M Vallade

B Houchmandzadeh

Analytical solution of a neutral model of biodiversity

Keywords: Pacs numbers: 87.23.-n, 87.10.+e, 02.50.Cw

The unified neutral model of biodiversity proposed by S. Hubbell is solved analytically: The distributions of species abundance in the metacommunity and in a local community are calculated exactly as a function of speciation and migration rates and of the size of the community. In the limit of large population sizes the densities of species of given relative abundance are found to be given by universal functions depending only on two parameters.

One of the major goals of biodiversity theories is to explain the distribution of relative species abundance in ecological communities. Recently S. Hubbell has given an extensive description of a unified neutral theory of biodiversity [START_REF] Sp | The unified neutral theory of biodiversity and biogeography[END_REF] relevant for the description of taxons where trophically similar species such as trees in forests or benthic marine invertebrates communities are competing for resources. In this framework the population dynamics obeys a zero-sum game: large landscapes are essentially biotically saturated with individuals and every death is rapidly followed by the birth of an individual belonging to the same or to a different species. The time dependence of relative species abundance in a given community (an "island") is then the result of both internal competition and immigration from outside (the "metacommunity"). The second major Hubbell's hypothesis is that the game rules obey a principle of neutrality: all the species are equal competitors with the same per capita chances of dying and reproducing ( the plausibility of such an assumption relies on the fact that bad competitors have been eliminated by Darwinian selection). For such a neutral theory, population dynamics is essentially a stochastic process and is expected to obey universal laws depending only on a few number of parameters independent of specific properties of the species involved. This is at variance with the so called " ecological niche theories" for which the particular fitness of a given species to a particular environment is the predominant feature. The neutral model provides a "null-hypothesis" to which actual data can be compared and the influence of other parameters can be assessed. In this respect, various aspects of neutral models have been reviewed by Bell [START_REF] Bell | Neutral Macroecology[END_REF]. Since its apparition, this model has generated considerable debate (see for example a critical review by Riklefs [START_REF] Re | Riklefs, a comment on Hubbell's zero-sum ecological drift[END_REF] Hubbell's reply [START_REF] Sp | Modes of speciation and the lifespans of species under neutrality[END_REF], and [START_REF] Bj | A test of the unified neutral theory of biodiversity[END_REF] and references therein).

In addition to immigration, the species evolution depends also on speciation. Mutations, although being rare events, drive the long term drift of large communities. In Hubbell's theory they are considered as the fundamental process in determining the equilibrium distribution of species abundance in the metacommunity. He introduced a dimensionless parameter θ (the "fundamental biodiversity number") proportional to the product of the mutation rate ν with the total number of individuals in the metacommunity J M (the time scale being fixed by the average lifetime of individuals).The relative species abundance in a local community depends essentially on its size J, the immigration rate from the metacommunity m and the mutation rate ν (through θ). The Hubbell's formulation of the problem can only be solved through numerical calculations. The purpose of the present paper is to report on an exact analytical solution of the model which gives directly the equilibrium distributions of species abundances both in the metacommunity and in the local community.

Let us first consider the metacommunity dynamics under the influence of mutations.We assume that the death of an individual in a metacommunity of size J M is immediately followed by the birth of another one.The lifetimes and the mutation rates are assumed to be the same for all the species according to the neutral and the zero sum rules of the Hubbell's model. In the continuous time limit, the probability P k (t) that k individuals belonging to the same species are present at time t obeys a simple master equation:

dP k /dt = A k-1 P k-1 + C k+1 P k+1 -(A k + C k )P k (1)
where the coefficients A k and C k are respectively the increase and decrease rates of a species of abundance k , expressed in units of individual lifetime. These coefficients are readily found to be given by [START_REF] Sp | The unified neutral theory of biodiversity and biogeography[END_REF]:

A k = (J M -k)k J M (J M -1) (1 -ν) (2)
C k = k(J M -k + (k -1)ν) J M (J M -1) (3)
The increase rate A k for example is proportional to the probability of death of an individual which does not belong to the considered species (J M -k)/J M , times the probability of birth of an individual which belongs to the considered species k/(J M -1), times the probability of no mutation (1 -ν).

Let φ k (t) M designate the average number of species of abundance k. In the long time limit, the species which contribute to φ k (t) M are those which have appeared by mutation at an earlier time (t -u) and have reached the size k at time t . As all species are assumed to be equivalent, they have the same probability p(u)du = νdu to appear between times u and u + du . The time evolution of φ k (t) M is then simply given by :

φ k (t) M = t 0 P k (t -u)p(u)du = ν t 0 P k (u)du (4)
where P k (t) is the solution of eq. 1 with initial condition P k (0) = δ k,1 . Using Laplace transformation, the equilibrium distribution of the number of species with a given abundance is then found to be (see Appendix ):

φ k M = θΓ(J M + 1)Γ(J M + θ -k) kΓ(J M + 1 -k)Γ(J M + θ) (5)
where θ is defined by:

θ = (J M -1)ν 1 -ν (6)
This definition of θ coincides (within a factor 2) with Hubbell's universal biodiversity number in the limit J M ≫ 1 and ν ≪ 1. One can easily check that φ k M agrees exactly with the expression calculated at small J M by the Hubbell's method. The total average number of species S M = JM k=1 φ k M can be put under the form :

S M = JM -1 i=0 θ/(θ + i) (7)
in agreement with [START_REF] Ewens | The sampling theory of selectively neutral alleles[END_REF]. Typical distributions corresponding to Eq.5 are shown in fig. 1 using Preston plots (histogram of the number of species per octave of abundance).They are in perfect agreement with our numerical simulations of the problem.

For large J M and finite θ, g M (ω) = lim JM →∞ J M φ k M , which represents the density of species of relative abundance ω = k/J M , reads:

g M (ω) = θ(1 -ω) θ-1 ω (8)
This last result could have been obtained directly from the continuous reformulation of the evolution equation of P k (t) (Fokker-Planck equation), analog to the approach taken by Malécot [START_REF] Malécot | Our eq.8 actually coincides with eq[END_REF].

Let us now consider the distribution of species in a local community of size J in contact with the above described metacommunity. If J ≪ J M mutations within the community can be neglected and the equilibrium distribution in the metacommunity is negligibly modified by migrations from or towards the community. Let us now consider the probability P n (t; ω) of finding a given species with abundance n in the community knowing that this species has relative abundance ω = k/J M in the metacommunity. Because of the large size of the metacommunity compared to the community, ω can be considered constant over time scales relevant for the evolution of the community. Thus P n (t; ω) obeys a differential equation similar to Eq 1 but with coefficients A n and C n given by:

A n = (J -n) J ( n J -1 (1 -m) + mω) (9)
C n = n J ( J -n J -1 (1 -m) + m(1 -ω)) (10)
The equilibrium solution P n (ω) can be calculated (see Appendix) and it takes a concise form by introducing a re-scaled immigration parameter µ defined in a way similar to θ:

µ = (J -1)m 1 -m (11)
P n (ω) = J n (µω) n (µ(1 -ω)) J-n (µ) J (12)
In this expression J n is the binomial coefficient and

(a) n = Γ(a + n)/Γ(a)
is the Pochhammer coefficient [START_REF] Abramowitz | Handbook of mathemat-ical functions[END_REF] .

Note that P n (ω) is a polynomial of degree J in ω which can be conveniently written:

P n (ω) = ω J-1 k=1 f nk (1 -ω) k (13)
where the coefficients f nk depend on J and µ.

The important point is now that eq. 5 and eq. 12 can be combined to give the distribution of species φ n C in the local community:

φ n C = JM k=1 P n (k/J M ) φ k M ( 14
)
This equation is the main result of the present paper. It expresses the way the internal population dynamics of an island is modified by immigration from the environment.

