Farhang Radjai

Michel Jean

Jean-Jacques Moreau

Stéphane Roux

Force Distributions in Dense Two-Dimensional Granular Systems

Relying on contact dynamics simulations, we study the statistical distribution of contact forces inside a confined packing of circular rigid disks with solid friction. We find the following: [START_REF] Dantu | Proceedings of the 4th International Conference on Soil Mechanics and Foundations Engineering[END_REF] The number of normal and tangential forces lower than their respective mean value decays as a power law. [START_REF] Travers | [END_REF] The number of normal and tangential forces higher than their respective mean value decays exponentially. (3) The ratio of friction to normal force is uniformly distributed and is uncorrelated with normal force. (4) When normalized with respect to their mean values, these distributions are independent of sample size and particle size distribution.

Despite the highly uniform density of a random packing of noncohesive particles, photoelastic visualizations provide a striking evidence of the heterogeneous distribution of contact forces on a scale definitely larger than the typical particle size [START_REF] Dantu | Proceedings of the 4th International Conference on Soil Mechanics and Foundations Engineering[END_REF][START_REF] Travers | [END_REF][3]. A quantitative characterization of these distributions is relevant both to mechanical processing (compression, compaction, flow, grinding) and fundamental understanding (mesoscopic scales, instability thresholds) of granular media [4][5][START_REF]Disorder and Granular Media[END_REF][START_REF] Wolf | Computational Physics: Selected Methods -Simple Exercises-Serious Applications[END_REF].

This Letter is concerned with a numerical study of this problem in confined two-dimensional packings at static equilibrium. We are interested in the statistical distributions P N and P T of normal forces and (absolute values of) friction forces N and T, independently of contact orientations. We also study the distribution P h of the dimensionless variable h T ͞N, which is a measure of friction "mobilization" within the Coulomb range ͓0, m͔, where m is the coefficient of friction between disks. Scaling with sample size and relation among the three distributions will be considered too.

Numerical results will be presented here for four samples of 500, 1200, 4025, and 1024 particles, referred to as samples A, B, C, and D, respectively. Particle radii are uniformly distributed between 3.8 and 7.5 mm in samples A and B, and between 1.5 and 7.5 mm in sample C. Sample D contains 192 particles of radius 1.6 mm, 320 particles of radius 1.05 mm, and 512 particles of radius 0.65 mm. Particles are contained in a rectangular frame composed of one planar base, two immobile walls, and one horizontal plane (the lid) free to move vertically and on which a downward force of 6600 N is applied. The acceleration of gravity is set to zero in order to avoid force gradients in the sample. Particle-particle and particle-base coefficients of friction are 0.2 and 0.5, respectively. All other coefficients of friction are zero.

For this investigation, we have relied on the contact dynamics (CD) approach to the dynamics of perfectly rigid particles with unilateral contacts. Since particles cannot interpenetrate, the allowed configurations of the system, characterized by a set of inequalities, define a region in the configuration space presenting a large number of edges and corners. Moreover, the basic Coulomb's law of friction, relevant to most of the granular media of interest, is a nonsmooth law in the sense that friction force and sliding velocity at a contact are not related together as a function. Finally, in the case of collisions velocity jumps occur, so that the evolution is not globally governed by differential equations in the classical sense.

The most commonly used algorithms are based on regularization schemes. In this way, impenetrability is approximated by a steep repulsive potential and Coulomb's law by a viscous friction law, to which smooth computational methods can be applied. The dominant feature of the CD method is that the conditions of perfect rigidity and exact Coulombian friction are implemented, with no resort to any regularization. At a given step of evolution, all kinematic constraints implied by lasting interparticular contacts and the possible rolling of some particles over others are simultaneously taken into account, together with the equations of dynamics, in order to determine all contact forces in the system. The method is thus able to deal properly with the nonlocal character of the momentum transfers-resulting from the perfect rigidity of particles in contact.

Detailed descriptions of the CD method can be found in the literature [START_REF] Moreau | [END_REF][START_REF] Jean | Mechanics of Geometrical Interfaces[END_REF][START_REF] Radjai | [END_REF]. In relation with the present investigation, we would just like to underline the point that dynamics is an essential ingredient of this approach. It is well known that a granular system at static equilibrium is hyperstatic; i.e., for given boundary conditions there is a continuous set of possible contact forces. This is due both to the absence of an internal displacement field (because of perfect rigidity) and to the nonsmooth character of the friction law [11]. In the CD method, the force network at static equilibrium is determined through the dynamic processes from which it relaxed. In other words, as in real granular systems, the static values of forces are reached asymptotically as the kinematic energy of the system is dissipated in friction and collisions.

Of course, this does not mean that the statistical distribution of forces is necessarily dependent on the preparation process. The most probable force distribution may well result from the generic disorder of granular systems [3]. However, density is a major control parameter of the mechanical properties of granular materials, and only in the steady state, reached after enough shear-induced volume change, it acquires a rather well-defined value for a given confining pressure [START_REF] Schofield | Critical State Soil Mechanics[END_REF]. That is why we applied the same procedure to prepare all samples in the same state: Filling the box with particles under gravity, shearing by moving the base horizontally (dilation occurs then), stopping shear and applying the confining load on top of the sample, and, finally, setting the gravity to zero and allowing the system to relax to equilibrium under the load. Although the algorithm is quite efficient compared to other available techniques, the whole procedure requires hundreds of CPU hours on a fast Unix workstation (Sparc 20) for each sample.

Figure 1 shows the network of normal forces in sample D. One can observe both large contact-to-contact fluctuations and a subnetwork of "force chains" that seem to carry a significant portion of the applied external stress. Forces range from 0.003 to 1127 N, i.e., a range of 6 orders of magnitude, which clearly requires a scaling analysis. The mean normal force is ͗N͘ 249 N and more than 60% of contacts carry a force lower than the mean. the mean are well fitted by an exponential decay. In order to see the behavior at low forces, we have shown in Fig. 3 the normalized log-log plots of the distribution of the logarithm of the forces. The data for forces lower than the mean have a power-law distribution. We conclude that the normalized distribution of normal forces is independent of our sample sizes and can be approximated by a power-law decay with a crossover to an exponential cutoff,

P N

~Ω ͑N͗͞N͒͘ a , N , ͗N͘, e b͑12N͗͞N͒͘ , N . ͗N͘.

(

) 1
We find a 20.3 and b 1.4. It is important to notice the collapse of normalized data on the same distribution in spite of the fact that the size dispersity of particles is not the same in all samples. The mean values seem, however, to depend on size dispersity since they do not scale with system size as shown in Table I. On the other hand, the lack of statistics at low normal forces in sample D as compared to sample B, giving rise to the fluctuations observed in Fig. 3, suggests that the "branching process" generating low forces from the high applied force on the system is more efficient in systems with a continuous distribution of particle sizes.

The semilogarithmic and log-log plots of the probability distributions of the T are displayed in Figs. 4 and5. The data are normalized with respect to the mean ͗T ͘ in each sample, and, as we see, they nicely collapse on the same distribution. This is again essentially a power-law decay with a crossover to an exponential cutoff,

P T

~Ω ͑T͗͞T ͒͘ a 0 T , ͗T ͘ , e b 0 ͑12T͗͞T͒͘ , T . ͗T ͘ .

(

) 2
We find a 0 20.5 and b 0 1. We also studied the probability distribution P h of h T ͞N. This is a uniform distribution except for a small peak at h m. The uniformity of this distribution may be attributed to the random structure of the contact network. On the other hand, it is likely that the rather weak singularity at h m is a "signature" of the dynamics of preparation. Indeed, only at sliding contacts is the friction force fully mobilized. If a granular assembly relaxes asymptotically towards static equilibrium, then the set of the last sliding contacts at the equilibrium threshold might remain fully mobilized. We checked that when the system is sheared by the motion of the basal plane, the peak at h m can rise to 50% of contacts, whereas the distribution remains uniform within ͓0, m͓. Finally, we note that the normal forces for which h m are much smaller than the average, so that the peak may well result also from an imperfect relaxation.

Another important result regarding friction mobilization is the statistical independence of h with respect to N. Whatever the value of N, friction is indifferently mobilized the Coulomb range ͓0, mN͔ (apart from the above discussed small peak). Such an assumption allows one to relate in a simple way P N to P T . Let P͑N, T͒ be the joint probability distribution of normal and friction forces. Since h is statistically independent of N, we may write P͑N, T͒ as a product of P N and P h times the Jacobian of the transformation ͑N, T ͒ ! ͑N, h͒, One may check that integration of the two members of Eq. ( 3) with respect to N and T over ͓0, 1`͔, with the substitution T hN in the right-hand side together with the constraint h [ ͓0, m͔, implies a normalized P h over the Coulomb range ͓0, m͔. Introducing the uniform distribution P h ͑h͒ 1͓͑0, m͔͒ in Eq. ( 3) and integrating with respect to N over ͓0, 1`͔ with the substitution N T͞h in the right side, we get the following relation between P N and P T :

P͑N, T ͒ dN dT 1 N P N ͑N͒P h ͑h͒ dN dT . (3)
P T ͑T ͒ 1 m Z 11 ͞m P N ͑xT ͒ dx x . (4)
This equation implies that the initial power law of the two distributions P N and P T should be the same: a a 0 . Moreover, an exponential upper cutoff of normal forces yields an exponential-integral cutoff for friction forces, i.e., essentially an exponential decay times a slowly varying function. Going back to Figs. 2345, we see that such refinements are out of reach within the statistical precision. On one hand, the cutoff may well be an exponential-integral function. On the other hand, the equality of exponents is consistent with the rough determination of these exponents.

Equation ( 4) can, however, be directly checked from the data. In Fig. 6 we have plotted both P T and the probability distribution obtained from P N via Eq. ( 4) for sample C. They are almost the same with a very good precision, although we assumed a uniform distribution of h with no additional peak on the edge h m. This validation of Eq. ( 4) is also an indirect check of the statistical independence of h with respect to N.

