marginal cost of the good that it is selling or by the difference between the remuneration to the holder of a production factor and that factor's maximum marginal productivity.

Following a similar approach, the international neo-classical equilibrium model described by Heckscher, Ohlin, and Samuelson (the HOS model) can be interpreted as the standard of equal trade, conflictually neutral, from which all dominance relations are axiomatically excluded [START_REF] Sandretto | Inégalités transnationales. Une application de la théorie des jeux[END_REF]. Measurement of economic power by deviation from the model of pure trade (or the ideal model of perfect competition) is both simple and attractive on the conceptual level.

But is it the most operative and significant in practice? According to Perroux, the answer is no, because it refers not to a particular concrete situation, but to an unrealistic model -a fiction.

Power, keystone of the Perrouxian analysis

In L'Économie du XXe Siècle [START_REF] Perroux | L'Économie du XXe siècle[END_REF], Perroux shows the importance of the dominance effect within his work. The structure itself of this book reflects this prominence.

This major work begins, in fact, with a section devoted to the dominant economy (Part 1). It is followed by a study of spatial, linkage, and agglomeration asymmetries -in other words, the formalization of the growth poles that are a direct application of the dominance theory (Part 2).

Then comes the concept of macro-decisions, a clear example of the structural decision-making power of a dominant actor: with the help of the irreversible and asymmetrical influence that it is capable of exerting, the macro-decision imposes the rules of the game on and shapes the environment of the other units (Part 3). The analysis then turns to the process of development and underdevelopment, which is dependent on the coupling mechanisms that link the various parties in the global economy and the asymmetries that it supports (Part 4). This process leads to identification of the forces of dynamism and progress, the main one of which is the search for power (a motivation "as powerful as the search for well-being or monetary gain" [Part 5]).

Economic movements are accomplished by human beings, innovation, and power. They result from the intersection of the behaviours of "diversely and unequally active" units (Part 6). We can thus see that dissymmetries and irreversibilities of power relations, far from being dispersed instruments in an analytic toolbox, are essential aspects of an overall interpretation.

In this work -no doubt Perroux's most important synthesis -the dominance effect appears to be the common denominator in most of his key concepts. Later, it became the bedrock of an overall theoretical reformulation and of his last project: the construction of a theory of general equilibration [START_REF] Perroux | Unités actives et mathématiques nouvelles: révision de la théorie de l'équilibre économique général[END_REF].

The concept of economic power elaborated by Perroux is deduced from his analysis of asymmetries, irreversibilities, and constraint "in a universe of actors." It is no exaggeration to state that this concept of dominance is the cement that gives his complex body of work its coherence.

A prefiguration of the most recent analyses of power

Perroux's concept of power can be compared to more recent concepts of power. In the American neo-realist approach, power is relational. First, in a context of strong asymmetries, power can be applied through constraints. In the contemporary American neo-realist analysis, power is defined as the capacity of unit A (state, firm) to directly force unit B to do what it would not have done spontaneously, in order to better satisfy the interests of unit A. This is called hard power, because it relies on the comparative strengths of units A and B: military power, natural resources, demography, capacity to inflict damage on another or to avoid such damage. The "hard power" is one of the key concepts of the American neo-realist school of thought, whose one of the most prominent representative is Kenneth Walz (1979). In contrast to this, the American liberal institutional approach has emphasized the quite different concept of soft power based on cultural ideological and political attraction, and on the attractiveness of the way of life of the leading country(ies) (Nye 1990: 167). Actually, in the globalized multipolar and complex world in which we are living, the reinforcement of global interdependences creates a situation such that hegemonic (hard) power is increasingly difficult to exert. Force cannot always easily impose power. Power then tends to change in nature. Leading states attempt more and more frequently to exert influence through other instruments than military force or economic constraint, using state's capacity to seduce, convince, or yet induce through cultural and/or ideological attraction. More than traditional means, soft power is based on intangible assets (culture, way of life).

Another important recent contribution to power analysis has been achieved by Susan Strange.

Similarly to François Perroux, Susan Strange suggested a structural approach of power, that is a concept of power basically linked to structures and, more generally, to the environment in which agents' actions take place. She defines power as the capacity of an individual or a group to influence a situation in such a way that the preferences of the individual or group have priority over others' preferences [START_REF] Strange | The Retreat of the State: The Diffusion of Power in the World Economy[END_REF]. In other words, power is the capacity to conceive, legitimize, implement, and control rules for individual and collective action. This amounts to the capacity to shape structures within which other actors will have to evolve. The strangeian concept of power is also structural in so far as it relies on structural components.

Strange suggests four basic power structures:

1. Security structures, the way in which each society organizes and manages its protection against various risks (wars, terrorists threats, natural catastrophes, epidemics, food and environmental security) The above brief contextualization of approaches to power shows the extent to which Perroux's own approach was seminal. Half a century earlier, Perroux had framed an approach that incorporates American neo-realism, liberal institutionalism and the Strangeian approaches, each of them appears as specific cases of this Perrouxian unified theoretical framework, since this last one includes both relational and structural powers. Perroux' point of view suggests that hard power, soft power and structural powers can be regarded as different aspects of a more general conceptualization.

Indeed, it is easy to recognize the hard power as a modern expression of imposition or coercion, while the soft power is quite similar to influence in the Perrouxian typology. Similarly, structural power, as described by Strange, is reminiscent of unintentional dominance along with the Perrouxian suggestion that intentional dominance can rely on unintentional dominance. In both

Perroux and Strange we can also find the idea that power relationships are structurally conditioned.

Conclusion

Perroux's acceptance at the outset of asymmetrical and irreversible actions explains why his analysis was so strongly distinct from the major traditional currents of economic analysis. It may also explain why his analysis tends now to sink into oblivion. In several publications, Perroux criticized the various processes whereby the mainstream economic analysis eludes the power relationship, namely:

-the waterproof partitioning between economics (often considered as science of means) and politics (as science of ends), which lead to a tendency to associate power only with state power and extract it from the economic sphere (belonging to the private sector) ;

-the rudimentary separation of economic relations (superficially conceived as merchant relations governed by private profitability) and social relations (often trivially considered as an obstacle or a corrective to economic activities) ; -the separation of economic variables (prices and quantities) from extra-economic data (rules of the game, institutions, ownership regimes, power relations, and so forth).

Finally, Perroux was fundamentally opposed to reductionist simplifications -the neo-classicists' irenicism (total absence of conflicts) and the Marxists' polemicism (unavoidable confrontation between two inherently antagonistic classes) [START_REF] Perroux | Les Conceptualisations implicitement normatives et les limites de la modélisation en économie[END_REF](Perroux, : 2271)). For Perroux, all exchanges are of a hybrid nature: they mix free and reciprocal transfers and power relations [START_REF] Perroux | Pouvoir et Économie[END_REF].

Economic relations, as any social relations, intimately blend conflict and co-operation.

One of the main questionings that we find in several publications of Perroux was: can the neoclassical model be amended? François Perroux believes that the very foundations of the model are defective. In his opinion, the neo-classical theory would not be improved by the introduction of power, for it would certainly then be ruined. Thus, he considers that a complete reconstruction on other foundations is necessary.

Perroux tried to perform this reconstruction by replacing equilibrium with equilibration of active units' energy for change: "Equilibration is a chain of decisions and acts over a period of time.

The state that we call equilibrium is the more or less durable persistence of sequences conveying, under explicit structural constraints, the cross-compatibility of actors' projects and activities" (Perroux, 1975: 148). Thus reformulated, the general equilibration of an economic set is attained when the sum of the actors' energies for change is close to zero.

