Sylvie Charlot
email: charlot@enesad.inra.fr.

Sonia Paty
email: .paty@enesad.inra.fr.

TAXABLE AGGLOMERATION RENT: EVIDENCE FROM A PANEL DATA by

Keywords: spatial autocorelation panel, economic geography, …scal agglomeration rent. JEL classi…cation: H2 H3 H7 C21 1 Introduction

The main purpose of this paper is to test the existence of a taxable agglomeration rent in the French local tax setting by taking account the tax interactions among the urban jurisdictions.

After presenting a simple economic geography model with …scal interactions, we estimate a model of tax setting for the local business tax using the econometrics techniques on panel data for 1993 to 2002. We observe that the relationship between tax rate and …scal base gives presumption of the existence of a " taxable agglomeration rent".

As economic activities tend to concentrate in a small number of places (typically in urban area), some literature considers the e¤ect of agglomeration forces on tax competition between jurisdictions. More speci…cally, the new economic geography literature uses the monopolistic competition framework, with internal increasing returns, to study agglomeration in general equilibrium models [START_REF] Krugman | Increasing returns and economic geography[END_REF]. The increasing returns to scale mean that industrial producers want to be close to consumers (or …rms when there is vertical linkage) to satisfy a large demand, while consumers want to be close to producers to bene…t from more varieties of goods without sustaining transport cost. Thus, there is a cumulative process of agglomeration whose intensity depends on the values of transport cost, on the magnitude of the preference for diversi…ed goods and on the share of the monopolistic competition sector.

Following this large literature (see [START_REF] Baldwin | Public Policies and Economic Geography[END_REF], for a complete survey) recent papers have started to focus on the taxation of factors and their income when …rms are in monopolistic competition and when trade costs on goods are present. They show that capital mobility is not the only factor a¤ecting the impact of tax competition on tax rates. The level of trade openness and the extent of agglomeration forces not only have e¤ects on location but also on tax rates in equilibrium, when localities or countries engage in tax competition.

In a pioneer paper, [START_REF] Andersson | Tax competition and economic geography[END_REF] build a model where taxation on factors is used by local government to produce a local public good. They show that taxation on immobile (resp. mobile) workers stabilises (resp. destabilises) the dispersed equilibrium. One of the major explanations is the production's technology of the public good which constitutes a new agglomeration force; regions with more mobile factors own resources to produce more public goods, attracting more mobile factors. This e¤ect is reinforced when mobile factors are not too much taxed comparatively to the immobile ones. When regions are asymmetric, in terms of immobile factors endowment, [START_REF] Ludema | Economic geography and the …scal e¤ects of regional integration[END_REF], [START_REF] Andersson | Tax competition and economic geography[END_REF] and also [START_REF] Baldwin | Agglomeration, integration and tax harmonisation[END_REF] show that agglomeration creates rents for the mobile factor that can be taxed, increasing the equilibrium tax rates. In this setup, the result, according to which the mobile factor may not respond to marginal changes in tax rates, di¤ers from the standard tax competition theoretical predictions. They show how an agglomerated region can tax more without losing its mobile activities. Firms accept to bear a higher tax rate in order to bene…t from agglomeration economies and from local public goods. This leads to a "race to the top" instead of a "race to the bottom", as described by the vast body of literature on tax competition.

The main purpose of this paper is to assess the existence and the magnitude of the taxable agglomeration rent, by taking into account the tax interdependencies among the French local tax setting. In order to perform that test, we estimate a tax setting equation using a panel data set from 1993 to 2002 and spatial panel econometric techniques.

We essentially con…rm a positive relationship between the potential tax base and the tax rate, suggesting the existence of a "taxable agglomeration rent"for urban governments. We also observe signi…cant mimic behaviour between the French localities when they choose their rate of local business tax as well as the existence of a vertical interaction between municipalities and counties. Our paper is in line with the growing empirical literature which generally con…rm the positive relationship between competing regions (or states), that is the existence of horizontal externalities, and provide some strong empirical support for the hypothesis of vertical tax interactions between the federal government and lower layers of government but obtain contrasting results with respect to the sign of the vertical reaction functions (see [START_REF] Goodspeed | Tax structure in federation[END_REF][START_REF] Goodspeed | Tax competition and tax structure in open federal economies: Evidence from OECD countries with implications for the European Union[END_REF][START_REF] Hayashi | An empirical analysis of intergovernmental tax interaction: The case of business income taxes in Canada[END_REF][START_REF] Brett | The determinants of municipal tax rates in British Columbia[END_REF][START_REF] Revelli | Spatial patterns in local taxation: tax mimicking or error mimicking?[END_REF]Esteller-Moré and Solé-Ollé, 2003;Andersson, Aronsson and Wikström, 2004).

The structure of the paper is as follows. In the next section we present a simple model of new economic geography with tax interactions in order to derive testable hypotheses. The third section presents the econometric procedure we use in the empirical analysis and the data set based on local business taxation for the period 1993 to 2002. Main results arise in section 4.

The …fth section concludes.

Theoretical considerations: An economic geography model with …scal interactions

In order to understand how agglomeration forces in ‡uence the local tax setting, we develop an economic geography model with a mobile capital model without income e¤ect. Local governments tax local capital and produce a local public good which bene…t to all residents of the municipalities.

