Hugo De Vries
email: hugo.de-vries@inrae.fr

Mechthild Donner

Monique Axelos

A New Conceptual 'Cylinder' Framework for Sustainable Bioeconomy Systems and Their Actors

Keywords: Sustainable bioeconomy, Conceptual framework, Complex adaptive systems, Game theory, Business cases

Concepts for sustainable bioeconomy systems are gradually replacing the ones on linear product chains. The reason is that continuously expanding linear chain activities are considered to contribute to climate change, reduced biodiversity, overexploitation of resources, food insecurity, and the double burden of disease. Are sustainable bioeconomy systems a guarantee for a healthy planet? If yes, why, when, and how? In literature, different sustainability indicators have been presented to shed light on this complicated question. Due to high degrees of complexity and interactions of actors in bioeconomy systems, trade-offs and non-linear outcomes became apparent. This fueled the debates about the normative dimensions of the bioeconomy. In particular, the behavior of actors and the utilization of products do not seem to be harmonized according to the environmental, social, and economic pillars of sustainability. Potential conflicts require a new conceptual framework that is here introduced. It consists of a 'sustainability' cylinder captured between an inner-cylinder, representing order, and an outer-cylinder for chaos, based on the laws of physics and complex adaptive systems. Such a framework permits (bioeconomy) systems to propagate in the sustainability zone only if they follow helical pathways serving as the new norms. Helices are a combination of two sinusoidal patterns. The first represents here the sustainable behavior of interacting actors and the second the balanced usage of resources and products. The latter counteracts current growth discourses. The applicability of the conceptual cylinder framework is positively verified via 9 cases in Europe, which encompass social-organizational and product-technological innovations.

Introduction

In 2018, the European circular and sustainable bioeconomy strategy [START_REF] Patermann | The origins of the bioeconomy in the European Union[END_REF]EC DG R&I, 2018) and the circular bio-society 2050 reports (Biosociety, 2020) provide clear, largely supported, ambitious visions for bioeconomy systems. They are supposed to contribute to the highly challenging Sustainable Development Goals (SDG) of the United Nations [START_REF] Lu | Policy: Five priorities for the UN Sustainable Development Goals[END_REF]. Recently, the European New Green Deal and Fork-to-Farm strategy have been setting the scene for the new research and innovation programs for the bioeconomy, including the food domain (EC, 2020a;EC, 2020b;EC, 2020c).

These strategies are responses to the current linear 'take -make -consume -dispose of' chains, which are associated with mass consumption and unsustainable behavior of actors. These chains often result in waste [START_REF] Fusions | Estimates of European food waste levels[END_REF][START_REF] Morone | Food waste: Challenges and opportunities for enhancing the emerging bio-economy[END_REF], over-exploitation of natural resources (Meadows et al., 1972; EC, 2011 1 ), and competing claims for resources [START_REF] Tuck | Valorization of Biomass: Deriving More Value from Waste[END_REF], food and nutritional insecurity. Numerous indicators show (exponential) growth patterns (e.g. for climate change, biodiversity loss, overweight and obesity, energy, and water usage, urbanization, social inequalities), possibly with severe consequences for the planet, profits, and the well-being of people [START_REF] Barnosky | Approaching a state shift in Earth's Biosphere[END_REF]IPCC, 2019;[START_REF] Ipbes | Summary for policymakers of the global assessment report on biodiversity and ecosystem services of the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services[END_REF][START_REF] Sapea | A sustainable food system for the European Union[END_REF]. The importance of these challenges is reflected by their prominence in most of the 17 SDGs and even more accentuated by the current COVID-19 crisis.

Systems showing continuous overall (exponential) growth patterns tend to end up in chaos or order as explained by the laws of thermodynamics [START_REF] Georgescu-Roegen | The Entropy Law and the Economic Process[END_REF][START_REF] Prigogine | Order Out of Chaos: Man's New Dialogue with Nature[END_REF] via a series of small and large scale events following power laws, like avalanches on a growing sand pile [START_REF] Andriani | From skew distributions to power-law science[END_REF][START_REF] Bak | Self-organized criticality[END_REF]. The zone in between order and chaos, called the melting zone [START_REF] Carbonara | Making Geographical Clusters More Successful: Complexity-Based Policies[END_REF], is narrow, however, with a certain bandwidth. One can hypothesize that systems continuously evolving in this zone are sustainable by nature, as further discussed below. This should also hold for bioeconomy systems that are here defined as systems that organize the utilization of bio-based products (including natural resources) within certain boundaries, appreciating its wider environmental, social, political, and economic context.

Sustainability and sustainable bioeconomy systems (SBS) are now widely discussed (e.g. [START_REF] Dubois | How sustainability is addressed in official bio-economy strategies at international, national and regional levels; An overview[END_REF][START_REF] Bugge | What Is the Bioeconomy? A Review of the Literature[END_REF][START_REF] D'amato | Green, circular, bioeconomy: A comparative analysis of sustainability Avenues[END_REF][START_REF] Szekacs | Environmental and Ecological Aspects in the Overall Assessment of Bioeconomy[END_REF], utilizing the Brundtland definition as the basis (WCED, 1987); hence, they integrally consider the three pillars 'planet, people and profit' and specific actions that will not compromise future generations. However, the understanding of the functioning of bioeconomy systems and the way to change the current trends are less obvious, in particular at the Global and European levels but 1 EC, 2011; 'Over the twentieth century, the world increased its fossil fuel use by a factor of 12, whilst extracting 34 times more material resources. Today in the EU, each person consumes 16 tons of materials annually, of which 6 tons are wasted, with half going to landfill. Whilst demand for food, feed and fiber may increase by 70% by 2050, 60% of the world's major ecosystems that help produce these resources have already been degraded or are used unsustainably.'. also local levels. The appealing concept of a circular economy, as re-introduced by the Ellen MacArthur Foundation (2015), has widely been promoted in the past decade. It largely emerged from legislation [START_REF] Murray | The circular economy: An interdisciplinary exploration of the concept and application in a global context[END_REF], even though closed-loop thinking already exists since the beginning of agricultural production by feeding back essential nutrients to the soil. The success of the circular bioeconomy approaches will depend on transformation costs (like money, water, energy, and safety measures) for the recuperation and utilization of nutrients somewhere in the bioeconomy. To establish whether or not environmental sustainability is also at stake, a sound scientific basis is required e.g. based on thermodynamics and system boundaries [START_REF] Korhonen | Circular Economy: The Concept and its Limitations[END_REF]. Social sustainability deserves attention as well [START_REF] Ostrom | A general framework for analyzing sustainability of social-ecological systems[END_REF]. Here, we like to remark that the mathematical representation of a circle implies (i) 'equally fair and just distances' for all actors at the circle to its center and (ii) the absence of a beginning or end, hence shared responsibilities for all being suppliers and demanders at the circle. In contrast, traditional linear food and other fossil-based product chains, from producers, manufacturers, retailers to consumers, generally show end-of-chain dominance.

SBS needs metrics and joint actions to understand and measure the impacts of current actions [START_REF] Bracco | Indicators to monitor and evaluate the sustainability of bioeconomy[END_REF][START_REF] Ronzon | Socioeconomic Indicators to Monitor the EU's Bioeconomy in Transition[END_REF]. Besides, they require resources, multi-level and landscape-oriented approaches [START_REF] Geels | Technological transitions as evolutionary reconfiguration processes: A multi-level perspective and a case-study[END_REF]; the landscape refers to the overall socio-technical setting for interactions of actors. Finally, they ask for renewed considerations of planetary boundaries presented as radars [START_REF] Rockström | A safe operating space for humanity[END_REF]; the boundaries are associated with the planet's biophysical subsystems or processes. An alternative image is a Doughnut in which also social limits are incorporated [START_REF] Raworth | A doughnut for the Anthropocene: Humanity's compass in the 21st century[END_REF]; the image of a doughnut shows an inner circle representing the 'social foundation' and the outer circle serving as the 'ecological ceiling (or planet's bio-physical limits)'. Beyond the ecological ceiling, one can speak about unacceptable environmental degradation, while below the social foundation the human primary needs are fundamentally challenged.

Radars and doughnuts partially provide information about the spaces within which human beings can act. In the case of planetary, environmental, boundaries only upper limits are given, while for social boundaries only lower limits are presented. Here, we state that one should also define lower limits for planetary boundaries and upper limits for social ones; however also for economic ones. This results in sets of social -or socio-economic -foundations and ceilings as well as ecological foundations and ceilings. As we will see later, this corresponds with the thoughts about correct interpretations of the order-melting-chaos zones. The chaos zone corresponds then to the zone beyond these ceilings, while the order zone is below the foundations. It should also be noted that radar and doughnut are presented as twodimensional images, hence they are explicitly lacking the time dimension. This does not make them suitable for visualizing dynamic behavior and (un)sustainable outcomes in time. These two considerations will form the basis for constructing our conceptual 'cylinder' framework (see Fig. 1).

We hypothesize and discuss that sustainable (bioeconomy) systems are characterized by their balancing evolution between order and chaos, hence between social-environmental-economic foundations and ceilings. However, this immediately asks for a reflection on the normative dimension of sustainability, which is inherent in its conceptions and debates but very complex, as it involves different (conflicting) visions among various societal actors and contested pathways [START_REF] Schlaile | Innovation systems for transformations towards sustainability? Sustainability[END_REF]. The normative dimension also refers to the question of ethical leadership [START_REF] Blok | Technocratic Management Versus Ethical Leadership Redefining Responsible Professionalism in the Agri-Food Sector in the Anthropocene[END_REF] in bioeconomy systems as well as of dedicated innovation systems [START_REF] Pyka | Dedicated innovation systems to support the transformation towards sustainability: Creating income opportunities and employment in the knowledge-based digital bioeconomy[END_REF] and responsible research and innovation pathways [START_REF] De Saille | Innovating innovation policy: the emergence of 'Responsible Research and Innovation[END_REF][START_REF] Schomberg | A Vision of Responsible Research and Innovation[END_REF]. Without such a reflection, bioeconomy systems may pass ceilings and foundations. Also, the visions on desirable ceilings and foundations as well as on the pathways to sustainability may be quite different [START_REF] Schlaile | Innovation systems for transformations towards sustainability? Sustainability[END_REF]. This immediately poses the following questions: (a) In what way can the three dimensions of sustainability (environmental, social, and economic) be harmonized to avoid conflicting visions and outcomes of bioeconomy systems? (b) Which interacting system elements propagate in a sinusoidal manner under changing conditions? (c) Which system elements provide the 'environments' and 'limits' such that balancing behavior may appear? (e) Which system elements reveal (un) sustainable pathways? (f) Which real-life cases provide insights and allow formulating policy options?