Finally, integration of Eq. ( 4) with respect to T yields the following relation between the mean values:

͗T ͘ m 2 ͗N͘. ( 5
)
This relation is approximately satisfied for our samples, as can be seen in Table I.

In view of these findings, we would like to underline some salient aspects of the problem. One important point concerns the scale of statistical homogeneity of granular systems. Despite local force fluctuations, the present study shows that for a sample as small as 1200 particles the force distributions are clearly defined over several decades. An increase in sample size does nothing but improve statistics. Hence, as far as stress is concerned, the linear scale of statistical homogeneity in a 2D assembly is a few tens of particle diameters. This is what comes out also from the study of anisotropy in angular distributions of contact forces [START_REF] Rothenburg | [END_REF][START_REF] Cambou | Powders and Grains 93[END_REF]. This observation is crucial for a continuum approach to the mechanics of granular media, needed in most of the usual technological problems.

Another point is that only the exponential tail of the distribution of normal forces, comprising nearly 40% of contacts in our simulations, has been observed in FIG. 6. Log-log plots of the distribution P T of normalized friction forces and the one obtained by applying Eq. ( 4) to P N in sample C.

experiments [3]. Weaker forces are technically difficult to measure, and their distribution has not been observed. The exponential tail has also been obtained through the usual simulation methods [15], and, what is more, a recent theoretical model provides plausible statistical arguments in favor of it [3]. This statistical model is likely to apply only to the subnetwork of force chains, which carries in effect most of the applied external load and in our simulations belongs to the exponential tail. The characteristic force at this scale is essentially imposed by the external load and the ratio of the system size to the largest particle size. On the other hand, the power-law decay of weak forces, if confirmed by other investigators, indicates the self-similar nature of weak contacts that do not belong to the subnetwork of large forces. Indeed, such contacts do not feel the external load, and hence their distribution can give rise to a power law through a self-similar branching process with no intrinsic scale. This observation also suggests that the exponents a and a 0 depend on the interparticular friction coefficient m.

We gratefully acknowledge many fruitful conversations with D. E. Wolf. This work has been supported by the Groupement de Recherche "Physique des Milieux Hétérogènes Complexes" of the CNRS.

Figure 2

 2 FIG. 1. Network of normal forces in sample D; see TableI. Forces are encoded as the widths of intercenter connecting segments.

FIG. 2 .

 2 FIG. 2. Semilogarithmic plots of the probability distributions of normalized normal forces N͗͞N͘.

FIG. 3 .

 3 FIG. 3. Log-log plots of the probability distributions of normalized normal forces N͗͞N͘.

FIG. 5 .

 5 FIG. 5. Log-log plots of the probability distributions of normalized friction forces T ͗͞T ͘.

TABLE I .

 I Number of particles p, number of contacts c, width L, mean normal force ͗N͘, and mean friction force ͗T͘ in our samples A, B, C, and D.

						FIG. 4. Semilogarithmic plots of the probability distributions
						of normalized friction forces T ͗͞T͘.
	Sample	p	c	L (mm)	͗N͘ ͑N͒	͗T͘ ͑N͒
	A	500	806	260	592	51
	B	1200	1969	389	213	18
	C	4025	6293	620	219	21
	D	1024	1498	65	249	23


Farhang Radjai

Dietrich E Wolf

Michel Jean

Jean-Jacques Moreau

Bimodal Character of Stress Transmission in Granular Packings

The correlation between contact forces and the texture of a packing of rigid particles subject to biaxial compression is analyzed by means of numerical simulations. Four different aspects are investigated: stress tensor, dissipation due to friction, angular distribution of forces, and fabric tensor characterizing the anisotropy of the texture. All of them provide evidence that the contact network can be decomposed unambiguously into two subnetworks with complementary mechanical properties.

The plasticity of a packing of rigid spheres is maybe the simplest example in which the dynamics is dominated by topological constraints: Forces are transmitted only through the interparticle contacts. This leads to strong inhomogeneities of the forces [START_REF] Dantu | Proceedings of the 4th International Conference on Soil Mechanics and Foundations Engineering[END_REF][START_REF] Liu | [END_REF][3][4]. Moreover, an initially isotropic packing develops an anisotropic contact network under shear, because new contacts are formed along the major principal axis of the strain-rate tensor, while some are lost perpendicular to it [5][6][7]. This geometrical anisotropy leads in turn to a mechanical anisotropy of the contact forces. Both the geometrical and the mechanical anisotropy enter the expression of the stress tensor and are thus essential for the resistance of a granular medium to shear [8,[START_REF] Cambou | Powders and Grains 93[END_REF].

In this Letter, we analyze the transmission of stress in a two-dimensional dense packing of rigid spheres by taking for the first time both the inhomogeneity of the forces and the anisotropy of the texture into account. It will be shown that the forces belong to two distinct classes which contribute differently to anisotropy, stress, and dissipation. This bimodal character of the force network is quite naturally suggested by the observation of the "buckling" of strong force chains supported by weak lateral forces during shear [START_REF] Cundall | Mechanics of Granular Materials: New Models and Constitutive Relations[END_REF]. The results presented in this Letter provide an unambiguous demonstration of this intuitive picture for all the aspects considered.

The main idea of our analysis is to evaluate internal variables such as the geometrical anisotropy for subsets of contacts with a given absolute value of the force. Thereby important aspects of the inhomogeneity of the system can be taken into account. For example, the contribution of contact chains with strong forces may be evaluated separately from the rest of the packing. This is, however, not practical because of the bad statistics of contacts within a small force interval. Instead, we consider the subset of contacts which carry a force lower than a given cutoff j. We shall refer to this subset as the "j-network." The variation of a quantity evaluated for the j-network as j is varied from 0 to the maximal force in the system allows us then to estimate its correlation with the contact force.

For the numerical simulations, we used the relatively new method of contact dynamics. This method allows us to integrate the equations of motion for multicontact systems composed of rigid bodies with Coulombian friction. The method tackles the nonsmooth character of the interactions with no resort to regularization schemes often used in numerical algorithms for granular systems. An account of the mathematical basis and the discretization procedure of this approach can be found in [START_REF] Moreau | [END_REF].

The simulation was carried out for a two-dimensional system with 4012 circular particles contained in a frame of four rigid walls. The radii were uniformly distributed between 3.8 and 7.5 mm. The particle-particle and particlewall coefficients of friction were 0.5 and zero, respectively. No gravity acted on the particles. The sample was biaxially compressed (see Fig. 1) by imposing a constant velocity of 1 cm͞s on the upper wall. The left wall was free to move under a horizontal confining force of 500 N. The initial sample was prepared with an isotropic contact network. As a consequence of compression the amplitude of anisotropy and the stress ratio Q ͑s 1 2 s 2 ͒͑͞s 1 1 s 2 ͒ increased, where s 1 and s 2 are the principal values of the stress tensor. We investigate below several quantities as a function of j at Q 0.18.

The texture is characterized by the probability density E͑u, j͒ of finding a contact with direction u in the jnetwork. In general the first deviatoric component in the Fourier expansion of E provides an adequate measure of geometrical anisotropy [START_REF]This is in general true for simple histories of deformation[END_REF]:

E͑u, j͒ ഠ 1 2p ͕1 1 A c ͑j͒ cos 2͓u 2 u c ͑j͔͖͒ . (1)
The parameter A c defines the amplitude of anisotropy, and u c is its principal direction. For the calculation of these parameters from the numerical data, it is convenient to use the "fabric tensor" defined by f ij ͗n i n j ͘, where n i is the i component of the unit vector along the contact direction and the average is taken over all contacts in the j-network.

Using (1) to evaluate the average of n i n j , it is easy to see that f 1 2 f 2 A c ͞2, where f 1 and f 2 1 2 f 1 are the eigenvalues of the fabric tensor. u c and u c 1 p͞2 are the directions of the corresponding eigenvectors. We found that the principal directions of the fabric tensor in the j-network coincide with those of the strainrate tensor irrespective of the value of j. Therefore we set u c ͑j͒ u c ͑`͒ 0, i.e., the direction of the axis of compression in [START_REF] Dantu | Proceedings of the 4th International Conference on Soil Mechanics and Foundations Engineering[END_REF]. Then a positive A c indicates that the direction of anisotropy is parallel to the axis of compression, whereas a negative A c corresponds to the orthogonal direction. Figure 2 shows the amplitude of geometrical anisotropy A c in the j-network as a function of j. For large j it approaches the geometrical anisotropy FIG. 2. Amplitude of geometrical anisotropy A c in the jnetwork as a function of j normalized with respect to the average force ͗F͘; see text. The inset shows the polar diagrams of the probability density E of contact directions for "weak" contacts (F , ͗F͘) and for "strong" contacts (F . ͗F͘).

of the whole system. The anisotropy of the network complementary to the j-network is given by A c ͑`͒ 2 A c ͑j͒ and can be obtained from Fig. 2.

Surprisingly, the direction of anisotropy is orthogonal to the axis of compression (A c , 0) for weak forces (small j). The anisotropy becomes more pronounced as j increases, and reaches a maximum for j ͗F͘, where ͗F͘ is the average force in the system. When j is increased beyond ͗F͘, A c becomes less negative and finally changes sign. This shows that contacts which carry a force larger than the average force ("strong contacts") are preferentially oriented parallel to the axis of compression. Although these are less than 40% of all contacts, their positive contribution to A c overcompensates the negative contribution of the contacts with a force lower than the average force ("weak contacts"). This means that the strong network (composed of strong contacts) is more anisotropic than the weak network (composed of weak contacts), as shown in the inset of Fig. 2.

The orthogonal anisotropy of the weak network cannot be simply understood as a result of the process of loss and gain of contacts induced by the deformation. The latter predicts only a positive anisotropy, i.e., parallel to the axis of compression. Our result, Fig. 2, proves that a sheared granular packing is not only inhomogeneous with respect to the forces, but also with respect to the geometrical anisotropy, and that these inhomogeneities are correlated.