In the extreme cases, if m = 1, φ n C = φ k M (complete "thermalisation") and if m = 0, the isolated community undergoes total dominance by a single specie as will be discussed below. The proof of this statement can be derived in the following way. Let P jC (n) be the probability that a given specie j has an abundance n in the community and P jM (k) the probability that this same specie has an abundance k in the metacommunity . Since P n (ω) has the meaning of a conditional probability, one has:

P jC (n) = JM k=1 P n (k/J M )P jM (k)
so that, if s is the total number of species:

φ n C = < s j=1 δ n,nj > C = s j=1 P jC (n) = JM k=1 P n (k/J M ) s j=1 P jM (k) = JM k=1 P n (k/J M ) φ k M
In the limit J M → ∞ , φ n C can be computed using eqs. 8 and 13:

φ n C = 1 0 P n (ω)g M (ω)dω = J-1 k=1 f nk θ/(θ+k) (n ≤ J-1) (15)
Preston plots corresponding to this result are shown in Fig. 2 . Our analytical results are again in very good agreement with numerical simulations. The existence of a maximum in these curves is a feature often observed in nature. It corresponds to an intermediate situation between full dominance of a single species in absence of immigration (µ = 0 ) and full equilibrium with the metacommunity ( µ = ∞ ). Typical ecosystems for which the distribution of species abundance has been experimentally measured and can be well described by the present model are closed canopy forests ( in Malaysia and Panama) [START_REF] Condit | Species-area and species-individual relationships for tropical trees[END_REF] as cited in [START_REF] Sp | The unified neutral theory of biodiversity and biogeography[END_REF] .

The average total number of species in the local community S C can be put in a form which generalizes eq. 7:

S C = J-1 i=0 θ (θ + i)(µ) J J j=i+1 α j µ j ( 16
)
where α j are the coefficients of the polynomial expansion of the Pochhammer coefficient (µ) J = J j=1 α j µ j For large J , the density of species g C (ω) = lim J→∞ J φ n C in the continuum limit (ω = n/J ) is:

g C (ω) = µθ 1 0 µ µu (1 -ω) µu-1 ω µ(1-u)-1 u θ du (17)
In this equation µ ≃ mJ is considered as finite when J → ∞ . This equation describes the asymptotic behavior of large local communities, as a function of only two parameters θ and µ . Fig. 3 shows ωg C (ω) for several values of µ. This function which is normalized to 1, represents the probability density of finding an individual belonging to a species of relative abundance ω . This figure clearly shows the crossover from dominance at small µ to diversity at large µ . When µ increases at constant θ, ωg C (ω) approaches continuously ωg M (ω) . This is the full "thermalisation" of the community with the metacommunity when the immigration rate m approaches unity.

Eq.17 however must be used cautiously. Our numerical simulations show that species distribution depends critically on the ratio J/J M when both J and J M are large . This emphasizes the importance of discrete formula (eq. 14).

To conclude we have derived an analytical solution of the Hubbell's "unified" model of biodiversity: exact expressions for the equilibrium distributions of species abundance and for the total number of species have been found for a community and a metacommunity of finite sizes. In the limit of large population sizes we have shown that the equilibrium distributions of species are described by universal functions depending only on two scaling parameters, θ and µ, related respectively to the mutation and migration rates. The model discussed above is essentially "zero dimensional", which means that no spatial inhomogeneous distribution of the species has been considered. There is an obvious interest in extending the present results to 1 and 2 dimensional systems : important results have been obtained for the probability of sampling the same species at two different locations as a function of their separation, both theoretically [START_REF] Malécot | Our eq.8 actually coincides with eq[END_REF][START_REF] Chave | A spatially explicit neutral model of β-diversity in tropical forests[END_REF] and from field measurements [START_REF] Condit | β-diversity in tropical forest trees[END_REF]. The present work opens the way to further analytical results in that direction, specially for deriving the full species distribution similar to eq. 14.

Appendix

The set of master equations (1) can be written under a matrix form: dP/dt = H.P with P a (J + 1) dimensional vector corresponding to P n (t) ( n = 0 to J ) and H a matrix defined by:

H =      -A 0 C 1 A 0 -(A 1 + C 1 ) C 2 A 1 . . . . C J A J-1 -C J     
Using the Laplace transformation Q(E) = L[P(t)] and defining the matrix G(E) = (EI -H) -1 one has:

P(t) = L -1 [G(E)].P(0)
The long time behavior of P(t) is obtained by considering the limit E → 0 of G(E).

A1 -Metacommunity:

The probability P k (t) that a specie which has appeared at time t = 0 has an abundance k at time t is given by :

P k (t) = L -1 [G k1 (E)]
According to eq. 2, A 0 = 0 . Using a recurrence method one finds that, when E → 0 :

G 01 (E) = 1/E + O(1) G 11 (E) = 1/C 1 + O(E) G k1 (E) = k-1 j=1 A j k j=1 C j + O(E) (1 < k ≤ J M )
Therefore, when t → ∞ , P k (t) → δ k,0 : every specie disappears by mutation. However, as new species appear continuously, the population distribution goes to a well-defined stationary value which can be calculated by taking the Laplace transform of eq.4:

< φ k > M = νL -1 [G k1 (E)/E] E=0
and one gets:

< φ 1 > M = ν/C 1 < φ k > M = ν k-1 j=1 A j k j=1 C j (1 < k ≤ J M )
Using the definition of θ (eq.6) , the coefficients C j in eq.2 can be written:

C j = j(J M -j + θ) J M (J M -1) (1 -ν)
so that one gets:

< φ k > M = θ k k j=1 (J M -j + 1) (J M -j + θ) = θ k Γ(J M + 1)Γ(J M + θ -k) Γ(J M + θ)Γ(J M + 1 -k)
which is eq.5. One can easily check that this distribution satisfies correctly the sum rule:

JM k=1 k < φ k > M = J M
Using this relation, the total average number of species in the metacommunity < S(J M ) > M = k < φ k > M can be shown to obey the recurrence relation:

< S(J M + 1) > M =< S(J M ) > M + θ θ + J M
Using < S(1) > M = 1, one gets eq. 7

A2-Community:

In this case A 0 = 0. In the limit E → 0 one then finds that:

G nm (E) = M n E J n=0 M n + O(1)
with:

M n = n-1 j=0 A j J j=n+1 C j (0 < n < J) M 0 = J j=1 C j M J = J-1 j=0 A j
Introducing µ as defined in eq.11 into the coefficients A n and C n given in eq.9 and 10, one gets:

A n = m Jµ (J -n)(n + µω) C n = m Jµ n(J -n + µ(1 -ω))
When t → ∞ the probability P n (t; ω) goes to a stationary value P n (ω) given by:

P n (ω) = M n J n=0 M n
The denominator of this expression is found to be to be independent of ω and the probability P n (ω) can be written:

P n (ω) = n-1 j=0 (J -j)(j + µω) J j=n+1 j(J -j + µ(1 -ω))

J-1 j=0 (J -j)(j + µ) (0 which finally leads to eq.12. P n (ω) is a polynomial of degree J which can be written:

P n (ω) = ω J n µ (µ) J n-1 j=1 (µ+j-µ(1-ω)) J-n-1 j=0 (µ(1-ω)+j)
which is of the form eq.13 and defines the coefficients f nk in that equation. Fig. 2 Preston plot of local community species distribution obtained by Monte-Carlo simulation for J M = 1024 , J = 128 and 2 values of µ and θ. Dashed lines represent theoretical species distribution, as given by eq.14 Fig. 3 Probability density of finding an individual in a species of relative abundance ω in the local community for J → ∞ (eq.17). θ = 5, and various values of µ as indicated on each curve. µ = ∞ corresponds to the metacommunity distribution.

  Figure Captions.