To answer these questions, we will stepwise introduce a conceptual framework for understanding and analyzing SBS in the following section. First, a cylinder

Graphic representaƟon of key system elements & helical pathways in between boundaries

Time (z-axis)

2050

Self-fulfilment needs

Scenario 1

Primary needs

Playing fields

the safe and unsafe operaƟng spaces Fig. 1 The cylinder confinement for sustainable bioeconomy (incl. food) systems evolving in the safe and fair operating space (SFOS), in between order and chaos, hence following scenario 3; the SFOS is identical to the melting zone in Fig. 3 in which Complex Adaptive Systems evolve. Bioeconomy (including food) systems that are unsustainable enter either in the chaos or order zone, following respectively the scenarios 1 or 2. Note the interconnectedness, via a helix, between the behavior of players and biomass utilization in a sustainable way. Source: Modified image of https:// www. radar tutor ial. eu/ 06. anten nas/ pic/ zirku lanim. gif is included concept is constructed for dynamic systems that encompass all system elements (playing fields, players, pieces, moves, rules, win/lose, and duration). It includes the notion that sustainable systems continuously evolve in a melting zone in between order and chaos, hence following combined helical pathways. Second, it incorporates the mathematical description of helices as constructs of 2 sinusoidal-like waves. In bioeconomy, this brings the behavior of players and the utilization of products in harmony. Also, both the overall global bioeconomy system and the multiple local systems should be able to perform sustainably. Third, the theory of complex adaptive systems -i.e. systems that continuously evolve in the 'melting' zone also if challenged by extreme conditions -is linked with the conceptual framework, thus revealing which player networks proceed harmonically in the melting zone. The same should hold for the utilization of products.

Scenario 3

Moves

Here, we take into account that the earth is an open thermodynamic system, i.e. fueled by solar energy input and emission outputs of greenhouse gases. In the 'case studies' section, the conceptual framework is elucidated via practical cases. In the 'discussion' section, the framework serves the debates on the normative dimensions of SBS and its actors. Finally, conclusions are drawn and options are given how stakeholders, including policymakers, could act while operating within the here proposed normative dimensions of a sustainable bioeconomy.

Towards a Conceptual Framework for Analyzing Sustainable Bioeconomy Systems (SBS)

From Radar and Doughnut to a Cylinder Confinement Which 'confinement' area allows systems to follow sinusoidal-like patterns? We start with the integration of the time dimension in the previously presented 'doughnut' and 'radar'. This yields a novel cylinder configuration with three zones (Fig. 1), the order, melting, and chaos zones. The melting zone is a hollow cylindrical tube centered around a 'highly ordered (rigid) zone'. This inner cylinder represents e.g. the non-vital planet earth that is not able to respond to primary needs. A third, outer, cylinder represents a 'highly chaotic zone', e.g. the over-exploited or over-heated planet earth where excessive behavior leads to extreme and irreversible inequalities. Consequently, the melting zone can also be called a safe operating space in socialecological systems [START_REF] Anderies | Knowledge infrastructure and safe operating spaces in social-ecological systems[END_REF][START_REF] Rockström | A safe operating space for humanity[END_REF] or fair and safe operating space (this publication); the latter refers to the reflections on framings of food as a commodity, commons, and human right (SAPEA, 2020). The cylinder configuration allows defining contrasting outcomes -presented as 3 different scenarios -for bioeconomy systems ('win-lose' in game theory; like SDG outcomes). Besides, the other 6 key elements of systems or game theory [START_REF] Neumann | Theory of Games and Economic Behavior[END_REF] are presented, namely players, pieces, rules, moves, playing fields, and duration/time (the light blue text boxes).

The element 'players' include all actors in bioeconomy systems (like producers, NGOs, public institutions, citizens); their overall behavior should follow pathways in the green area to reach a sustainable output. The element 'pieces' includes renewable resources, transformed functional and healthy products, recycled products, and services like safety & security & health insurance, labor, etc. Overall, their utilization should also follow pathways in the green area. The element 'moves' refers to all steps dealing with the handling of pieces including production, manufacturing, distribution, consumption, usage/digestion, and recycling; the outcomes of moves should guarantee that pathways remain in the green area. The element 'playing fields' regards all kinds of territories from planetary scales to local environments (geographic, political, legislative, etc.). These should be chosen such that pathways can be followed in the green area. The element 'rules' encompasses legislation and incentives, hence defines the freedom to play, the rights, and the obligations for players to reach sustainable outcomes. The final element is the duration, or time axis, for exploring pathways.

Interacting Helices, as Compositions of 2 Sinusoidal Waves, Converge into an Overall Concentric Helix in the Cylinder Confinement

Does the cylinder confinement enable systems to evolve in a sinusoidal-like manner? Yes, one can learn from fluid dynamics that under specific thermodynamic conditions and considering interacting (nano-)particles with short-range attraction and long-range repulsion, cylindrical confinement promotes the formation of helical structures [START_REF] Jung | Confinement induces helical organization of chromosome-like polymers[END_REF][START_REF] Serna | Assembly of Helical Structures in Systems with Competing Interactions under Cylindrical Confinement[END_REF]. Their morphology depends on pore size and boundary conditions (Fig. 2a). If a short-range attraction is absent, only repulsive interactions govern the system; this behavior is not observed. Helices have mathematically well-described characteristics and are known as essential natural compound structures like those of DNA (Fig. 2b) and of proteins (see for example the α-helix from a top and side view; Fig. 2c). One also recognizes helix structures in living species [START_REF] Forterre | Generating Helices in Nature[END_REF]) like plants, shells, sunflowers, and strawberries (spiral structures, following Fibonacci sequences, Fig. 2d). In food and bio-based product processing, stable helices are also rather easily created (see Fig. 2e for ropes, cakes, and pasta).

Helices are among the elementary shapes that are observed in the filamentary and molecular structures of nature. Even though, they are quite complex from mechanical properties points of view and minimum energy configurations [START_REF] Chouaieb | Helices[END_REF]. The conformation of proteins is directed towards the lowest free energy. Although the overall conformation of each protein is unique, two regular folding patterns are often found in parts of them, one is the alpha-helix structure [START_REF] Alberts | The Shape and Structure of Proteins[END_REF]. The formation of helical structures is also far from trivial, as shown for example in the food domain for gelatin via covalent functionalization [START_REF] Zaupa | Influence of Tyrosine-Derived Moieties and Drying Conditions on the Formation of Helices in Gelatin[END_REF].

For our discourse, it is important to note that, mathematically speaking, helices2 are three-dimensional structures formed by 2 sinusoidal waves propagating in time (z-axis) in two perpendicular planes (one sinus in the x-z plane and one in the y-z plane). This is presented in Fig. 2f, and implicitly in Fig. 1 via the dotted curves. If one supposes that the x-axis represents 'utilization of pieces (either resources, products or services)', the y-axis the 'behavior of players' and the z-axis the 'time' (see Fig. 1), then endless propagating helical structures should be formed by needs and behaviors following balancing, sinusoidal-like patterns in between order and chaos. Remarkably, this three-dimensional configuration allows connecting the behavior of stakeholders with the utilization of products in a harmonic way. One could notice similarities between the here presented balancing curves and patterns for predator and prey populations in time within a specific territory, as shown in Fig. 2g. The boundaries are set by socially-accepted norms, ecological boundaries, and economic constraints, hence, the dimensions of the three pillars of sustainability. These social norms, boundaries, and constraints should always have both lower -the social foundation guaranteeing the fulfillment of human primary needsand upper limits -the social ceiling avoiding excessive behavior and extreme inequalities -as mentioned before, to present an operational window for actors (or utilized products) in a bioeconomy system to endlessly propagate in a balancing way.

As outlined above, the normative dimensions of SBS are now appearing in the form of a conceptual cylinder framework; in other words, the normative dimensions of sustainable bioeconomy seem to reveal 'cylindrical symmetry' in mathematical terms. This implies that ethical leadership, responsible research and innovation programs, decisions of policymakers, or ethical behavior of other players should lead to clearly defined social, environmental, and economic foundations and ceilings. They also should provide acceptable options to continuously balance in the melting zone, here phrased as the safe and fair operating space (Fig. 1).

One could ask if the cylinder framework is also relevant in the case of multiple, interacting, local bioeconomy systems. Figure 2a shows the co-evolution of multiple, intertwining, helices finally converging into an overall concentric helix, under well-defined thermodynamic conditions. The helicoid representation of the overall concentric bioeconomy system is in particular interesting to underline, since these are forms of minimal surfaces when bounded by a closed space, like a spiral staircase; this also holds for catenoid structures and planes [START_REF] Colding | Shapes of embedded minimal surfaces[END_REF]; partly based on Meusnier J.B. work in 1776; Fig. 2h). Even if such a scheme is a simplification of reality, it serves to explain how multiple local SBS could interact, show co-evolutionary pathways and form the overall, global, concentric SBS.

