Bernard Teissier

Jean Petitot

ON OBJECTIVITY AND MEANING IN MATHEMATICS

In a first part, I shall explore the consequences of distinguishing the foundations of meaning and the foundations of truth in mathematical statements, or imagination and rigor as motors of mathematical development. The foundations of meaning can be sought in our largely unconscious perception of the world, which modern cognitive science is exploring. In a second part, I shall illustrate this by comparing two approaches to understanding mathematical problems: creating appropriate abstract structures, which is exemplified by Galois, Hilbert, Bourbaki and Grothendieck, or creating geometric models where we can use our intuition of space, of which Riemann, Poincaré and Thom were masters. This part requires some basic mathematical knowledge.

The moving power of mathematical invention is not reasoning but imagination. (W.R. Hamilton, 1805-1865) For a recent Academic Seminar at the Bulgarian Academy of Sciences, it has been suggested that I talk about René Thom and the Bourbaki group, with both of whom I have had scientific contact. It is a very interesting suggestion because they correspond to different modes of mathematical activity and both had a strong influence. It is also very appropriate because Jean has been close to Thom for decades and has explained and greatly developed, with his extraordinarily penetrating mind, the consequences of Thom's approach to Science in many fields: Linguistics, Semiotics, Philosophy of Science, Epistemology, Esthetics, and more.

But before I can describe that difference I think it is useful to reflect on the forces which animate the search for objectivity and its ally rigorous reasoning, as well as the search for meaning, an obsession indispensable for creativity.

My title is provocative because Mathematics is supposed to be, by its very nature, objective in the sense that its structure is independent of the subject who studies it or makes use of it. This is interpreted by some philosophers as implying that Mathematics exists independently of human understanding in a world of ideas of which we humans perceive only projections, or shadows. It is a simplified but all too common version of platonism with which I am not sure that even Plato would agree.

Anyway, I hope to convince the reader that Mathematics is a human science whose origin and growth are the result of extremely complex interactions between our mostly unconscious perception of the world and pulsions which are just as unconscious and force us to organize those perceptions. The world of ideas is actually the product of concrete but extremely complicated processes. The impression of objectivity is due to the fact that humans share this perceptual system and those pulsions. It is indeed independent of any one individual but that does not make it superhuman.

The other option is that there is indeed an abstract universe of ideas of which we explore only the part we can understand with our limited abilities and that understanding is what 1 we call "meaning". I do not find this satisfactory but for a long time we had no way of finding a firm basis for the human alternative. What is new in our time is that cognitive sciences allow us to begin to get an idea of how the perceptual system works to create, among other activities, what one can call "protomathematical objects". I claim that such objects are the foundation upon which -with much elaboration and many layers-the meaning we give to Mathematics is built.

Poincaré had the intuition of this: In summary, for each attitude of my body, my first finger determines a point and it is that, and only that, which defines a point in space. Henri Poincaré, in La Science et l'hypothèse, Flammarion. In other words, the (unconscious) tensions of the muscles which position the finger are a system of coordinates for (our perception of) space.

My favourite example (see [START_REF] Teissier | Géométrie et Cognition: l'exemple du continu, in Ouvrir la logique au monde[END_REF]) is the protomathematical continuum which results from the extremely strong interaction in our perception/action system of the vestibular line, the visual line, and the motor system.

The vestibular line

Our vestibular system is an inertial navigation system which detects accelerations, rotations, etc. with great accuracy. It is strongly connected to the motor system in order, for example, for a biped to be able to react very quickly when it stumbles, thus creating a high acceleration of its head.

More precicely, in our inner ear are three semicircular canals, each of which detects rotations of our head around one of the directions of our three dimensional space. They are semicircular tubes filled with a fluid which, in case of movement, rubs against cilia on cells of the inner surface of the tube, thus creating a signal for the brain. There are also, next to the canals, sacculae which are small chambers containing tiny calcium carbonate crystals, the otoliths which detect linear acceleration, again by rubbing against cilia.

Moving at constant speed in a constant direction (inertial motion) corresponds to a particular state of the assembly of neurons which manages the vestibular information. According to Galilean relativity, the vestibular system sends no signal to the brain during the inertial motion. Of course the head goes up and down, which does send some signal, but this is compensated for. There are only two ways to measure the distance covered during an inertial motion: the time elapsed, assuming we know the speed, and the number of steps.

The visual line

The optic nerve transmits the electric impulses from the retina to the visual areas of the brain at the back of the skull. The retina cells are already specialized, and then the impulses are subjected to a filtering. There is a quite specific and extremely complicated architecture of the neurons in the first visual area of the brain (see [START_REF] Petitot | Neurogéométrie de la vision[END_REF], [START_REF] Petitot | Vers une Neuro-géométrie. Fibrations corticales, structures de contact et contours subjectifs modaux[END_REF]) which implies in particular that if a neuron detects in a certain direction of sight a segment with a given orientation, it excites the neurons in its neighborhood to reinforce the detection of a segment with a similar orientation. This is a gross oversimplification but the end result is that our visual system can detect curves, contours, and especially lines, which correspond again to a special state of an assembly of neurons in the visual cortex. Note that the visual line has no orientation and by itself no measure of progress. Professor Alain Berthoz has conducted many experiments in his lab at the Collège de France to study the integration of visual, vestibular and muscular perceptions. It makes a very strong case (see [START_REF] Berthoz | Le sens du mouvement[END_REF]) for the idea that our unconscious perceptual system almost identifies the visual and vestibular lines. In addition, visual perception is strongly coupled with muscular tension, which supports Poincaré's intuition. I call this indentification the Poincaré-Berthoz isomorphism (see [START_REF] Teissier | Géométrie et Cognition: l'exemple du continu, in Ouvrir la logique au monde[END_REF]). Of course it is not an isomorphism in the strict mathematical sense, but in the sense that it allows transporting structure from one to the other. For example, the natural orientation of the vestibular line, and its notion of distance, are carried over to the visual line, which is our model for the real line, and this allows us to think of it as parametrizing time. The steps measuring the vestibular line become the integers disposed on the visual line, etc. This leads also to the concept of trajectory parametrized by time, a fundamental notion, One cannot overestimate the consequences of the fact that the Poincaré-Berthoz isomorphism carries the continuity of motion to the continuity of the visual line.

Einstein said that one of his basic intuitions was to think of himself as moving along a ray of light.

The construction of the real line from the integers, then the rationals, then Cauchy completion, does not provide us with such a vision. It does provide a construction from set theory, considered as being objective and providing a foundation of truth for the statements concerning for example the convergence of sequences, continuous functions (intermediate value theorem), etc. But does it provide a foundation of meaning?

For example, we can imagine without difficulty walking indefinitely on the vestibular line from where we are. It is much more difficult to imagine having walked indefinitely to arrive where we are. I think it took the invention of -1 as an operator one can iterate to imagine this. And it is perhaps the origin of the concept of well ordered set where there are no infinitely decreasing sequences. The vestibular line has its notion of boundary which, when it is parametrized by time, is the instant and when it is parametrized by walking is the end of the motion. The visual line has also an obvious (sic!) notion of boundary. It is a fundamental intuition of Dedekind that important characters of the difference between the real line and a set of points given in bulk are that it is totally ordered, is divisible (one can cut intervals into parts) and is made of boundaries, the Dedekind cuts.

In conclusion, the Poincaré-Berthoz isomorphism creates a protomathematical object blending the attributes of the visual and vestibular lines, which will serve as a source of meaning for many statements concerning sequences, arithmetical operations, parametrized curves, etc. Of course mathematicians learn by usage to give meaning to much more elaborate objects and statements, but I claim that at the bottom of it there are similar protomathematical objects and amazing properties of adaptation of our perceptual system to the world aroud us.