Fig. 1

 1 Fig. 1 Preston plot (binned by octave) of metacommunity species distribution obtained by Monte-Carlo


Bernard Gazier

Labour market institutions

Introduction

In order to properly function, labour markets need a set of rules, organizations, policies and resources. Among them, unemployment insurance, wage setting rules, employment services, retraining programmes and employment protection legislation are developed to some degree in all countries, as well as a collective bargaining framework. All these elements can be considered as labour market institutions, used -and transformed -by labour market actors: firms and workers, social partners and government, this last one with a dual role: legislator and controller on one side, and a particular employer on the other. Labour markets are deeply embedded in the societies they belong to. Robert Solow summed up this point when he chose as a title for one of his books "The labor market as a social institution" [START_REF] Robert | Vietnam develops a new way to prevent labor disputes: Technical assistance and experiences from the United States promote first multi-employer collective bargaining agreement[END_REF].

When one considers these institutions among countries, one is struck by their wide diversity and even heterogeneity. To take one example, apprenticeship is a key labour market institution in some countries where the bulk of the workers come from this training and recruiting route, while it remains marginal in others. The diversity comes from the specificity of societal contexts and history, but also from the variety of objectives pursued by each scheme and rule: e.g. efficiency and equity considerations may be combined in multiple ways. Labour markets are usually segmented in different submarkets. Some groups, benefitting from long -term and secured careers with promotional ladders, may be favoured by some institutions, while others are left aside or excluded. Another essential source of variety is the degree of implementation on the rules, depending on the size of the informal sector, on the political will and the amount of resources devoted to detecting and sanctioning noncompliance. There may be a big gap, and even an abyss between laws or signed agreements and their implementation. Last, one should take into consideration the interaction of all these institutions between each other and also with the whole social and economic sphere.

Beyond this diversity, unifying views have been elaborated by actors, experts and researchers. Several policy-oriented views emerged in the 90s, proposing different "labour market reforms" ensuring that these institutions bring or ease labour market adjustments to short term and long term needs. Among them, one may cite the "flexibility agenda" advocated by the OECD , the World Bank and the IMF, the "decent work" agenda promoted by the ILO, the "flexicurity" agenda developed by the European Union, and the "Transitional Labour Market" (TLM) perspective elaborated by a group of European researchers.

In this contribution, we shall not focus on the content, relevance or limits of each perspective (for a short discussion, see Auer and Gazier 2008), but we shall take stock of previous ILO work [START_REF] Peter | Protected Mobility for Employment and Decent Work: Labour Market Security in a Globalised World[END_REF]and 2007[START_REF] Peter | Flexicurity : Still going strong or a victim of the crisis?[END_REF] and propose, connected to the "decent work" and TLM agendas, the concept of "protected mobility" as a synthetic priority for analyzing labour market institutions in their contribution to the creation of productive employment, in the context of the persisting difficulties created by the world crisis triggered in 2007.

The period before the crisis was characterised by a big push for labour market deregulation. The idea was that with increasing globalisation, labour markets had to adapt quickly to shifts in demand, production technologies and new markets. In general it was believed that when all other markets (e.g. goods and financial markets) became increasingly liberalized, the labour market could not remain unreformed. The crisis seemed in a first phase have led to a renewed interest in (re-) regulation, because it was believed that excessive deregulation of the financial market was the major cause of the crisis. However, very soon, reregulation of the financial sector was watered down, and the pressures for labour market reforms continued and became even stronger. In addition the idea that microeconomic factors weighing on the supply side of the economy (e.g. all institutions touching the price of labour) has again taken its dominant place, whereas during the crisis the (aggregate) demand side of the economy was seen as the lever to be pushed for resolving some of the most damaging effects of deregulation.

This facts are to be seen in all proposals and action plans for the countries still in crisis, e.g. the Southern European countries, where we can see policy packages that combine budget austerity with labour market deregulation, leading to reduced wages, social benefits and employment protection.

The benefits of regulation, and policies concerned with a high level of aggregate demand, requiring decent wages, both as stabilizing factors for the economy, are today largely forgotten. If at all, only a minimum level of LMIs is accepted by the main economic players and austerity policies dominate everywhere. This text, while posing also some critical question in regards to excessive regulation as well, , supports the beneficial effects of labour market institutions, when they are well designed. This requires also that these labour market regulations and their reforms are not dictated top down but are bargained between the socio-economic partners.

While the text supports also ideas about the positive interaction of "smart" regulation and a more assertive demand side macroeconomic policy, it cannot develop these ideas in any length.

The chapter is organized as follows. Section 2 discusses in some detail the meaning, justification and implications of the concept of "protected mobility". In section 3, we shall separately review four main components of labour market institutions, analyze their objectives and means in this perspective, and provide examples of interesting practices. Section 4 will be devoted to some remarks on the interplay of these institutions in the perspective of the productive transformation of an economy. Section 5 provides a short conclusion.

The concept of protected mobility: from job security, employment security to labour market security

Emerging at the beginning of this century from empirical as well as normative work done under the aegis of the ILO, the concept of "protected mobility" has been developed as a contribution to the long lasting debate on the "structural labour market reforms" advocated by international organizations such as the OECD, the IMF and the World Bank. While anybody agrees on the idea that labour markets should enhance smooth and quick adjustments to the changing conditions of our globalized world, researchers and social actors strongly diverge on the role that should be played by market flexibility: flexibility of wages, of employment contracts, of hours… A related and more consensual idea is that labour market institutions should convey flexibility as well as security: flexibility for firms and security for workers, even if this statement is simplistic2 . Against this backdrop, "protected mobility" appears as a way to combine flexibility (here: mobility across jobs, firms, sectors, occupations, regions…) and security (here achieved by employment protection rules and labour market adjustment policies). But how to understand this combination and which role should it play?

We shall proceed in two steps. First we shall sum up the main arguments introducing "protected mobility" as an overarching objective for labour market institutions and reforms. Second, inspired by the "Transitional Labour Market" (TLM) perspective (see Gazier and Gautié 2011 for a recent synthesis) we shall show that in order to go further it is necessary to consider together two elements too often taken separately: transitions and positions in the labour market and around it. We shall introduce the idea of "transition capacity" from the worker's viewpoint, and show that it is critical in order to efficiently promote "protected mobility".

"Protected mobility": the core arguments

Workers' mobility as a central labour market adjustment channel On any market, there exist three main categories of variables that may, in a separate or in a simultaneous way, contribute to the adjustment between supply and demand: prices, quantities and qualities. In the case of the labour market, prices are wages; quantities are the number of available jobs, hours and workers; "qualities" are the skill level and competences of workers, and the skills requirements and attractivity of jobs. Wages are a variable depending on complex and multiple determinants: reflecting the productive contribution of a worker or a group of workers and / or their relative scarcity, but also reflecting hierarchical positions and career profiles, acting as an incentive and often influenced by moral, political or social norms (e.g. workers, unions and public opinion are strongly opposed to massive wage cuts3 ). This may explain that while some wages in some sectors prove to be highly flexible and even volatile, in most sectors of the formal economy they are "sticky" i.e. they change in a smooth and organized way, for example through the translation of a wage grid as a result of a periodical wage bargaining session taking into account inflation and productivity expectations. Quantities are very often used as adjustment channels in firms and on the labour markets: modulation of working time, supplementary hours or short-time working; but also hiring and firing decisions, downsizing; these adjustments accompany the reallocation of the remaining workers inside firms; on the labour market, one may consider the size and evolution of unemployment, the case of workers taking a leave, and also the number of persons in early retirement schemes (although early retirement schemes have been widely criticized and became less relevant). Discouraged workers can also be considered as a quantity adjustment (an undesirable one) on the labour market in the case of widespread unemployment. Last, "quality" adjustments may consist in training and retraining the workforce, and in improving (or downgrading) the skill content of a given job. Of course these three categories of variables often play together and interact, each sub-variable bearing part of the needed adjustment. They can act either as complements, for example when workers' reallocation combines part-time bridging jobs and training measures and/or as substitutes, for example in the case of training that does not lead to a wage increase, which is a functional equivalent to a "hidden"wage cut, because trained and thus more productive workers are paid the same as before.