A similar analysis can now be applied to investigate the mechanical anisotropy of the average normal force F n ͑u, j͒ and the average friction force F t ͑u, j͒ as a function of the contact direction. As for E, a second order Fourier expansion provides an adequate representation:

F n ͑u, j͒ ͑͗F͘͞2p͒ ͕1 1 A n ͑j͒ cos 2͓u 2 u f ͑j͔͖͒ , F t ͑u, j͒ ͑͗F͘͞2p͒A t ͑j͒ sin 2͓u 2 u f ͑j͔͒ , (2)
where A n and A t are the magnitudes of mechanical anisotropy. The analytical form of F t results from the fact that the spherical component of F t is zero due to static equilibrium and its principle axes are rotated to those of F n by an angle of p͞4. Again we found that the principal directions are independent of j, so that we shall set u f 0 in the following.

For the calculation of A n and A t we introduce two tensors x ͑n͒ ij ͑1͗͞F͒͘ ͗F n n i n j ͘ and x ͑t͒ ij ͑1͗͞F͒͘ ͗F t t i n j ͘, where t i is the i component of the unit vector t orthogonal to n and such that ͑n, t͒ preserves the same parity for all contacts. It can then be shown that ͑x are the principal values of x ͑n͒ and x 1 and x 2 are those of x x ͑n͒ 1 x ͑t͒ . In Fig. 3, A n and A t in the j-network are plotted as a function of j. The two parameters remain positive, i.e., the mechanical anisotropy is always oriented along the axis of compression. However, the contribution of normal forces to the total anisotropy begins to increase FIG. 3. Amplitudes of mechanical anisotropy A n and A t in the j-network as a function of j͗͞F͘.

significantly only after j ͗F͘, where both A n and A t have an inflection point.

The physical importance of mechanical anisotropy becomes clear when it is considered in connection with the stress tensor. The stress tensor s for a granular system in a quasistatic state is given by [START_REF] Christoffersen | [END_REF] s ij r͗F i d j ͘ , (3) where r is the number of contacts per unit volume, F i is the i component of the contact force F F n n 1 F t t, and d j is the j component of the intercenter vector joining the centers of two particles in contact. For spherical particles, we have d dn. Neglecting the weak correlation between d and F, we get s ij r͗d͘ ͗F i n j ͘. Now, introducing the two components of F into this expression and comparing with the expression of x , we see that s r͗d͘ ͗F͘x , and accordingly [8] Q͑j͒

1 2 ͓A c ͑j͒ 1 A n ͑j͒ 1 A t ͑j͔͒ . (4)
In Fig. 4, both the stress ratio Q and the sum ͑1͞2͒ ͑A c 1 A n 1 A t ͒ are displayed as a function of j. We see that Eq. ( 4) holds for all j with very weak deviations due to a weak correlation between d and F. Figure 4 reveals an unexpected property of the stress tensor: the shear stress Q for all forces lower than the average force is negligibly small compared to the total deviatoric load Q͑`͒ sustained by the system. Those forces contribute only 28% of the average pressure ͑s 1 1 s 2 ͒͞2 in the medium. This means that the weak network behaves essentially like an interstitial liquid, whereas the strong forces carry the whole deviatoric load and in this respect behave like a solid. Furthermore, Eq. ( 4) shows that this property is related to a compensation between the negative anisotropy of fabric and the positive anisotropy of forces, so that A c 1 A n 1 A t Ӎ 0 for forces lower than the average.

Another aspect of stress transmission in a granular packing is the appearance of chainlike structures of relatively strong forces. This observation is suggestive of long-range correlations over a scale far larger than the particle size. In our numerical experiments, we can check these correlations as a function of j in the complementary network to the j-network. At large values of j, say j . 2͗F͘, strong contacts are distributed in the form of relatively isolated clusters. As j is decreased, these clusters grow [see Fig. 5(a)] and finally at j ͗F͘ there is directed percolation along the axis of compression [Fig. 5(b)]. The fact that the whole deviatoric load is supported by a percolating network of strong chains makes it plausible that buckling of the directed chains under the action of compression occurs. Their stability then requires lateral forces in the complementary network. This is the origin of a negative geometrical anisotropy in the weak network. This mechanism goes with a peculiar scheme of the "mobilization" of friction, defined by the ratio h jF t j͞F n . Figure 6 shows the proportion of sliding contacts to the total number of contacts in the j-network as a function of j. At sliding contacts the friction force takes its maximum mobilized value, h m, where m is the coefficient of friction. At nonsliding contacts, particles roll over one another and h , m [14]. Almost 8% of contacts are sliding in the whole volume of the system at Q 0.18, and Fig. 6 shows that 96% of them are in the weak network for j ͗F͘. In other words, almost the whole dissipation by friction occurs at contacts bearing a force lower than the average force. Almost all contacts with a force larger than the average, corresponding to the buckling chains, are thus nonsliding.

In all the cases briefly discussed above, the average force appears as a characteristic force separating two complementary networks: a "load-bearing" percolating network of contacts carrying a force larger than the average force, and a "dissipative" network of contacts carrying a force smaller than the average force. The load-bearing network carries the whole deviatoric load, while the dissipative subnetwork contributes only to the average pressure. All contacts within the load-bearing network are nonsliding, whereas nearly the whole dissipation due to sliding takes place inside the dissipative network. The load-bearing subnetwork carries a direct geometrical anisotropy induced by shear, but it gives rise via buckling to an indirect anisotropy inside the dissipative network with a preferred direction orthogonal to the major principal direction of the stress tensor.

For all the variables studied here, this distinction between the two networks disappears in the particular case where the shear stress is zero. But it still holds for the statistical distribution P F of forces. P F is a power law with a weak negative exponent for forces lower than the average force, and an exponentially decreasing function for forces larger than the average [3]. The same behavior is observed in 3D systems as well [15].

The central message is that the inhomogeneous distribution of forces on the particle scale does not average out at the macroscopic level. It induces a bimodal behavior for the macroscopic variables of interest. More particularly, we find that a more precise description of stress transmission in a dry granular packing requires two stress tensors corresponding to two complementary phases. This property of a quasistatic granular medium is in contrast to both liquids and solids.

It is a great pleasure to acknowledge many stimulating discussions with S. Roux and L. Brendel.

FIG. 1 .

 1 FIG. 1. Velocity field in the center-of-mass frame during the biaxial compression.

2 ͒

 2 ͑1͞2͒ ͑A c 1 A n ͒ and ͑x 1 2 x 2 ͒͑͞x 1 1 x 2 ͒ ͑1͞2͒ ͑A c 1 A n 1 A t ͒,where x ͑n͒ 1 and x͑n͒2

FIG. 4 .

 4 FIG. 4. Stress ratio Q and the sum 0.5͑A c 1 A n 1 A t ͒ in the j-network as a function of j͗͞F͘. The inset shows the eigenvalues and the directions of the stress tensor for weak (F , ͗F͘) and strong (F . ͗F͘) contacts. The orientation of the weak tensor is irrelevant since its deviatoric component is nearly zero.

FIG. 5 .

 5 FIG. 5. The forces F for (a) F . 1.3͗F͘ and (b) F . ͗F͘, where ͗F͘ is the average force, in the upper halves of the sample. The line thickness is proportional to the force.

FIG. 6 .

 6 FIG. 6. Proportion r s of sliding contacts to the total number of contacts in the j-network as a function of j͗͞F͘.


IPBES mandate and governance

D.Pesche; G.Futhazar; S.Maljean-Dubois

The Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES) faces various challenges, as highlighted in chapters 2 and 3. How can biodiversity regime complex initiatives be coordinated and integrated to improve the science-policy interface? How can an intersubjective understanding of the contents of biodiversity science be achieved in a setting of different knowledge systems, competing policy priorities, and rival agendas? How can intergovernmental dynamics be combined at different scales in selecting and assembling knowledge?

The Platform design is the result of a relatively long and laborious process of international negotiations (2008 to 2012) in the context of a biodiversity regime complex characterized by a large number of international conventions of various scopes (both general and thematic) and at all scales (global, regional and even bilateral) (see chapter 2). IPBES is governed by an array of rules and procedures which have been developed throughout this slow genesis (2008 to 2012) and regularly enhanced in every plenary session. These rules are related to the decision-making mechanism but also to the working procedure to provide a framework for and implement scientific assessments and other activities linked to the IPBES work program.

The aim of this chapter is to provide a broad overview of the dynamics of governing IPBES on two aspects, i.e. institutional functioning and its core business, namely the production of assessments on biodiversity issues. When striving to understand the dynamics of IPBES, we focus on some aspects that have been controversial among the participants, including the question of the legal status of IPBES.

The plenary sessions highlight of IPBES functioning process1 . Generally, an IPBES Plenary agenda is structured as follows. Firstly, the organizational matters aim to finalize the agenda, to specify the membership of the Platform and validate the presence of observers. The representatives' credentials enable an evaluation of the exact number of members represented at the Plenary. Secondly, the work program and then the financial and budgetary arrangements for the Platform are discussed in the Plenary sessions. Further, the Platform operating rules and procedures are discussed, followed by debates on communications and stakeholder engagement strategies. Then the members discuss the institutional arrangements, including United Nations collaborative partnership arrangements for the work of the Platform and its Secretariat. Finally, the provisional agenda, date and venue of future plenaries are tabled, followed by the adoption of decisions and reports of the session.

Throughout this chapter, we strive to grasp the main elements of this conventional IPBES Plenary structure. This chapter could be a useful guide for readers who have not participated in an IPBES Plenary, while giving them some insight into the Plenary process.

We have grouped these elements in two main parts:

1. What is the legal status of IPBES and how is it governed? (section 1) This part focuses mainly on the decision-making process, including the organizational matters, rules of procedure of the Plenary, the Bureau and MEP. We also include the institutional arrangements and financial and budgetary arrangements that shed light on the IPBES governing dynamics. 2. What is IPBES doing? (section 2) This part focuses on IPBES activities, including the IPBES work program and some elements on its budgetary dimension that highlight the priorities of the Platform.