Helical Structures in Cylinders, Complex Adaptive Systems, and Open Thermodynamic Systems

In our conceptual cylinder framework, the adaptation capacity and the resilience of SBS is lacking. This is of crucial importance for our debate on normative dimensions and ethical considerations concerning the behavior of players. So far, the complex adaptive system (CAS; [START_REF] Gell-Mann | Complex Adaptive Systems; Complexity: Metaphors, Models, and Reality[END_REF][START_REF] Holland | Emergence: From chaos to order[END_REF][START_REF] Kauffman | At Home in the Universe, The Search for the Laws of Self-Organization and Complexity[END_REF] theories are rarely mentioned and not yet systematically explored for integral SBS (de Vries, 2017), except for specific domains like e.g. climate-smart food villages [START_REF] Jagustović | Contribution of systems thinking and complex adaptive system attributes to sustainable food production: Example from a climate-smart village[END_REF]. CAS is based on the thermodynamic plot in which the diversity of N agents (or actors or stakeholders) versus their interactions K is sketched in 2-dimensions, see Fig. 3 (Kaufmann, 1995;[START_REF] De Vries | Meeting new challenges in food science technology: the development of complex systems approach for food and biobased research[END_REF]. Herein, three zones are shown: an order, melting, and chaos zone. The melting zone is in between the order and chaos zones, i.e. the same green zone as in the 'cylinder configuration' in Fig. 1. It is the zone of self-organization, auto-catalytic behavior, adaptation, and resilience [START_REF] Martin | Complexity thinking and evolutionary economic geography[END_REF], emergence, and co-evolution. Co-evolution describes the coupling of fitness landscapes such that adaptive moves by one player deform the fitness landscapes of its immediate partners; this is similar to the interacting individual helices of Fig. 2a resulting in the helicoid in Fig. 2h. In the melting zone, CAS maintains quasi-equilibrium states 3 [START_REF] Nicolis | Exploring Complexity: An Introduction[END_REF][START_REF] Kauffman | Even peptides do it[END_REF]. Properties include non-linear behavior, scalability, and butterfly effects [START_REF] Carbonara | Making Geographical Clusters More Successful: Complexity-Based Policies[END_REF]. The latter implies that minor changes at sensitive intervention points may either maintain the self-organized behavior of actors or push the overall system over the edge of order and chaos [START_REF] Farmer | Sensitive intervention points in the post-carbon transition[END_REF]. This notion is highly relevant today in the discourses about COVID-19. The edges and the bandwidth of the melting zone are determined by external constraints and rules, e.g. acceptable climate conditions, a certain level of (bio-/cultural-) diversity, social limits for the actors, and resource usage. Each constraint -environmental, social, economic -has both a lower and an upper limit in between which a system balances as mentioned before.

The NK model of [START_REF] Kauffman | At Home in the Universe, The Search for the Laws of Self-Organization and Complexity[END_REF], described as the number of interactions 'K' between diverse players 'N', teaches us the following. If the NK model is applied for either a purely linear or circular food chain configuration (number of interactions 'K' = 2, i.e. each stakeholder 'N' deals with only one supplier and one customer; see Fig. 3; bottom left), the configurations are rigid. If applied for multiple cascading business configurations (very high number of interactions 'K' between various stakeholders 'N'; Fig. 3; top right), the configurations are chaotic. However, if utilized for interactive networks of stakeholders with an intermediate number of interactions 'K' between stakeholders 'N' (Fig. 3; center), then the configurations become self-organized, showing sinusoidal patterns. The linear and circular concepts may become sustainable in only exceptional cases e.g. if the number of stakeholders becomes very high (N very large; see Fig. 3). The same holds for cascading Fig. 3 The 'CAS' scheme shows four different configurations of actors in bioeconomy systems, either in the order or chaos or melting/sustainability zone; in the latter complex adaptive systems evolve business pathways with appropriate sets of relatively low N, K-values. This is an important observation for debates about the circular economy, the linear chains for food and other bio-based products, and the cascading concepts for the valorization of resources. Quite often it is stated that strategies are in development to make them sustainable, however, this isn't always possible as explained here. Finally, a model for the utilization of products, either as raw agro resources or as processed bio-based products, or services in the melting zone is required (see Fig. 1) which allows revealing sinusoidal-like curves. This model needs to take into account the huge variety of production schemes for renewable resources, the multitude of conversion pathways to assembled products, and the heterogeneity of recyclable products. Second, external inputs are to be considered in all those steps, such as (solar) energy, water, minerals, and gaseous molecules. Third, the potentially unavoidable losses are to be addressed such as heat and the emission of greenhouse gases (GHG). Fourth, the temporal storage or buffering capacity of soils and marine environments for nutrients are to be included. Finally, the planetary lower and upper boundaries (see the introduction and [START_REF] Rockström | A safe operating space for humanity[END_REF] require attention like the carrying capacity of the planet [START_REF] Szekacs | Environmental and Ecological Aspects in the Overall Assessment of Bioeconomy[END_REF], the limitations for greenhouse gases, and the maintenance of nature and biodiversity. Such a model is thus quite complex. However, a simplified first-order 'input -moves -output -moves -input -…' model suffices in the context of our conceptual cylinder framework. We call this here an Open Thermodynamic and Circular Model (OTCM), because of the solar energy input as the driving force, and as outputs the recycled nutrients, unavoidable emissions, and temporal storage of (bio-)matter.

If appropriately and ethically [START_REF] Blok | Technocratic Management Versus Ethical Leadership Redefining Responsible Professionalism in the Agri-Food Sector in the Anthropocene[END_REF] steered, this simplified model allows sinusoidal patterns in the utilization of resources and products to evolve between limits. This implies that mass consumption, avoidable waste streams, over-exploitation of the planetary capacities, GHG emissions above limits, hunger, and poverty, etc. are thus unacceptable options leading to either chaos or order. Responsible research and innovation pathways are foreseen to counteract these options [START_REF] Schomberg | A Vision of Responsible Research and Innovation[END_REF]. This suggests e.g. that science becomes part of the societal contract (De Saille, 2015) and companies voluntarily carry societal responsibility as expressed in their Corporate Social Responsibility (CSR) reports [START_REF] Luhmann | Corporate Social Responsibility in Agribusiness: Literature Review and Future Research Directions[END_REF].

Case Studies

To exemplify the conceptual framework, we have selected and analyzed cases in Europe in which we have been involved. These cases cover at least seven system elements: (i) a relatively well-defined playing field, (ii) a group of interacting actors, (iii) specified resources and products, (iv) conversion schemes for resources up to 'consumed' bio-based products, (v) rules and constraints like regulations, subsidies and external changing conditions, and (vi) a notion of win-lose. The element 'duration' is implicitly present via the starting date of the case. This may be extended for all cases to 2050, which is the time horizon for the Green Deal. The bold values are used for the NAME of each case, that is later on systematically used in the main text

In our experience, the number of case studies covering all elements is rather limited in the bioeconomy literature; most cases are focused on one or only a few system elements. The here selected case studies have not been set up with system or game theories in mind before. They are only selected as they contain sufficient information to exemplify the conceptual framework and to get a notion of its applicability. Future case studies preferably address a larger scope, higher level of complexity, strategic behavior of players, and a territorial setting that encompasses a certain geographical scale, a wide range of actors, pieces, moves, rules, and (intermediate) win/ lose outcomes. However, for a first test of the usability of the cylinder-helix-CAS-OTCM-conceptual framework-in short, conceptual cylinder framework-the case studies already have their purpose (see Table 1).

The Conceptual Cylinder Framework Exemplified by Case Studies

Nine Cases Characterized for Seven Elements of Systems (or Games)

Nine case studies originating either from European, Mediterranean, or national projects have been selected in which the authors have been involved either as an initiator, a (sub-)project coordinator, an advisor, or a researcher. To further test the framework, other described cases may be explored (BBI, 2020;[START_REF] Stadler | New innovative ecosystems in France to develop the Bioeconomy[END_REF]. For each case, the presented first observations for the seven system elements have been extracted from project proposals, reports, deliverables, website communications, scientific publications, field visits, and/or discussion meetings with project partners. It should be noted that the observations are here not serving for in-depth analysis and presentation of each case. The latter has been the purpose of (scientific) publications within a European Horizon 2020 project for the first 5 cases, of the final publishable report of a European Six Framework Program project for the 6th case, of the website information of the 7th and 9th cases, and the scientific publication for the 8th case. Our analysis is restricted to (i) verifying if specific data can be presented for each system element, (ii) which information is available about players and their interactions (Fig. 3), (iii) how products are utilized, and (iv) how cases evolve in time (exploiting Fig. 1).

The majority of cases are oriented towards new valorization pathways for agricultural by-products and waste via new business models, innovative technologies, and facilitating public measures. Consequently, the cases address the challenge of the sustainable usage of pieces (resources, products, and services; see Fig. 1) by a group of actors interacting in a concerted way (see Fig. 3). Also, the groups of actors contribute to a revalorization of territorial bioeconomy assets, often in a circular economy context, even though the latter can be questioned from a sustainability point of view (see the remarks about the NK model for bioeconomy above). Others are responding to public measures ('rules') by reducing external inputs in agriculture, processing, or in storage and transport ('win'). Some are reacting to unhealthy diets (a 'loose'). The observations are summarized in Table 1.

Interactions Between Players Following the CAS Scheme in Fig. 3 For each case, interactions between actors have been analyzed regarding their positioning in the order-sustainability-chaos scheme of Fig. 3. Overall, the rules and constraints are recognized as clear and transparent; also, the potential scenarios are well-defined as either 'win' ('1′) or 'lose' ('2 & 3′) outcomes of evolving systems responding to specific rules. The 'Agropark','Wine', 'CEET', and 'Manure' cases are rather mature, self-organized, dynamic, and autonomously evolving in the melting zone. Agropark and CEET are propagating in the melting or sustainability zone already for quite some years showing a dynamic but stable business behavior. 'Wine and Manure' are still not fully stabilized for various reasons like lack of agro resources, larger sourcing areas, and strong competition with manufacturers of conventional products. Hence, Wine and Manure can be positioned at the edge of the order and melting zones.

The NovelQ and PlantProtein examples are near-mature with a strong business potential, competitive advantages due to unique and partly protected technologies and wide application areas. However, they continue to work on a sound and stable technology and business model.

The Food&Energy and Cereals cases are promising examples for the future, however, actually in immature phases. The geographical playing fields are well-defined. The business and technology models are currently in development. There is a need for new actors and interactions, to cross the frontier of the rigid and melting zones.

Flexiprocess is fully dependent on the support of external parties and yet immature as a business. However, as a more food-chain technology-oriented concept it already has an added value as research has shown. Their positioning is still in the rigid zone.

Balanced Utilization of Products via the OTCM Coupled to the Conceptual Cylinder Framework

If one considers the simplified OTCM for products, the cases are in general showing a balanced utilization of resources and products within the green melting zone of the conceptual cylinder framework. This is in particular due to circular flows of biomass, efficient input of energy and water (key examples are Agropark and Food&Energy), prioritizing valorization of by-products above loss and accumulation of waste (Manure, Wine, Cereals, Plantprotein), and lowering energy input in conversion and handling steps (NovelQ, CEET). This is further supported by the change towards resources that are demanding fewer inputs, the provision of more sustainable diets (Flexiprocess), the exploration of territorial production capacities without striving for the usage of external inputs while respecting seasonal fluctuations (Wine, Cereals). It should be noted that all cases intend to optimize the production and utilization of resources and products in a well-balanced way.