Wages are often "sticky" and difficult to adjust; most labour market adjustments are a mix of quantities (volume of hours, jobs created or destroyed) and "qualities", because, compared to destroyed jobs, new jobs appear in other plants, other firms, other sectors and / or other regions, and may be more qualified. Together with on-the-job training, this continuous process of creation and destruction of jobs is one key determinant of the productivity growth in a given country. This makes job reallocation and workers' mobility a central stake on today's labour markets and explains why, either left to deregulated processes or organized to some degree, either alone or combined with other devices such as retraining, workers mobility is at the heart of currently discussed labour market reforms proposals.

From job security to employment security… and to labour market security Following here Auer and Chatani 2011, section 5, we can start from the widely accepted and quite commonsense idea that security for workers mainly stems from holding stable jobs. This was the traditional picture offered by the first analysts of labour market segmentation (Doeringer and Piore 1971): the success criterium for a worker is, after having experienced some short-term jobs, to get a long-term work contract and become a stabilized employee in a so-called "internal labour market". This is all the more the case today, in a world where stable jobs seem to become less numerous and more difficult to obtain and keep, and where unstable, precarious jobs, seem to trap their holders into a vicious circle of marginality and poverty.

However one frequent idea popularized by analysts and policymakers is that the security ensured by firms through stable jobs is no more sufficient and that this deficiency will be durable4 . Accordingly, they propose to complement (stable, firm-provided) job protection by the ability to shift from one employer to another, what implies other actors and sources, ie. employment protection.

However this shift, which has been advocated by the promoters of "flexicurity" in Europe, proved to be misleading on two important points. First, it seems to end up into a more or less virtual "employability" protection. As say Auer and Chatani 2011 (op. cit): "… the problem with selling employability as employment security is that it sells a potentiality (access to jobs) for a fact (holding a job)". Second, it neglects the key role of firms in securing their workers by organizing internal shifts from one job to another -what has been termed "employment security" in an initial and more relevant meaning. Such role has been highlighted in the case of Japanese firms developing polyvalence (ability to perform multiple tasks). This is the reason why it is better to speak of "labour market security". Job security and employment security (in this last, restrictive sense, as provided by a single firm), cannot protect workers in increasingly flexible labour markets.. Labour market security gives additional layers of security, by organizing protected mobility, i.e. protected transitions in and around the labour market, through labour market policies and social rights. This perspective is grounded, as it has been shown by the "Transitional Labour Market" researchers, on a dynamic view on careers and workers' trajectories. Holding a stable job remains central, but as a matter of fact during the whole life course people undertake many transitions, e.g. from school and training to work, and back in the case of retraining leaves, from full-time to parttime work, from one employer to another and so on. Labour market security consists in avoiding "bad" transitions leading to durable unemployment and/or poverty, and promoting "good" transitions leading to stable and productive jobs at the end of the day. As Auer and Chatani 2011 (op. cit) conclude: "Employment security with internal adjustment flexibility and protected transitions are the two sides of labour market security".

Transitions, positions and transitions capacities

The key question now becomes: how to understand and combine both sides of "labour market security"? A risk would be that, for some favoured workers, firms and labour market institutions cooperate in order to organize secure careers, while for other workers the Public Employment Service will try to compensate the indefinitely renewed instability of short-term contracts. An important observation is that a complete definition of a "transition" involves not only information about the transitory period to be secured but also information about the starting point and the arrival point. A transition starts from somewhere and should lead somewhere. Taken seriously, this remark brings at least three consequences.

The first one is that policymakers intending to ensure "protected mobility" should consider not only the intrinsic characteristics of the transitions they want to foster, but also the characteristics of the "positions" they start from and they lead to. They should make sure that exist "stability poles" as safe arrival points for workers engaged into some mobility, either geographical or sectoral. The basic list of such "stability poles", beyond the public sector and private firms when they offer stable employment, is the following: the branch/sector, the trade/craft, the "territory", non-profit organizations (NPO). NPO and public employers are of course direct job providers. Branches and sectors, and trade, play as "stability poles" because for a worker with a given set of competencies it is easy and natural to contact plants and firms in the branch/sector to which belonged the firm (s)he comes from, and to apply to the same kind of work (s)he is entitled to. This leads to underline the key role played by the transferability of skills. Workers recruited in traditional "internal labour markets" sometimes develop high level competencies, but they are often specific to their firms, and then, not transferable. This may become a major source of difficulties if they are dismissed5 . Last, the "territories" (regions, municipalities…) may act as a "stability pole" when proximity networks of information provide job opportunities to "local" workers. All these elements show that the fields of labour market policies and of macro-economic and productive development policies are closely intertwined.

The second consequence is that transitions and positions should be carefully considered in their gender asymmetries. During their whole career, given the current specialization of family roles, women most often face the dual constraints of care and work. This explains that they are most of the time engaged in more transitions than men (typically women take parental leaves while for men it remains an exception, or limited to a very short period), and that they often hold positions (typically part-time jobs) combining paid work and domestic work. How to make progress in gender equality and how to secure women's transitions and positions is a strategic issue.

The last consequence is that "protected mobility" is a subset of work and employment quality 6 . Work quality is today assessed through a set on indicators comprising wages, work intensity, work interest etc. but also the security given by the employment contract, the ability to be trained, to conciliate family duties and professional tasks… all these elements are at the core of "protected mobility".

The outcome of a mobility decision is highly contextual, and depends first on the set of opportunities available to the worker. In the case of countries, sectors or regions in a situation of tight labour market, close to full employment, mobility is easier, even if the question of labour market segmentation remains relevant. We have already seen that transferable skills also are important conditions for a successful outcome. Considering the departure situation of workers and combining both dimensions of context and transferability, the analysis proposed by T. Korver and G. Schmid 2012 puts into evidence that their transition capacity may vary from strong to very weak. In a situation of rare employment opportunities and non transferable skills, some workers may become trapped into long-term unemployment, losing their employability and confidence as they remain unemployed. Some others, still employed but under the threat of being dismissed, try to keep their current job on any condition. This entails two consequences. The first is that ensuring trust in one's own initiative and developing enabling capacities is a necessary ingredient of protected mobility. The second consequence is that workers should be aware of their rights and of the institutions organizing labour market mobility. They should understand the way they function, and be able to choose the best fitting option among options available. This leads to underline the key, sine qua non role played by social dialogue in "protected mobility". in providing information about available adjustment packages..

Labour market institutions and policy tools for protected mobility

It will not be possible, within the limited format of this chapter, to examine, even quickly, the whole set of labour market institutions. They comprise wage setting institutions (bargaining practices at different levels -national, branch, firm and even plant level -, the complex set of working time regulations (normal length of a working day, holidays, supplementary hours…), training and (re)training institutions and arrangements and other active as well as passive labour market policy measures. As labour market training will be discussed in another chapter of this book, we focus our analysis on four key sets of institutions: social dialogue, Employment Protection Legislation, income protection for the Unemployed, and labour market policies including employment services which constitute a policy package relevant for protected mobility.

Social dialogue

Social dialogue involves all the social partners, who share information, diagnoses and who bargain. It may also involve national and local government bodies (tri-or quadripartite conferences or negotiations). Social dialogue can be appraised first in the functioning of specific labour market institutions: it may be allowed, encouraged or even practiced like a routine. And it may appear, in a more transversal way, as an overarching style of governing employment relations and labour market policies7 .