In particular, Euclidean geometry would not exist if our perceptual system did not detect lines, angles, parallelism.

For example, as mentioned above, the "parallel transport" of orientations of segments, which is a concept of differential geometry is already cabled in the architecture of our visual system. We detect it in the world around us and this gives us the meaning of the abstract notion. This is not at all a reductionist discourse because I very strongly believe that the complexity of the physiological structures and dynamics which we would use to rationally provide meaning to mathematical objects and statements is literally beyond human comprehension.

Indeed, what is superhuman, or transcendental, is the complexity of the functional architecture and the dynamics of the brain. But this is the place where meaning resides, and any progress in that direction would be fascinating.

Let me now come to the unconscious pulsions which push mankind to elaborate protomathematical objects into Mathematics. They are in a sense similar to Freud's libido but quite distinct. I can name only a few of what I believe to be a long list.

• Detecting structures, for example periodicities and repetitions. Most importantly, detecting boundaries of all kinds. • Capacity of creating mental images to simplify and abstract independently of language. • Comparing comparable objects without consciously asking the question. This leads to consciously comparing and measuring lengths, areas, etc. • Above all, an extremely strong need to find causes and origins. In particular, if A implies B, does B imply A? Our basic intuitions of space is based on this kind of subconscious interiorization, through evolution, of our experience of the world into for example protomathematical objects. When submitted to these unconscious forces or pulsions, it produces Mathematics, in particular when faced to something contrary to intuition. This happens especially when some infinite process comes into play. Think of Zeno's paradox, or the discussions about the actual or virtual existence of the infinite. Think of Cantor discovering that there are as many points in a square or a cube as in a segment of the real line. He wrote: "I see it but I cannot believe it". A lot of Mathematics are born of such questionings (search for causes) and astonishments. For example, the ancient Greeks had a method, called Anthyphairesis, to describe the exact relationship of two lengths. Count how many times the smaller one goes into the larger one. This is an integer a 0 . In general, there is a remainder r 0 which is smaller than the smaller length. Then, one counts how many times the remainder goes into the smaller length. This gives a second integer a 1 . Again, there is in general a remainder r 1 which is smaller than r 0 , and one continues in this manner. The ratio of the two lengths is expressed as a sequence of integers. If the sequence is finite, the two lengths are commensurable, which etymologically means that they can be expressed as integral multiples of a unit length, the last non zero remainder. Their ratio is a rational number. Otherwise, the ratio is irrational. There is a Lemma in Euclid's Elements which implies that if one performs anthyphairesis for the diagonal of a square and its side, the sequence of integers obtained is 1, 2, 2, . . . , 2 . . .. This is a geometric lemma, using constructions of Euclidean geometry. Hint: If s and d are the lengths of the side and diagobal of our square, build a larger square of side S = s + d with a side extending the diagonal of our square. Easy geometric considerations will give you the value D = 2s + d of the length of the large diagonal. Then compute the ratio

D+S S = 1 + D S = 1 + d s = 2 + s s+d .
You see that the anthyphairesis will keep giving 2. This Anthyphairesis of 1 + √ 2 proves the irrationality of √ 2. According to Fowler in [START_REF] Fowler | The Mathematics of Plato's Academy: A new reconstruction[END_REF] this did not really cause an intellectual upheaval in Greek science, because a constant, or even periodic, sequence of integers is still amenable to reason. Anyway this proof is far superior to the proof taught in schools because it provides approximations of √ 2 by rational numbers as good as one wishes by computing the rational number obtains by keeping only the first k 2's and increasing k. Anthyphairesis is known nowadays as continued fraction expansion of a positive real number. For much more in this direction, I recommend the excellent book [START_REF] Fowler | The Mathematics of Plato's Academy: A new reconstruction[END_REF]. I believe that Mathematics develop in part to compensate the failures of our perceptual grasp of the world, and because of our overwhelmind desire to find causes, explanations. As I tried to explain above, it is much closer to our human nature than some philosophers would have us believe.

For example, we have a good perceptual, or intuitive feeling for distances, but our intuition of areas and volumes is poor. I believe that the invention of the concept of area was a great mathematical moment. A large part of Euclid's elements is devoted to considerations on area and volume, a hot mathematical topic at the time. In Homer, the size of the city of Troy is 10200 steps. At the time, the size of a city or indeed any area, was its perimeter, because that is what one could measure. Proclus (411 -485) reports court cases of members of Greek communities in which, in the first century A.D., it was decided to divide the land equitably, according to perimeter. There were surprises at the time of harvest. We note that the perimeter measures the length of the boundary of a plane domain. . . 24 centuries before the physicist Sokal derided (see [START_REF] Sokal | Impostures intellectuelles[END_REF]) the (mis)use of very elaborate modern mathematical or physical concepts by some philosophers, Plato was making fun of the followers of Pythagoras who put numbers everywhere. In The Republic, 587d he gives a farcical proof of the following statement:

The measure of the area of the image of the tyrant's pleasure is a perfect square. Plato "proves" that it is 9. It is probable that in those days, the concept of area was not as common as today.

More seriously, the astonishment of Cantor discovering that there are as many points in a square or a cube, etc. was obviously a booster for the development of the axionatic method and set theory. One needed to be able to provide incontrovertible proofs based on undisputable axioms and well defined logical reasoning of these counterintuitive results.

The price to pay is that the roots of Mathematics in the world around us disappeared under this solid slab on which Mathematics was supposed to be built by the axiomatic method. A vision of Mathematics as a purely logical construction whose main quality was to ensure the truth of its statements emerged.

Thanks to the recent progress in cognitive science, we can begin to study scientifically the foundations of meaning in Mathematics, which I think must be clearly distinguished from the foundations of truth provided by axioms and logic. One does not understand a proof by following the logical arguments but rather as a succession of links between statements which have meaning.

However, the part of our subconscious activities which is related to the pulsions mentioned above remains mysterious. It seems to me that a possible origin for them is a blending of the need to simplify and organize the enormous amount of information which the perceptual system provides (below our consciousness) to the brain and the idea proposed by cognition scientists that the brain has a Bayesian approach to this information, which means that it is constantly making conjectures about the next batch of information. One can imagine that this unconscious Bayesian interaction with the world emerges into our consciousness as curiosity and in particular curiosity about the causes.

Let us now turn to Bourbaki and Thom who, in my view, illustrate in strikingly different manners three of those pulsions.

Nicolas Bourbaki

Let me provide background with some pictures. They were influenced by Hilbert's ideas on axiomatization. Youth and talent being what they are, and were, this dissatisfaction turned into an enterprise to rewrite most of Mathematics in a particular frame of mind, the exposition of the underlying structures. This enterprise continues to this day, at its own pace (see the pictures above). Bourbaki adopted the axiomatic method of constructing Mathematics but went much further in taking as basic objects not sets, to which earlier mathematicians had painfully tried to give a firm axiomatic status, meeting paradoxes all too often, but structures which, according to Bourbaki, exist independently of set theory.

The method of exposition we have chosen is axiomatic and abstract, and normally proceeds from the general to the particular. This choice has been dictated by the main purpose of the treatise, which is to provide a solid foundation for the whole body of modern Mathematics. Nicolas Bourbaki, in the foreword to his books.