Combined Results for the Conceptual Cylinder Framework and Capacity to Respond to Changes

The results show that modifications in one element, like technological (moves) or organizational (player) innovations, or the introduction of new rules are always leading to modifications in the other elements. This is needed to reach a favorable outcome. For example, for the new valorization steps of by-products, also new business models are emerging (e.g. Food&Energy). For a new territorial organizational innovation (e.g. Agropark and Flexiprocess), new connections for flows of biomass are established between actors. Another rule-incentive (e.g. changing subventions in the case of Manure) generates a new business model and production of alternative added-value products. This means that elements are interconnected, however, not yet per se sustainably. This should be tackled in forthcoming research and innovation projects focusing on a more in-depth understanding of all interconnected elements, appropriate indicator sets, and variable constraints settings like in Game Theory.

It should be noted that the selected cases do not allow analyzing inter-dependencies between playing fields, hence looking to the integration of helices into a helicoid structure for an overall, planetary, bioeconomy system (see discussion for Fig. 2a). This remains to be done in the next studies.

Discussion

This section deals with (i) the need for a new conceptual framework for Sustainable Bioeconomy Systems (SBS), (ii) a detailed discussion of the cylinder framework, its applicability and understanding of sustainability in a dynamic system, and (iii) the potential of the framework to study interacting (local) systems.

(i) While the first and second bioeconomy strategies and agendas of the European Commission have been product-and biotechnology oriented [START_REF] Bugge | What Is the Bioeconomy? A Review of the Literature[END_REF], the third is more an ecological and circular bioeconomy strategy. These strategies do not guarantee that the global and local bioeconomy systems are sustainable from an environmental, social, and economic point of view.

Neither is the understanding of the positive or conflicting intentions from public and private stakeholders to strive for sustainable solutions based on a well-founded theory. This makes all debates about the normative dimensions of the bioeconomy systems so complicated and challenging. Here, we have attempted to provide a unifying conceptual framework as the theoretical basis for these debates. This framework underlines the challenge and importance of a coherent and integrative approach based on concomitantly addressing the seven system or game theory elements in a cylinder configuration, the interactions (K) between diverse agents (N) according to CAS-theory, and balanced production and utilization of products and resources following the OTCM.

As compared to previous 2-D configurations like the radar and doughnut, the here introduced cylinder configuration allows visualizing and understanding pathways of SBS avoiding entering in chaos or rigidity zones. The cylin-der configuration also permits to link the seven key elements of systems (or games), namely playing fields, players, pieces, moves, rules, outcomes, and duration. (ii) A deeper insight into the 3 zones (order, chaos, and melting or sustainability or safe and fair operating space) is obtained via complex adaptive system theories. These theories are partly founded on thermodynamic laws, in particular on the graph describing the diversity of agents versus their interactions leading either to order, chaos, or self-organized behavior. Intuitively it is known that if many diverse actors are all interacting with each other, the outcome is chaotic (like for all people speaking at meetings at the same moment). Also, if there are no interactions or nearly no actors, the outcome is highly static or rigid (like for nobody saying a word at a party). Somewhere in between the discussions make sense and are dynamic. As explored by [START_REF] Kauffman | At Home in the Universe, The Search for the Laws of Self-Organization and Complexity[END_REF], these interactions can be mimicked by Boolean networks with N different agents and K number of interactions. In a network of 'N' stakeholders with a reasonable amount of interactions 'K', bioeconomy systems are becoming selforganized, dynamic with overall sinusoidal behavior (Fig. 3; core). Endless growth of economies due to increasing N-K values will undoubtedly lead to chaos (Fig. 3; top right). Consequently, these economies will be ethically hard to defend if not additional considerations like pressure valves [START_REF] Zwier | The Ideal of a Zero-Waste Humanity: Philosophical Reflections on the Demand for a Bio-Based Economy[END_REF] are introduced to equilibrate systems. Passive approaches and inactivity will lead to rigidity and highly static food systems (see Fig. 3; bottom left).

The unifying conceptual framework is not complete if the notion of the planet as an open thermodynamic system is not taken into account. This implies that there is a driving force (solar energy), several conversion steps, and a re-balancing output (stored biomass or emitted particles or infrared radiation). In a very simplified way, this is described as OTCM. The consequence is that an ideal circular concept doesn't make sense; dynamic systems follow helical pathways.

As shown above, the cylinder framework seems to be useful for analyzing diverse bioeconomy cases. Most importantly, it reveals that elements are interconnected. If 'interacting actors' and 'product utilization' both show sinusoidal patterns and are interfering, in well-defined playing fields, with transparent rules, and appropriate moves (conversion steps), then the overall outcomes are 'wins'. The patterns reveal helical pathways in the zone between order and chaos, i.e. following scenario 3 in Fig. 1. If one of the behavior patterns shows steady growth (or decline) patterns, then the overall outcome is 'lose', the system ends up in chaos (scenario 1) or rigidity (scenario 2). Systems are sustainable if they follow scenario 3, and unsustainable for scenarios 1 and 2.

The systems following scenario 3 have a certain capacity to respond to external changes like increasing levels of agro-and food waste in chains, loss of nutritional quality, new incentives, and excessive energy inputs as shown by our cases. For example, changing subsidies in the Manure or banning of insecticides in the CEET cases have led to new organizational and technological innovations and sound business cases. However, it finally depends on the resilience and adaptation capacity of bioeconomy systems, their capacity to find new equilibria whether or not this also holds for climate change, drought, viruses like COVID-19, biodiversity loss, financial crisis, new laws, etc.

The unifying conceptual framework may help in better understanding how sustainability pathways could be reached, which are leverage points and (remaining) constraints. As an illustration and based on the insights obtained in our cases and framework, some very first and preliminary suggestions are provided here:

• The connection of bioeconomy systems with agroecology [START_REF] Caquet | L'agroécologie: des recherches pour la transition des filières et des territoires[END_REF] may be the only way to make the agroecology transition sustainable. If the sustainable evolution of new food and bio-based products, sustainable behavior of all interacting actors, and adopted rules in the full system are not taken into account, the agroecology transition may enter either the order or chaos zones (Fig. 1). • Valorizing entire plant resources and waste streams via cascading schemes may be beneficial from a resources efficiency point of view, however, may unintentionally lead to chaos (see Fig. 3); the number of interactions between (new) actors in the cascading systems should be taking into account and being 'manageable'; also policy measures are to be considered to guarantee self-organized dynamical solutions and sustainable outcomes. • The choice of playing field dimensions -like for urban metabolisms [START_REF] Bezama | Resources, collaborators, and neighbors: The three-pronged challenge in the implementation of bioeconomy regions[END_REF] -should very critically be re-considered because sustainable outcomes may never be reached in these playing fields; hence, interactions with other playing fields (nearby territories like rural-coastal areas) and/or external players and resources should then be taken into account. The 'ensemble' of playing fields, via fair and compensating exchange mechanisms for all system elements, should be sustainable. The considerations about uncompensated unsustainability measures in one playing field, and leaving the burdens to other playing fields, are ethically and scientifically unjustifiable. • The circular bioeconomy in itself is highly rigid (Fig. 3), except if the number of actors in the circle is extremely high. The business model typology for local circular economy initiatives [START_REF] Donner | A new circular business model typology for creating value from agro-waste[END_REF] shows in majority networkmodels revealing 6 different cooperation types between robust but flexible actors striving for integrated usage of resources locally. To avoid rigidity, insights in resilience and adaptation capacity are crucial, especially when subsidies are altered for resource usage or new European competition rules are introduced for interacting SMEs [START_REF] Gerbrandy | Agricultural Policy and EU Competition Law: Possibilities and Limits for Self-regulation in the Dairy Sector[END_REF].

(iii) Our 9 selected cases do not yet show the interactions and trade-offs between different local bioeconomy systems. This is very important in the case of e.g. sustainable urban bioeconomy systems (see above) or for food sovereignty as currently debated. For example, if one country or region strives for autonomous supplies to feed its population, what are the consequences for other countries? Which mutual support options should be put in place to keep systems overall viable and ethically justified (like emergency aids, migration, and additional support externally)? And should each local system be sustainable as our framework strongly suggests? What does this imply for the normative dimensions of both the overall system and local systems? One can draw a parallel with an orchestra of individual musicians: the overall outcome could only be harmonic (like the helicoid structure in Fig. 2a) in case all individual contributions are harmonic.

Conclusions

The here presented unifying conceptual cylinder framework allows analyzing and discussing diverse SBS. This is in a very preliminary way done via the 9 cases, and provides the following conclusions: • Here, the conceptual cylinder framework reveals that (i) player behavior and usage of biomass sustainably are interconnected and should jointly follow helical pathways to be sustainable (see Fig. 1), (ii) the helicoid, as the sum of individual helices representing co-evolving local systems, is the lowest energy (thus preferable) state for SBS at our planet (like DNA or protein triple helices in nature) (cf.

Figure 2), (iii) the top view of the cylinder reveals a circle which currently serves as the basis for circular economy thinking, however without the time dimension and thus without the possibility to analyze sustainable evolutions, (iv) helical structures are highly stable but dynamic structures in nature, hence they are perfectly well suitable for being resilient and adaptive to external shocks.

Overall, the unifying conceptual cylinder framework (theory) now permits us to define Sustainable Bioeconomy Systems as Complex Adaptive Systems dealing with food and other bio-based products, showing helix-like moves in the sustainability zone. This is due to the coherence between Complex Adaptive System, NK models, open thermodynamic models, helical moves in cylinders between order and chaos, and the exploitation of system or game theory elements; a synthesis is presented in Fig. 4. This integrally includes playing fields, dynamically interacting (existing and new) actors, (novel) bio-resources and products, all eco-friendly conversion steps, critical conditions and rules, duration and timings, and win-lose scenarios which are crucial for finding sustainable solutions and steering (policy) measures.

The notion of territories as evolving playing fields requires further reflection because their characteristics are modified by the dynamics of the (replicating) agents themselves. The traditional way of considering fixed country or regional borders as political choices may be inadequate for considering territories from a sustainability point of view. Those should encompass e.g. geographical, atmospheric, political, or sectorial dimensions to provide freedom to sustainably operate within limits. Hence, an intelligent re-design of playing fields, adapted case studies, and the analysis of external conditions -arriving from other 'playing fields' -are imperative for concluding about all possible interactions in the systems and ethically justified sustainable outcomes (wins).