Even though the theoretical reconstruction begun by Perroux was not completed, it remains an original attempt. His last book published in 1975 is full of intuitions and suggestions aimed at transforming the concept of general economic equilibrium from its initial description as a balance of forces applying to objects to the topological representation of a process which tends to make compatible agents' plans as well as the change energies that they develop individually and collectively.

The fact that this project has not been completely brought to a successful conclusion is assuredly a limitation. However, in one sense, it remains also a potential: an invitation to present and future generations not to give in to mental laziness but to follow the rocky path that Perroux opened up.

  2. Production structures (e.g., multinationals, innovation) 3. Financial structures (with financial globalization) 4. Knowledge structure, a domain in which asymmetries of acquisition and holding of knowledge have increased dramatically with recent changes in communication technology On the basis of these concepts, Strange puts forward two major theses: first, she contests the thesis of a U.S. decline. Second, all states (including the United States) see their capacity to act on society and the economy decline in comparison with private actors. Therefore, zones of ungovernance -spheres in which neither state nor non-state actors can master events (in particular in the field of finance and the environment) -evolve. Consequently, S. Strange considered that if the most important global risk in the long run is related to environment, the closest risk of global crisis will have to do with the world financial system.


domain: spi phys

text:
Koffi Ahanogbe

J Alvarez

Alexandre Jaffré

James P Connolly

Marie-Estelle Gueunier-Farret

E Fourmond

A Fave

S El-Whibi

Zakaria Djebbour

Jean-Paul Kleider

A Jaffre

Electroluminescence analysis of Silicon Interdigitated Back Contact for three-terminal tandem applications

come   L'archive ouverte pluridisciplinaire

A very promising new concept of 3-terminal (3T) tandem cells with selective band offset barrier (3T-SBOB) tandem cells has been developed at GeePs and has many advantages over 2-and 4-terminal cells. The ANR THESIS project aims at 3T-SBOB tandem cell. The perovskite based top subcell absorbs energy photons while the silicon based interdigitated back contact (Si-IBC) bottom subcell absorbs lower energy photons. We focus here on the optoelectronic properties of IBC-Si « that will be used as bottom cell in 3T », investigated using the spatially and spectrally resolved electroluminescence (EL) characterization. EL consist of light emission by application of an electrical bias enables rapid characterization of the entire cell and allows the visualization of microscopic defects on micrometer scale of the cell that can not be detected by photoluminescence (PL) imaging on the device. Figures 1 and2 show examples of the spatially resolved EL and PL of a 13.8% efficiency Si-IBC solar cell fabricated at INL-Lyon and characterized at GeePs. The fill factor of this cell is of about 67%. Absorption is quite homogenous as shown in PL image. But in EL image we notice locally reduced emission which may caused by resistive losses, low surface recombination velocity and low diffusion length. In Figure 3 we present spectrally resolved EL emission(red curve) and the directly mesured quantum efficiency (EQE) (magenta curve). By scaling the EL emission with the EQE and integrating it, one can obtain the correct saturation current density and then quantify the radiative recombination open circuit voltage (𝑉 𝑜𝑐,𝑟𝑎𝑑 ). The difference between 𝑉 𝑜𝑐,𝑟𝑎𝑑 and 𝑉 𝑜𝑐 directly mesured (∆𝑉 𝑜𝑐 = 𝑉 𝑜𝑐,𝑟𝑎𝑑 -𝑉 𝑜𝑐 ) gives the losses due to non-radiative recombination in the cell.

Fig. 1 :

 1 Fig.1: EL image of 1cm 2 monocristalline Si-IBC at 0.9V bias applied. We note locally reduced EL emission due to variation of electronic properties.

Fig. 2 :

 2 Fig. 2 : PL image of 1cm 2 monocristalline Si-IBC. Beam used is laser 532 nm at room temperature.

Fig. 3 :

 3 Fig. 3 : Comparison of EL spectra (red curves) and quantum efficiencies (magenta point). The blue points represent the quantum efficiencies that follow from the EL spectra.


Emeline Roux

Aurélie Nicolas

Florence Valence

Grégoire Siekaniec

Victoria Chuat

Jacques Nicolas

Yves Le Loir

Eric Guédon

The genomic basis of the Streptococcus thermophilus health-promoting properties

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

METHODS

RESULTS

ü S. thermophilus is a Gram-positive bacterium used as starter in dairy industry and traditional fermented products ü Well adapted to the milk environment due to its genomic plasticity and population evolution ü Used as probiotics for several years with various beneficial effects (alleviation of lactose intolerance, inhibition of pathogens, prevention or treatment of inflammatory gut diseases...)

CONCLUSION

Strain characteristics

Antioxidative activity ü STH can produce various molecules that decrease the risk of reacIve oxygen species such as glutathione, GABA, CLA, folate, EPS, betalactoglobulin-released pepIdes ü glutathione peroxidase acIvity is predicted in 12 strains

Produc4on of bioac4ve pep4des

ü

Resistome and Virulome

ü No virulence factors are found. ü Only two genes potentially conferring resistance to antibiotics were detected in nine strains: ü 4 strains encode mefE; but mefE alone is likely not able to confer high-level macrolide resistance in STH ü 5 strains encode tet(S) leading to a tetracycline resistance à the absence of virulence factors and the low occurrence of antibiotic resistance genes contribute to the safety status of the species.

Produc4on of GABA

ü 29% of STH strains contain the gadB and gadC genes coding for the glutamate decarboxylase enzyme involved in the irreversible conversion of glutamate into GABA and the GABA/Glutamate anIporter, respecIvely. ü The gadBC-containing region tends to undergo mulIple evoluIonary events and may have been acquired by HGT.

Produc4on of conjugated linoleic and linolenic acids

ü The genome of six strains encodes a protein annotated as linoleate isomerase involved in CLA/CLNA synthesis

Produc4on of biogenic amines

ü Only a few STH strains (6/79) contains genes coding for histamine producIon from hisIdine (the HcdA hisIdine decarboxylase proenzyme, the HdcP hisIdine/histamine anIporter, and HdcB, which is involved in HdcA maturaIon). ü Concerning tyramine, tryptamine, phenylethylamine and putrescine producIon, no protein/genomic region with homology to known decarboxylase is detected in the 79 STH genome sequences.

The results of this comparative genomic study provide a sound basis for future studies on STH. Notably our analysis provides targets for further phenotypic characterizations and experimental validations. While some beneficial traits are widely shared among isolates suggesting their central physiological and ecological role for the species (e.g., degradation of lactose, folate production), others including the tagatose-6-phosphate pathway involved in the catabolism of galactose, and the production of bioactive peptides and GABA are highly strain-specific. Most of strain-specific health-promoting features seems to have been acquired via horizontal gene transfer events. The natural intra-species diversity of STH, therefore, represents an interesting source for innovation in the field of fermented products enriched for healthy components that can be exploited to improve human health. A better knowledge of the health-promoting properties and their genomic and genetic diversity within the species may facilitate the selection and application of strains for specific biotechnological and human health-promoting purpose.

Lactose and galactose metabolism

ü 100% of STH strains are Lac+ ü 21% of strains could display Gal+ phenotype: ü 15 strains contain the same nucleoIde G-to-A subsItuIon in the -10 box of Gal+ mutants ü 2 strains contain genes coding for the tagatose-6-phosphate pathway

FigureFigure 2 :

 2 Figure 1: Health-promo4ng proper4es of S. thermophilus

Figure 3 :

 3 Figure 3: Comparison of the genomic region harboring the gpx gene in various S. thermophilus strains, S. ves'bularis NCTC12167 and S. salivarius CCHSS3.