Bourbaki's goal is not to prove theorems but to provide mathematicians with a toolbox of clear and well founded definitions and results which help mathematicians to attack difficult problems by relating them to well studied structures. The historic example of such structures is that of group, which appears in so many fields of Mathematics, Physics, Chemistry, etc. Then there is the structure of topological space, of topological vector space, Lie groups, integration, and so on. The structure of group, which is an operation with certain properties, can manifest itself in a set, for example the set of rotations around an origin in the plane, giving a group.

Bourbaki's idea is that this will produce a considerable economy of thought because instead of proving results in special cases adapted to special problems, it suffices to recognize that they are results in the theory of some structure.

The common feature of these notions which we have designated under this name (of structures) is that they apply to sets of elements whose nature is not specified. Nicolas Bourbaki in "L'architecture des Mathématiques", in [START_REF]Les grands courants de la pensée mathématique[END_REF].

But Bourbaki is conscious that the tools do not suffice to produce Mathematics: One cannot insist too much on the role played in the mathematician's research by a particular intuition, which is not the vulgar intuition of the senses. It is rather a sort of direct divination (prior to any reasoning) of the normal behavior which he can expect from mathematical beings which a long interaction has made almost as familiar to him as the beings of the real world. Nicolas Bourbaki in "L'architecture des Mathématiques", loc. cit. As the reader will have guessed, I agree only partially with this formulation. But Bourbaki at that time could not guess the role of the "vulgar intuition of the senses". For a lot more on the role of structures and structuralism in Bourbaki, I recommend [START_REF] Heinzmann | The Functional Role of Structures in Bourbaki[END_REF]. If the founders of Bourbaki, who were at the beginning ostracized by some important mathematicians, were dissidents in their time, René Thom was also a dissident but in an entirely different manner and at a later age. René Thom was born in 1923 and received the Fields medal in 1958 for his work on cobordism. This notion is based on the fact that for a manifold or a union of manifolds, being the boundary of some manifold of one more dimension imposes strong conditions. Two manifolds are cobordant if their union is the boundary a manifold. This led to a beautiful classification of manifolds up to cobordism. The following is an example of composition of two cobordisms between sets of circles:

After his Fields medal, Thom embarked on an extremely ambitious project of providing qualitative models for the discontinuous behavior which dynamical systems depending on parameters can exhibit. This includes for example the (relatively) sudden change of shape of an embryo during its growth.

Thom's goal is very wide. He wants to provide geometric and qualitative models (for him, to understand is to visualize) which help to understand how discontinuous changes in shape, in behavior occur. The notion of a qualitative model was difficult to accept for scientists of the time. This qualitative aspect is also the reason why Thom's ideas apply to humanities as the work of Thom, Zeeman (see [START_REF] Zeeman | Catastrophe theory[END_REF]), and Petitot illustrates. A basic intuition for him is that of a boundary but in a geometric, not quantitative sense.

Discontinuous changes (hence the name "Catastrophe theory") in the shape (hence the word "morphogenesis") or the behavior of a system depending on parameters occur when the parameters cross a certain boundary in the parameter space and he wants to provide "universal boundary shapes" which will appear in any parameter space depending of course on the nature of the system. Another fundamental idea of Thom is that these discontinuous changes, or bifurcations, must appear in a stable manner in order to be observable, because of the inevitable "noise" in nature. Here stable is a technical term for his mathematical models.

This allowed him to give a classification of the stable families of gradient dynamical systems depending on at most four parameters (because they are supposed to manifest themselves in space-time) and the corresponding bifurcation sets, or boundaries of the domains of parameters where no brutal change occurs. One could say that for Thom what gives meaning to the behavior of a family of dynamical systems is the geometry of this boundary.

The essential idea of our theory that a certain understanding of the morphogenetic processes is possible without having recourse to special properties of the substrate of the shapes, or to the nature of the acting forces, may seem difficult to admit. . . René Thom, in Chapter 1 of "Mathematical models of morphogenesis".

The following is a picture of the extrema of the potential V = z 4 + bz 2 + az in one variable z depending on two parameters a, b. The gray zone corresponds to a maximum of the potential, which is an unstable extremum. It is one of Thom's 7 elementary catastrophies. The parameter space is the a, b plane below and Thom's boundary is the cusp drawn in black, although there are other conventions to define the boundary. The next picture describes how the extrema change with the parameters. competition of minima of potential (courtesy of AIP Publishing) Let me say a word on the relations between Thom and Bourbaki:

The collaborators of Bourbaki retire at age 50. Bourbaki recruits new members by inviting some promising young mathematician to one of his meetings, where redactions of new chapters are read and criticized.

The invitee is known as "guinea pig" because the redactions are tested on him or her. Depending on the level of interest exhibited, the guinea pig is invited to become a member, or not. Thom was invited to such a meeting and . . . fell asleep during the reading. Thom has sometimes criticized not the Bourbaki enterprise itself, but the abuses, for which Bourbaki bears little to no direct responsibility, which the "structuralist" approach has generated in the teaching of Mathematics.

Jean-Pierre Serre, a Bourbaki member, helped Thom to put his thesis in shape. Thom lectured in the Bourbaki seminar. But the Bourbaki goal is definitely not Thom's cup of tea. . . The following quotation illustrates this. If one must choose between rigour and meaning, I shall unhesitatingly choose the latter.

René Thom

Conclusion

Bourbaki wants to define and study the abstract "structures" which exist independently of individual sets which they organize, while Thom wants to define and study abstract "morphologies" and morphogenetic processes independent of the substrates and the dynamics which they structure.

Is there not a common set of pulsions at work, like pulsions 1, 2 and 4 of our list?

  Bourbaki at work, ca. 1982 Published 2016 Published April 2023. Bourbaki started in the middle 1930's with a group of young mathematicians dissatisfied with the manuals from which they had to teach. They were especially dissatisfied with the proofs of Stokes' formula, which is an n-dimensional generalization of the formula b a f (t)dt = f (b) -f (a). which computes the differences of the values of a function f (t) on the boundary of an interval [a, b] on the line from the values of its derivative on the interval (boundaries again!).

  Let me provide background with a few pictures: René Thom à son bureau (D.R., courtesy of I.H.E.S.) Thom's mathematical works, published between 2017 and 2022

Cusp Catastrophy (courtesy of AIP Publishing)


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Sangalli Coronel

Soil and water bioengineering: Practice and research needs for reconciling natural hazard control and ecological restoration

Keywords: Benefits, Biodiversity, Ecological engineering, Ecosystem services, Erosion, Vegetation

come   L'archive ouverte pluridisciplinaire

Development and issues in soil and water bioengineering 1.Definition, applications and benefits of soil and water bioengineering

Soil and water bioengineering combines the implementation of techniques using plants as living building materials, through knowledge of their mechanical and/or biological properties (Figure 1) [START_REF] Barker | Ground and water bioengineering for erosion control and slope stabilization[END_REF][START_REF] Stokes | Eco-and ground bioengineering: the use of vegetation to improve slope stability[END_REF]. Bioengineering is a well-recognized component of ecological engineering, itself defined as "the design of sustainable systems, consistent with ecological principles, which integrate human society with its natural environment for the benefit of both" [START_REF] Mitsch | Ecological engineering: a field whose time has come[END_REF][START_REF] Mitsch | What is ecological engineering?[END_REF]. Bioengineering is used to: (i) control natural hazards (e.g., [START_REF] Norris | Slope stability and erosion control: ecotechnological solutions[END_REF][START_REF] Dhital | Soil bioengineering application and practices in Nepal[END_REF], (ii) restore or reintroduce plant and animal species onto degraded lands and disturbed environments (e.g., [START_REF] Li | Soil bioengineering and the ecological restoration of riverbanks at the Airport Town, Shanghai, China[END_REF][START_REF] Rauch | Installation of a riparian forest by means of soil bio engineering techniques-Monitoring results from a river restoration work in Southern Brazil[END_REF], and (iii) increase soil, air and water quality (e.g., [START_REF] Pretty | River rehabilitation and fish populations: assessing the benefit of instream structures[END_REF][START_REF] Woolsey | A strategy to assess river restoration success[END_REF].