One may distinguish three modalities of social dialogue. The first is sharing information and diagnosis. The second is sharing decisions through collective bargaining; the third is the comanagement of some labour market institutions.

• Sharing information and diagnosis is a key and basic ingredient of social dialogue.

This ensures a sense of common fate and mutual respect, ending up in a feeling of security for workers. Among the important ways of sharing information, one may cite early notice in the case of restructuring decisions involving mass dismissals, which allows workers and unions to react and take initiatives in a pondered way, opens some space for negotiated arrangements and avoids short-term interactions dominated by fear and anger. Early notice (at least six months in advance) is a frequent practice in several countries, and often stipulated by law. Other information sharing devices, are systematic and periodical meetings with social partners on the future evolution of jobs, competencies and work organization, which may prevent or better organize employment adjustment. Such meetings do not always end up into a shared diagnosis. Disagreements may persist among employers and unions, but at least partners may refer to a common basis

• The importance of constructive collective bargaining cannot be over-emphasized. It prevents labour disputes, and it leads parties in conflict to reach negotiated resolution of disputes when they arise. It helps improve working conditions, too. Some economists regard trade unions as pressure groups negotiating for undue high wages above the market clearance level, thus disturbing the function of labour markets. This view is quite biased since it neglects the positive contribution of social dialogue to productivity gains. A rich body of literature has documented the contribution of kaizen, improvement at workshop level based on social dialogue, to the rapid productivity growth realized in Japan. ILO's SCORE project replicated the model in developing countries where industrialization has been taking place. 8 In addition to the benefits at the micro level, collective bargaining also contributes to a fair distribution of productivity gains, which supports the aggregate demand. Arguably, collective bargaining is more important in developing countries where production is rapidly expanding but labour market institutions, especially labour administration, are weak. Mutual agreement between workers and employers is not a substitute for enforcement of labour regulations, but a supplement to them. In this sense, building the capacity of representatives of workers and employers in engaging in collective bargaining and forging trust among them are conducive not only to industrial peace and productivity gain but also to a broader development agenda that drives industrialization process. Nevertheless, promotion of collective bargaining often meets with challenges in many developing countries where the safeguard for fundamental workers' rights stands on a fragile ground.

Building the capacity for collective bargaining: the case of Viet-Nam

Viet Nam upholds a strategic socio-economic development objective that the nation will be a modern industrialized one by 2020 with socio-political stability (The government of Viet Nam, 2010). In this context, it has taken steps to build sound industrial relations at the national level, as well as in export-oriented sectors. The National Industrial Relations Committee (NIRC), a tripartite advisory body to the Prime Minister in the field of labour regulations and policies, was established in 2007. Since the coverage of enterprise-based collective bargaining agreements was limited, the Ministry of Labour Invalids and Social Affairs (MOLISA) implemented a pilot project to train negotiating parties and generate collective agreements in the garment and textile industry with the support of USAID and the ILO. Workers and employer representatives of the sectors negotiated employment and employment security; working and rest hours; wages, bonus and wage allowance; labour norms; workplace safety and social insurance for workers. The pilot project noted some challenges such as representation issues, negotiation skills and a lack of understanding of applicable labour regulations (ILO, 2010).

Today more collective bargaining agreements are reached with multiple employers in the same sector, but without sector-wide coverage. Under multi-employer Collective Bargaining Agreements (CBA), workers receive standardized benefits and wage packages.

It is reported that this approach has seen a success in improving workplace communications between unions, workers, and employers and reducing strikes (USAID, web page). Multi-employer CBAs were reached in the garment, textile, leather, footwear and seafood sectors as of August 2011. The Vietnam Chamber of Commerce and Industry notes the importance of involving more enterprises under multi-employer CBAs [START_REF] Hiep | Collective employment agreement: Universal application needed, Vietnam Chamber of Commerce and Industry News[END_REF].

Social dialogue may directly foster bargained "protected mobility". In Sweden, the law governing mass redundancies (Employment Protection Act, 1974) stipulates that in order to protect the workers with long tenure, the dismissing order is "LIFO" (last in, first out) but it also stipulates that if social partners bargain and agree on a different order (typically because the firm will demand to retain younger and more skilled workers, and offers compensating resources for the older workers to be dismissed through redundancy payments and intensive re-training and placement services), their decision will dominate the law's provision. This enables social partners to bargain and take their own responsibility9 . A recent selection of in-depth case studies collected all around the world (from Australia to Egypt, Mexico and China) showed the crucial role played by social dialogue in the management of displaced workers (ILO 2013).

• Examples of co-management of labour market institutions remain quite rare. One may cite the apprenticeship systems, co-managed by the social partners in Germany and Austria. Most often, social partners are involved in a tripartite management process with the State, this actor keeping the dominant role.

It is of course difficult to directly assess the importance and consequences of constructive social dialogue as institutionalized practices in the labour market and employment relationships. A recent attempt has been made in the case of France [START_REF] Gilbert | Labour Relations Quality and Productivity: an Empirical Analysis on French Firms[END_REF]). This study is based upon a survey of French manufacturing firms collected by the Banque de France over the period 1991 -2008, including variables such as profitability and productivity, as well as variables depicting the quality of labour relations and the social climate. It considers the impact of "regulatory constraints" on the total factor productivity (TFP) in different social dialogue contexts. When social dialogue is weak and labour relations are characterized by "workforce or union opposition", the influence of "regulatory constraints" is negative on the TFP. When firms are characterized by a good social climate and the presence of branch or firm agreements, these traits offset the negative impact of "regulatory constraints" on TFP, and the interaction of the variables "regulatory constraints" and "branch or firm agreement" yields a positive significant impact on TFP.

Employment Protection Legislation

Employment Protection Legislation (EPL) is very often seen as a major culprit for "rigid" labour markets and is thus very often subject of reforms to allow more flexibility in labour market adjustment. It has three main components: first, the rules and constraints regarding the ability to hire and fire through open-ended work contracts; second the rules and constraints regarding short-term work contracts; and thirdt, the rules and constraints regarding mass dismissals (early notice, negotiated arrangements, severance pay…). However, even from a "pure market" point of view, EPL has strong justifications. When they dismiss workers, firms generate social costs such as income and consumption losses, unemployment, skills attrition, costs for labour market policies, etc. In this perspective, it is fair and efficient to ask firms to minimize such "negative externalities" by maintaining a fair degree of EPL.

The key question becomes of course the "optimal" level of EPL. While excessive levels of EPL may deter employment creation, there is indeed a wide variety of EPL levels and modalities with many exceptions (e.g. for small firms) all around the world (for a careful balance, see Skedinger 2011). For example, firms only hiring their workforce on short-term contracts will not be able to reap the gains from on-the-job training and from a continuous adaptation and progress. Firms facing relatively high levels of EPL may develop efficient tools for adapting their workforce internally and many studies show that there is a positive correlation between the level of EPL and (training) investments in the labour force.. However, in many developing countries, while formal levels of EPL seem sometimes excessive, enforcement is dramatically low and positive or negative effects of EPL can in fact not be analysed without (usually lacking) empirical evidence of enforcement. Thus, while many economists argue that EPL is a determining factor for widespread informality in the labour markets, this argument is usually assessed on legal rules only, but not on their enforcement.