Figure 4 :

 4 Figure 4: Gene4c organiza4on of genes coding for the tagatose 6P pathway in strain JIM10116 and CIRM-BIA336.


Lisa Weiss
email: lisa.weiss@univ-perp.fr

Wolfgang Ludwig

Serge Heussner

Miquel Canals

Jean-François Ghiglione

Claude Estournel

Mel Constant

Philippe Kerhervé

The missing ocean plastic sink: gone with the rivers

come

2.4 to 4.0 Mt yr -1 [START_REF] Lebreton | River plastic emissions to the world's oceans[END_REF][START_REF] Schmidt | Export of plastic debris by rivers into the sea[END_REF]. Among the different plastic size categories generally recognized, the <5 mm microplastics (MPs hereafter) represent the size fraction for which both river flux and surface oceanic MP stock estimates rely on equal sampling techniques, thus allowing direct comparison (Supplementary Materials and Methods 3.1). Narrowing the figures to this better-documented category yields an average MP river input of 1.5 Mt yr -1 [START_REF] Lau | Evaluating scenarios toward zero plastic pollution[END_REF]. Furthermore, the amount of plastic floating at the ocean surface, mainly composed by MPs [START_REF] Morét-Ferguson | The size, mass, and composition of plastic debris in the Western North Atlantic Ocean[END_REF][START_REF] Van Sebille | A global inventory of small floating plastic debris[END_REF], is currently estimated at 14.4 kt [START_REF] Cózar | Plastic debris in the open ocean[END_REF], [START_REF] Xiong | Occurrence and fate of microplastic debris in middle and lower reaches of the Yangtze River -From inland to the sea[END_REF].5 -66.1 kt [START_REF] Eriksen | Plastic pollution in the world's oceans: more than 5 trillion plastic pieces weighing over 250,000 tons afloat at sea[END_REF] or even 236 kt [START_REF] Van Sebille | A global inventory of small floating plastic debris[END_REF], depending on data availability, modeling approach and the upper particle size limit considered. So far, compelling evidence for a rapid growth of the floating plastic stock in the ocean is missing [START_REF] Law | Plastic accumulation in the North Atlantic subtropical gyre[END_REF][START_REF] Law | Distribution of surface plastic debris in the eastern Pacific Ocean from an 11-year data set[END_REF]. Therefore, dividing the relevant amount by the annual MP flux from rivers provides a conservative indication of the average residence time of MP debris at the ocean surface. A global river discharge in the range of million tons per year accordingly implies an unrealistic short residence time of MPs at the ocean surface, i.e. in the range of days to weeks.

As with the "missing carbon sink" concept [START_REF] Keeling | A three-dimensional model of atmospheric CO2 transport based on observed winds: 4. Mean annual gradients and interannual variations[END_REF] that fostered fundamental research on the global carbon cycle in the early 1990s, the idea of a "missing ocean plastic sink" emerged from such an overwhelming difference between the amount of MPs supposedly brought by rivers and the stocks accumulating at the ocean surface [START_REF] Cózar | Plastic debris in the open ocean[END_REF][START_REF] Thompson | Lost at Sea: Where Is All the Plastic?[END_REF][START_REF] Ter Halle | Understanding the fragmentation pattern of marine plastic debris[END_REF] and triggered research on the fate of plastic debris in the marine environment. Several processes have been proposed to be prime actors in preventing ever-growing plastic accumulation at the ocean surface. Among them is rapid accumulation in living biomass [START_REF] Davison | Plastic ingestion by mesopelagic fishes in the North Pacific Subtropical Gyre[END_REF], quick loss of buoyancy and settling to deeper water layers and the seabed [START_REF] Woodall | The deep sea is a major sink for microplastic debris[END_REF][START_REF] De Haan | on behalf of the NUREIEV1 Shipboard Scientific Party, Floating microplastics and aggregate formation in the Western Mediterranean Sea[END_REF][START_REF] Pabortsava | High concentrations of plastic hidden beneath the surface of the Atlantic Ocean[END_REF][START_REF] Kane | Seafloor microplastic hotspots controlled by deep-sea circulation[END_REF][START_REF] Boucher | The Mediterranean: Mare plasticum[END_REF], rapid stranding on beaches [START_REF] Liubartseva | Tracking plastics in the Mediterranean: 2D Lagrangian model[END_REF][START_REF] Ourmières | The boundary current role on the transport and stranding of floating marine litter: The French Riviera case[END_REF], degradation through physical fragmentation [START_REF] Ter Halle | Understanding the fragmentation pattern of marine plastic debris[END_REF], microbial alteration [START_REF] Jacquin | Microbial ecotoxicology of marine plastic debris: a review on colonization and biodegradation by the "plastisphere[END_REF] and/or photochemical dissolution [START_REF] Zhu | Photochemical dissolution of buoyant microplastics to dissolved organic carbon: Rates and microbial impacts[END_REF]. None of these studies has nevertheless questioned the robustness of so short residence times of MPs at the ocean surface as those derived from the comparison between river fluxes and floating ocean stocks.

Contrary to measurements at sea, MP studies in rivers were scarce at the time of initial river flux estimates and disregarded differences in sampling techniques. However, recent studies on MPs in rivers allowed us to reassess river fluxes based on a more exhaustive data compilation than previously made (Fig. 1 and Table S1). We consequently identify three main methodological biases that magnified errors in the process leading from the quantification of plastic debris in individual rivers to the calculation of global river budgets. Correcting these errors leads to flux estimates that are orders of magnitude (OM hereafter) smaller than previous values. The quest for a major missing plastic sink in the ocean becomes then needless. S1). With respect to the world total, the 89 sampled rivers represent 14% of water discharge.

The first source of error refers to the choice of a representative mass for MPs in rivers. Since most field studies only determined MP number concentrations, the accurate estimate of MP mass transport depends on knowing how to convert numbers to mass. Based on our extended dataset (n = 129), a median mass of 0.23 mg item -1 (Weiss conversion factor 1, Wf1) for non-fiber MPs is obtained (Supplementary Materials and Methods 1.3 and Figs. S1, S2), which is significantly lower than those used in previous estimates, i.e. 3.0 mg item -1 (7) or 0.96 mg item -1 (8), referred as Lf and Sf conversion factors hereafter (according to initial letters of the first authors in [START_REF] Lebreton | River plastic emissions to the world's oceans[END_REF] and (8), respectively). Our estimate for MP fibers is 0.75 µg item -1 (Weiss conversion factor 2, Wf2). Since bulk samples can be largely composed by fibers (up to >90%, Table S1), composite MP mass (estimated using a composite Weiss factor, Wf) often represents only a small fraction of Wf1, and Wf frequently is 1-2 OM lower than Lf or Sf.