Natural hazards such as soil erosion, torrential floods, and landslides, are phenomena that have severe consequences globally [START_REF] Poesen | Gully erosion and environmental change: Importance and research needs[END_REF][START_REF] Smith | US billion-dollar weather and climate disasters: data sources, trends, accuracy and biases[END_REF][START_REF] Poesen | Soil erosion in the Anthropocene: research needs[END_REF]. The use of vegetation for protecting against natural hazards and attaining economic and/or social goals is typical of traditional forest and hydraulic engineering programs in Europe, such as the 'Restauration des terrains en montagne' (RTM) in France [START_REF] Vallauri | An analysis of forest restoration 120 years after reforestation on badlands in the Southwestern Alps[END_REF], 'Wildbach und Lawinen Verbauung' (WLV) in Germany and Austria, or 'Sistemazioni Idraulico-Forestali' (SIF) in Italy [START_REF] Bresci | A historical survey on the evolution of some forest watershed management techniques (part II: stream channel works)[END_REF][START_REF] Bischetti | On the origin of soil bioengineering[END_REF]. Today, the control of these types of hazards using herbaceous and woody vegetation through bioengineering remains a major challenge in areas where technical, socioeconomic, and ecological issues are confounding factors that can hinder success [START_REF] Phillips | Revegetation of degraded steeplands in France and New Zealand: a comparison of geomorphic and policy responses[END_REF][START_REF] Dhital | Soil bioengineering application for flood hazard minimization in the foothills of Siwaliks, Nepal[END_REF]. Bioengineering in areas that are difficult to access, e.g. torrential catchments, riverbanks and lakes, as well as on disturbed lands, such as agricultural zones, road and rail embankments, ski slopes, mines, quarries and in urban areas [START_REF] Lin | Assessment of vegetation recovery and soil erosion at landslides caused by a catastrophic earthquake: A case study in Central Taiwan[END_REF], requires understanding of the interdependency of hydrological, ecological, and biophysical processes underway at the site. Bioengineering solutions should provide a combination of the benefits of immediate hazard control, comprising techniques such as (Figure 1): (i)brush layers (that provide deep-seated protection), (ii) drain fascines or live pole drains (which drain excess water to allow vegetation establishment), (iii) vegetated crib walls (that immediately protect stream banks), (iv) brush mattresses (providing roughness from establishment against flow), and the long-term stabilization due to plant reinforcement effects. As with any stabilization technique, there is a stress (or load) transfer between the soil and the structure, but, in contrast to other solutions, this initial response is modified by the evolving role of the living material used in the bioengineering structure [START_REF] Preti | Root reinforcement and slope bioengineering stabilization by Spanish Broom (Spartium junceum L.)[END_REF][START_REF] Graf | Soil aggregate stability related to soil density, root length, and mycorrhiza using site-specific Alnus incana and Melanogaster variegatus s[END_REF][START_REF] Yildiz | Effects of roots and mycorrhizal fungi on the stability of slopes[END_REF][START_REF] Yildiz | An assessment of plant-induced suction and its effects on the shear strength of root-permeated soils[END_REF][START_REF] Tardio | Implementation of eco-engineering design into existing slope stability design practices[END_REF]. This latter feature must be reflected in the bioengineering work design methodologies.

Ecological restoration encompasses all actions for repairing degraded lands, with the aim of reestablishing both form and function to attain autonomous and stable ecosystems [START_REF] Clewell | Ecological restoration: principles, values, and structure of an emerging profession[END_REF]. Ecological engineering in general and bioengineering in particular, can be employed for the restoration of a degraded environment [START_REF] Mitsch | Ecological engineering and ecosystem restoration[END_REF]. Actions can include: (i) rehabilitating degraded land, which requires techniques aimed at recovering the natural succession of the ecosystem, especially by installing pioneer vegetation and enhancing its development; and (ii) monitoring and maintaining the rehabilitated land, thereby guiding the natural dynamics of the degraded systems so that they recover with a structural and functional autonomy [START_REF] Aronson | Restoration and rehabilitation of degraded ecosystems in arid and semi-arid lands. I. A view from the South[END_REF]. A significant advantage of bioengineering actions is the incorporation of vegetation establishment and succession processes into the design stage. Therefore, the need for further intervention or maintenance is reduced and a long-term solution is provided. Bioengineering could also make restoration faster in the sense that, if the path of plant succession is known, it is possible to establish vegetation at the most advanced stage which will be compatible with the soil and microclimatic conditions of the site. Moreover, considering the energy balance of any civil engineering construction, a benefit from using soil bioengineering techniques is that although we need energy for its construction, we "save" energy with the development of the plant biomass. Finally these actions not only include ecological restoration, but also water and soil quality restoration or depollution (e.g., [START_REF] Wang | Theory and application technology of riparian wetland[END_REF].

Soil and water bioengineering is an emerging discipline globally, with regulatory frameworks (including the European Water Framework Directive or more recently the European Green Infrastructure Strategy) introducing the need to implement "soft" techniques for natural hazard control instead of "hard" techniques (engineered concrete and steel structures such as check dams), in the pursuit of restoring degraded environments or preventing further degradation during new construction. Prioritizing soil and water bioengineering techniques is now highly encouraged in the European Community and in many countries worldwide, often promoted through various incentives (e.g., European Commission, 2013). The International Union for the Conservation of Nature (IUCN) is proactively endorsing the use of Nature-based solutions for disaster risk reduction (EcoDRR), and includes soil bioengineering as a technique for protecting against natural hazards [START_REF] Furuta | Helping nature help us: transforming disaster risk reduction through ecosystem management[END_REF]Renaud et al., 2016). Questioning practitioners and scientists about their experience, successes, and failures will allow a better understanding of the multiple benefits and services that natural habitats and human populations derive from bioengineering actions (Table 1).

An interactive process between researchers and practitioners

Soil and water bioengineering implies an interface between the researcher and the practitioner, i.e. between the improved knowledge base and its application [START_REF] Stokes | Engineering the ecological mitigation of hillslope stability research into the scientific literature[END_REF][START_REF] Stokes | Ecological mitigation of hillslope instability: ten key issues facing practitioners and researchers[END_REF][START_REF] Mitsch | When will ecologists learn engineering and engineers learn ecology?[END_REF]. The questions raised are increasingly complex and many practitioners are now involved in research projects, improving dialogue and mediation between different stakeholders. Bioengineering projects could also benefit from more multi-and inter-disciplinary approaches, as well as from a better understanding of practical issues experienced by practitioners (e.g., choice of materials, costs, insurance, health and safety, and management of human resources).

For those working in the field of bioengineering, a specific framework is required at three levels:

(i) questions: identification of the technical, socio-economic, and ecological problems, evaluated by the practitioners. Researchers and practitioners should then work together to solve specific objectives.

(ii) applied research: translation of the technical, socioeconomic, and ecological concerns into scientific questions, and increase of knowledge by observations and experiments. Soil and water bioengineering can be implemented based on relevant knowledge from several scientific domains, especially geosciences (e.g., geomorphology and soil science), ecology (e.g., restoration ecology, landscape ecology, and plant sciences), engineering (e.g., fluvial hydraulics, civil and geotechnical engineering), sociology (e.g. community engagement and social acceptability of the methods and tools proposed; legitimate design approach), and economics (e.g. project financial management, carbon accounting) [START_REF] Petrone | Soil bioengineering for risk mitigation and environmental restoration in a humid tropical area[END_REF][START_REF] Stock | Defining Terms for Integrated (Multi-Inter-Trans-Disciplinary) Sustainability Research[END_REF].