Finally, one could suppose that the normative dimensions of the bioeconomy have cylinder symmetry. Such a cylinder symmetry enables bioeconomy systems -constituted of different interacting players utilizing bio-based products in welldefined playing fields -to endlessly evolve in a balanced or sustainable manner in the melting zone between order and chaos (scenario 1 in Fig. 1), hence, respecting boundaries. In other words, the cylinder framework also provides a direction to ethical, philosophical, and esthetical debates in the bioeconomy. The Open Thermodynamic Circular Model (OTCM) for uƟlizaƟon of pieces (bio-based products) combines solar energy input as driving force for biomass producƟon, with circular usage of nutrients and unavoidable emissions and temporal storage of (bio-) maƩer as outputs, i.e. the moves in systems.

The helix is the sum of two sinusoidal curves for behavior of players and uƟlizaƟon of pieces, describing balancing (or harmonic) evoluƟon. Bioeconomy systems are here defined as systems that organize the uƟlizaƟon of bio-based products (including natural resources) within certain boundaries, appreciaƟng its wider environmental, social, poliƟcal and economic context.

Ɵme

  plane (actors in bio-economy) UƟlizaƟon of Pieces: sinusoidal in xz plane (resources & products) Time (z-axis)* *The helix is the sum of two sinusoidal curves for the behavior of players and the uƟlizaƟon of pieces Scenario 2

Fig. 2

 2 Fig. 2 Helical structures; a A single, double, and triple concentric helix in the cylinder confinement (modified from Serna et al., 2019); b DNA c Alpha-helix with top and side views; d spiral structures in nature; e spiral structures in food and non-food products; f two propagating sinusoidal curves form a helix; g predator-prey populations in time; h helicoid structure. Source: Fig. 2a-Helices in a tube, own design, based on work of Serna et al., 2019; Fig. 2d-Spiral growing plant, wikipedia commons; https:// commo ns. wikim edia. org/ wiki/ File: Dirkv dM_ natur al_ spiral. jpg; Fig. 2f-Helix -2 sinusoidal curves: own design, based on picture of wikipedia commons image: https:// www. radar tutor ial. eu/ 06. anten nas/ pic/ zirku lanim. gif; Fig. 2g-Own design, inspired by https:// en. wikip edia. org/ wiki/ Lotka% E2% 80% 93Vol terra_ equat ions#/ media/ File: Lotka_ Volte rra_ dynam ics. svg; Fig. 2h-Helocoid: slightly modified, based on https:// en. wikip edia. org/ wiki/ File: Helic oid. svg. From Wikimedia Commons, the free media repository

  The major system or game elements are players, pieces, moves, playing fields, rules, win-lose outcomes and Ɵme/duraƟon Safe and fair operaƟng space = melƟng zone = sustainability zone = green zone between social-environmental-economic foundaƟons and ceilings Order (rigid) zone Chaos zone Scenarios are either 'win' ('1') or 'lose' ('2 & 3') outcomes of evolving systems responding to rules The NK model describes the number of interacƟons 'K' between diverse players 'N'. One disƟnguishes rigid (linear & pure circles), chaoƟc or self-organized dynamic networks.

  systems that conƟnuously evolve in the 'sustainability' zone (following scenario 3), also if challenged by extreme condiƟons.Sustainable bioeconomy systems areComplex AdapƟve Systems dealing with bio-based products, showing helix-like moves in the sustainability zone.

Fig. 4

 4 Fig. 4 Synthesis of the major building blocks of the Conceptual Cylinder Framework for Sustainable Bioeconomy systems. Source: Modified image of https:// www. radar tutor ial. eu/ 06. anten nas/ pic/ zirku lanim. gif is included

Table 1

 1 The observations for seven elements of a system or a game (horizontal) presented for nine different cases(vertical)

	Win / lose			Valorization of over	10,000 tons of organic	waste/year	New products and	markets for local	producers; some new	jobs created. Public-	private cooperation	model	Valorization of over	hundreds of thou-	sands of tons of grape	marc, of Hls of lees	and wine must per	year; all collected	by-products are	valorized, no ultimate	waste (except process	wastewater)	Social: over 100 jobs	Economic: Almost no	cost for wine-makers
	Rules / constraints			Odor limits, public	subsidies, the time	limitation for feed-in	tariffs						Changing regulations	for the treatment of	wine waste and by-	products
	Conversion steps /	moves		Recycling, bioenergy	conversion, bio-	fertilizer manufac-	turing						Recycling, manufac-	turing of feed, food,	and cosmetics, dis-	tilling and extract-	ing constituents,	optimizing logistics
	Resources and / or	products / pieces		By-products and agro-	waste: pig, cattle	and horse manure,	vegetables, and	energy crops					By-products from	wineries and wine	processing, nutra-	ceuticals (grape	seed extracts),	sugars, natural	colorings, animal	nutrition, alcohol &	spirits
	Interacting actors /	players		Farmer and owner of	a biogas plant, local	farmers, technol-	ogy supplier, own	logistics, Town Hall,	citizens				Union of wine	cooperatives special-	ized in food and	non-food oriented	products based on	wine by-products	Wine producers,	Manufacturers,	R&D institute,	Cooperatives
	Playing field	& Time/indicated	starting date	A community in	Germany,	since 2000							A region in France	since 1970
	Element	Bioeconomy Case	& motivation	Local manure and agro-waste initiative	Entrepreneurial	initiative to initially	transform waste in	bioenergy, partly	supported by sub-	sidies	(NOAW, 2020)	New cooperative	'from cost to value	for wine by-prod-ucts'	Joint cooperative ini-	tiative to transform	waste into bio-based	products, partly sup-	ported by subsidies	(NOAW, 2020)

  Without a coherent conceptual frame, including the time axis, coherent sets of both lower and upper limits for social, environmental, and economic indicators, and a linkage between the 7 key system or game theory elements, one cannot distinguish if systems are sustainable or not. Continuous growth (or decline) strategies -and related discourses -are automatically leading to chaos or rigidity and are ethically and scientifically not justified. Feedbacks and interventions in the 7 elements are necessary to keep balancing outcomes in between order and chaos. This implies that interventions always include counter-balancing actions to keep the system within boundaries (Fig.1), expressed by Latour as 'Down to Earth' (2017). • Disrupting or innovating one element (e.g. technology, business, regulation, or social) impacts the other six elements. If this destabilizes systems and results in unsustainable outcomes, then integral measures for all elements are required (like today discussed for climate change, biodiversity loss, COVID-19, etc.). If not, individual and mono-disciplinary, single domain or sectororiented interventions make sense for local optimizations in the system.

•

It should be noted that our representation of a helix is not referring to the helix systems described by[START_REF] Carayannis | Creative Destruction in International Trade: Insights from the Quadruple and Quintuple Innovation Helix Models[END_REF]. The latter are linking knowledge, innovation and environment, either as 'university-industry-government relations' (triple helix), an additional "media-based and culture-based public" (quadruple helix) and a final extension to the inclusion of the "environment" (quintuple helix).

INRAE-French National Research Institute for Agriculture, Food and Environment, 147 Rue de l'Université, Paris, France

Acknowledgements Colleagues of the Case Studies, the European SCAR working group on food systems (WG-FS) and the SAM-SAPEA WG-FS, the Foresight reflection group on Bioeconomy of INRAE, and members of the French Academies of Agriculture and Technologies, are acknowledged for discussions on system approaches.

Data Availability All references are given.

Declarations

Conflict of interest The authors declare that they have no competing interests

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Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Authors and Affiliations

Hugo de Vries


5. Triathlon and ultra-endurance events in tropical environments

Physical performance in tropical environments, which combine heat and high humidity, is a challenge that requires specific preparation. The high humidity of a tropical climate alters thermoregulatory capacity by limiting the rate of sweat evaporation. Proper management of wholebody temperature is thus essential to complete an endurance event like a long-distance triathlon or an ultramarathon in such an environment. In triathlon and ultra-endurance races, which can last from 8 to 20 h, performance in tropical settings is closely linked to the capacity to maintain hydration status. Indeed, the rate of withdrawal in these longer events has been associated with water intake, with many finishers showing alterations in electrolyte (e.g. sodium) balance. To counterbalance the impact of a tropical climate and maintain performance, several countermeasures can be adopted, such as using hydration and cooling strategies, and heat acclimation.

1 Influence of heat on performance and health 1.1 Specificity of the triathlon The Ironman and Challenge triathlon series are trademark brands for long-distance triathlons consisting of a 3.8-km swim, 180-km cycling leg, and full marathon (42.195 km). The best professional triathletes complete the distance in under 7 h and 50 min, whereas age group athletes vary from 9 to 13 h and more, making this one of the longest endurance races. The duration depends on several factors, including terrain (i.e. course route and geography) and environmental conditions.

For example, hot and humid climates impact on performance and the rate of withdrawal, as observed in the Kona (Hawaii) Ironman World Championships every October [START_REF] Giambelluca | Evapotranspiration of Hawaiʻi: final report to the US Army Corps of Engineers-Honolulu District and the Commission on Water Resource Management[END_REF][START_REF] Stiefel | Analysis of performances at the'Ironman Hawaii triathlon'and its qualifier events with respect to nationality[END_REF]): top age-groupers were slower at Hawaii than at their qualifier races [START_REF] Stiefel | Analysis of performances at the'Ironman Hawaii triathlon'and its qualifier events with respect to nationality[END_REF], and abandon rate can reach 10%, a high proportion considering the fitness level of athletes participating in this particular event, more resistant to heat stress (Cheung and McLellan 1998;Ironman 2018b). Similarly, more than 25% of the athletes did not reach the finish line at the inaugural Ironman Vichy in 2015, which was held in unusually hot conditions (31~35°C), in contrast to North American races with a minimum 95% finish rate [START_REF] Britt | North American Ironman DNF Rates: Finishers and DNF by Race[END_REF].

The following sections detail how thermal stress can specifically impact each of the triathlon legs: swimming, cycling and running.