The second source of error results from the inappropriate mixing of data collected with different sampling techniques. MPs at sea are usually collected with plankton nets [START_REF] Hidalgo-Ruz | Microplastics in the Marine Environment: a review of the methods used for identification and quantification[END_REF], which is also the most common sampling technique in rivers (30) (hereafter "plankton net sampling"). However, in a number of studies, MPs have been collected using other techniques (hereafter "miscellaneous sampling") including filtration through pore sizes smaller than the minimum mesh size of plankton nets (80 µm). Our data clearly show that filtration collects much larger numbers of MPs (Fig. 2A) and, particularly, small-sized MPs, which is consistent with previous studies that found distributions of MPs sampled with this method skewed toward the lower size range in rivers [START_REF] Dris | Microplastic contamination in an urban area: a case study in Greater Paris[END_REF], atmospheric deposits [START_REF] Allen | Atmospheric transport and deposition of microplastics in a remote mountain catchment[END_REF] and seawater [START_REF] Poulain | Small Microplastics as a Main Contributor to Plastic Mass Balance in the North Atlantic Subtropical Gyre[END_REF]. Major biases arise when such small plastic fragments are included in mass conversions using factors obtained from plankton net sampling. A striking example is the Yangtze River for which miscellaneous sampling on filters [START_REF] Zhao | Suspended microplastics in the surface water of the Yangtze estuary system, China: first observations on occurrence, distribution[END_REF] produced MP number concentrations 3 to 4 OM larger than sampling with plankton nets [START_REF] Xiong | Occurrence and fate of microplastic debris in middle and lower reaches of the Yangtze River -From inland to the sea[END_REF]. The mass offset rises to almost 5 OM when the number concentrations based on filtration are converted to mass concentrations by using Lf [as applied in [START_REF] Lebreton | River plastic emissions to the world's oceans[END_REF]] and the number concentrations based on plankton net sampling are converted by using Wf.

A box plot of MP mass concentrations highlights the combined effect of inappropriate conversion factors and misleading mixing of measurements from different sampling techniques (Fig. 2B). Applying uniformly the Lf factor to the reported number concentrations in our exhaustive data set yields a mass concentration range encompassing 7 OM. MP mass concentrations would be in some cases as low as those of natural trace metals during low flow conditions [START_REF] Martin | Elemental Mass-Balance of Material Carried by Major World Rivers[END_REF] while in other cases they would be as high as total suspended sediment concentrations during flood conditions [START_REF] Meybeck | Global variability of daily total suspended solids and their fluxes in rivers[END_REF]. Such an extended mass range has never been reported for any kind of particulate matter in rivers before. Using however the Wf factor not only lowers the median mass concentration by more than a factor of 30, but also narrows its variability by one OM. Restricting the outcomes from field studies to those from plankton net sampling further lowers median concentrations and leads to the strongest reduction of variability. Values now only stretch over 3 OM, which is more in line with the maximum seasonal variability for MP concentrations reported in case studies [START_REF] Constant | Microplastic fluxes in a large and a small Mediterranean river catchments: The Têt and the Rhône, Northwestern Mediterranean Sea[END_REF][START_REF] Faure | Plastic pollution in Swiss surface waters: nature and concentrations, interaction with pollutants[END_REF][START_REF] Lechner | The Danube so colourful: a potpourri of plastic litter outnumbers fish larvae in Europe's second largest river[END_REF]. The third source of error concerns global MP flux estimates based on the relationship between MP river fluxes and MPW. Our calculations yield MP fluxes as high as millions of tons when using the above-mentioned Lf or Sf conversion factors (4,610 and 1,479 kt yr -1 respectively) and correlating river mass fluxes with MPW stocks in drainage basins (Table 1). Nevertheless, the associated values of the coefficient of determination are quite low (r² = 0.53), suggesting that the models are far from fully explaining the calculated river loads. Applying the composite factor Wf drops the global MP flux to 129 kt yr -1 , while r² increases to 0.59. Restricting the regression to the plankton net data subset further improves the correlation (r² = 0.66) and reduces the global flux to 31 kt yr -1 . Interestingly, with this latter subset of data, MPW is no longer the best predictor for MP river loads, since the associated coefficient of determination is greater (r² = 0.69) if correlated to total basin population (Pop). Processing the large-scale extrapolations with the parametric equation based on regression with Pop instead of MPW still decreases the global MP flux by about one OM down to 3.5 kt yr -1 . We also tested whether multi-regression models can improve the statistics (Supplementary Materials and Methods 2.2 and Table S3). For the plankton net dataset, we identify a significant relationship between specific MP fluxes, population density (sPop) and drainage intensity (sQ). This relationship increases again the coefficient of determination to r² = 0.80 (Table 1), although global budgets only change moderately (6.1 kt yr -1 ). However, regression analyses alone do not allow rejection of MPW as the best predictor for riverine MP fluxes but the heterogeneity that MPW values implied in the spatial distribution of riverine MP discharges into the ocean does. Indeed, this heterogeneity does not match the observed accumulation patterns in the different ocean basins (Fig. 3). The discrepancy is particularly striking for the North Atlantic Ocean. Although this basin should have a MP concentration at least as large as the North Pacific Ocean [START_REF] Cózar | Plastic debris in the open ocean[END_REF][START_REF] Poulain | Small Microplastics as a Main Contributor to Plastic Mass Balance in the North Atlantic Subtropical Gyre[END_REF][START_REF] Lebreton | Evidence that the Great Pacific Garbage Patch is rapidly accumulating plastic[END_REF], it always receives less than 6% of the global river inputs when extrapolations are calculated from MPW (Table 1). This is because MPW estimates for Europe and North America are quite low compared to Asia and Africa (Fig. S3). Extrapolations based on Pop and/or on sPop and sQ better fit with observed MP accumulation at the ocean surface (Fig. 3). Very recently, a modeling study [START_REF] Mai | Global Riverine Plastic Outflows[END_REF] proposed a scenario of global river plastic fluxes based on a Human Development Index (HDI). Although the authors found clearly lower and spatially more equilibrated values compared to [START_REF] Lebreton | River plastic emissions to the world's oceans[END_REF] and (8), discrepancies with the accumulation patterns at the ocean surfaces still exist. They are more important than in our approach, which is not giving more credit to HDI compared to Pop.

Table 1. Regression models for observed MP river fluxes and potential controlling factors in the respective

drainage basins for the data subsets shown in Fig. 2. The resulting global MP fluxes are further detailed according to the main ocean basins to which they are discharged. The "Others" column includes discharges into the Mediterranean Sea, the Black Sea and the Arctic Ocean. MPW: Mismanaged plastic waste; Pop: basin population; sPop: population density; sQ: drainage intensity. 1). Both surface ocean stocks for the listed ocean basins and river fluxes close at 100%. Extrapolations of MP river fluxes based on Pop and/or sPop and sQ generally fit better with observed MPs accumulation at the ocean surface according to Cózar's et al.,observations (12) than extrapolation based on MPW. Nevertheless, discrepancies exist, especially for the Indian Ocean in the Southern Hemisphere. The oceanic gyre is here connected to the South Atlantic via the Agulhas Current leakage [START_REF] De Ruijter | Indian-Atlantic interocean exchange: Dynamics, estimation and impact[END_REF] and to the South Pacific via the Great Australian Bight and the Tasman Sea [START_REF] Maes | A surface "superconvergence" pathway connecting the South Indian Ocean to the subtropical South Pacific gyre[END_REF], suggesting that the stocks in these two ocean basins could be partly fed by MPs originating from the Indian Ocean.