(iii) management in bioengineering: as soil and water bioengineering is consistent with policies aimed at encouraging "soft" solutions, in particular by including environmental concerns into standard technical practices such as civil engineering, it is essential that current and improved knowledge is included at the work design stage. For example, features such as natural wood deterioration rates [START_REF] Barré | Assessment of the level of decay of small-diameter silver fir logs degraded in natural conditions in the French Northern Alps using two different methods[END_REF][START_REF] Tardio | Implementation of eco-engineering design into existing slope stability design practices[END_REF], plant development and successional trajectories [START_REF] Walker | Applying lessons from ecological succession to the restoration of landslides[END_REF]Gonzalez-Ollauri and Mickovski, 2017a), must be incorporated into the routines and protocols of bioengineering projects. Research results should then be used to develop methods and tools to assist management, conceptualization and action.

Adaptation of these tools needs to be performed in collaboration with practitioners, while the knowledge transfer and learning should occur in training courses at every educational level [START_REF] Mitsch | When will ecologists learn engineering and engineers learn ecology?[END_REF][START_REF] Mickovski | Development of Eco-Engineering Sector Specific Routines and Curricula for the Mediterranean Region[END_REF]. The application of knowledge to real cases using newly gained expertise should be verified. Long term monitoring programs, with accurate benchmark data, are also required to compare similar case studies and establish databases on the successes and failures of various techniques and plant material used [START_REF] Tardío-Cerrillo | Monitoring of erosion preventive structures based on eco-engineering approaches: the case of the mixed check dams of masonry and forest residues[END_REF][START_REF] Perez | An open access database of plant species useful for controlling soil erosion and substrate mass movement[END_REF][START_REF] Tardio | Bamboo structures as a resilient erosion control measure[END_REF]. Such considerations should improve practitioners' understanding of recent knowledge in ecology and geosciences, as well as increasing scientists' understanding of practical needs in soil and water bioengineering.

For soil and water bioengineering, all the above features are essential and, for a project to be successful, close interactions between stakeholders and bioengineers are necessary. Improved communication and interaction between the stakeholders will allow bioengineering interventions to both become more effective over time and take advantage of the accumulated experience within the sector.

Natural hazard control and/or ecological restoration?

Depending on the precise objective of a project, the choice of the bioengineering intervention and the desired long-term strategy can vary considerably. For example, soil or streambed erosion can cause different types of damage: (i) loss of topsoil, organic matter and nutrients, which lowers soil quality and hence crop yields and, in turn, threatens agricultural activities (e.g., [START_REF] Jin | Soil management effects on runoff and soil loss from field rainfall simulation[END_REF]; it can also cause imminent risk of structural failure of roads, bridges, and railway lines (e.g. [START_REF] Mickovski | Resilient design of landslip prevention measures: a case study[END_REF]; (ii) topographic changes (terrain deformation) in the case of gully channel development, landslide triggering and suffusion risk phenomena (e.g. [START_REF] Poesen | Gully erosion and environmental change: Importance and research needs[END_REF]; (iii) biodiversity loss, which affects vegetation and animal habitats [START_REF] Mkanda | Contribution by farmers' survival strategies to soil erosion in the Linthipe River Catchment: Implications for biodiversity conservation in Lake Malawi/Nyasa[END_REF]; (iv) silting of reservoirs, as a consequence of soil erosion and sediment transport, compromising the functioning of these structures (e.g. [START_REF] Schleiss | Reservoir sedimentation, vision paper[END_REF] and (v) increased floods, caused by sediment deposition in river channels (e.g. [START_REF] Steiger | Sediment deposition along the channel margins of a reach of the middle river Severn, UK[END_REF]. Strategies to control soil erosion rates will vary depending on the type of problem requiring action. For example, if reducing the sediment yield in rivers and reservoirs is the final objective, then the only intervention required is sediment control. Hence, it may be possible to allow hillslope erosion to take place, but to aim at trapping and retaining sediment before it reaches the river channel [START_REF] Rey | A strategy for fine sediment retention with bioengineering works in eroded marly catchments in a mountainous Mediterranean climate (Southern Alps, France)[END_REF]. If riverbed erosion causes lateral displacement and bank failures, and impacts nearby infrastructure, the main objective is to protect facilities with highly specialized and adapted bioengineering solutions, e.g. based on geotechnical preliminary investigations during design and monitoring stage [START_REF] Peklo | L'apport d'un programme de modélisation hydrodynamique bidimensionnel au travail de l'ingénieur[END_REF]. However, if soil and biodiversity conservation are the final objectives, then both erosion control and ecological restoration are required to prevent soil particles from being detached and removed [START_REF] Petrone | Soil bioengineering for risk mitigation and environmental restoration in a humid tropical area[END_REF].

The current challenge when using bioengineering techniques is to define rules that satisfy a set of diverse functions and benefits, particularly those that reconcile natural hazard control and ecological restoration (Figure 2). This approach requires innovation from the practitioners, and also raises new questions for scientists, as part of an interactive process that necessitates the designing and testing of bioengineering actions that reconcile the competing demands of both natural hazard control and ecological restoration. As soil and fluvial bioengineering operates on complex systems (ecosystems) intrinsic adaptive management strategies and feedback loops are necessary to ensure that the project and the intervention is well informed.

From practice to research needs

One of the currently pressing challenges is to define bioengineering actions for a range of different situations. Although techniques are well described (e.g., Schiechtl andStern, 1996, 1997;[START_REF] Gray | Biotechnical and soil bioengineering slope stabilization: a practical guide for erosion control[END_REF][START_REF] Zeh | Soil Bioengineering Construction Type Manual[END_REF][START_REF] Florineth | Bioengineering methods of strengthening slopes in the Alps: protection of deep soil and subsoil horizons[END_REF][START_REF] Hacker | Ingenieurbiologie[END_REF][START_REF] Efib | European guidelines for soil and water bioengineering[END_REF], quantitative recommendations on how and which materials to use in specific situations are lacking, especially when the objective is to reconcile natural hazard mitigation and ecological restoration. To overcome this knowledge gap, scientists should heed practitioners' needs through discussions during projects, conferences or training, and conduct research at different spatial scales, with specific objectives in mind (Figure 3).

Selection of plant species

Numerous studies have already dealt with the performance of specific species in protecting against different hazards (e.g. plant species potential to control gully erosion rates in a Mediterranean ecosystem; De [START_REF] De Baets | Methodological framework to select plant species for controlling rill and gully erosion: application to a Mediterranean ecosystem[END_REF], in a specific climate (Gonzalez-Ollauri and Mickovski, 2016), environment or topographic location [START_REF] Bochet | Topographic thresholds for plant colonization on semiarid eroded slopes[END_REF]). Furthermore, an open access plant species database has recently been developed by [START_REF] Perez | An open access database of plant species useful for controlling soil erosion and substrate mass movement[END_REF], allowing users to access the database or add information about species suitable for controlling erosion and shallow landslides in different climates. Traditionally, a limited number of plant species has been used for this purpose, although there are countless species available that could perform equally well, many of which have not yet been tested for suitability [START_REF] Preti | Soil bioengineering for watershed management and disaster mitigation in Ecuador: a short-term species suitability test[END_REF][START_REF] Perez | An open access database of plant species useful for controlling soil erosion and substrate mass movement[END_REF]. In general, although using pioneering species in soil bioengineering projects is sometimes necessary to initiate the successional processes that will maintain vegetation on the site, native species should be preferred over exotic species and ecological succession trajectories should be included in the bioengineering intervention design [START_REF] Clemente | Effect of hydroseeding components on the germination of Mediterranean native plant species[END_REF][START_REF] Xiao | Experimental study on the soil mixture to promote vegetation for slope protection and landslide prevention[END_REF].