Swimming

Most long distance triathlons allow neoprene wetsuits to be worn for the swim leg as long as water temperature does not exceed 24.5°C. Between 24.5°C and 28.8°C, athletes who choose to wear a wetsuit are allowed to participate, but are not eligible for age-group awards or for qualifying slots for the Ironman World Championships, and over 28.8°C wetsuits are prohibited (Ironman 2018). With its enhanced buoyancy, the neoprene wetsuit reduces ventilation and O 2 consumption ( O 2 ) at a given swimming speed, and therefore metabolic heat production [START_REF] Trappe | Physiological responses to swimming while wearing a wet suit[END_REF].

However, wetsuits reduce heat dissipation capacity and can lead to high core body temperatures and dehydration [START_REF] Kerr | Hyperthermia during Olympic triathlon: influence of body heat storage during the swimming stage[END_REF][START_REF] Laursen | Core temperature and hydration status during an Ironman triathlon[END_REF]). Hence, although banning wetsuits in warm water might impair swimming performance, it might also decrease the risk of hyperthermia.

Interestingly, [START_REF] Kerr | Hyperthermia during Olympic triathlon: influence of body heat storage during the swimming stage[END_REF] showed in a simulated Olympic triathlon that core temperature did not change by wearing a wetsuit, thought to limit thermoregulatory mechanisms through heat-insulating properties of neoprene, as excess heat was still transferred at the periphery, leading to a higher skin temperature. A subsequent field study confirmed that core temperature remained around 38°C in well-trained athletes wearing a wetsuit in 20.5°C water during a 3.8 km swim [START_REF] Laursen | Core temperature and hydration status during an Ironman triathlon[END_REF]. This was again confirmed by a case report in which an athlete's core temperature was continuously monitored during an Ironman [START_REF] Laursen | Hyperthermic fatigue precedes a rapid reduction in serum sodium in an ironman triathlete: a case report[END_REF]). In 29.5°C water, another study showed that the core temperature of moderately trained athletes increased by an average 0.7°C and remained under 38°C during a non-wetsuit half-Ironman (Figure 1; [START_REF] Baillot | Hydration and thermoregulation during a half-ironman performed in tropical climate[END_REF]). Thus, no study appears to have shown a dangerous elevation in core temperature during the swim leg of long-distance triathlon events. Moreover, while 13 of the 14 deaths in triathlon races from 2006 to 2008 occurred during the swim leg, pre-existing cardiovascular abnormalities seem to have been the major factor, ruling out hyperthermia as a potential cause [START_REF] Harris | Sudden death during the triathlon[END_REF].

Cycling

When cycling, some of the heat produced by the muscles is dissipated via convection. This however, depends on a sufficient temperature gradient between the skin and ambient air.

Convection is therefore limited in hot conditions when air temperatures exceeds 35°C. Heat is also dissipated during cycling via the evaporation of sweat, which depends on the water vapor partial pressure gradient between air and skin. Like convection, this mechanism is reduced in humid environments, making performance in a tropical environment challenging as thermoregulatory efficiency is reduced [START_REF] Nybo | Cycling in the heat: performance perspectives and cerebral challenges[END_REF]. In a tropical climate (31-33°C, 70-75% RH), one-hour of pedalling at a submaximal intensity increases core temperature, heart rate, sweat rate and water loss (Saat et al. 2005a;Saat et al. 2005b;[START_REF] Voltaire | Influence of a hot/wet environment on exercise performance in natives to tropical climate[END_REF]. These results can be extrapolated to describe the physiological impact of 4-6-h events, especially if the cycling course includes hills, where the diminished air speed reduces heat dissipation [START_REF] Nybo | Cycling in the heat: performance perspectives and cerebral challenges[END_REF]. Laboratory-controlled studies showed that increasing ambient temperature impaired cycling capacity when relative humidity was clamped at 70% [START_REF] Galloway | Effects of ambient temperature on the capacity to perform prolonged cycle exercise in man[END_REF][START_REF] Maughan | Influence of relative humidity on prolonged exercise capacity in a warm environment[END_REF]. During a 9-day (2.5 h/day) cycling race held in Guadeloupe (31.1°C, 75.6% RH), tympanic temperatures measured immediately after the stages never exceeded 2°C of resting pre-race values [START_REF] Hue | Heart rate, thermoregulatory and humoral responses during a 9-day cycle race in a hot and humid climate[END_REF]. In contrast to the variability associated with stage racing in a peloton, triathletes will adopt a much steadier pace during racing in some cases to "save their legs" for the following marathon [START_REF] Wu | Pacing strategies during the swim, cycle and run disciplines of sprint, Olympic and half-Ironman triathlons[END_REF]. Interestingly, Baillot et al. [START_REF] Baillot | Hydration and thermoregulation during a half-ironman performed in tropical climate[END_REF] showed a negative correlation between body mass and the evolution of core temperature throughout the cycling leg, implying greater heat storage and inertia. A bigger body thus presents a larger surface to preserve heat exchange at high velocity, even in a hot and humid environment [START_REF] Nielsen | Olympics in Atlanta: a fight against physics[END_REF].

In summary, the high velocities and individual nature of cycling in the triathlon support heat dissipation by convection on the condition that air temperature is lower than skin temperature. In a thermally challenging environment, sweat evaporation is the main avenue for heat dissipation but it is limited by the high humidity of a tropical environment. Nevertheless, triathletes appear to show adequate thermoregulatory capability to prevent excessive hyperthermia, mainly through intensity management and pacing strategies [START_REF] Baillot | Hydration and thermoregulation during a half-ironman performed in tropical climate[END_REF].

Running

Of the three sports in the triathlon, running may carry the greatest risk of hyperthermia for triathletes competing in a tropical climate. Several factors come into play. Firstly, although running is faster than swimming, air possesses neither the heat capacity nor transfer celerity of water, hence limiting the quantity of heat energy transferred from the body. Secondly, unlike in cycling, the lower speed associated with running does not allow for excess heat dissipation via convection [START_REF] Nielsen | Olympics in Atlanta: a fight against physics[END_REF]. These factors can have a strong negative impact on running performance [START_REF] Kenefick | Thermoregulatory function during the marathon[END_REF], particularly the marathon [START_REF] Ely | Impact of weather on marathon-running performance[END_REF]. This negative impact is amplified (i) by a heavier body mass, which, at a given pace, requires more energy for running propulsion and therefore produces more heat, and (ii) in heavier athletes running in a hot/humid environment limiting heat exchange by convection and evaporation, who display greater imbalance between heat production and dissipation, even at slower paces [START_REF] Marino | Advantages of smaller body mass during distance running in warm, humid environments[END_REF].

While the core temperature data of professional triathletes in the Hawaii Ironman or other tropical locations are currently not available, a few studies of moderately to very well trained age group athletes have shown that none of them suffered from heat-related illness and excessive increases in core temperature [START_REF] Laursen | Core temperature and hydration status during an Ironman triathlon[END_REF]) (Figure 1; [START_REF] Baillot | Hydration and thermoregulation during a half-ironman performed in tropical climate[END_REF][START_REF] Coso | Relationship between physiological parameters and performance during a half-ironman triathlon in the heat[END_REF]). In the report from Laursen et al. [START_REF] Laursen | Core temperature and hydration status during an Ironman triathlon[END_REF] [START_REF] Baillot | Hydration and thermoregulation during a half-ironman performed in tropical climate[END_REF]. These values are not surprising given the relative intensity and absolute workload at which most long-distance triathlon races are performed, which is in contrast to shorter events performed at a higher intensity and thus higher heat production [START_REF] Siegel | Ice slurry ingestion increases core temperature capacity and running time in the heat[END_REF][START_REF] Baillot | Hydration and thermoregulation during a half-ironman performed in tropical climate[END_REF]. The importance of exercise intensity was confirmed in dryer conditions in a study showing that the fastest athletes exhibited the highest core temperatures [START_REF] Coso | Relationship between physiological parameters and performance during a half-ironman triathlon in the heat[END_REF].

1.2 Specificity of ultra-endurance events Marathon races have more standardized characteristics, facilitating the comparison of performances in order to study the role played by heat (see chapter 12). Based on the analysis of winners' times in several marathons, [START_REF] Maughan | Distance running in hot environments: a thermal challenge to the elite runner[END_REF][START_REF] Maughan | Distance running in hot environments: a thermal challenge to the elite runner[END_REF] determined that the best running temperature is between 10°C to 12°C for elite athletes. Beyond this temperature, the analysis of 136 marathons performed between a wet-bulb globe temperature (WBGT) of 5 and 25°C showed a decrease in performance with an increase in WBGT (Figure 2; [START_REF] Ely | Impact of weather on marathon-running performance[END_REF]). Interestingly, these authors also showed that slower runners, who are exposed to heat for a longer time than faster runners, are more affected by temperature. For ultramarathon distances, the same effect of hot environments on performance was observed in a study that examined running times in the Western States Endurance Run (161 km and 6000 m D+) in 2006 and 2007 [START_REF] Parise | Influence of temperature and performance level on pacing a 161 km trail ultramarathon[END_REF]. In these two editions (Figure 3), the authors followed 50 runners who had finished the race in both years to investigate the effect of temperature changes from 7-38°C in 2006 to 2-30°C in 2007. Independently of their level, the athletes were 8% slower in the hot condition (2006) than in the cooler environment (2007), and the withdrawal rate was 14% higher in 2006. In this study, slower runners did not appear to be more impacted by the hot environment, but this observation was probably due to the longer time running at a comfortable temperature (i.e. night).

Hydration requirements during ultra-endurance exercise in the heat

During muscle contraction, only ~25% of the substrate energy is converted to mechanical work, with the other ~75% released as heat. Effective thermoregulation during exercise depends on the balance between the absolute mechanical work generated by the athlete and the heat loss process (Chapter 2). Ultramarathons, characterized by the maintenance of a low relative exercise intensity over very long periods, do not significantly challenge the heat balance in temperate environments.