Fig. 3. Comparison between relative distribution of estimated MP stocks at the surface of the different ocean basins (12) and relative distribution of riverine MP fluxes according to the "plankton net sampling" model outputs (Table

Lowering the global river plastic flux down to a few thousand tons per year has of course major implications for our understanding of MPs cycling in the sea. Conservatively dividing the oceanic stock of 14.4 kt (12) by our best MP flux estimate of 6.1 kt yr -1 yields residence times around 2.4 years for the floating stock at the ocean surface. Although associated with significant uncertainties (Supplementary Materials and Methods 3), such values support the idea that surface oceanic MP stocks result from rather slow accumulation processes and thus conflicts with the concept of ocean MPs being a highly reactive pool in terms of biological and chemical degradation and sequestration processes. Longer residence times are also in accordance with the observed long-distance transport of invasive species living on rafting plastics that may be part of the "plastisphere" [START_REF] Jacquin | Microbial ecotoxicology of marine plastic debris: a review on colonization and biodegradation by the "plastisphere[END_REF][START_REF] Zettler | Life in the "Plastisphere": microbial communities on plastic marine debris[END_REF]. Slow accumulation does not exclude selective sorting and sequestration of MPs on their way from land to the oceanic gyres. The average mass of a floating oceanic MP is generally higher (between 0.97 and 7 mg [START_REF] Morét-Ferguson | The size, mass, and composition of plastic debris in the Western North Atlantic Ocean[END_REF][START_REF] Cózar | Plastic debris in the open ocean[END_REF][START_REF] Eriksen | Plastic pollution in the world's oceans: more than 5 trillion plastic pieces weighing over 250,000 tons afloat at sea[END_REF][START_REF] Ter Halle | Understanding the fragmentation pattern of marine plastic debris[END_REF][START_REF] Lebreton | Evidence that the Great Pacific Garbage Patch is rapidly accumulating plastic[END_REF]) than the value we found for non-fiber MPs in rivers and tends to increase in accumulation areas (Supplementary Materials and Methods 3, and Fig. S1). This difference could reflect selective sequestration of smaller MPs, for example through turbulent dispersion in the water column [START_REF] Poulain | Small Microplastics as a Main Contributor to Plastic Mass Balance in the North Atlantic Subtropical Gyre[END_REF] or ingestion by a wide range of organisms [START_REF] Law | Plastic accumulation in the North Atlantic subtropical gyre[END_REF][START_REF] Thompson | Lost at Sea: Where Is All the Plastic?[END_REF][START_REF] Deudero | Mediterranean marine biodiversity under threat: reviewing influence of marine litter on species[END_REF] and subsequent transfer to seafloor sediments where they form the bulk of plastic litter [START_REF] Woodall | The deep sea is a major sink for microplastic debris[END_REF][START_REF] Kane | Seafloor microplastic hotspots controlled by deep-sea circulation[END_REF][START_REF] Courtene-Jones | Microplastic pollution identified in deep-sea water and ingested by benthic invertebrates in the Rockall Trough, North Atlantic Ocean[END_REF].

Our finding that MP river fluxes are much lower than previous estimates should not be misunderstood as an attempt to minimize the severity of the plastic pollution problem. On the contrary, it implies that even if riverine plastic inputs were to cease immediately, the floating MP stocks and their deleterious effects on the marine environment would persist for many years. We neither claim that plastic cycling in the oceans is fully understood. There are many size classes, oceanic compartments and land-to-sea transfer processes on which further research is urgently needed to properly evaluate the exposure of marine biota to this novel type of pollution and design cleaning strategies. Reliable mass quantification of plastic stocks and fluxes both in the lower micrometer to nanometer scale and in the form of macroplastics are on top of the priority list for action. However, as we clearly demonstrate with our results, in all of these approaches, great effort should be spent on the development of standard sampling techniques and reliable extrapolation methods in order to avoid major errors in budget calculations that are uncritically accepted. We finally demonstrate that MP pollution in the world ocean is not restricted to MPW-designated hot spot countries in Asia or Africa. Collective initiatives aiming at reducing the ocean's MP load therefore should rely more on global land-based actions at much larger spatial scales than previously thought.

SUPPLEMENTARY MATERIALS AND METHODS

Data collection on MPs in rivers 1.Data mining

Our dataset on microplastics (MPs) in rivers has been compiled based on an extensive bibliographic search and a careful analysis of the collected data (Table S1). All retrieved values have been thoroughly verified in the respective original source publications. The resulting database contains 127 average MP concentration values corresponding to 127 sampling stations from 42 published studies on 89 rivers and connected surface waters all over the world (Fig. 1). Most of them are located in Europe, North America and South-East Asia. Our study goes far beyond previously published compilations [START_REF] Lebreton | River plastic emissions to the world's oceans[END_REF][START_REF] Schmidt | Export of plastic debris by rivers into the sea[END_REF] in terms of number of measurements (n = 340) and diversity of studied environments and protocols. Our 127 average values have been calculated from these 340 referenced measurements. Repeated seasonal measurements for a given river station have been averaged to one single data point. For conversion to instantaneous fluxes we have used, whenever possible, the reported literature values for water discharges and basin areas. In many case studies, however, the associated water discharge was not cited, and we have used instead the long-term estimate extracted from our drainage intensity data layer (see below). Research on plastic pollution in rivers is recent. The first papers on this topic were published in 2004 and 2005 [START_REF] Thompson | Lost at Sea: Where Is All the Plastic?[END_REF]47,48). It took another decade to develop the first field protocols for quantifying MPs in rivers [Danube [START_REF] Lechner | The Danube so colourful: a potpourri of plastic litter outnumbers fish larvae in Europe's second largest river[END_REF], Los Angeles rivers (49), Tamar (50), Seine (51)]. Up to now, there is no standardized protocol and our database encompasses a great diversity of sampling and analytical procedures. Mesh or pore sizes for recovering MPs in freshwater samples are highly variable (3 µm to 2 mm).

Data subsets

In order to test whether the diversity of the sampled environments and the applied sampling methods could influence the calculation of MP concentrations and global budgets, collected data have been categorized according to two binary classifications. On the one hand, river studies have been classified according to sampling locations ("river-like" column, Table S1). Sampling in rivers sensu stricto (flag = 1, n = 101) have been differentiated from other locations (flag = 0, n = 26), such as artificial canals, channelized streams, tidal estuaries or connected bays. On the other hand, data have been classified according to sampling techniques ("plankton net" column, Table S1).

Here, we distinguished sampling based on trawling with plankton nets (flag = 1, n = 96), which is the most common technique used for MP sampling in freshwaters and open ocean environments [START_REF] Hidalgo-Ruz | Microplastics in the Marine Environment: a review of the methods used for identification and quantification[END_REF][START_REF] Dris | Beyond the ocean: contamination of freshwater ecosystems with (micro-) plastic particles[END_REF]. The other methods (flag = 0, n = 31) comprise continuous pumping through filters, bulk sampling with bottles and successive filtration, and/or micro-layer sampling with sieves. These methods normally use much smaller mesh or pore sizes to retain MP particles compared to plankton nets (i.e. 80-1000 µm, with most of them corresponding to 300 or 333 µm, e.g. mantatrawl).

Conversion to mass concentrations

MP quantities in the literature are generally expressed as concentrations by numbers (i.e. number of items per unit volume), and mass concentrations are rarely provided. Only 8 of the 42 articles in our data compilation provide measured mass concentrations. Thus, standard conversion factors had to be determined to calculate MP mass concentrations for the remaining 34 studies. To do so we have used the 8 studies that simultaneously measured both number and mass concentrations, separating the fraction of synthetic fibers from non-fiber MPs (such as fragments, beads, films, foams). Indeed, according to Constant et al. [START_REF] Constant | Microplastic fluxes in a large and a small Mediterranean river catchments: The Têt and the Rhône, Northwestern Mediterranean Sea[END_REF]52), synthetic fibers account for more than 90% of the number concentrations, but only for 4 to 7% of the mass concentrations. Ideally, conversions should be performed specifically for the different size classes, shapes and polymer types, but the information that would be needed to do so is lacking.