When choosing which species to use on a site, and considering ecological restoration principles, the local and regional environmental conditions need to be considered carefully, so that an optimal and sustainable system is created [START_REF] Mickovski | A decision support system for the evaluation of ecoengineering strategies for slope protection[END_REF]. For the successful creation of a bioengineering system, the initial phase is of major importance. For the last 30 years, practitioners and scientists have been studying the installation phase, by e.g. examining the relationship between the richness of pioneer species and soil aggregate stability [START_REF] Pohl | The relationship between plant species richness and soil aggregate stability can depend on disturbance[END_REF], or the efficacy of using mycorrhizal inoculations to improve plant growth and soil structure on eroded soil [START_REF] Powell | Mycorrhizal infectivity of eroded soils[END_REF][START_REF] Yildiz | Effects of roots and mycorrhizal fungi on the stability of slopes[END_REF][START_REF] Bast | Does mycorrhizal inoculation improve plant survival, aggregate stability, and fine root development on a coarse-grained soil in an alpine eco-engineering field experiment[END_REF][START_REF] Demenois | Does arbuscular and ectomycorrhizal fungal inoculation improve soil aggregate stability? A case study on three tropical species growing in ultramafic Ferralsols[END_REF]. These studies concluded that the key to fully understanding ecological processes at eroded sites requires similar long-term experiments in the field.

Species adapted for hazard protection are not necessarily those used for ecological restoration. One of the most difficult questions a manager can ask is: is it better to use only one or a few species that can efficiently mitigate a specific hazard, or should a diverse range of species, sometimes less efficient, be used? Promoting species diversity is generally recommended in ecological restoration projects, but could an increased diversity result in less effective hazard control? Investigating this problem, [START_REF] Erktan | Morphological diversity of plant barriers does not increase sediment retention in eroded marly gullies under ecological rehabilitation (Southern Alps, France)[END_REF] showed that a morphological diversity of plant species used in vegetation barriers did not increase sediment retention in eroded marly gully floors in the French Southern Alps, compared to monospecific barriers (Figure 4). Such a consideration of plant biodiversity is a critical issue, as it generally corresponds to a more ecologically stable system [START_REF] Preti | Soil bioengineering for watershed management and disaster mitigation in Ecuador: a short-term species suitability test[END_REF]. A stable and healthy planting system would be less vulnerable to abiotic (e.g., flooding, storms, snow loading and landslides) and biotic stress (e.g., pathogens and grazing). A diversity of plant species would also enable a manager to "cover all options"; for example in the case of a particular species becoming susceptible to abiotic/biotic factors, the loss of one species would be less likely to compromise the aims of the project. Referring to the study of [START_REF] Erktan | Morphological diversity of plant barriers does not increase sediment retention in eroded marly gullies under ecological rehabilitation (Southern Alps, France)[END_REF], [START_REF] Rey | Resprout and survival of willow (Salix) cuttings in marly gullies in a mountainous Mediterranean climate: a real size experiment in the Francon catchment (Southern Alps, France)[END_REF] suggested using only one species to build brush layers and mats in eroded gully floors, but to use different species between structures along the gully floor, thus reconciling natural hazard mitigation with improved biodiversity.

Selection of bioengineering structures

The choice of the appropriate structure to use in a bioengineering project largely depends on the objective. When considering natural hazard control, the first principle to follow is to use structures and plants that have sufficient mechanical resistance to withstand gravitational or hydrological forces linked to the hazard process. Firstly, although technical drawings describing structures and their mechanical resistance exist in guidelines, we do not necessarily know their origins and performance or reliability for the myriad of field situations likely to be encountered [START_REF] Schaff | Effects of soil conditions on survival and growth of black willow cuttings[END_REF]. With the exception of gravitational structures (e.g. crib walls and fascines), whose design procedures are well established, and apart from a few cases (e.g. brushlayers and riverbank protection, [START_REF] Bischetti | Quantifying the effect of brush layering on slope stability[END_REF], most bioengineering techniques have not yet been sufficiently studied. At the individual plant scale, it is not well known to which topographic (e.g. [START_REF] Bochet | Topographic thresholds for plant colonization on semiarid eroded slopes[END_REF][START_REF] Nadal-Romero | Effects of slope angle and aspect on plant cover and species richness in a humid Mediterranean badland[END_REF] and hydrological forces plants resist before failing, and which plant traits are important for mechanical resistance [START_REF] Burylo | Species traits as practical tools for ecological restoration of marly eroded lands[END_REF], therefore this topic needs significantly more attention from the scientific community. Questions also remain concerning the types of hazard and their different return periods depending on geographic situation and climate, especially under extreme climates such as in tropical countries. This knowledge gap calls for large-scale experiments taking into consideration all the variables and elements to which the structures are subjected [START_REF] Schwarz | Spatial characterization of root reinforcement at stand scale: theory and case study[END_REF]. Secondly, it should be kept in mind that certain plant species or conditions may destabilize a structure. For example, along river embankments, vegetated crib walls (Figure 1D) can act as a slope buttress or slope break when placed on an eroding embankment to mitigate gully erosion processes [START_REF] Florineth | Bioengineering methods of strengthening slopes in the Alps: protection of deep soil and subsoil horizons[END_REF]. Vegetated crib walls help protect the shoreline and promote revegetation because plants are incorporated within the structure and root growth stabilizes soil (Stangl, 2007). Although some long-term observations have demonstrated that root development and tree stem growth did not adversely affect the structure of vegetated crib walls (K. Peklo, unpublished data), practitioners may hesitate to choose this type of structure because of the way that vegetation interacts with the structure over time.

There is a need to assess more precisely the interrelationships between inert and living materials in bioengineering structures. Questions remain, in particular with regard to wooden structures, where wood decay has to be assessed over time, as vegetation grows and develops around the structure [START_REF] Barré | Assessment of the level of decay of small-diameter silver fir logs degraded in natural conditions in the French Northern Alps using two different methods[END_REF]. Although the role of plants in stabilizing slopes over the long-term is crucial, the growth dynamics of plants used in bioengineering structures are basically unknown and more research is needed to address this gap. Questions particularly arise with regard to the desirable biodegradation of wooden structures. When inert structures are used to enhance vegetation development, for example certain small-scale wooden structures, their initial rigidity has to allow the triggering of new natural processes such as an improved resilience, an improved ecological functioning, and vegetation succession processes, before these inert structures disappear [START_REF] Stokes | Ecological mitigation of hillslope instability: ten key issues facing practitioners and researchers[END_REF]. The initial rigidity achieved by means of the inert elements used in the bioengineering intervention must exist long enough so that plants are capable of developing their reinforcing effect. This evolution must be reflected well at the design stage related to a predefined construction aim.

Deterioration models of the material used in the work (such as wood) must also be included in the design [START_REF] Tardio | Implementation of eco-engineering design into existing slope stability design practices[END_REF]. All these considerations call for research to evaluate the level and speed of decay of wooden structures, as well as the dynamics of vegetation within bioengineering structures, in relation to the development and diversification of vegetation and to the desired stage of natural hazard mitigation [START_REF] Barré | Assessment of the level of decay of small-diameter silver fir logs degraded in natural conditions in the French Northern Alps using two different methods[END_REF].