Through flashbacks, we reconsider some elements of debates which have taken place in IPBES preparatory meetings since 2008 in order to underline the possible diversity of options, which were then discussed, finally leading to an agreement. We also try to underline the challenges and potential controversies linked to some rules and procedures. Most of the rules were defined at the Panama meeting [START_REF] Cbd | Guide for working group chairs at COP and SBSTTA meetings[END_REF], where 94 consenting governments formally established "an independent intergovernmental body to be known as the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services" (UNEP, 2012c)2 . Since 2012, the members have been meeting almost on a yearly basis and the Secretariat is based in Bonn (Germany).

1.

IPBES status and governance

IPBES founding: A first that is not 'the' first

As shown in the chapter on the IPBES history, the Busan meeting, held in 2010, ended with the agreement that IPBES 'should be established'. It would now be interesting to look more closely into the legal aspect of this emergence process.

The meeting detailed the exact mission of the Platform and agreed on a number of principles that would constitute the foundation its future structure (UNEP, 2010). The final meeting document was submitted at the 65 th session of the United Nations General Assembly (UNGA). UNGA adopted a resolution calling for UNEP to organize a Plenary meeting in order to operationalize the Platform as soon as possible (UNEP, 2011a). This resolution was taken into account by the UNEP governing council during its 26 th session in February 2011, where it stated: "Decides, based on the request by the General Assembly in its resolution 65/162 of 20 December 2010, without prejudice to the final institutional arrangements for the intergovernmental science-policy platform on biodiversity and ecosystem services and in consultation with all relevant organizations and bodies, in order fully to operationalize the platform, to convene a Plenary meeting providing for the full and effective participation of all member states, in particular representatives from developing countries, to determine modalities and institutional arrangements for the platform at the earliest opportunity" (UNEP, 2011b). But did UNGA really establish IPBES? Considering the fact that the Platform Plenary was scheduled to take place in October 2011, one might rightfully think that it did. However, in this existential limbo, negotiators felt it was necessary to ask the UN Office of Legal Affairs (OLA) this crucial question on this matter, but the office came to a different conclusion: "the General Assembly, by merely taking note of the relevant decisions in paragraph 17 of resolution 65/162 of 20 December 2010, did not express approval or disapproval of the arrangement outlined therein, and accordingly did not establish the platform as a United Nations body" (UNEP, 2011c). It also added that the Busan Outcome provided declarations on the Platform that were recommendations but did not make the decision to establish it.

Thus, the mandate of the October 2011 meeting, which was referred to as a 'plenary', was to determine the modalities and institutional arrangements of the Platform. OLA also underlined that it did not have the mandate to operationalize the Platform, as it was not truly the first meeting of IPBES. If so, then what was the exact status of the ongoing Plenary? Was it part of an official intergovernmental process? According to OLA it was actually an intergovernmental process convened following a request by UNGA and in conformity with a decision from the UNEP governing council that had defined its relevant mandate. But this situation raises numerous questions. If the Platform was not yet established, who had the responsibility for doing so? And under what conditions? Would the IPBES be within or outside of the UN system? Would it have a legal status?

At the end of this 2011 'pseudo plenary', several options were available for the establishment of the Platform. It could be established by the ongoing meeting that could then turn into a Plenary. According to the opinion of OLA, it could also be established by the relevant organizations through a decision of their secretariat heads. In this situation, the Platform could work in an autonomous fashion and be independent of the decision-making process of these organizations, while still remaining in their institutional framework as an intergovernmental body. Other options were also considered, such as the creation by UNGA or the UNEP governing body or even by converging decisions by the executive heads of UNEP, UNDP, FAO and UNESCO3 . According to the latter hypothesis, IPBES would then be similar to IPCC in its creation. These different options are not negligible as each of them has repercussions on the independence of the Platform to be established.

Finally, a year later, on April 21, 2012, IPBES was formally established by a resolution during the second Plenary meeting in Panama. At the time of the resolution's adoption, representatives from Bolivia, Egypt and Venezuela indicated that their governments were not to be listed as supporting this resolution. Most notably, they expressed dissatisfaction on the fact that a UN status had not been attributed to the newly established Platform from the outset.

As though to stress their intention to maintain as much control as possible over the Platform, the 2012 resolution specifically states that, "any future decisions of the Platform have a legally non-binding nature." Also, some of its members are prompt to recall that the IPBES has no international legal capacity thus limiting its autonomy to act outside of what its members have formally agreed to [START_REF] Enb | Third Session of the Plenary meeting of the Intergovernmental Platform on Biodiversity and Ecosystem Services[END_REF].

However, this tendency to promote state sovereignty at all costs has some limits-the resolution and the future decisions will inevitably have a 'normative strength' [START_REF] Thibierge | La force normative. Naissance d'un concept[END_REF] and measurable practical consequences, e.g. decisions on the geographical location of the Platform or the way it operates [START_REF] Brunnee | COPing with Consent: Law-Making Under Multilateral Environmental Agreements[END_REF]. Of course, States will be able to leave the Platform as freely as they have joined it, but the distinction between binding and non-binding, hard and soft, is not a crucial concern when considering the repercussions of the different instruments used. Most of them, despite having an uncertain normativity, are nevertheless being applied on a daily basis without the issue of their legal nature ever being raised. On the other hand, many conventional or customary obligations are simply not enforced. Ultimately, "so long as the stage of mutual interest continues relatively undisturbed, the legal aspects of the relationship may seem of minor importance" [START_REF] Lachs | Some Reflections on Substance and Form in International Law, Transnational law in a changing society[END_REF]. Could legitimacy be the most important factor in the 'compliance pull' [START_REF] Boyle | The Making of International Law[END_REF] of many customary and conventional obligations? This statement does not imply that the procedures and processes of normative creation are irrelevant. On the contrary, the more open, transparent and inclusive they are, the more these norms will satisfy legitimacy criteria [START_REF] Brunnee | COPing with Consent: Law-Making Under Multilateral Environmental Agreements[END_REF]. This is a crucial stake for the Platform.

Plenary sessions -the main power arena for members

Since its official launch during the Panama meeting (2012), the Plenary has become the Platform's decision-making body, consisting of all Platform members. The latter are UN state members who have expressed their intent to be Platform members.

The main IPBES rules of procedure were agreed at this 2012 meeting and amended at the first IPBES Plenary in Bonn (IPBES, 2013b). Those rules were based on the relevant rules of procedure of the UNEP Governing Council (UN, 1988). The Platform members agreed that the meeting would make its decisions by consensus or, if not possible, by a two-thirds vote of present and voting Platform members (rule 36) 4 .

The issue of membership of regional economic integration organizations remains under discussion. In the Busan meeting (2010), it was agreed that the Platform would be open to regional economic integration organizations-a provision that concerns the European Union, which is part of numerous multilateral conventions, and international organizations (such as WTO) under this status. However, during the Panama meeting, the United States, followed by the African group and GRULAC opposed the fact that EU could access membership. The voting rules and the possibility for the European Commission to have electoral functions within the different IPBES bodies through one of its representatives caused some internal tension between the Commission and the member states. In the end, the Panama Resolution stated that, "the Platform is open to state members of the United Nations, who may become members by expressing their intent to do so". For the time being, the European Union only has an observer status5 , and it seems unlikely that this situation will change in the foreseeable future (see rule 5). The last Plenary, held in 2015 in Bonn, did not even address this issue, suggesting that there was a general understanding that an agreement was still impossible to reach at this point in the process (IPBES, 2015b).

Platform members are represented by a delegation consisting of a head of delegation, other accredited representatives, alternate representatives and advisers. The credentials of representatives of Platform members assigned by or on behalf of a head of state or a foreign affairs minister must be submitted to the Secretariat and approved by the Plenary (rule 11 to 14). The presence of a majority of Platform members participating in the session is required for any decision to be made (rule 35).

Opening the process -observers and/or stakeholders

After an early stage of the negotiation process generally open to all stakeholders, would IPBES end up having a usual intergovernmental composition, or would it be more 'modern', participative, open to private actors such as NGOs, scientists and even businesses and industry?

Non-state actors have actually been integrated in the IPBES process since the outset. In the first IPBES preparatory meeting (2008, Malaysia), a strict intergovernmental option was presented with a second option more open to other stakeholders: "The Platform is open to all states that are members of the United Nations or specialized agencies, in addition to relevant organizations and stakeholders. Each government has one vote. The relevant organizations and stakeholders also have qualified votes, the total number of which should not exceed the total number of votes of participating governments" (UNEP/IPBES/1/4). This meeting did not make any decisions on that aspect and most of the participants expressed their preference for an intergovernmental platform (UNEP/IPBES/1/6). This was the choice at the Busan meeting (2010), confirming a quite common approach, calling for the participation of UN states and regional economic integration organizations, the document states that "Intergovernmental organizations and other relevant stakeholders should participate in the plenary as observers" and would therefore have no role in the formal decision-making process (UNEP, 2012a).

IPBES communicated on this will to provide open and easy observer access to the Plenary, with particular reference to the inclusion of intergovernmental organizations, non-governmental organizations, indigenous peoples and local communities. Some specific rules were established to regulate this openness.

Firstly, IPBES define who are potential observers: "observers" are "any state not a member of the Platform and any body, organization or agency, whether national or international, governmental, intergovernmental or non-governmental, including organizations of and representatives of indigenous peoples and local communities, which is qualified in matters covered by the Platform" (UNEP, 2012b).

Secondly, IPBES define the procedure for admitting an observer. The question reached a deadlock during the first Platform Plenary in Bonn on the question of consensus or vote for the admission of new observers (ENB, 2013a). An interim procedure for the admission of new observers has thus been applied since then (IPBES, 2013a). This interim procedure reflects the will of some Platform member states to have complete control over the process by regulating the participation of non-state actors as much as possible. Basically, the current procedure automatically grants a Plenary observer status to any institution that has attended the previous session. Any actor wishing to be an observer to an upcoming Plenary has to send a formal request to the Platform Secretariat. The request is then scrutinized by the Platform Bureau, which then puts forward its observations to the Plenary on the admission of the new observer. However, a member state can oppose the admission of an observer. If such an opposition were to happen, it could only be overruled by a two-thirds majority of present and voting Platform members. Considering the danger of such a situation in a process that strives to promote consensus6 , it can be argued that this interim procedure could ultimately lead to a situation where one state could issue a discretionary opposition to the participation of an observer.