Based on 129 samples for non-fiber MPs [from refs. [START_REF] Constant | Microplastic fluxes in a large and a small Mediterranean river catchments: The Têt and the Rhône, Northwestern Mediterranean Sea[END_REF][START_REF] Faure | Plastic pollution in Swiss surface waters: nature and concentrations, interaction with pollutants[END_REF]49,(53)(54)(55)(56)(57)], and 96 samples for fiber MPs [from refs. [START_REF] Constant | Microplastic fluxes in a large and a small Mediterranean river catchments: The Têt and the Rhône, Northwestern Mediterranean Sea[END_REF](54)(55)(56)], we calculated an average particle mass per sample dividing the mass concentration by the number concentration. Then, we analyzed the distribution of average particle masses for the two shape categories, fiber and non-fiber MPs (Fig. S1A,B). Both histograms followed a normal distribution, although the fiber histogram was more irregular, which might be related to the smaller number of related studies. A probability density function was fitted to the data and showed that the maximum probabilities were approximately met at median particle masses of Wf1 = 0.23 mg item -1 for non-fiber MPs and Wf2 = 0.75 µg item -1 for fiber MPs. We therefore retained these values for number to mass conversions. The composite MP mass (Wf) was consequently determined according to the following equation:

Wf = ( Wf1 * Cnf + Wf2 * Cf ) / ( Cnf + Cf )

with Cnf and Cf being the number concentrations (item m -3 ) of non-fiber and fiber MPs, respectively. As expected, conversions with Wf fit much better observations (Fig. S2A-D) compared to the previously proposed factors of Lf = 3.00 mg item -1 (5) and Sf = 0.96 mg item -1 (6).

Regression analysis

Potential predictor factors

For extrapolating riverine MP fluxes to regional and global scales, we performed regression analyses to find the best predictors among a series of georeferenced and globally available gridded parameters such as MPW (5), Pop (58), sPop or/and sQ (59). Previous modeling studies correlated the observed river MP fluxes (in tons per year) with MPW (4, 7, 8) alone, or MPW together with drainage intensity sQ [START_REF] Lebreton | River plastic emissions to the world's oceans[END_REF] in their respective drainage basins. For MPW we used the newer data set of Lebreton and Andrady (5), although for ease of comparison also the older data set of Jambeck et al. [START_REF] Jambeck | Plastic waste inputs from land into the ocean[END_REF] was considered. This data set was originally used in the modeling studies cited above. For sQ we took the data set of Ludwig et al. (59) and further integrated data sets on population numbers in 2015 (Pop) (58) and riverine particulate matter fluxes in general (60). Their spatial variability at global scales is summarized in Table S2 according to the main ocean basins to which they are connected.

Quantification of MPW stocks on land is strongly linked to total population numbers, but also depends on socio-economic behavior of the populations. MPW is hence more variable than Pop (Fig. S3). In the study of Lebreton and Andrady (5), MPW was estimated at much finer spatial scales than in the original study of Jambeck et al. [START_REF] Jambeck | Plastic waste inputs from land into the ocean[END_REF], rendering this dataset more suitable for our purpose. Both data sets are nevertheless highly correlated and have in common that they predict relatively low MPW stocks in the drainage basins connected to the North Atlantic (Table S2). Waste management is considered sophisticated in North America and Europe, reducing waste leakage rates to the environment. The two studies differ, however, on their evaluations of MPW stocks in drainage basins of the North Pacific, which is proportionally a larger hot spot for Jambeck et al. (4) than for Lebreton and Andrady [START_REF] Lebreton | Future scenarios of global plastic waste generation and disposal[END_REF]. It should also be noticed that the latter study predicts a global MPW stock that is only about two thirds of the predicted MPW stock in the former study.

We extracted the average values for each potential predictor factor upstream of river sampling stations for all basins. Regressions were calibrated with our dataset of observed MP fluxes. The resulting equations were applied to the predictor parameters of each river basin worldwide in order to obtain the corresponding MP fluxes. For these extrapolations of average river MP fluxes at regional and global scales we used a simplified river routing scheme (61) allowing both identifying the main world river basins in a 0.5x0.5 degree grid cell resolution (30 arc minutes), and conservatively tracking riverine matter fluxes from headwaters down to the receiving ocean basins. This approach has the advantage that many global environmental data sets exist at this resolution, which consequently eases combinations for extrapolation purposes, at the cost of spatial resolution. For characterization of the 127 studied catchments, a second drainage basin data layer was created for the drainage basins and sub-basins holding stations that had been sampled for MPs (Fig. 1). Both were delineated by including all basin grids upstream of sampling points.

Multi-parametric regressions

A single controlling parameter may not be sufficient to explain the observed variability of MP fluxes in rivers, and multi-regression models can help identifying additional controlling factors. We therefore tested this type of regression based on specific, i.e. normalized by basin area, values for MP fluxes (sMP) and drainage basin characteristics (sMPW, sPop, sQ). Regression analyses with absolute values are strongly dominated by observations in the largest river basins, which can consequently be a source of statistical bias. When restricting the data to our plankton net data subsets, we find that the following model best fits our observations:

sMP = b * sPop a1 * sQ a2

The regression coefficients a1, a2 and b are listed in Table S3. Correlation is rather weak for both data subsets (r² = 0.35 and r² = 0.38) but is significant for all parameters. Applying this model and converting the values into absolute MP fluxes increases the correlations in Table 1 to r² = 0.80. In addition, in our specific multi-regression models, sPop is a more powerful predictor for sMP than sMPW.

Constraints and uncertainty assessment

Residence time

Our approach of estimating plastic residence time in the surface ocean only considers the MP size fraction of plastic debris. Both MP sampling in the oceans and MP sampling in freshwaters rely on common techniques (plankton net trawling) and sufficiently large data sets could be assembled to produce reliable quantitative estimates at the global scale. The surface ocean stocks were determined from hundreds to thousands of MP plankton net samples [START_REF] Van Sebille | A global inventory of small floating plastic debris[END_REF][START_REF] Cózar | Plastic debris in the open ocean[END_REF][START_REF] Eriksen | Plastic pollution in the world's oceans: more than 5 trillion plastic pieces weighing over 250,000 tons afloat at sea[END_REF] and extrapolated together with oceanic circulation models to distinguish between accumulation (i.e. gyres) and nonaccumulation zones. Also, most plastic flux estimates in rivers rely on measurements of MP concentrations. They are clearly more frequent than measurements of macroplastic (>5 mm) concentrations [START_REF] Lebreton | River plastic emissions to the world's oceans[END_REF][START_REF] Schmidt | Export of plastic debris by rivers into the sea[END_REF] and often serve as extrapolation basis for the calculation of total plastic fluxes assuming constant MPs to macroplastics ratios [START_REF] Mai | Global Riverine Plastic Outflows[END_REF][START_REF] Lebreton | River plastic emissions to the world's oceans[END_REF]. Often macroplastic fluxes in rivers were not determined independently. However, accumulation of plastic at the ocean surfaces also involves larger plastics and other sources than rivers. This introduces uncertainty into our results, which has to be addressed.

Size limits

Variable or unclear definition of the size limits between MPs, macroplastics and total plastics both in the surface ocean stocks and in the river fluxes is definitively a source of uncertainty. On the one hand, plankton net sampling of MPs in the oceans not always excluded plastic debris larger than 5 mm (as in rivers), but used instead an upper size limit of 100 mm [START_REF] Cózar | Plastic debris in the open ocean[END_REF] or 200 mm [START_REF] Eriksen | Plastic pollution in the world's oceans: more than 5 trillion plastic pieces weighing over 250,000 tons afloat at sea[END_REF]. Only one study [START_REF] Eriksen | Plastic pollution in the world's oceans: more than 5 trillion plastic pieces weighing over 250,000 tons afloat at sea[END_REF] quantified this effect in terms of mass stocks and concluded that plastic debris in the 5-200 mm range contributed with about 43% to the total (<200 mm) stock collected by plankton net sampling. Macroplastics >200 mm such as plastic bottles are not included in the surface stock estimates in our study because they were determined by field observation surveys and not by plankton net sampling [START_REF] Eriksen | Plastic pollution in the world's oceans: more than 5 trillion plastic pieces weighing over 250,000 tons afloat at sea[END_REF].