However, maintaining mechanical load over a longer time may challenge heat balance in athletes, especially when competing in hot and/or humid environments. Furthermore, environmental heat stress (i.e. temperature) reduces dry heat loss, due to the small (or even negative) temperature gradient between the skin and air, which progressively places sweat evaporation as the only mechanism available for the organism to dissipate endogenous heat [START_REF] Brotherhood | Heat stress and strain in exercise and sport[END_REF][START_REF] Taylor | Challenges to temperature regulation when working in hot environments[END_REF]. Indeed, at in 30°C conditions a dry heat loss of 75 W is observed whereas at 40°C, it induces a dry heat gain of 75 W, increasing the sweating rate require to maintain body core temperature [START_REF] Gagnon | The evaporative requirement for heat balance determines whole-body sweat rate during exercise under conditions permitting full evaporation[END_REF]. Thus, ultramarathons performed in a hot environment require bigger volumes of water intake to compensate for increased water losses. During the Badwater Ultramarathon of Badwater. According to these corrected distances, the Badwater runners drank almost twice as much water as the Biel runners (0.13 L.km -1 and 0.069 L.km -1 , respectively), despite the higher mechanical workload developed during the Biel Ultramarathon due to its shorter distance and lower elevation change (6.6 min.km -1 vs. 8.5 min.km -1 for Badwater). The characteristics of the 2007 Peninsula Ultra Fun Run (PUFfeR) of South Africa (80 km and 1000 m D+) were close to those of the Biel Ultramarathon, but the participants were subjected to lower environmental temperatures (8-20°C). The runners drank less during this more temperate race than during the Biel Ultramarathon (0.028 L.km -1 and 0.069 L.km -1 , respectively) [START_REF] Tam | Fluid intake and changes in blood biochemistry, running speed and body mass during an 80 km mountain trail race[END_REF]). Analysis of the hydration status of 16 ultramarathon runners (161 km, 7000 m D+) in a hot environment (4.8-37.8°C) showed that finishers (n=6) had drunk significantly more water at the 48 th kilometer than non-finishers (n=10) [START_REF] Stuempfle | Race diet of finishers and non-finishers in a 100 mile (161 km) mountain footrace[END_REF]). However, the authors were unable to determine whether beverage intake was directly linked to finishing capacity or if it was due to other factors, such as the experience or endurance capacity of the runners. A second study performed during a 160-km foot race (positive elevation not known) in temperatures that peaked at 38°C followed only those runners who had completed at least one previous ultramarathon among the top 50% [START_REF] Glace | Food intake and electrolyte status of ultramarathoners competing in extreme heat[END_REF]. The authors showed that, despite the homogenous level and experience of these runners, non-finishers also drank significantly less than finishers (-35%, p<0.01). All these data confirmed the relationship between event temperature and water intake that is crucial to health and performance. A study during the Gwada Run of 2011, a 6-day multi-stage race for a total of 142 km under tropical conditions (30±2.4°C and 82±4% RH) showed a sweat loss of 0.19 L.km -1 (Hue et al.

2014

). Yet water intake (1.5±0.3 L per stage) was probably distorted by the shortness of the stages (from 16 to 21 km), which enabled athletes to tolerate transient dehydration during the races (-4.2±0.9 L per stage).

2 Countermeasures to optimize performance and health

Hydration

Limiting dehydration during triathlons and ultramarathons in hot environments seems to be essential to maintain the exercise workload over many hours. The role of hydration in a tropical climate (see chapter 6) is critical since it has been shown that hyperthermia and dehydration are worse than hyperthermia alone [START_REF] Sawka | Hydration effects on thermoregulation and performance in the heat[END_REF][START_REF] Sawka | Does dehydration impair exercise performance?[END_REF]. Despite contradictory observations on influencing thermoregulation and core temperature [START_REF] Latzka | Hyperhydration: thermoregulatory effects during compensable exercise-heat stress[END_REF][START_REF] Ross | Effects of lowering body temperature via hyperhydration, with and without glycerol ingestion and practical precooling on cycling time trial performance in hot and humid conditions[END_REF], it seems that hyperhydration can delay the development of dehydration [START_REF] Latzka | Hyperhydration and glycerol: thermoregulatory effects during exercise in hot climates[END_REF][START_REF] Latzka | Hyperhydration: thermoregulatory effects during compensable exercise-heat stress[END_REF][START_REF] Sawka | Influence of hydration level and body fluids on exercise performance in the heat[END_REF]. However, hyperhydration does not seem to lead to better performances during a laboratory-based 46 km cycling time trial by elite cyclists [START_REF] Ross | Effects of lowering body temperature via hyperhydration, with and without glycerol ingestion and practical precooling on cycling time trial performance in hot and humid conditions[END_REF] or a 60 min run in endurance trained runners [START_REF] Scheadler | Glycerol hyperhydration and endurance running performance in the heat[END_REF]. As hyperhydration results in non-negligible added body weight, it may not be an advantage for running performance, which is greatly affected by extra weight [START_REF] Teunissen | Effects of independently altering body weight and body mass on the metabolic cost of running[END_REF]. In addition, it does not enhance thermoregulation in a hot and humid climate and augments the risk of hyponatremia [START_REF] Noakes | Water intoxication: a possible complication during endurance exercise, 1985[END_REF]).

In the triathlon, although hydration depends very much on the availability of adequate means set up by the race organization, the descriptive papers to date report that no triathlete has suffered from dehydration symptoms in hot and humid events, despite occasional significant water loses [START_REF] Baillot | Hydration and thermoregulation during a half-ironman performed in tropical climate[END_REF][START_REF] Coso | Relationship between physiological parameters and performance during a half-ironman triathlon in the heat[END_REF][START_REF] Laursen | Core temperature and hydration status during an Ironman triathlon[END_REF][START_REF] Speedy | Fluid balance during and after an ironman triathlon[END_REF]. This suggests that the hydration strategies employed by the athletes meet the body's water requirements [START_REF] Kenefick | Drinking Strategies: Planned Drinking Versus Drinking to Thirst[END_REF].

Maintaining optimal hydration is more complicated than it would seem in the ultramarathon.

Indeed, analysis of the hydration status of ultramarathon runners in 2 different races showed that finishers had drunk significantly more water than non-finishers, even if the runners' experience was taking into account [START_REF] Glace | Food intake and electrolyte status of ultramarathoners competing in extreme heat[END_REF][START_REF] Stuempfle | Race diet of finishers and non-finishers in a 100 mile (161 km) mountain footrace[END_REF]. In contrast, slower runners became over-hydrated because they feared dehydration, which may lead to hyponatremia [START_REF]Statement of the Second International Exercise-Associated Hyponatremia Consensus Development Conference, New Zealand[END_REF][START_REF] Noakes | Drinking guidelines for exercise: what evidence is there that athletes should drink "as much as tolerable", "to replace the weight lost during exercise" or "ad libitum[END_REF]. Hyponatremia however, is not only due to over-hydration, but may be the consequence of insufficient sodium intake during the race [START_REF] Glace | Food intake and electrolyte status of ultramarathoners competing in extreme heat[END_REF][START_REF] Stuempfle | Race diet of finishers and non-finishers in a 100 mile (161 km) mountain footrace[END_REF].

In a hot environment, hyponatremia affected 30-50% of ultramarathon finishers, reflecting the inadequate or incorrect hydration strategies of many runners [START_REF] Glace | Food intake and electrolyte status of ultramarathoners competing in extreme heat[END_REF][START_REF] Hoffman | Hyponatremia in the 2009 161-km Western States Endurance Run[END_REF][START_REF] Lebus | Can changes in body mass and total body water accurately predict hyponatremia after a 161-km running race?[END_REF]). Thus, better sodium intake during ultramarathons could contribute to better performances by stimulating thirst, increasing voluntary fluid intake, enhancing intestinal glucose and water absorption, optimizing extracellular and intracellular fluid balance, and potentially mitigating the occurrence of clinically significant episodes of hyponatremia [START_REF] Maughan | Fluid and electrolyte loss and replacement in exercise[END_REF][START_REF] Shirreffs | Fluid and electrolyte needs for training, competition, and recovery[END_REF][START_REF] Speedy | Hyponatremia in ultradistance triathletes[END_REF][START_REF] Vrijens | Sodium-free fluid ingestion decreases plasma sodium during exercise in the heat[END_REF].

Hydration policy and implementation

In a triathlon field study, oral salt supplementation improved half-Ironman performance through faster cycling (p<0.05) and showed a similar trend in the running leg (p=0.06), with reduced sweat rate and limited electrolyte deficit [START_REF] Coso | Effects of oral salt supplementation on physical performance during a halfironman: A randomized controlled trial[END_REF]. The consensus recommendation is thus to ingest 0.5 to 0.7 g.L -1 .h -1 for long endurance races (Von [START_REF] Duvillard | Fluids and hydration in prolonged endurance performance[END_REF]) and up to 1.5 g.L -1 .h -1 for athletes prone to develop muscle cramping [START_REF] Bergeron | Heat cramps: fluid and electrolyte challenges during tennis in the heat[END_REF].

However, adding salt to the consumed water is not sufficient to avoid hyponatremia if athletes overdrink during a race (73% of severe symptomatic hyponatremia found after an Ironman [START_REF] Speedy | Hyponatremia in ultradistance triathletes[END_REF]).

(Hoffman and Stuempfle 2014) observed no advantage to sodium-enriched beverages during a 161-km ultramarathon performed by all levels of athletes in heat (38°C). This result may have been due to a variation in sodium intake from solid food and/or to the tolerance of faster runners to hypohydration and hyperthermia [START_REF] Baillot | Fluid replacement strategy during a 27-Km trail run in hot and humid conditions[END_REF][START_REF] Hue | Thermoregulation, hydration and performance over 6 days of trail running in the tropics[END_REF]).

Cooling

Cooling strategies such as cold drink ingestion or cold-water immersion to reduce the thermal load may enhance performance in the heat (see chapter 7). This effect has been manifested in cyclists (Figure 4; [START_REF] Burdon | The effect of ice slushy ingestion and mouthwash on thermoregulation and endurance performance in the heat[END_REF][START_REF] Riera | Precooling does not enhance the effect on performance of midcooling with ice-slush/menthol[END_REF][START_REF] Trong | Ingestion of a cold temperature/menthol beverage increases outdoor exercise performance in a hot, humid environment[END_REF]) and runners as a longer time to exhaustion [START_REF] Siegel | Ice slurry ingestion increases core temperature capacity and running time in the heat[END_REF][START_REF] Siegel | Pre-cooling with ice slurry ingestion leads to similar run times to exhaustion in the heat as cold water immersion[END_REF][START_REF] Yeo | Ice slurry on outdoor running performance in heat[END_REF]. Wearing cooling garments prior to or during exercise has proven to be performance-effective in hot and humid climates [START_REF] Arngrimsson | Cooling vest worn during active warm-up improves 5-km run performance in the heat[END_REF][START_REF] Hasegawa | Wearing a cooling jacket during exercise reduces thermal strain and improves endurance exercise performance in a warm environment[END_REF][START_REF] Luomala | Adding a cooling vest during cycling improves performance in warm and humid conditions[END_REF]), but they are difficult, impractical and potentially not allowed to be used during official long-distance events.