Employment Protection Legislation: the case of Indonesia

Employment protection legislation is often seen as a cause of sluggish employment growth by observers since it increases the cost of hiring and firing workers. This view, however, is far too simplistic for understanding labour market dynamism, especially that of developing countries. Here we take the case of Indonesia to illustrate the point. The Manpower Law of 2003 stipulates hiring and firing practices, severance pay, and minimum wage setting, among other labour issues in Indonesia. The effect of the Law on employment has been a subject of debate. Some observers claim that rigid labour regulations have deterred job creation because tight employee protection and high severance pay discourage investment in Indonesia and hiring workers (World Bank 2010). Rapid increase in the minimum wages was blamed for stagnant growth in job opportunities in the formal economy (ibid.). Would reducing rigidity in employment protection legislation create more formal employment as predicted by proponents of flexible labour market? The answer for the case of Indonesia is largely no. If such a labour market reform had any effect on job creation, it would be most probably modest. This is because the causal relation between employment protection legislation and job growth is not as straightforward as is believed by observers in favour of more labour market flexibility. One must note that a variety of factors affects creation of productive employment: employment protection is merely one of such factors (ILO 2010); the weight of each factor differs depending on the country specific contexts.

In the case of Indonesia, employee protection, though it is relatively tight in the region, has turned out not to be among the most influential factors affecting creation of productive employment. An investment climate survey by the University of Indonesia ranked labour regulation as the eleventh constraints, with macroeconomic instability, transport and corruption as the top three constraints. An executive opinion survey by the World Economic Forum echoed the finding and excluded labour market rigidity from the top five impediments to business operation in Indonesia. Therefore, it is unlikely for labour market reforms of weakening employment protection legislation to have substantial employment creation effect, if critical constraints to job growth are left intact. Further, a growth diagnostic report by the Asian Development Bank, the ILO and the Islamic Development Bank identified inadequate and poor quality of infrastructure, weaknesses in governance and institutions, and unequal access to and poor quality of education as critical constraints to inclusive and sustainable growth (ADB-ILO-IDB, 2010). Fine-tuning the suspension, when the engine is in defect, would not help the car run.

Income Protection for the Unemployed

Social Security programs mainly replace lost income in specified situations such as illness, maternity, retirement and unemployment. Although it is essential in many countries to develop Social Security, especially "provident funds" enabling workers to accumulate pensions rights for their old age, we focus here on unemployment insurance (or unemployment benefits, hereunder UI).

UI mitigates the adverse impact of job loss and enables the unemployed to seek for suitable jobs and/or receive training without incurring high financial and psychological costs associated with joblessness. It functions not only as an important safety net in the labour market, protecting transition capacities, but also as an automatic stabilizer of fluctuation in economic activities. Given these crucial roles played by UI, most developed countries have implemented mandatory and large UI 10 .

Although the importance of UI is widely recognized, it is often considered as challenging to introduce it in developing countries since these countries hold a large share of workers in the informal economy and lack necessary administrative capacity. OECD-style UI is seen as unsuitable to developing countries and tailor-making UI to the country contexts is suggested [START_REF] Vodopivec | Introducing unemployment insurance to developing countries[END_REF]. Despite the challenges, many developing countries have implemented UI. Although a prevalence of informal employment does pose a significant challenge in expanding the coverage of UI, 7 to 13% of the unemployed in Argentina, Brazil, China, South Africa and Turkey were covered by UI in 2008(ILO, 2010).

Unemployment insurance: the case of Brazil

Brazil' Federal Constitution of 1988 has established social security in the country. Protection for unemployed workers fired without a justified reason and with at least 6 months of formal work prior to dismissal was introduced by Law no. 7998 on unemployment insurance in 1990. Unemployment benefit (seguro-desemprego) replaces lost income, the amount of which is equivalent to the average monthly salary of the past three months prior to job loss but no less than the monthly minimum wage and no more than the predetermined upper ceiling. The duration of benefit is for three to five months, depending of the employment history over the past three years. Sales tax on firms funds UI in Brazil, while in most other countries contributions by workers and employers finance UI. UI supported income of 7.5 million job seekers in 2010 and mitigated the impact of the global financial crisis.

Recent studies on Brazil's UI have found positive labour market and welfare impact of the UI (Gerard and[START_REF] Gerard | Unemployment insurance in developing countries: The case of Brazil[END_REF]2012). Although some observers argue that UI may discourage job losers from actively seeking jobs, little distortionary effect on the job-finding behaviour was observed in Brazil. In addition, welfare effect of extending UI programme is found to be positive and sizable. The case of Brazil indicates that a country with a large informal economy can still implement and administer UI successfully.

Employment services

10 Space precludes here a discussion on the correct design of an UI scheme, addressing the two classical stakes of "moral hazard" and "adverse selection". For a recent and concise presentation, see Schmid 2013.

An important mechanism that corrects labour market failure is employment services. They comprise career guidance, job placement services and referral to training programmes. Without such services, matching the labour demand and supply may be suboptimal. For instance, jobseekers may spend more time to find suitable jobs or may take up less suitable jobs. Similarly, employers may not be able to recruit necessary workers with right skills and lose business opportunities.

Considered in their interaction with UI, employment services may play an important role in enhancing transition capacities and ensuring a quick way back to work. It is often said that employment services are "active" while UI is "passive". In developed countries this may lead to "activation" strategies, trying to limit UI and extend employment services. However, an efficient UI is a precondition for good matches in the labour market, and should be considered, combined with employment services, as an "active" investment in the workforce (Auer et al 2005).

A One of the challenges of providing employment services is outreach to jobseekers. Due to budget constraint, employment service centres are not ubiquitous in developing countries. In fact, jobseekers living in rural areas have limited physical access to employment service centres that are often located in large cities. Disseminating useful information in a costeffective manner to jobseekers remains as a challenge. An increasingly popular solution to this is the use of the Internet. Some employment services have developed online job database in which jobseekers search suitable jobs. YES Cameroon has been utilizing a popular social media to overcome this challenge. By utilizing an existing web platform, it saved the cost of developing and maintaining a website. Information on job fairs is widely disseminated thought the social media at no cost.

Protected mobility and the productive transformation of an economy

In this last section we go back to a more global level and consider, from a dynamic point of view, the interaction of labour market institutions between themselves and with the overall economic and social productive transformation of a given country.

It would be necessary here to explicitly introduce the variety of "employment regimes" and the macroeconomic context: the diversity of situations is large all around the world. , as well as the dependency of labour markets on business cycle movements. To take but one example, the world crisis triggered in 2007 has had very different outcomes in the European Unions, some countries like Spain and Greece seeing a doubling or even a tripling of their unemployment rates, while others such as Germany or Austria, keeping the same (low) unemployment rate and benefitting, among other things, from the flexibility effects of shorttime working scheme, which are traditional labour market institutions used through all recessions (Schmid 2013).

However, place constraints lead us to focus on the contribution of labour market institutions to the long-term growth process and to limit ourselves to some remarks. We shall evoke two general points and end up with an example of adaptable labour market institution.

• First, the question of the "optimal" level of mobility, often left implicit, has been discussed by ILO researchers. Auer 2007a and b showed that available statistics setting a correlation between labour productivity and the length of tenure do not deliver a single message. A wide range of tenure lengths, between 5 to 13 years seems to be compatible with the same high level of productivity. In the case of Eastern and Central Europe countries, Cazes and Nesporova 2003 identify some evidence of excessive labour market mobility: they observe for these countries "a countercyclical movement of labour turnover and a pro-cyclical movement of job tenure, in direct contrast to developments in the (western) OECD countries" (p. 138), suggesting that even in economic booms workers prefer staying in their (stable) jobs, whereas the contrary is true in the West. There many workers look for new jobs in a positive growth context, but tend to stay on their jobs in recessions. These analyses have been recently confirmed from a more theoretical point of view by a working paper of the IMF [START_REF] Olivier | Labor Market Policies ans IMF Advice in Advanced Economies During the Great Recession[END_REF] showing the limits of external labour reallocation which may induce competencies losses and hinder on-the-job training. • A second line of remarks suggests that a homogeneous, adaptable and motivated workforce can be considered as a public good. Looking at the employment performance of countries all around the world, it has been observed that there is no systematic trade-off between quantity and quality of work [START_REF] Erhel | Job quality: A comparative perspective on the basis of EU indicators[END_REF]. Competitive countries are characterized by a high quality workforce, benefitting from high quality work and jobs, and by the same token they generate a larger quantity of jobs. An additional observation concerns gender considerations. The productive potential of women remains enormous and should be tapped more intensively, especially in developing countries. In the long run this can only be achieved though a better sharing of domestic and labour market work, i.e. through jobs allowing a better conciliation between both spheres and tending towards equality between women and men.