On the other hand, previous mass flux estimates from rivers were often only reported in the form of total plastics without further discrimination between MPs and macroplastics (e.g. [START_REF] Mai | Global Riverine Plastic Outflows[END_REF][START_REF] Lebreton | River plastic emissions to the world's oceans[END_REF]. Based on compilations of field studies that reported independently riverine MP and macroplastic mass concentrations for individual rivers, it can be roughly estimated that MPs represent on average about half of the total plastic mass concentrations (41% according to [START_REF] Lebreton | River plastic emissions to the world's oceans[END_REF] with n=6 and 48% according to (8) with n=33) in rivers. Since a few larger particles can contribute a large fraction of the total plastic mass concentration [START_REF] Schmidt | Export of plastic debris by rivers into the sea[END_REF], estimating this contribution is nevertheless problematic. Assuming that up to half of the MP mass stock at the ocean surface could be composed by particles in the 5-200 mm sizerange, it may therefore be concluded that size effects might represent an error factor of <2 in the calculation of average residence times based on MP river loads and surface ocean stocks, and of <4 based on total river loads (which may contain, although associated with large uncertainty, as much macroplastics as MPs). This is clearly less than the almost three OM difference we find between previous mass estimates of riverine MP fluxes and ours.

The smallest MPs at the lower micrometer scale and nanoplastics also contribute to oceanic stocks and river fluxes. Recent studies [START_REF] Ter Halle | Understanding the fragmentation pattern of marine plastic debris[END_REF][START_REF] Pabortsava | High concentrations of plastic hidden beneath the surface of the Atlantic Ocean[END_REF] highlighted that these particles could represent a significant or even dominant part in the oceanic plastic stocks (mainly below surface). Our data confirm their abundance in rivers, at least in terms of number concentrations. However, this should have no impact on our calculations of residence times as we only refer to MP debris collected by plankton net sampling, which do not retain such small particles.

Other terrestrial MP sources

Beyond rivers, other pathways involved in the land-to-sea transfer of plastics are atmospheric transport and deposition, direct wastewater inputs from coastal cities, settlements and the areas nearby, and direct dumping from the shoreline. Unfortunately, all these sources are poorly quantified at global scale. Would they be quantitatively much greater than MP discharge from rivers, the residence time of MPs at the ocean surface would indeed decrease much further. But OM calculations indicate that these sources are clearly less important than rivers. Besides the smallest MPs and nanoplastics, atmospheric MP deposits on land correspond almost exclusively to fibers [START_REF] Constant | Microplastic fluxes in a large and a small Mediterranean river catchments: The Têt and the Rhône, Northwestern Mediterranean Sea[END_REF]62,63). Consequently, fibers should also be the dominant MP form from atmospheric deposition at sea. It could be eventually assumed that atmospheric fiber deposits on land are integrally transferred to the sea by rivers via surface runoff. However, this would lead to an overestimation as fibers can also originate from other sources such as wastewaters. The average mass percentage of fibers in our "Plankton net -River" subset of data in Table 1 is 1.1% (n=68 when omitting the case studies in which fibers were not measured), which corresponds to a global mass flux of 0.08 kt yr -1 of MPs. Assuming an equal deposition rate over the entire ocean, i.e. over an area about 3 times larger than the land area draining into the sea, atmospheric fiber deposits at sea should therefore be <0.25 kt yr -1 . Again, smallest fibers and MPs may not be retained in plankton nets and actual atmospheric deposition rates could be greater. But as we compare plankton net sampling in rivers with plankton net sampling at the sea surface, this should have no impact on the average residence times we calculate. Very recently, a study detected airborne MP particles in the marine atmosphere over the Atlantic, which were all clearly smaller than 300 µm in size (64).

To our best knowledge, only one global modeling study (65), although poorly constrained by observations, quantified MP discharges to the sea by wastewaters. The authors estimated them to be 9.4 kt yr -1 , i.e. in the same range we found for riverine MPs in general. In their study, all wastewater inputs are supposed to enter the oceans via rivers, hence being included in our estimate. However, in coastal areas, wastewaters may be directly discharged into the sea via submarine outfall systems, specially off large cities. According to our GIS, 18.9% of the world population lives in coastal areas within <50 km distance to the sea and could potentially be connected to such systems. Assuming approximately that wastewaters from up to one quarter of this population may be drained through submarine outfall systems would consequently produce an additional flux estimate of 0.44 kt yr -1 . This is clearly lower than riverine MP loads as a whole.

Fragmentation

Fragmentation of larger plastic debris can also contribute to the floating MP stock at sea. Because of the difficulties in studying this process under field conditions, there is no estimate quantifying its significance at the global scale. However, comparison of the average MP particle masses both in rivers and at the ocean surface is indicative in this respect. If fragmentation happens rapidly, and rivers remain a dominant source, ocean MPs would be expected to be smaller on average than riverine MPs. If the opposite, small MPs of riverine origin could be preferentially withdrawn from the ocean surfaces as they would have lower buoyancies [START_REF] Poulain | Small Microplastics as a Main Contributor to Plastic Mass Balance in the North Atlantic Subtropical Gyre[END_REF]66) compared to large MPs. In that case, it would be the larger MPs that accumulate at the ocean surface.

The study of Cózar et al. (12) is of interest in this context because it allows estimating the representative standard mass of MP debris at the ocean surface from regression analysis. Based on the relationship between mass and number densities the authors published in their supplementary data section, together with the average MP density derived from their mid-estimate MP stock (44.5 g km -2 ), we calculated that this mass is about 0.97 mg item -1 . Regionally, it ranges from approximately 0.3 mg item -1 in low-density (~10 2 items km -2 ) areas to 3.0 mg item -1 in high-density (~10 7 items km -2 ) areas. Due to the log-log nature of the cited relationship, which implies normal data distribution, the standard MP mass in the ocean can be directly compared to our MP mass estimate. This consequently represents about 4 times the median mass of 0.23 mg item -1 we retained for riverine non-fiber MPs (for this purpose fibers can be neglected since they were often not accounted for in marine samples). The studies of Eriksen et al. [START_REF] Eriksen | Plastic pollution in the world's oceans: more than 5 trillion plastic pieces weighing over 250,000 tons afloat at sea[END_REF] and van Sebille et al. [START_REF] Van Sebille | A global inventory of small floating plastic debris[END_REF] solely reported average number and mass budgets according to which the average MP weight in the oceans is 4.6-7.3 mg item -1 , i.e. 10-15 times our average value for non-fiber MPs in rivers (0.48 mg item -1 , see Fig. S1A). In all cases, oceanic MPs are hence heavier on average than riverine MPs, which does not support the idea that plastic debris undergo rapid fragmentation into floating MPs when they arrive to the marine domain.