Other studies have focused on cooling strategies, but the exercise duration has been relatively short compared with ultra-endurance events. Nonetheless, they show interesting results that may be extrapolated for long to ultra-long events. Spraying or pouring water over the face and/or body can improve performance in tropical conditions. For example, pouring cold water over the skin will reduce skin temperature before dripping off the body, and transiently improve thermal comfort.

Cooling the head in this manner resulted in a 51% increase in cycling time to exhaustion at 75% VO 2max [START_REF] Ansley | The effects of head cooling on endurance and neuroendocrine responses to exercise in warm conditions[END_REF], with similar effects recently observed in running (Stevens et al. 2017b). Neck cooling during a 90-min running trial in a hot environment (30.4°C and 53% RH) increased the distance covered by 7.4% with no change in rectal temperature [START_REF] Tyler | Neck cooling and running performance in the heat: single versus repeated application[END_REF]. A similar effect was found with menthol ingestion, as it activates cold dermal sensors [START_REF] Stevens | Menthol: A Fresh Ergogenic Aid for Athletic Performance[END_REF]. Mixed into a cold beverage, menthol did not lower core body temperature but had a positive effect on thermal sensation and running/cycling performances over various distances in tropical climate [START_REF] Stevens | Running performance and thermal sensation in the heat are improved with menthol mouth rinse but not ice slurry ingestion[END_REF][START_REF] Trong | Ingestion of a cold temperature/menthol beverage increases outdoor exercise performance in a hot, humid environment[END_REF]. Indeed, [START_REF] Stevens | Running performance and thermal sensation in the heat are improved with menthol mouth rinse but not ice slurry ingestion[END_REF] showed that a menthol mouth rinse every kilometre (25 mL at a concentration of 0.01%) during a running time trial in the heat significantly improved 5-km performance time by 3%. A cumulative effect of menthol and ice slurry or cold water was observed on performances during a 20-km cycling trial in hot environment (30.7±0.8°C and 78±0.03% RH) [START_REF] Trong | Ingestion of a cold temperature/menthol beverage increases outdoor exercise performance in a hot, humid environment[END_REF].

Ultimately, menthol mouth rinsing and ingesting influence thermal perception and thermal comfort, which in turn might contribute to enhance performance in hot climates (Stevens et al. 2017a;[START_REF] Stevens | Running performance and thermal sensation in the heat are improved with menthol mouth rinse but not ice slurry ingestion[END_REF].

Cooling policy and implementation

According to the literature, pre-cooling by ice or cold water has been successfully studied during short duration exercise (<60 min) that is too brief to be a key factor of performance during ultra-endurance trials [START_REF] Siegel | Pre-cooling with ice slurry ingestion leads to similar run times to exhaustion in the heat as cold water immersion[END_REF]Stevens et al. 2017b). Conversely, per-cooling by cold water or ice slurry ingestion during exercise seems to be a very interesting intervention to improve performances in a hot environment and possibly increase fluid intake, particularly for well-trained athletes (see chapter 7). Indeed, most high-performing runners show the biggest increase in internal temperature, probably due to higher thermogenesis consecutive to higher workloads [START_REF] Baillot | Fluid replacement strategy during a 27-Km trail run in hot and humid conditions[END_REF]Hue et al. 2014). Faster trail runners (27 km;[START_REF] Baillot | Fluid replacement strategy during a 27-Km trail run in hot and humid conditions[END_REF]) and multi-stages trail runners (127 km on 6 days; [START_REF] Hue | Thermoregulation, hydration and performance over 6 days of trail running in the tropics[END_REF]) also present greater post-race dehydration, which could be reduced by cold water due to its effect on voluntarily increasing water absorption during exercise.

The higher temperatures and greater dehydration observed in faster trail runners also seem to indicate that performance in heat is associated with a better tolerance to hyperthermia in elite athletes (McKeag and Moeller 2007).

Heat acclimation

Heat acclimation (HA) before a race is an efficient way to increase performance in a hot environment [START_REF] Armstrong | The induction and decay of heat acclimatisation in trained athletes[END_REF][START_REF] Williams & Wilkins | Heat stress and acclimation[END_REF]) (see chapter 8 for further details). The physiological adaptations of HA lead to better cardiovascular function (output, stroke volume, heart rate) and a decreased core temperature at rest and during exercise, in part due to an enhanced sweat rate and expanded plasma volume [START_REF] Armstrong | The induction and decay of heat acclimatisation in trained athletes[END_REF]. HA is also known to reduce sodium loss by sweating [START_REF] Kirby | Plasma aldosterone and sweat sodium concentrations after exercise and heat acclimation[END_REF]. However, HA does not fully restore long to ultra-long endurance performance to the level reached by athletes in temperate conditions [START_REF] Voltaire | Effect of fourteen days of acclimatization on athletic performance in tropical climate[END_REF].

If early arrival at the race location is not possible, HA in an environmental chamber is a strategy that may help preserve ultramarathon performance. [START_REF] Costa | Heat acclimation responses of an ultraendurance running group preparing for hot desert-based competition[END_REF]) examined the effects of six 2-h sessions of running at 60% of VO 2max on a motorized treadmill in an environmental heat chamber at 30°C or 35°C. From the third session onward, mean heart rate was lower at 30°C, whereas mean heart rate and thermal comfort were lower at 35°C. The authors concluded that two bouts of running at 60% of VO 2max in a 30°C air temperature conditions were sufficient to induce heat acclimation in ultra-runners, which may enhance their performance in such environments.

.

Conclusions

The maintenance of triathlon or ultramarathon performance in a hot environment is a considerable challenge which requires meticulous preparation and management during the race. To limit the performance decrements induced by these harsh environmental conditions, several countermeasures have been proposed, such as cold-water or ice slurry ingestion, external pre-and per-cooling and/or menthol use. However, the limited duration of exercise performed in these studies does not allow for direct application of the results to an ultra-endurance or ultra-triathlon context. Thus, further studies are required to validate these approaches in long to triathlon and ultraendurance events.

Currently, one of the most relevant strategies to employ when performing in the heat is to consume adequate fluids. Maintaining water availability along different race courses is thus crucial due to the detrimental effects dehydration has on fluid balance and consequently heat loss via sweating. Individual sweat rates are highly dependent on the athlete's morphology, the intensity of exercise and the environment temperature and humidity. Sweat losses are accompanied by electrolyte losses, particularly sodium, which may contribute to hyponatremia if not compensated.

To limit this risk, exogenous intake by enriched sodium beverages is the most effective strategy. In addition to the traditional compounds found in most sport drinks (e.g. glucose, magnesium,), it seems that ultramarathon beverages should contain about 0.7-1.2 g.L -1 of salt when conducted in the heat. However, sodium-enriched beverages are insufficient if athletes overdrink by fear of dehydration during the race, placing management of water intake as a key determinant of performance. Drink Temperature interaction (P<0.004), respectively [START_REF] Trong | Ingestion of a cold temperature/menthol beverage increases outdoor exercise performance in a hot, humid environment[END_REF].

  than 6 h[START_REF] Zaryski | Training principles and issues for ultra-endurance athletes[END_REF]. In the past decade, trail running races have become a major ultra-endurance sport. Since the first edition of the Ultra Trail du Mont Blanc (160 km and +10,000 m of elevation), the number of finishers has grown from 67 in 2003 to 1685 in 2017. This kind of effort involves several physiological and psychological parameters that are modulated by environmental factors. Ultramarathon races are performed with a variety of off-road terrains, elevation profiles (positive: D+ and negative: D-changes), and distances, all of which greatly complicate the attempt to understand how environmental conditions affect performance.

  2012 (217 km and 4000 m D+), the temperature oscillated from 10.1°C at night to 46.6°C during the day. The follow-up of 4 runners who completed the race in 36±3 h showed a mean water intake of 34±13 L[START_REF] Brown | Food and Fluid Intake During Extreme Heat: Experiences From The Badwater Ultramarathon[END_REF]. On average, each athlete drank 0.93 L.h -1 , whereas on completion of the Biel Ultramarathon in Switzerland (100 km and 645 m D+), in a temperate environment varying from 8 to 28°C, the runners consumed 0.65 L.h -1[START_REF] Knechtle | Low prevalence of exercise-associated hyponatremia in male 100 km ultra-marathon runners in Switzerland[END_REF]. When the distances of these two races were linked to elevation changes (100 m D+ corresponds to 1 km of distance), the corrected distance for the Biel Ultramarathon was 106.45 km and 257 km for

FiguresFigure 1 .

 1 Figures

  Figure 1. Individual and mean values (±SD) of core temperature at each stage of the Guadeloupe half-Ironman held in tropical climate. T1: just before the race; T2: after the swim phase; T3: after the cycle phase; T4: at the end of the run phase (Baillot and Hue 2015). Temperatures were obtained from telemetric intestinal temperature devices ingested at least 6 hours before the race.

Figure 2 .

 2 Figure 2. Nomogram representing the impact of WBGT on the relation between marathon finishing times according to quartiles and relative performance decrement in comparison with WBGT at 5°C (Ely et al. 2007).

Figure 3 .

 3 Figure 3. Proportion of runners abandoning the Western States Endurance Run (161 km; 6000m D+) race at each checkpoint along the course (A), and relationship between finish times for the 2006 (7-38°C) and 2007 (2-30°C) edition (B). (Parise and Hoffman 2011).

Figure 4 .

 4 Figure 4. Trial times for 5 successive blocks (4 km cycling + 1.5 km running) with the ingestion of Neutral water (orange), Cold water (blue) and Ice-slurry (green). a Significantly different from Neutral water Cycling and Running Performance Using Ice-Slurry/Menthol (P<0.05). b Significantly different from Cold (P<0.05). Mean values and SD are shown. β, † denote that block performance was affected by Time Period (P<0.007) and the Time Period x

Heat acclimation is also a relevant strategy that may enhance ultra-endurance and triathlon performance in hot environments. Most of the acclimation benefits occur in the first 14 days of exposure, but a short-term protocol of 5 days will induce significant early adaptations.