Finally, a maintenance schedule of the living material used in bioengineering structures may be required. These maintenance tasks are usually needed to avoid vegetation becoming too heavy, resulting in the overturning of the bioengineering structure. On riverbanks, this maintenance should also aim at keeping vegetation flexible enough to avoid excessive hydraulic resistance, which can cause an increase of water levels, and to reduce stem and branch breakage, which produce debris obstructing bridges and narrow sections of the river (EFIB, 2015).

Design of bioengineering structures

To improve the adoption of bioengineering methods by a wider community, new tools (e.g. soilvegetation interaction models, technological frameworks, enhanced methodological approaches and guidelines) must be developed for use in the design of bioengineering structures. In particular, it is necessary to know how to use living plants to attain the expected objectives, and to predict the spatial-temporal development of the installed bioengineering structure, while considering the climate and ecological conditions of the site. During the pre-design phase, the designer must be able to decide if the bioengineering techniques are feasible or must be used in combination with other conventional techniques (so called 'mixed' techniques), in order to improve the resistance of the structure and resilience of the system. Finally, a global, long-term vision of the project at all spatial scales, from local to catchment, is needed.

Improved knowledge is required to design bioengineering structures and optimize their performance in terms of hazard mitigation while enhancing plant diversity. For example, where is it most effective to install a structure at a site? How many plants or cuttings should be used within a structure? Particular attention should be paid to improving our understanding of the efficiency of different plant species and their traits, depending on the final goal of the intervention [START_REF] Burylo | Species traits as practical tools for ecological restoration of marly eroded lands[END_REF]. To design technical solutions, the bioengineer can sometimes use physical scale models. This approach is often not feasible, as plant effects on e.g. slope stability or erosion control and the impact of vegetation on discharge capacity cannot be downscaled appropriately at reasonable laboratory scales such as 1:30 to 1:40 (Wilson et al., 2006). Prototype scale (1:1) tests remain a viable solution for scientists and practitioners, but are often not feasible because of time, space, and cost [START_REF] Schwarz | Spatial characterization of root reinforcement at stand scale: theory and case study[END_REF].

Therefore, most engineers use readily available numerical geotechnical models that include the effects of vegetation. Different types of models have been implemented over the years to predict landslide risk (see [START_REF] Stokes | Ecological mitigation of hillslope instability: ten key issues facing practitioners and researchers[END_REF]Gonzalez-Ollauri and Mickovski, 2017b), many of which calculate a global Factor of Safety (FoS) at the slope level, but are not suitable for calculating the efficacy of individual bioengineering structures. Several uncertainties exist in model parameters, which can be overcome by using a probabilistic approach to e.g. synchronize the mechanical behavior of roots and soil throughout the development of the shear surface [START_REF] Tardio | Method for synchronisation of soil and root behaviour for assessment of stability of vegetated slopes[END_REF].

Further information on the hydrological effects of root water uptake is also required, particularly for herbs, shrubs and trees [START_REF] Chirico | Role of vegetation on slope stability under transient unsaturated conditions[END_REF][START_REF] Tron | Mean root depth estimation at landslide slopes[END_REF][START_REF] Arnone | Modeling the hydrological and mechanical effect of roots on shallow landslides[END_REF][START_REF] Kim | Vegetation as a driver of temporal variations in slope stability: The impact of hydrological processes[END_REF].

Upscaling to the catchment level is still a significant challenge, partially because of a lack of suitable data to either parameterize or validate models, but also because of a lack of understanding of biophysical processes at different scales. However, [START_REF] Rossi | Sensitivity of the landslide model LAPSUS_LS to vegetation and soil parameters[END_REF] demonstrate that the physical landslide model LAPSUS_LS is suitable for calculating the effects of vegetation on slope stability at the catchment level. Nevertheless, parallel studies should investigate how soil hydrological and physical processes at the slope level are altered over a larger scale and vice versa [START_REF] Bogaard | Landslide hydrology: from hydrology to pore pressure[END_REF].

Reconciling qualitative experience and quantitative engineering

Statutory constraints related to building structures used for natural hazard control require quantitative engineering methodology, whereas bioengineering often, but not always, comprises more qualitative experience. Thus there is a need to develop research that will reconcile these qualitative and quantitative issues for natural hazard control, but also for ecosystem restoration. Methods for identifying precise performance thresholds for bioengineering installations at local scales could be very helpful. Questions to ask include: (i) is a stepwise strategy necessary and therefore an initial plant protection plan needed? (ii) what is the most efficient spatial distribution of bioengineering structures and plants for hazard control with regard to the physical forces to which they are subjected? (iii) what is the necessary, but adequate, rate of vegetation cover to control a given natural hazard, while considering also ecological processes at this spatial level? Answers to these questions are strongly related to the objectives, which will be different in the case of natural hazard mitigation or ecological restoration. A need also expressed by practitioners is to define appropriate indicators that allow managers to determine the thresholds of efficiency when reconciling natural hazard control and ecological restoration. Finally, the need for case study analysis in terms of bioengineering work performance has been suggested as a useful tool for proposing improvements at the design, construction, and monitoring stages.

One further crucial issue determining the success of a bioengineering project is to know if bioengineers can have the financial freedom to create the "best" solution to each problem (EFIB, 2014). For example, for a project in which ecological restoration is required and when significant financial means can be used to implement optimal actions, such actions are able to achieve effective restoration, and enable the damaged ecosystem to recover its original condition. But when constraints are imposed in budgeting and financing bioengineering projects, such as in underdeveloped countries, it is necessary to minimize interventions. In this later case, complete 'restoration' is not economically possible. Therefore, recovering the ecosystem to a state before degradation is not the final objective, but reaching a specific ecosystem objective in line with the current technical, socio-economic and ecological problems, such as controlling a specific natural hazard, becomes the main aim [START_REF] Rey | A strategy for fine sediment retention with bioengineering works in eroded marly catchments in a mountainous Mediterranean climate (Southern Alps, France)[END_REF]. This situation also calls for reconciling possible qualitative issues linked to the definition of precise objectives of a bioengineering project, and quantitative engineering, corresponding to the design of the bioengineering structures and the related financial means.

Defining actions at the catchment and landscape scales

Soil and water bioengineering techniques are usually targeted to discrete locations, whereas their design often needs to be considered at the catchment and landscape scales [START_REF] Bifulco | Renewing dangerous highway slopes in Portugal[END_REF]. The variables with the greatest influence on a bioengineering structure's final design are usually structural, hydraulic or related to plant characteristics, especially when natural hazard mitigation is the main objective. Using bioengineering for natural hazard mitigation at the catchment scale, especially with regard to water and sediment transport, implies taking into account the connectivity between slopes and the river or gully channel, and between upstream and downstream parts of the catchment. For example with respect to flood reduction, a key objective can be to reduce runoff and particularly to interrupt the fine sediment connectivity between various parts of the catchment (e.g. [START_REF] Verstraeten | The use of riparian vegetated filter strips to reduce river sediment loads: an overestimated control measure?[END_REF][START_REF] Borselli | Prolegomena to sediment and flow connectivity in the landscape: A GIS and field numerical assessment[END_REF][START_REF] Rey | Can bioengineering structures made of willow cuttings trap sediment in eroded marly gullies in a mountainous and Mediterranean climate (Southern Alps, France)?[END_REF][START_REF] Mekonnen | Soil conservation through sediment trapping: a review[END_REF]. The spatial distribution of control measures such as planted areas also needs to be considered at the wider catchment scale, as does the climatic regime. In some cases it will be possible to provide a level of control for more frequent climatic events that generate sediment. Nevertheless, designing structures or bioengineering solutions to deal with extreme, infrequent or high magnitude events remains problematic.