Surface ocean stocks

It is finally also important to mention that estimates for the average residence time of MPs at the ocean surface not only depend on annual river loads but also on the quality of estimates of the floating MP stock in the ocean. For quantification of the latter, we refer to the study of Cózar et al. [START_REF] Cózar | Plastic debris in the open ocean[END_REF] as a conservative low-end estimate. Larger stocks would consequently increase the calculated average residence time. Although Cózar et al. (12) did not cut off plastic debris >5mm in their data compilation (they used an upper size limit of 100 mm, see above), the mid-estimate plastic stock they propose only corresponds to 41% of the estimated stock of Eriksen et al. [START_REF] Eriksen | Plastic pollution in the world's oceans: more than 5 trillion plastic pieces weighing over 250,000 tons afloat at sea[END_REF] for plastic debris below this size. The former study assembled a larger number of field observations than the latter and covered many low-density areas in the oceans. At the high-end of estimates, the oceanic MP stock can reach more than 10 times Cózar's et al. [START_REF] Cózar | Plastic debris in the open ocean[END_REF] stock and differ significantly in terms of spatial distributions according to a series of modeling studies that are summarized in van Sebille et al. [START_REF] Van Sebille | A global inventory of small floating plastic debris[END_REF]. However, whereas these studies still increased the number of observations for calibration, all models involved accounted for dynamic MP interactions at the land-to-sea interface (i.e. prediction of the land-derived inputs and/or outputs via beaching along the coastlines), thus making them less suitable for independent comparisons with observations, as the load estimates they produce directly depend on the algorithms controlling the land-to-sea interactions.

Regression uncertainties

The multi-parametric regression models we determined using the specific prediction parameters sPop and sQ only yield moderate coefficients of determination for the prediction of specific MP fluxes (Supplementary Materials and Methods 2.2). Based on the standard error of both regressions (total fluxes + standard error), the corresponding error intervals for the fluxes reported in our Table 1 stretch from 1.3 to 30.1 kt yr -1 (n=96) and from 1.3 to 31.7 kt yr -1 (n=84). Weak coefficients of determination and large error intervals are not surprising given the constraints under which the MP flux estimates had to be established. These constraints include standard per item mass conversions instead of size specific mass conversions, missing information on hydrological conditions and seasonal variations, and restriction of plankton net sampling to low discharge conditions. The global fluxes we calculated should consequently be considered as OM estimates. To quantify the confidence we can associate to these estimates, we further submitted our regressions to a bootstrap . sMPW is about two orders of magnitude (OM) more variable than sPop, which can explain why MPW-based extrapolations generally lead to much greater budgets than extrapolations with the Population. Specific MPW generation rates are generally higher in African, South American and Asian countries than in European and North American countries. Table S1. Compiled literature studies providing MP concentrations in rivers. For data categorization as "plankton net sampling" and "river-like" see Supplementary Materials and Methods section 1.2 and for details on the calculation of MP mass concentrations see section 1.3.

Table S1 (continued). Compiled literature studies providing MP concentrations in rivers.

For data categorization as "plankton net sampling" and "river-like" see Supplementary Materials and Methods section 1.2 and for details on the calculation of mass concentrations see section 1.3. Table S3. Regression and correlation coefficients for the multi-regression models performed in this study. All parameters are significant with p < 0.03. sPop: population density; sQ: drainage intensity. For the parametric equation, see Supplementary Materials and Methods 2.2.

Fig. 1 .

 1 Fig. 1. Global watershed delineation (0.5 x 0.5 degree grid cell resolution) and representation of the river catchments for which MP flux estimates can be established from the literature. They represent 340 measurements at 127 sampling locations in 89 rivers and have been compiled from 42 published studies (TableS1). With respect to the world total, the 89 sampled rivers represent 14% of water discharge.

Fig. 2 .

 2 Fig. 2. MP concentration variability in rivers. (A) MP number concentrations (items m -3 ) in different data subsets combining sampling techniques and study locations. Retention limits correspond to mesh (plankton net sampling) or filter pore sizes (miscellaneous sampling) used to retain MP particles according to the compiled studies. "River-like" sampling considers data obtained in rivers sensu stricto, i.e. excluding connected surface waters such as artificial canals, channelized streams, tidal estuaries or bays (Supplementary Materials and Methods 1.2). (B) Box plot representation of MP mass concentrations as a function of different combinations of sampling techniques and number to mass conversion factors (Lf, Sf, Wf). The similarity of the two box plots at the right (all plankton net data and plankton net data restricted to rivers) indicates that the high variability observed in the other box plots is mostly related to miscellaneous sampling.

Fig. S1 .

 S1 Fig. S1. Mass histograms and probability density functions. (A) For non-fiber MPs and (B) for fiber MPs. Both were calculated from literature studies in TableS1in which both mass and number concentrations have been determined (see Supplementary Materials and Methods 1.3).

Fig. S2 .

 S2 Fig. S2. Comparison between measured and calculated MP mass concentrations. Determined from (A) the combination of median masses of fiber and non-fiber MPs (Wf) in Fig. S1, (B) the combination of average masses of fiber and non-fiber MPs in Fig. S1, (C) the average MP mass proposed by Lebreton et al. (7) (Lf), and (D) the average MP mass proposed by Schmidt et al. (8) (Sf).

Fig. S3 .

 S3 Fig. S3. Comparison between specific Mismanaged Plastic Waste (MPW) generation (5) and 2015 population densities (58)for each exorheic basin in our global GIS (0.5 x 0.5 degree grid cell resolution). sMPW is about two orders of magnitude (OM) more variable than sPop, which can explain why MPW-based extrapolations generally lead to much greater budgets than extrapolations with the Population. Specific MPW generation rates are generally higher in African, South American and Asian countries than in European and North American countries.

ACKNOWLEDGMENTS

We thank the anonymous peer reviewers for their suggestions and comments, which improved this manuscript. We are indebted to P. Döll who kindly supplied the WATERGAP river routing file in a 0.5-degree grid cell resolution and to S. Pinel for performing the calculations with the bootstrap statistical method. Funding: This work was supported by doctorate school ED305 of the University of Perpignan Via Domitia through attribution of PhD grants to L.W. and M.Co. M.Ca. acknowledges support from Generalitat de Catalunya 2017 SGR 315 grant to GRC Marine Geosciences, Red Española sobre BAsuras MARinas (BAMAR, ref. CGL2016-81854-REDT) and Institut d'Estudis Catalans (IEC) I-MarCat grant (ref. PR2015-S06-CANALS). Author contributions: L.W. collected and assembled the MP data in rivers from the literature, performed the statistics, implemented the river GIS, and extrapolated and analyzed the global MP fluxes. W.L. steered the study design, conducted the discussion and contributed to data analysis. W.L., L.W. and S.H. wrote the manuscript with significant contributions from M.Ca., J-F.G. and C.E in their respective domains of expertise. M.Co. contributed to data mining from literature. M.Co., P.K. and M.Ca. supplied individual data on riverine MPs from previous studies. All authors discussed the results and commented on the manuscript. Competing interests: The authors declare no competing interests. Data and materials availability: The data frames used for the analyses are provided as Table S1 and in the Supplementary Materials and Methods and also are freely available online at the links specified in the references. The code for statistical analyses is based

on the OLS statsmodels and scikit-learn Python libraries (online documentation hosted at statsmodels.org and scikit-learn.org).

SUPPLEMENTARY MATERIALS

Supplementary Materials and Methods

5

References

Figs. S1-S3

Tables S1-S3

Supplementary Materials for

Figs. S1-S3

Tables S1-S3

Table S2. Characteristics of the 0.5 x 0.5 degree resolution river basin GIS and integrated data layers used in this study. Parentheses correspond to percentages of global values. For data sources, see Supplementary Materials and Methods 2.1.