Currently, there are two opposing views at each Plenary on the observer issue. China requested the incorporation of a consensus requirement in the rule of procedure from the outset. The consensus requirement would then allow any state to regulate the admission of observers. EU states, on the other hand, have called for the establishment of a voting procedure where the admission of an observer could only be rejected by one third of the members [START_REF] Enb | Third Session of the Plenary meeting of the Intergovernmental Platform on Biodiversity and Ecosystem Services[END_REF]. This would prevent any excessive exclusion of observers. However, these two options are radically opposed and it has been acknowledged within the Plenary that these 'strong views' (Ibid.) have not changed throughout the negotiation process. Consequently, each Plenary has eluded the problem by inviting the next one to deal with the issue. Ultimately, it is very probable that the interim procedure will be perpetuated even for IPBES-5 (in 2017). Indeed, it seems unlikely that this sensitive issue will be addressed in a definitive way considering the heavy workload of the upcoming fourth Plenary where the first reports are due to be discussed.

Since 2013, a stakeholder engagement strategy has been drawn up, closely linked to the IPBES Communication and Outreach Strategy. In fact, the standard corporate communication of IPBES per se (dissemination of Platform products) is enhanced by the aim to mobilize a large array of stakeholders to support implementation of the IPBES work program. Stakeholders and observers claim to be highly involved in the IPBES process. They regularly highlight the lack of adequate funding to support stakeholder engagement and the stakeholder engagement strategy, and dependence on in-kind contributions to participate as stakeholders. The stakeholder group requested that IPBES estimate the in-kind contributions to the work plan including, for example, the cost of expert time in preparing assessments. However, stakeholders are not a group per se nor a community (see chapter on stakeholders). In the Plenary session, a stakeholder is not allowed to be accepted as an observer.

Bureau -a political balance

The question of subsidiary bodies was identified early in the 2008 meeting (UNEP, 2008) and strongly discussed during a further meeting without reaching a consensus (Nairobi, 2011). Two options were tabled-a first one with a single subsidiary body, including an expanded Bureau and a second option with a dual structure, an executive body plus a scientific advisory group. The first option was defended by EU, Norway, Mexico, Turkey, inter alia, arguing for a more coherent and less cumbersome body 7 . The second option, advocated by Japan, Brazil, US, China, Indonesia, inter alia, arguing that "this would facilitate efficiency in administration and foster the independence of the scientific functions" (ENB, 2012). Finally, the Panama meeting decided on this dual option. The IPBES Plenary thus has two subsidiary bodies, i.e. a Bureau and a multidisciplinary expert panel (MEP). Much of the discussion at this meeting focused on MEP, about its strictly or not scientific character and the nomination mechanism, based on UN regions or more biogeographical criteria 8 . Finally, the first Plenary (Bonn 2013) established the first Bureau and an interim MEP.

The Plenary Bureau includes the Chair, four Vice-Chairs, and five other officers. Each UN region is represented by two Bureau officers 9 . Candidates for the Bureau are proposed by governments for nomination by UN regions and elected by the Plenary for a 3-year mandate. The Chair and four Vice-Chairs are selected with due consideration to scientific and technical expertise. The Chair "will be rotated among the five United Nations regions every 3 years without the possibility of re-election as Chair" (rule 15). "The Bureau meets regularly "to advise the Chair and the Secretariat on the conduct of business of the Plenary and its subsidiary bodies" (rule 16).

The above chart cites the Chairs and Vice-Chairs elected for the first mandate (2013)(2014)(2015). 7 This option is similar to the IPCC organization with a large Bureau including three working groups: (1) the physical science basis of climate change, (2) climate change impacts, adaptation and vulnerability, and (3) mitigation of climate change. 8 Regularly, some countries highlight the underrepresentation of Antarctic and high seas regions. 9 The five UN Regions are the African Group (54 member states), the Asia-Pacific Group (53), the Eastern European Group (23), the Latin American and Caribbean Group (33), the Western European and Other Group (28). The Bureau Chair presides over Plenary meetings. In each Plenary, members can establish contact groups (CGs) to assist in the consensus forging process (CBD, 2010). In IPBES-2, three CGs were trained on the Platform work program, conceptual framework, budget and financial arrangements, and policies and procedures. CG meetings are organized so as to avoid overlap with Plenary meetings. There is usually a lot of discussion in those informal meetings. The groups are open to observers with some exceptions, as in IPBES-2 for the budget group: "some participants expressed the view that observers have a strong case to be involved in budget discussions, noting that many of them have provided inkind contributions to the Platform and are key to its success" (ENB, 2013). Other informal meetings are organized around the official plenary schedule, inter alia, regional meetings and stakeholders meetings.

Multidisciplinary Expert Panel -in search of credibility

The second Plenary subsidiary body, the Multidisciplinary Expert Panel (MEP), involved 20 participants: five nominated by each of the five UN regions. This governance aspect was discussed in depth during the first Plenary in Bonn (2013). For many delegations, the independence of MEP and his focus on science issues was a key point for the credibility of IPBES. MEP embodies the IPBES willingness for independence of the mobilized expertise. MEP "will carry out the scientific and technical functions agreed by the Plenary" (rule 24). MEP candidates are elected by consensus in the Plenary for a 3-year mandate with a possibility of re-election for one consecutive term. The MEP composition is also based on UN region equilibrium: "Candidates for the Panel are to be proposed by members [and observers] of the Platform for nomination by regions and election by the Plenary" (…) "Taking into account disciplinary and gender balance, each region will nominate five candidates for membership to the Panel (rule 26)". This question of regional structuration of MEP was a point of discussion and some countries like Bolivia, Mexico, Colombia, Brazil and Japan advocate a regional network structure for MEP but, finally, the first Plenary in Bonn decided that "the members of the Panel are elected for their personal expertise and are not intended to represent any particular region (rule 25)". The notion of multidisciplinarity was defined in a sui generis manner: "multidisciplinarity connotes an approach that crosses many disciplinary boundaries, knowledge systems and approaches to create a holistic approach, focusing on complex problems that require expertise across two or more disciplines. Multidisciplinarity arises when scientists (including natural and social scientists), policy and technical experts, natural resource managers, other relevant knowledge holders and users, interact in an open discussion and dialogue giving consideration to each perspective"11 .

The procedures adopted during the second Platform Plenary regarding MEP promote regional, disciplinary and gender balance. Nevertheless, the nomination of MEP members remains the exclusive prerogative of states12 , despite voices among stakeholders calling for a role in the nomination of MEP members (ENB, 2013b).The question of criteria for MEP member selection was intensively discussed and the trade-off pooled a number of criteria: Links between MEP and the Bureau were the focus of discussion with the aim of guaranteeing both the independence of expertise mobilization and coherence. Formally, the Panama Plenary decided that Bureau members would also be Panel observers during the interim period (2013)(2014). The Bonn Plenary clarified the role of both subsidiary bodies: "The need for the Multidisciplinary Expert Panel to retain its independence (which was a crucial issue for the credibility of the Platform). Some of the delegates also highlighted the importance of the independence of the Platform. The point was also made that the Multidisciplinary Expert Panel must focus on scientific and technical issues, with political issues being addressed by the Bureau and Plenary. It was also noted that the MEP may wish to develop a code of practice for its members to ensure highest scientific integrity in its work" (UNEP, 2013). In fact, the Bureau and MEP try to meet at the same place and date, and Bureau members can attend MEP meetings as observers in order to improve the expected collaboration.

An interim period was decided to test the new IPBES organizational scheme. A mid-term 'self-assessment' was conducted after three MEP and Bureau meetings, in June 2014. MEP and Bureau members highlighted the fact that they did not have sufficient social scientists and economists, nor marine specialists. They also stressed the difficulty of achieving a discipline and gender balance within UN regions (IPBES, 2015a). A social network study on MEP and Bureau members in 2014 showed that natural science (36/41) and male membership (32/41) dominated [START_REF] Morin | Boundary Organizations in Regime Complexes[END_REF].

In 2015, the third Plenary led to the re-election of MEP members. Platform members tried to take the lessons learned from previous interim MEPs into account in order to constitute a more balanced Panel. Although some progress has been made in this respect, observers have underlined the fact that there is still room left for improvement [START_REF] Montana | IPBES and Biodiversity Expertise: Regional, Gender, and Disciplinary Balance in the Composition of the Interim and 2015 Multidisciplinary Expert Panel[END_REF].

Secretariat

During the inception phase (2008 to 2012), the Secretariat was supported by UNEP and based in Nairobi and then moved to Bonn (Germany) as decided at the Panama meeting ( 2012). The IPBES-1 Plenary (Bonn, 2013) "requests UNEP, UNESCO, FAO and UNDP to establish an institutional link with the Platform through a collaborative partnership arrangement for the work of IPBES and its Secretariat", and "UNEP to provide the Platform Secretariat, which will be solely accountable to the IPBES Plenary on policy and programmatic matters" (IPBES 1/EN Annex V). IPBES-2 (Antalya, 2013) establishes a collaborative partnership arrangement among the plenaries of IPBES and the United Nations Environment Programme (UNEP), the United Nations Educational, Scientific and Cultural Organization (UNESCO), the Food and Agriculture Organization of the United Nations (FAO) and the United Nations Development Programme (UNDP). This partnership aims to strengthen collaborations between them for implementation of the IPBES work program. The Secretariat staff is under the administrative responsibility of UNEP and other UN organizations provide staff support 13 .

The Secretariat has the following indicative administrative functions under the direction of the Plenary: organizing meetings, communication and outreach activities, support to budgetary functions and mobilization of financial resources, monitoring and evaluation of the Platform work (UNEP, 2012b). Recruitment for the Secretariat was carried out in 2014, with 9 staff and 3 more staff positions were requested in IPBES-3 (Bonn, 2015).