• Third: in some countries, interesting steps have been made towards inclusive, legitimate, pro-active and "smart" labour market institutions. We present here an example from Austria, insisting on the pragmatic stance behind it.

A case of institutional plasticity: The Work Foundations in Austria

Dating back to 1987, the "Work Foundations" (WFs) are training, placement and reemployment units used in cases of industrial restructuring and coping with mass dismissals. Their funding is original, because they were initially created by firms as foundations (independent bodies owning a stable capital given by a big firm engaged into restructuring) and benefit from three other resources: the full access to the Public Employment Services, a co-financing contribution coming from their "clients" (the dismissed workers) who give them 50% of the interests paid on the sums yearly accumulated in their life-long severance pay account (a specific Austrian institution), and a contribution coming from the workers remaining employed in the dismissing firm and used for financing the retraining costs (in general, this contribution is around 0.5 % of the wage bill). WFs provide classical services such as competencies diagnosis, referral, (re)training and placement of the workers, with two original traits. First, they may propose quite long and even very long training programs, up to three years. Second, their "clients" are volunteers, easily recruited because workers feel confident and backed by their colleagues as well as by the whole community. These traits explain why they benefit from a good reputation, especially from potential employers. The first WF has been set up by a big metalworking firm, Voest-Alpine, and from the start 12 firms were present. In 2011, 81 firms could benefit from this WF (Borghouts van de Pas 2011). A first generation of enlarged versions emerged, adapted to different categories of workers and different situations: "insolvency WFs" (with a capital given by local communities), sectoral WFs and regional WFs, the last category being adapted for small and medium sized firms and for workers in short-term work contracts. Since 2000, a second generation of enlargement appeared, with the idea that WFs should also help integrating unemployed workers by providing them the same services and guarantees. "In-placement" WFs have been created, offering intensive and long duration training sessions, especially to persons without apprenticeship records (In Austria apprenticeship is the main route from school to employment). In 2009, there were 141 WFs offering "out-placement" services and 175 WFs offering "inplacement" services. The WFs have enrolled 10743 workers during this year, i.e. 5% of the Austrian unemployed. The medium length of their intervention is 300 days. An early systematic evaluation (Winter-Ebmer 2001) showed a positive outcome of such "Work Foundations". More evaluation should be necessary in order to fully assess the costs and benefits of each type of WF. The case of the Austrian WFs shows how a legitimate and successful institution may be extended, diffused in other contexts, and adapted to different challenges and beneficiaries.

Conclusion

This short survey has suggested some important channels through which labour markets institutions, albeit diverse, foster "protected mobility" and contribute to a productive and inclusive growth. Most of economic theories tend to envisage a "pure" market and consider any institutions and mechanisms that hamper the smooth function of the market as "disturbances" which are desired to be removed. We showed that, properly designed and managed, labour market institutions are collective assets, protecting and enhancing not only transitions capacity but also a necessary core stability in the labour market (e.g. good and stable long-term jobs). It is the capacity of LMIs to maintain productive jobs as well as acting as a security device during necessary labour market adjustment processes that will determine their effectiveness in regard to a more assertive demand side macroeconomic policy.

In the future one may expect an even more ambitious role for these institutions, because the collective management of individual career discontinuities will call for new developments, involving more and more workers and promoting social inclusion as well as gender equality. For employment maintenance purposes new forms of internal adjustment have to be sought and for external adjustments one has to proceed from a narrow perception of unemployment insurance to a wider "employment insurance" (Schmid 2013). The task of these new or amended institutions should not only be to "make workers fit for the market", but also to "make the market fit for workers".

profit private employment services : the case of Cameroon Public

  central question regarding employment services is the role of public and private suppliers. Compared with most private recruitment agencies, public employment services support workers with relatively low skills and difficulties in placement. It is thus vital that public employment services help integrate low skilled workers in the labour market in order to enhance inclusiveness of growth. This could be done, either directly, or by developing partnerships with private organizations. employment services often face constraints including budget and service provision capacity. In this light, employment service in Cameroon is an interesting case. Youth Employment Service (YES) Cameroon was launched as a non-profit organization in 2006 (YES Cameroon 2013). It operates in partnership with government ministries (Ministry of Youth Affairs, Ministry of Employment and Vocational Training and Ministry of External Relations), UN agencies, schools and training centres, employment services in other countries, foundations and NGOs. Activities of YES Cameroon include offering career counselling, training courses and small grant to start a business. The NPO does not provide referral services, yet its grass-root approach to support youth's insertion in the labour market has been helpful.

	Non-

Some workers may demand more flexibility (e.g. for combining paid work and family duties) and firms may demand more security (e.g. employment contracts ensuring that trained workers stay employed during a minimum period).

Wage cuts have been observed in the current crisis, but they remain perceived as exceptional.

The question of the growing instability of the labour markets all around the world have been for many years a hotly debated topic. For a general assessment, showing that, on the long run, indicators such as job tenure remain stable and even increase, see Auer and Cazes 2003. However this statement is compatible with many observations of the growing number of unstable work contracts and the institutionalization of "precarious work", especially in the current crisis.

It is not the case with "professional labour markets", a specific version of "internal labour markets" because they recruit workers through the apprenticeship system, giving them transferable skills.

On this burgeoning field, see[START_REF] Lucie | Monitoring quality in work: European Employment Strategy indicators and beyond[END_REF][START_REF] Erhel | Job quality: A comparative perspective on the basis of EU indicators[END_REF]

In a wider perspective, Labour Market Institutions themselves can be seen as a result of social dialogue. We focus on the current functioning of LMIs.

Sustaining Competitive and Responsible Enterprises (SCORE) project implements a practical training and infactory counselling programme that enhances the productivity, while promoting respect for workers' rights. For more details visit http://www.ilo.org/empent/Projects/score/lang--en/index.htm

For a more systematic inquiry into the ways of setting up social dialogue in restructuring situations in the European context, see Gazier and Bruggeman (eds) 2008 and Bruggeman et al 2012.


M Cavarroc

M Mikikian

G Perrier

L Boufendi

Single-crystal silicon nanoparticles: An instability to check their synthesis

Keywords: numbers: 52.27.Lw, 52.35.-g, 52.70.-m

An instability occuring in electrical signals of the discharge is used as a mark to detect the end of the single-crystal silicon nanoparticle formation in Ar/SiH4 rf plasmas. Scanning electron microscopy and atomic force microscopy studies of depositions show that the exact beginning of the coalescence phase corresponds to the onset of the instability. At the end of the instability, no singlecrystal nanoparticles are remaining in the gas phase. These results based on a non-perturbative method allow to control depositions of single-crystal silicon nanoparticles of a well-defined size distribution with the highest density available during dust particle growth.

Dusty plasmas generated in radiofrequency (rf) discharges have been widely studied in the past few years. The range of interest spreads over industrial [1] as well as astrophysical concerns [START_REF] Cernogora | AIP Conference Proceedings[END_REF]. An active research has been induced by contamination phenomena in industrial plasma reactors. However, new applications of dust production have emerged. It can be used to produce analog aerosols of planet atmospheres like Titan [START_REF] Cernogora | AIP Conference Proceedings[END_REF]. The singlecrystal nanoparticles obtained by this way can be incorporated in thin film layers in order to improve their mechanical and/or optoelectronical properties [START_REF] Roca I Cabarrocas | [END_REF], or used for single electron device fabrication [4]. Many theoretical [5,6] and experimental [7,8] studies have dealt with the detection and dynamics of particles in silane based plasmas. Presently, many studies are being carried out on the production of silicon nanoparticles generated in plasma processes [9].