The need to define strategies for bioengineering at the catchment and landscape scales is well illustrated in the framework of Green infrastructure (GI), interconnected networks of natural or seminatural sites able to provide environmental, social, and economic benefits to human populations (known as ecosystem services). Soil bioengineering can play a fundamental role in creating networks because their capability is to bridge natural and man-made environments. It allows the restoration of ecosystems and is an effective tool in the implementation of GI [START_REF] Efib | Soil and Water Bioengineering and Green infrastructure[END_REF]. Although GI is included in several EU and International Agencies programs and policies (e.g. EU 2020 Biodiversity Strategy, Natura 2000, UNEP-DHI 2014 Green Infrastructure Guide for Water Management), the use of soil bioengineering techniques is generally implicit. The success in implementing a GI strategy strongly depends on the achievements of bioengineers. Soil bioengineering techniques, by including vegetation as an intrinsic component of installations, are able to provide several functions, such as slope and riverbank stabilization and protection from soil erosion, as well as habitat for animals, microclimate regulation and recreational use (Table 1, [START_REF] Stokes | Ecological mitigation of hillslope instability: ten key issues facing practitioners and researchers[END_REF]. Therefore, design of bioengineering structures can be thought for allowing them to provide both slope stabilization and ecological restoration (Figure 5).

The Blue infrastructures (BI) framework is also a good illustration of the complex questions facing bioengineers. Worldwide, two contrary eco-geomorphological management practices co-exist for rivers. In some catchments, aggradation of the river channel occurs, a phenomenon caused by excessive fine sediment in the river. Habitats for fish reproduction may be damaged, flood risks increase, and hydroelectric reservoirs can fill with sediment [START_REF] Rey | A strategy for fine sediment retention with bioengineering works in eroded marly catchments in a mountainous Mediterranean climate (Southern Alps, France)[END_REF]. In contrast, other catchments suffer from a lack of bed load in the river. As a consequence, groundwater levels can decrease and river beds incise, causing damage such as bridge destabilization [START_REF] Liébault | Landuse change, sediment production and channel response in upland regions[END_REF]. Vegetation cover in the surrounding landscape is an important factor controlling the erosion responsible for sediment yield in rivers. In case of bedload excess, eroding slopes and riverbanks are controlled through bioengineering measures and revegetation efforts, considered as restoration actions on degraded land (e.g., [START_REF] Vallauri | An analysis of forest restoration 120 years after reforestation on badlands in the Southwestern Alps[END_REF]. Conversely, where a deficit of bedload exists, slope erosion can be reactivated by destroying the vegetation on highly erodible soils. Sometimes, both situations co-exist within the river's catchment, but generally in different parts and at different times, as stated by [START_REF] Liébault | Landuse change, sediment production and channel response in upland regions[END_REF] who recorded both aggradation followed by degradation in the same catchment pre-reforestation and post-reforestation. Thus the influence of vegetation on a river's sediment production, especially in mountainous areas, is often difficult to understand.

Another situation showing the difficulty in reconciling natural hazard mitigation and ecological restoration is the management of dams on rivers. These structures often have a role in managing floods and many have been constructed over a century ago in different countries (e.g, [START_REF] Vallauri | An analysis of forest restoration 120 years after reforestation on badlands in the Southwestern Alps[END_REF] on French experience). However, today these structures are blamed for representing obstacles to aquatic fauna, and programs for removing them are developed, calling into question the impact of this kind of action on the river's stability. One solution consists in replacing dams with rough rock ramps with integrated fishway (Figure 6). All these examples call for more discussion between scientists and practitioners, as well as a better assessment of current knowledge. There is an urgent need to consider new research strategies and to determine whether ecological restoration actions should be carried out on areas where natural hazards occur, with different ecological and socioeconomic issues calling for different solutions in the management of these hazards.

Conclusion

In the sections above, we highlighted the practice and research needs in soil and water bioengineering through a critical review of the definition and development of bioengineering technology, while stressing the issues about the design, implementation, and monitoring of bioengineering actions. Based on the critical analysis presented above, we conclude that there is a need to reconcile natural hazard control and ecological restoration by posing new applied research questions aimed at meeting this purpose. More importantly, there is a need to define sound techniques that reconcile natural hazard control and ecological restoration. The key considerations helping succeeding bioengineering actions in the future can be summarized as: (i) considering a multidisciplinary approach for soil and water bioengineering projects, (ii) establishing practical guidelines and tools for designing bioengineering structures, (iii) implementing monitoring stages in bioengineering projects, (iv) transmitting knowledge and know-how on soil and water bioengineering, (v) analyzing existing bioengineering works in terms of their performance, successes and failures, and (vi) continuing to identify the needs of the bioengineering professional sector.

Table 1 :

 1 Illustration of some ecosystem services provided by grass buffer strips, grassed waterways, and small flood retention ponds (bioengineering techniques) installed to reduce soil erosion rates by water and muddy floods in the loess belt of Belgium (based on Vandaele (2010) and various unpublished data). * Maintenance and improvement of soil ecosystem services: e.g. food, fiber, fuel and other biomass production; environmental interactions such as water filtering, carbon storage (e.g., due to the change of cropland to grassland) and nutrient cycling (e.g. N and P), transformation of substances, biological habitat for soil micro-organisms, fauna and gene pool; archive of our past (artefacts and indicators of environmental change). * Maintenance and improvement of hydrological systems: e.g. on site water infiltration, retention and storage, flow energy dissipation, off site flood control through reduced peak flow discharge and reduced sediment overloads.* Increase of biodiversity: e.g. vegetation (such as properly managed species-rich grasses, herbs and multiple cover crops), providing food and habitats for spiders, insects (e.g. bees, ground beetles, Ichneumonidae, ladybirds that are important for pollination and pest control), birds (such as skylarks, partridges and birds of prey), mammals as well as amphibians (in ecologically designed flood retention pools).* Increase of ecological connectivity facilitating circulation of fauna in landscapes dominated by crops. Creation of ecological corridors for various kinds of animals, including potentially slow moving earth or water-bound species. Increase of genetic exchanges between distant populations of the same species.

Figure 1 .

 1 Figure 1. Examples of bioengineering structures and installations worldwide. A. Palissades (France)

Figure 2 :Figure 3 :Figure 4 :Figure 5 :Figure 6 :

 23456 Figure 2: Which bioengineering structures to use to restore this degraded stream while protecting the

Acknowledgements

We thank the French "Ministère de la transition écologique et solidaire" and the H2020 Erasmus project ECOMED (575976-EPP-1-2016-1-ES-EPPKA2-K1) for financial support. We also thank Mélanie Burylo for ideas and graphical assistance in Figure 2. This paper has been initiated from a discussion at the 4 th International Conference "Soil bio-and eco-engineering: the use of vegetation to improve slope stability" which was held from 11-14 July 2016 at the University of Sydney, Australia. We are grateful to members of the European Federation for Soil Bioengineering (EFIB) for useful discussion.

Funding was provided (A.S.) by theTALVEG2project (funded by Région Languedoc-Roussillon-Midi-Pyrénées and Projet Collaboratif Régional fond FEDER) and the BMU (Germany) International Climate Initiative funded project "Ecosystems Protecting Infrastructure and Communities" (EPIC). Finally the authors greatly thank the four anonymous reviewers for their helpful comments.