The IPBES-2 Plenary recognized that the needs for coordinating the work program deliverables would exceed the Secretariat's capacity and agreed that a cost effective way to provide the necessary additional technical support could be through different arrangements, such as technical support units (TSU), based on in-kind offers from governments and other stakeholders.

Since the IPBES-2 Plenary, three task forces were created on: (1) capacity building (see chapter 9), (2) knowledge and data, and (3) indigenous and local knowledge (ILK) systems14 . The capacity building and knowledge and data task forces are co-chaired by two Bureau members and include three MEP members, as well as nominated and selected experts. The ILK task force is co-chaired by two MEP members and includes two Bureau members, as well as nominated and selected experts. The Norwegian government accepted to host a technical unit for the capacity building group, while the South Korea government did the same for the knowledge and data task forces and UNESCO for ILK. Those engagements and others (e.g. UNEP suggested hosting the scoping meeting for the regional assessments) illustrate the multi-stakeholder dynamics in the implementation of the work program. Then, "technical support units had been established for all three task forces and for the thematic assessment on scenario analysis and modelling, and other technical support arrangements had been made for the assessment on pollination and pollinators associated with food production and for supporting the delivery of regional and subregional assessments" (IPBES, 2015b). This also led to a great challenge for the Secretariat, the Bureau and MEP to coordinate such disseminated combinations of human and financial resources.

Platform financial and budgetary arrangements

Since its inception in 2012, "a core trust fund to be allocated by the Plenary will be established to receive voluntary contributions from Governments, as well as from United Nations bodies, the Global Environment Facility, other intergovernmental organizations and other stakeholders such as the private sector and foundations, on the understanding that such funding will come without conditionalities, will not orient the work of the Platform and cannot be earmarked for specific activities" (IPBES Decision 2/7).

Three years later15 , the third Plenary conducted a first assessment of the IPBES funding process. The Platform received cash and in-kind contributions. Cash contributions fueled the trust fund and represented US$2,236,000 in 2012, US$4,277,000 in 2013 and US$13,621,000 in 2014. The main contributing countries were Norway (41%), Germany (24%), United Kingdom (11%), USA (7%) and four other countries, i.e. Netherlands, Japan, France and Sweden (2-3%). In-kind contributions are mainly technical staff (71%) and meetings facilities (28%) for and estimated amount of US$2,470,000. The main in-kind contributors were Germany, Norway, China, Netherlands and Korea, but also UN organizations (UNEP, UNDP, UNESCO and FAO) and IUCN 16 .

The

Institutional arrangements

One of the main institutional questions at the outset of IPBES concerned links to establish with other United Nations bodies. On this issue, opinions were divided between a minimalistic link, where UNEP, UNESCO, FAO and UNDP would provide their support to the Platform, or a formal attachment to the UN family. This second option was favoured by African states who saw several safeguards in this proposition. Indeed, an UN body would be compelled to comply with UN principles and its objectives would have to be in line with those set within the UN Charter. The institutional framework of the different responsible bodies would have to be applied, most notably the relevant norms concerning the communication of data. The affiliated body could also use the institutional framework of the concerned organizations (UNEP, 2011c). For an external body, these requirements would not apply. Moreover, the Platform-without institutional links with other UN bodies-would need additional funding for the supply of administrative services. Yet, USA still preferred to apply specific rules of procedure to the Platform and was against such links. Even the establishment of the Platform in 2012 did not end this debate and it was left to the first Platform Plenary to decide on the relation between the Platform and UN.

Discussions on this matter were heated during the first Plenary. Understandably so, as this issue raises the question of the role of other international institutions and UNEP, which is expected by the General Assembly to have a more important role in assisting in the decision-making process. In the end, it took two plenaries to draw up the procedural aspects of the relationship between the Platform and the other UN institutions. IPBES Decision 1/4 established the administrative and institutional arrangements of the Platform, where UNEP was requested to provide the Platform Secretariat (which is accountable to the Plenary) and UNDP, UNESCO and FAO were requested to establish institutional links, "through a collaborative partnership arrangement for the work of IPBES and its Secretariat"18 . IPBES Decision 2/8 further elaborated on this aspect and illustrated how the other institutions could assist the Platform in the implementation of its work program 19 . Finally, the framework of cooperation between IPBES and these other institutions is fairly straightforward-while UNEP is the only organization in charge of administering the Platform Secretariat, all organizations assist the Platform by participating in the implementation of its work program, sharing information, attending meetings or even providing staff.

This arrangement highlights the potential coordination role played by IPBES within the biodiversity complex regime (see chapter 2). One of the many questions regarding IPBES during its conceptualization concerned the exact potential relationship between CBD and the Platform. From the outset, the CBD COP followed negotiations on IPBES very closely but remained more of a passive observer than an actor. Its very brief resolution X/11 simply called for UNGA to study the possibility of establishing an IPBES as soon as possible 20 . This decision highlighted the necessity for the Platform to address the requirements of CBD and strengthen SBSTTA rather than entering in an obvious competition with it.

The decision also requested the CBD Secretariat, in collaboration with SBSTTA, to examine how CBD could make full and efficient use of IPBES by seeking complementarity and avoiding any duplication (UNEP, 2010).

This matter was and still is a focus of discussion within SBSTTA as the cooperation aspects between the Platform and the subsidiary body are yet to be clearly defined. For instance, SBSTTA of CBD issued a working document for its November 2015 meeting in which it discussed the different ways the Platform deliverables could fit into its own work program 21 . This document was produced following decision XII/25 of CBD which specifically requested SBSTTA to work on this issue 22 . SBSTTA will be able to put forward suggestions to the Platform following the approval of those suggestions by COP 23 (thus removing any possibility for SBSTTA to directly access the Platform). The same rationale is being promoted among the other expert organs of the biodiversity regime complex. For example, the most recent meeting of the CITES Animal Committee (Tel Aviv, 2015) addressed the issue as to how the chairs of the different MEA scientific bodies could be better coordinated in relation to MEP meetings 24 . These developments are more than welcome as the failure to develop partnerships with these bodies would hamper the Platform in efficiently performing some of its functions.

The whole process illustrates the complexity of global environment governance. This complexity and the necessity to constantly adapt to it is apparent in the reflexive design of the Platform, as illustrated in the Busan Outcome in which the members concluded that "the Platform's efficiency and effectiveness should be independently reviewed and evaluated on a periodic basis as decided by the Plenary, with adjustments to be made as necessary" (UNEP, 2012c). This demonstrates that the Platform is not conceptualized as being a rigid institution and has room for adaptation and evolution through iteration. All of those aspects concerning members, the Bureau, MEP, the budget and institutional arrangements constitute the institutional infrastructure of the Plenary and the intersessional activities25 . Those elements of IPBES governance are oriented towards developing products and managing processes that are linked within the IPBES work program.

2.

IPBES core activities -the work program

The Busan meeting (2010) clearly outlined the IPBES global mandate: "The Platform's objective is to strengthen the science-policy interface for biodiversity and ecosystem services for the conservation and sustainable use of biodiversity, long-term human wellbeing and sustainable development" (UNEP, 2012a) "Focusing on Government needs and based on priorities established by the Plenary, the Platform responds to requests from governments, including those conveyed to it by multilateral environmental agreements related to biodiversity and ecosystem services as determined by their respective governing bodies".

Four main functions were thus identified:

1. "The Platform identifies and prioritizes key scientific information needed for policy makers at appropriate scales and catalyses efforts to generate new knowledge by engaging in dialogue with key scientific organizations, policy makers and funding organizations, but should not directly undertake new research" 2. "The Platform performs regular and timely assessments of knowledge on biodiversity and ecosystem services and their interlinkages, which should include comprehensive global, regional and, as necessary, subregional assessments and thematic issues at appropriate scales and new topics identified by science and as decided upon by the Plenary". 3. "The Platform supports policy formulation and implementation by identifying policy relevant tools and methodologies (…) for decision makers" 4. "The Platform prioritizes key capacity-building needs to improve the science-policy interface at appropriate levels and then provides and calls for financial and other support for the highest-priority needs related directly to its activities" (UNEP, 2012a)

Interestingly, the fact that this option includes four functions in the IPBES work program, rather than focusing solely on assessment as previous related initiatives have done, is presented as an innovative challenge in comparison to other science-policy interfaces. In particular, the Platform provides the necessary means for effective participation of developing countries by promoting capacity building. This matter was neglected by IPCC when it was originally established.

As some countries have more biodiversity than others, it is crucial to ensure that appropriate research can be conducted within their territories.

After the Panama meeting, the development of the initial IPBES work program was directly linked to those four functions.

The work program -four pillars

During the IPBES-1 meeting, concerning the preparation of the work program, the participants, "identified a number of issues as being particularly important. These included: ensuring an appropriate balance across the four functions of the Platform; reducing potential bureaucracy in procedures; clarifying the respective roles of the Bureau and the Multidisciplinary Expert Panel in a number of activities; and the urgent need for further work on the conceptual framework" (IPBES 1, EN). The intersessional period between IPBES-1 and 2, was devote to a specific activity around the conceptual framework (see chapter 7) which was adopted during the second Plenary in Antalya, December 2013 (IPBES Decision 2/4).

The work program is supposed to address requests by governments. How does IPBES manage the process for receiving and prioritizing requests put to the Platform? Those requests could be formulated by government members but also by United Nations bodies related to biodiversity and ecosystem services or other relevant stakeholders26 . Requests, inputs and suggestions are to be presented to the Secretariat no later than 6 months. Then the Bureau and MEP prioritize those proposals based on a previous evaluation conducted on the basis of various criteria, inter alia, the relevance, urgency, geographic scope and level of complexity, and prepare a report to be disseminated 12 weeks prior to the Plenary meeting for consideration and decision (IPBES Decision 1/3). As shown in the chapter 2, governments remain clearly in the driver's seat in this process.