In previous experimental and theoretical works [7,10,11], the way particles grow has been brougth to the fore. The dust particle formation in Ar-SiH 4 low pressure rf plasmas has been shown to be a four step process occuring in the gas phase: nanocrystal growth (2-3 nm in diameter) from molecular species, accumulation phase, coalescence, and growth by deposition of the plasma species on the particle surface. Particle growth in the discharge leads to strong modifications of the plasma characteristics. Indeed dust grains affect many of the physical properties of the plasma (electron density, temperature, electric field, impedance, ...). The modification of the plasma impedance due to the particle formation and growth led us to use a diagnostic based on the time evolution of the amplitude of the third harmonic of the discharge current (3H) and the amplitude of the self-bias voltage (V dc ) [11]. This electrical diagnostic has been developed in the GREMI laboratory. The current and voltage probes are inserted between the matchbox and the powered electrode. The curves are visualized on a LeCroy scope LT364L (500 MHz bandwidth and 1 GS/s) and the results are recorded via a computer. This diagnostic has been shown to be able to follow the particle formation and growth in different chemistries such as silane and methane based ones [START_REF] Mezeghrane | Proceedings of the 31th EPS Conference on Plasma Physics[END_REF]. Thus, in a pure argon plasma, the amplitude of 3H and V dc remains constant in time. When silane is added to the the mixture, i.e. in a dust forming plasma, V dc and 3H show a time evolution due to the formation and growth of dusts in the discharge.

The main formation steps (accumulation phase, coalescence and growth by surface deposition) can be clearly identify thanks to this electrical diagnostic (fig. 1). Even though, some uncertainties are remaining concerning the exact transition from one step to another. As can be seen in figure 1 insert, an instability occurs in between accumulation and coalescence phase [START_REF] Cavarroc | [END_REF].

Until now it was still quite difficult to exactely define when the coalescence starts. The end of the accumulation phase is the most interesting point for nanocrystal deposition. In a previous study performed in our group in the same experimental conditions, nanocrystals have been shown to be single-crystal silicon nanoparticles of 2-3 nm in the FCC phase [14] and the critical density (i.e. the greater density of nanocrystals in the discharge) is reached just at the end of this phase. A precise control of the nanocrystal phase is very important for all industrial applications in nanotechnologies in which a well known nanocrystal size and density are required [15]. The aim of the present work is to determine the point on electrical signals corresponding to the exact end of the accumulation phase (i.e. to the exact beginning of the coalescence phase).

The experimental set up has already been described in details in a previous paper [8]. The rf discharge is produced in a grounded cylindrical plasma box (13 cm inner diameter and 3.3 cm for inter-electrode distance). The whole system is enclosed in a vacuum chamber. The upper electrode (driven electrode) is a shower-head one in order to ensure a homogeneous gas distribution at the entrance of the plasma zone. This electrode is connected to a 13.56 MHz rf generator through a match box including a blocking capacitor. The power can be varied from 0 up to 20 Watts. The experimental conditions are the following: 12 Pa total pressure, 20 sccm of argon flow In this work, depositions of dust particles at different instants have been performed. We used the instability occuring in the electrical signals as a mark. This instability has been studied in details in previous work [START_REF] Cavarroc | [END_REF]. We realized three different types of samples : a first one just before, a second one during, and a last one after the instability. Structural morphology of the formed dust particles is qualitatively analyzed from topographical observations of the samples by means of atomic force microscopy (AFM) operating in the tapping mode and scanning electron microscopy (SEM).The SEM images obtained are shown in figure 2.

Just before the instability (figure 2(a)), there are only single nanocrystals (around 2-3 nm) on the substrate. At the beginning and in the middle of the instability (figure 2(b) and (c)), two populations can be distinguished: there are both nanocrystals and small polycrystalline aggregates. At the end of the instability (figure 2(d)) deposited dust particles are mainly small polycrystalline aggregates. These results seem to place the beginning of the coalescence phase at the beginning of the instability. The AFM images obtained from the same samples are shown in figure 3. They are all normalized to the same height size scale in order to make the comparison easier. In the nanocrystal case, the AFM tip size is of the same order as the nanocrystal size. We are confronted to convolution troubles in the x and y directions. The only dimension we can use is the height because this dimension is less concerned by convolution troubles. The results are quite similar to the ones obtained by SEM. Before the instability (figure 3 The same analysis performed on a sample deposited during the instability (figure 4(b)) shows two peaks located at different heights. The higher peak around 1.5 nm corresponds to the nanocrystals and the smaller one around 4 nm corresponds to the first coalesced polycrystalline nanoparticles. On the last sample (figure 4(c)), a single peak appears around 5 nm, corresponding to bigger coalesced polycrystalline nanoparticles. Those dust particle radius distributions confirm our qualitative topographical observation.

The third harmonic/self-bias based diagnostic does not need any optical access to the plasma. Once it is calibrated, this diagnostic can provide precise information concerning the dust particle nature in the discharge. We performed the calibration for the first phases of formation (formation and accumulation of nanocrystals and beginning of the coalescence) in a typical dust forming Ar/SiH 4 plasma generated in a rf discharge. Presently, we can conclude that before the instability, the dust particles are single-crystal silicon nanoparticles of 2-3 nm in diameter in the FCC phase [14]. Their shape appears to be spherical and their density increases during the accumulation phase until reaching the critical value estimated to 10 11 to 10 12 cm -3 at room temperature [11]. Thereby, just before the instability the single-crystal silicon nanoparticle density in the plasma is the highest that can be reached. During the instability, nanocrystals agglomerate together to form the first polycrystalline dust nanoparticles of 4-5 nm. All the nanocrystals begin to agglomerate at least two by two. This is the early beginning of the coalescence phase and two populations can be distinguished. The first one corresponds to nanocrystals while the second one corresponds to first coalesced polycrystalline particles. At the end of the instability, no more single nanocrystals remain in the gas phase. Thus, the onset of the instability exactly corresponds to the beginning of the coalescence phase. This instability is certainly due to a charge effect of the nanoparticles becoming bigger and starting to attach more electrons. It can be related to attachment induced ionization instabilities observed in electronegative gases [START_REF] Cavarroc | [END_REF]16,17]. After the instability the dust nanoparticles are made of agglomerated nanocrystals. Their size increases from 5 nm at the beginning of the coalescence to about 45 nm at the end of the phase [1]. The dust particles are now polycrystalline and present a high specific surface (up to 115 m 2 .g -1 [18]) that can be of interest for applications in catalysis.

FIG. 1 :

 1 FIG.1:(Color online) Time-evolution of the amplitude of the discharge current 3 rd harmonic in a dust forming plasma.

  (a)), there are only small nanocrystals around 2-3 nm in height. At the beginning and in the middle of the instability (figure 3(b) and (c)), two populations of dust particles are present, one around 2-3 nm and another one around 4-5 nm. After the instability (figure 3(d)), a single population is visible, around 10 nm. Those results confirm the ones obtained by SEM.The radius distribution of dust particles corresponding to the first sample (figure4(a)) shows a single peak centered at 1.5 nm (corresponding to 3 nm in height).

FIG. 3 :

 3 FIG. 3: (Color online)AFM images of the samples deposited (a) just before (b) at the beginning of (c) during (d) after the instability.

FIG. 4 :

 4 FIG. 4: (Color online) Radius distribution diagrams corresponding to a sample deposited (a)before (b) during (c) after the instability.

The authors would like to thank M. Dudemaine, S. Dozias, M. Vayer, T. Baron and K. Aissou for technical support.