The IPBES work program adopted during the second Plenary session (IPBES Decision 2/5) is planned for 5 years (2014)(2015)(2016)(2017)(2018) and structured in 4 objectives and 16 deliverables.

Objective 1 aims to, "Strengthen the capacity and knowledge foundations of the science-policy interface to implement key functions of the Platform" (IPBES, 2013a). For that, four deliverables were identified 27 . The first two are related to capacity-building needs with the aim of identifying capacity-building needs clearly linked to achieving the Platform work program (deliverable 1a.) and to integrate the capacity-building needs into activities (1b.). Those two deliverables will be produced with the support of a specific task force on capacity-building supported by UNDP (see chapter 9). The third deliverable aims to produce procedures, approaches for participatory processes for working with indigenous and local knowledge systems developed (1c.) with the creation of an ad-hoc task force hosted by UNESCO since July 2014 (see chapter 10). The fourth one aims to identify and prioritize knowledge and data needs for policy making (1d.) and also led to the creation of an ad-hoc task force, which aims at, "helping to identify and prioritize key scientific information needed for policy makers at appropriate scales, and to catalyse efforts to generate new knowledge in dialogue with scientific organizations, policy makers and funding organizations".

The two next objectives are related to producing assessments on biodiversity and ecosystem services. Objective 2 aims to, "Strengthen the science-policy interface on biodiversity and ecosystem services at and across subregional, regional and global levels". Three deliverables are identified. The first one is a guide on production and integration of assessments from and across all scales (2a.), to address practical, procedural, conceptual and thematic aspects for undertaking assessments, taking different visions, approaches and knowledge systems into account. The second one is a set of regional and subregional assessments established through a regionally based scoping process (2b.). The third one is a global assessment on biodiversity and ecosystem services (2c.) to be prepared for the 2018 CBD COP.

Objective 3 aims to, "Strengthen the science-policy interface on biodiversity and ecosystem services with regard to thematic and methodological issues". Four deliverables are expected. The first one targets a fast-track thematic assessment of pollinators, pollination and food production (3a.) (see chapter 11). The second one aims to produce three thematic assessments (3b.) on land degradation and restoration, invasive alien species, and sustainable use and conservation of biodiversity and strengthening capacities/tools. The third one is related to policy support tools and methodologies for scenario analysis and modelling of biodiversity and ecosystem services (3c.). The fourth one aims to identify policy support tools and methodologies regarding the diverse conceptualizations regarding biodiversity values and nature's benefits to people, including ecosystem services (3d.)

The last one, Objective 4, aims to Communicate and evaluate Platform activities, deliverables and findings through five deliverables. The first one is a catalogue of relevant assessments (4a.). The second one will produce an information and data management plan (4b.), by creating a task force on knowledge and data (also responsible for deliverable 1.d.). The third one is a catalogue of policy support tools and methodologies (4c.). The fourth one is a set of communication, outreach and engagement strategies, products and processes (4d.). The last one is an evaluative deliverable and aims to review the effectiveness of guidance, procedures, methods and approaches to generate information that will be useful for future development of the Platform (4e.).

Implementation dynamics

More than a year before the launch of the IPBES programme, the first steps of the Platform clearly illustrate the ways of dealing with horizontal and vertical coordination challenges (see chapter 2). The existing bodies of the Platform (the Plenary, the Bureau, MEP and the Secretariat), all play a role in implementation of the work program, in conjunction with ad-hoc bodies like time-bound, taskspecific expert groups and task forces, web-based arrangements and technical support units, according to the procedures below.

Work program implementation procedure

comparison, 25% will be spent on all of the methodological and thematic assessments planned in Objective 3 30 . This unequal distribution of the budget underlines the priority given to assessment but could lead to criticism on the lack of resources allocated to capacity building initiatives 31 .

Assessments-both thematic and geographical-are considered as a main product for IPBES. They involve the credibility, legitimacy and visibility of the new Platform. In line with adopting the global work plan, the IPBES-2 Plenary session chose to select the issue of pollination and pollinators associated with food production as a flagship for his first thematic assessment (see chapter 11). Three other thematic assessments are also included: initiation of scoping for invasive alien species and for the sustainable use of biodiversity are planned for the fourth Plenary session. The first elements of the thematic assessment on land degradation and restoration will be presented for approval at the sixth Plenary (2018).

Regarding geographical assessment, the first initiatives were centered on four regional assessments concerning the Americas, Africa, Asia and the Pacific, Europe and Central Asia. This regional approach is innovative in global environmental assessments-the option to link regional and global assessments was tested during MA. Interestingly, some European countries like France, UK and the Nederlands have to deal with this option through a spatial distribution of their overseas territories in various regional assessments. The regional approach is also a better incentive for governement cash and/or in-kind contributions to the still incomplete IPBES core budget. Conventional regional approaches do not take some specific ecosystems into account-the IPBES-3 Plenary decided to consider the option of undertaking a regional assessment for the Open Ocean region.

In methodological terms, there is a substantial challenge in managing scales between regional and global assessments of biodiversity and ecosystem services. Global assessments could be considered as the legacy of the Millennium Ecosystem Assessment and will be a key product for IPBES. The actual global assessment scoping document highlights the numerous linkages within the biodiversity regime complex and, more broadly, within the development agenda, including contributions of biodiversity and ecosystem services to the implementation of the Sustainable Development Goals, while recognizing synergies and trade-offs associated with meeting multiple goals 32 . Such global assessments are also designed as an integrated product to make effective use of most other thematic and methodological assessments.

IPBES also implements methodological assessments on two topics: (1) on scenario analysis and modelling of biodiversity and ecosystem services; and (2) on the conceptualization of values of biodiversity and nature's benefits to people.

An assessment in concrete

To gain further insight into this process, we illustrate the operational structure of global assessments on multiple values of nature. These assessments are planned to mobilize 3 co-chairs, 80 authors and 14 review editors with the support of a technical support unit (one professional and one administrative). Each of the 5 main chapters will include 15 core authors, including 3 chapter co-chairs, experts from the academic community, key stakeholder groups and ILK knowledge holders to ensure coverage of diverse worldviews. The process in supposed to be coordinated with ongoing programmes such as the World Bank Waves initiative and the SEEA project of the UN Statistical Office. In terms of timetable, the scoping document will be approved in the next Plenary (IPBES- In parallel with the assessment production, IPBES manages some cross-cutting activities that aim to contribute to the various assessments, namely activities linked to the objectives of the first work plan conducted by the three task forces presented above on: (1) capacity building, (2) knowledge and data, and (3) indigenous and local knowledge (ILK) systems.

Mobilizing experts -between legitimacy and credibility

Each deliverable is under the supervision of an expert working group, supported by the Secretariat and or an ad hoc TSU, under the responsibility of the Bureau and MEP, as shown by the above example on assessments on multiple values of nature. The expert mobilization dynamics were assessed by the interim MEP for the March 2013-2014 period. MEP members noted that the current nomination process did not provide adequate representation across geographic regions, gender, scientific disciplines and knowledge systems. Stakeholders suggested relaxing the 80:20 split between government and stakeholder nominations, with a shift towards up to 50% of the selections based on stakeholder nominations, and making full use of the networks that stakeholders represent. Other aspects of importance to scientific experts were definitions of the assessment acceptance, adoption and approval process, and how changes to report languages could be incorporated, and whether authors could challenge changes requested by government. A more in-depth analysis of the dynamics of expert mobilization is provided in the case study on pollinators (see chapter 11). At this stage, the challenge of achieving a balance between scientific credibility, plurality of knowledge systems and political dimensions of the process remains open. The question of conflict of interest is a good illustration of possible tensions.

IPBES has defined a conflict of interest policy since the third Plenary session (Bonn, 2015). For IPBES, a 'conflict of interest' refers to any current interest of an individual that could: (1) significantly impair an individual's objectivity in carrying out his or her duties and responsabilities for the Platform, and/or (2) create an unfair advantage for any person or organization. Any request relating to a potential conflict of interest may be sent to the Platform Bureau. This policy applies to the members of the Bureau and MEP and any other subsidiary bodies contributing to the development of deliverables, authors with responsibility for report content (including report co-chairs, coordinating lead authors and lead authors), review editors and professional staff to be hired to work in a technical support unit established by the Platform, along with the permanent professional staff of the Secretariat. Implementation of this policy relies on a conflict of interest committee consisting of three elected members from the Bureau and five regional members, one per United Nations region, with one additional member with appropriate legal expertise from and appointed by the organization hosting the Secretariat (IPBES, 2015b).

Conclusion

The development of this international science-policy interface has not been trouble free. Even though the IPCC precedent provides a very useful source of experience on this subject, establishing the Platform has been a far more complex process than that which lead to the creation of the Panel. IPBES-as an intergovernemental body devoted to the science-policy interface-shares a lot of features with his often acclaimed model, i.e. IPCC. IPBES has innovative specific aspects regarding rules and procedure, e.g. those on stakeholder engagement and participation (see chapter 8). However, this inclusive policy is under control of governmental delegations and the dominant functioning spirit remains conventionally intergovernemental, resembling the UNEP procedure. This is in no way surprising considering the high political stakes that are shaping the whole process. North-South relations are still a sensitive topic and Rio +20, which was generally perceived as a failure, only further complicated the matter. Some dimensions of this functioning reveal usual tensions between Global North and Global South countries. The budgetary aspects clearly show an unbalanced financial contribution, with 65% of the budget provided by two countries, i.e. Norway and Germany. The balance of influence is assumed to be effective in IPBES global governance, with a UN regional way regarding the balance of participation and with an alternate position of the Chair between a south and North candidate.

The upcoming Plenary will constitute a significant stepping stone for this young institution. Its first two finalized assessments on pollination and scenarios and models will be presented to members and observers. In a context of controversy (see chapter 11), the negociation process for the adoption of the summaries for policy makers is likely to be heavily scrutinized. The way the Platform will apprehend this first ordeal will be crucial with regard to how its credibility, relevance and legitimacy are perceived.

  (a) Scientific expertise in biodiversity and ecosystem services with regard to both natural and social sciences and traditional knowledge among Panel members; (b) Scientific, technical or policy expertise and knowledge of the main elements of the Platform work program; (c) Experience in communicating, promoting and incorporating science into policy development processes; (d) Ability to work in international scientific and policy processes (rule 26). Linkage with other UN conventions is managed by cross participation: "The chairs of the scientific subsidiary bodies of the multilateral environmental agreements related to biodiversity and ecosystem services and the Intergovernmental Panel on Climate Change will be observers".

  Platform expenses amounted to US$2,327,018 for the 2013 financial year and US$3,247,838 for 2014 17 . The 2013/2014 variation was mainly due to implementation of the work program (+US$1.6 M) and to staff recruitment within the Secretariat after the arrival of the Platform Executive Secretary in February 2014. An estimated revised budget for 2015 was established at US$9,526,779, including the work program contribution (US$5.5 M) and staff recruitment (US$1.6 M). Those budget increases reflect the sudden increase in IPBES activities after the first meetings that were mainly devoted to drawing up the rules and procedures.

	The global estimated budget for the 2014-2018 work program is US$40.8 M. In
	late 2015, the Chair reminded members about the need to fuel the IPBES trust
	fund: US$13.6 M were still needed to reach the targeted budget.

  4, February 2016) and a first draft will be drawn up by late 2016 and then reviewed by experts for a second draft in May 2017. This second draft and a summary for decision makers will be submited to governments and experts to produce a final version to be discussed in the IPBES-6 Plenary in May 2018. The estimated cost of the entire process is around US$1 M.

	Extract from "IPBES -Draft Scoping Report for the methodological assessment
	regarding diverse conceptualization of multiple values of nature and its benefits,
	including biodiversity and ecosystem services -Online document for consultation
	(http://ipbes.net/images/documents/Letters/Draft_IPBES_Global_Scoping_Repor
	t_20151013.pdf, consulted December 1, 2015)

Four Plenary sessions have been organized since the inception of IPBES: IPBES-1 in Bonn -Germany (January

2013), IPBES-2 in Antalya -Turkey (December 2013), IPBES-3 in Bonn (January 2015) and IPBES-4 in Kuala Lumpur -Malaysia. Regarding the establishment ofIPBES (2008IPBES ( -2012)), see chapter 3 of this book)

In IPBES-1 (2013), 105 countries were IPBES members, 115 in IPBES-2 and 123 in IPBES-3.

 UNEP, 2011c, op. cit., pp.2 ss.

All citations to rule in this chapter refer to the online procedures document on the IPBES website, in particular the rules and procedures for the Plenary: www.ipbes.net/images/Rules%20of%20procedure%20for%20the%20Plenary%20of%20t he%20Platform_2013.pdf

During the Plenary, European Union countries meet every morning to exchange information and, in some case, coordinate their positions.

The rules of procedure of the Plenary states that "The Members of the Platform take decisions on matters of substance by consensus, unless otherwise provided in its rules" (IPBES1/1 Rules of procedure for the Plenary of the Platform)

R.T Watson Chairs the IPCC (1997[START_REF] Brunnee | COPing with Consent: Law-Making Under Multilateral Environmental Agreements[END_REF], Co-Chair of the Millennium Ecosystem Assessment(2000)(2001)(2002)(2003)(2004)(2005) and the IIASTD Director(2002)(2003)(2004)(2005)(2006)(2007)(2008).

Decision IPBES/1/1 Rules of procedure for the Plenary of the Platform, rule 2.

Decision IPBES-2/1: Amendments to the rules of procedure for the Plenary with regard to rules governing the Multidisciplinary Expert Panel.

Since the IPBES-2 Plenary, the Secretariat is headed by Anne Larigauderie, former director of Diversitas.

Those three task forces contribute to Objective 1 of the work program (see next section of this chapter).

All the data came from IPBES 2015b. Report of the Plenary of the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services on the work of its third session (IPBES/3/18). Bonn, Germany: United Nations Environment Program (UNEP). (pages 59 to 72).

In January 2015, IPBES had received in-kind offers from 12 governments and 24 organizations.

In comparison, the Millennium Ecosystem Assessment yearly budget was estimated at US$3,200,000.

Decision IPBES/1/4 IPBES administrative and institutional arrangements.

Decision IPBES-2/8: Collaborative partnership arrangement to establish an institutional link between the Plenary and UNEP, UNESCO, FAO and UNDP.

Between two plenaries, the members of the Bureau, MEP and other experts involved in the various task forces or working groups participate in the intersessional meetings.

This option was decided in Busan meeting (2010): other existing options discussed at this meeting envisage to manage requests through CBD only, or the six biodiversityrelated conventions or multilateral environmental agreements related to biodiversity and ecosystem services and United Nations agencies.

 27 All those deliverables are linked to the Aichi Biodiversity Target (18 and 19).

During the second Plenary, procedures for preparation of the Platform deliverables were defined (IPBES decision 2/3 in (IPBES, 2013a)). Three main classes of Platform assessment-related material are expected:

1. Platform reports include global, regional, subregional, eco-regional, thematic and methodological assessments, and synthesis reports and their summaries for policy makers. In general, Platform reports are accepted and their summaries for policy makers are approved by consensus in the Plenary. Regional and subregional reports and their summaries for policy makers are first accepted and approved by the relevant regional representatives of the Plenary and subsequently accepted and approved by the Plenary 28 . 2. Technical papers. They are not accepted, approved or adopted by the Plenary, but are finalized by the authors in consultation with MEP, which serves as an editorial board. 3. Supporting material, including intercultural and interscientific dialogue reports. Those document are not accepted, approved or adopted.

In particular, the rules defined the four levels for the procedure of transforming a writing product into an official IPBES product. 1. Validation is, "a process by which the Multidisciplinary Expert Panel and the Bureau provide their endorsement that the processes for the preparation of Platform reports have been duly followed". 2. Acceptance means that the, "Plenary signifies that the material has not been subjected to section-by-section or line-by-line discussion and agreement by the Plenary but nevertheless presents a comprehensive and balanced view of the subject matter". 3. Adoption is, "a process of section-by-section endorsement at a session of the Plenary". 4. Approval, "of the Platform's summaries for policy makers signifies that the material has been subject to detailed, line-by-line discussion and agreement by consensus at a session of the Plenary".

The IPBES procedures gave much more detail on the process of producing reports and documents, specifying the role of the Plenary, the Bureau and MEP in relation with the experts involved, namely report co-chairs, coordinating lead authors, lead authors, contributing authors, review editors and expert reviewer authors 29 .

Assessment -the raison d'être of IPBES

Regarding the budgetary aspect, assessments represent the main provisional activity: Objective 2 will mobilize 44.5% of the estimated budget, with a predominant allocation to the global assessment (deliverable 2c), with 31%. In 28 'Approval' means that the material has been subject to detailed, line-by-line discussion and agreement by consensus at a Plenary session. 'Adoption' is a process of section-by-section endorsement and 'Acceptance' at a Plenary session means that the material has not been subjected to line-by-line discussion and agreement, but nevertheless presents a comprehensive and balanced view of the subject matter.


Jérémy Rivière

Pascal Ballet

Vincent Rodin

NetBioDyn, a smart Agent-Based software to intuitively model and simulate complex biological systems

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

Modelling and teaching complex biological systems Scientific approach

Using an Agent-Based (discrete) approach (vs. continuous)  Focus on individuals (cells, molecules), their behaviour and their interactions, instead of population



Examples of applications

Self-adjusting mechanisms to calibrate the parameters of the model (test phase)

• Aiming at automatically find the proper values for all the parameters involved in a simulation • Based on real results provided by users, obtained for example in vitro.

A predator-prey relationship involving two marine bacteria (Bdellovibrio and Photobacterium leiognathi)

• Emergence of interdependences and cycles between the two populations observed in real predator-prey systems

The environment is a 2D or 3D grid where entities interact according to their behaviours

Objectives

To facilitate the process of investigating, teaching and learning complex biological systems • Creating realistic models and simulations of complex biological systems to investigate their dynamics and grasp complexity • Reducing the gap between the actual programming skills of (future) biologists and most modelling software needs • Stimulating students creativity by promoting abduction (observe, build and test hypothesis)

Proposal

To design an intuitive Agent-Based software aimed at biologists (students, teachers, researchers) to easily build and simulate complex biological mechanisms observed in multicellular and molecular systems

Water-blood 𝐎 𝟐 exchanges in Zebra Fishes

  applications, tutorials and the software sources are available at http://virtulab.univ-brest.fr/ Enzyme kinetics E + S -> ES -> P A simple autopoietic system • 4 entities: A, B and mA and mB (produced by A and B) • A and B entities use each other's products (mA and mB) to multiply • The system converges towards a balanced state

••

  Investigating the efficiency of the Zebra Fish counter-current respiratory system by changing easily the flow direction Guided by the Multi-Agent paradigm (entities, behaviours and environment)• No need of any prerequisite or knowledge in computer programming • Providing at any time a simplified and complete view of the system's state (suitable external representation)

NetBioDyn, a smart Agent-Based software to intuitively model and simulate complex biological systems

  Definition of local interactions leading to global emerging behaviours  Variability in cell population, cell differentiation  Easier to understand, do not require advanced mathematical skills  Model's parameters are closer to the field of biology  Design of an intuitive graphical user interface (GUI) guided by the Multi-Agent paradigm

	Jérémy RIVIERE 1 *, Pascal BALLET 2 , Vincent RODIN 1
	1 Lab-STICC, CNRS, UMR 6285
	2 LaTIM, INSERM, UMR 1101

Université de Bretagne Occidentale, Brest, FRANCE *

  jeremy.riviere@univ-brest.fr

http://virtulab.univ-brest.fr/ NetBioDyn,

an intuitive and open-source software

				Entities
	Complex biological phenomenon	Modelling Intuitive Agent-Based GUI	NetBioDyn model	Interactions & Behaviours Environment