Assumptions

Our model is a very simple two regions model, with a quasi-linear quadratic utility function .

Following [START_REF] Ottaviano | Market size and tax competition[END_REF], we use a linear foot-loose capital (FC) model, initially developed by [START_REF] Ottaviano | Home market e¤ects and the (in)e¢ ciency of international specialization[END_REF]. A very clear description of this model is given by [START_REF] Baldwin | Public Policies and Economic Geography[END_REF], more precisely in chapter 5, section 2. In this kind of model, capital is mobile and its spatial distribution gives the spatial equilibrium. As owners of capital, who are also labourers, are immobile, capital can be invested in one region and owned by someone living in the other region.

There are two regions, two factors of production, and two private sectors. We also consider two local governments. The traditional sector, A, is perfectly competitive, under constant returns to scale, and employs only labour. The good produced by this sector is freely tradable and, after normalisation of the marginal cost of production and considering this good as numéraire, price and wage are equal to unity.

The manufacturing sector, M, employs labour and capital, and is in monopolistic competition and under increasing returns to scale: there is a …xed cost, in terms of capital, in production function. Since wage is unity, the total cost of producing x units of a variety of the M good is J + a m x. Where J is the number of unities of capital employed to produce one variety (a …xed cost), and a m the variable cost in labour. J determines the number of …rms and therefore the number of varieties produced, N. is the net remuneration of capital.

Transport of a manufacturing good from one region to the other costs units of the A good.

Consumers localised in region j maximise the quasi-linear quadratic utility function:

U j = Z n 1 +n 2 i=0 c i d i 2 Z n 1 +n 2 i=0 c 2 i d i 2 Z n 1 +n 2 i=0 c i d i 2 + C A + H (G j )
where c i is consumption of variety i of the M good, C A is the consumption of the A good and n 1 and n 2 are the number of varieties produced in region 1 and 2. expresses the preference for the M goods, (> ) the preference for variety, and the substitutability between di¤erent varieties.

H is a function, concave in G j , the local public spending in region j.

Capital is mobile and is owned by workers who are immobile. As capital is mobile, it can be employed in one region while its owner is located in the other. The location of capital depends on the net return on capital in each region and determines the spatial equilibrium. s L L 1 =L is the share of total labour which is localised and employed in region 1. s K K 1 =K is the share of total capital owned by workers localised in region 1 and s 1 is the share of capital employed in region 1. We suppose that each layer of local government plays Nash relative to the two other layers of government. This means that each layer of government will set its own tax rate in order to maximise the indirect utility function of consumers subject to its budget constraint.

Local governments produce G j public goods.

Short-run location equilibrium

Short run equilibrium on private sectors, A and M, are the same as without governments, since public goods do not interact with private choices. In equilibrium, the prices of manufactured goods produced in region 1 and consumed respectively in region 1 and in region 2 are equal to

p 11 = 1 2 2 [a + a m (b + cN )] + cn 2 2b + cN ; p 12 = p 11 + 2 (b + cn 1 ) 2b + cN
Prices of manufactured goods produced in region2 are: p 22 = p 11 + (n 1 n 2 ) c 2(2b+cN ) ; p 21 = p 11 + 2 . Where N = n 1 n 2 are the total number of …rms and the …rms localised in region 1 and 2, and a + (N 1) , b a , c b . c measures the substitutability of goods and is therefore an inverse index of preference for diversity. The net return rate on capital in region 1 is equal to

1 = (b + CN ) (p 11 a m ) 2 M 1 + (p 12 a m ) 2 M 2 j t 1
where

M 1 = s L L + s K K and M 2 = (1 s L )L + (1 s K )K
n 1 = s 1 K L
, where s 1 is the share of manufacturing goods produced in region 1. We normalize K = J and then N = 1; n 1 = s 1 and n 2 = 1 s 1 . For having trade between regions, we have to assume that < trade 2(a bam) 2b+c

[see [START_REF] Baldwin | Public Policies and Economic Geography[END_REF] for details].

Long-run location equilibrium

Long-run location equilibrium is characterized by no incitation for capital to move from one region to the other, i.e. when the net return on capital localised in one region is greater than the net remuneration in the other:

1 = 2 , 0 < n 1 < 1, 1 > 2 , n 1 = 1, and 2 > 1 , n 2 = 1.
Spatial distribution of capital given the non-agglomerated equilibrium is equal to

n 1 = 1 2 + 2(2a 2ba m b ) c s E 1 2 2K(2b + c)(t 1 t 2 ) 2 c(b + c)M | {z } A (2) with s E M 1 M and M = M 1 + M 2 = K + L.
This equilibrium spatial distribution is the same as without taxation except the term A.

The tax rate di¤erential obviously decreases the attraction of the region. The more the share of capital in M is, the less important this impact is. Conversely, the more important are the trade cost the less the local tax rate di¤erential in ‡uences the equilibrium location. Otherwise the agglomerations forces and mechanisms are the same as those present in the linear FC model.

Local governments'behaviour and tax competition

The maximisation problem for the local level is: M axH

t j (G j ) subject to G j = t j n j K j . H is concave in G j .
To illustrate our purpose, we choose the simplest concave function: H =G j 2G 2 j . In spatial equilibrium, local taxes rate that maximise the public objective functions are equals to:

t 1 = (b + c) 3K(2b + c) + 3 4 c M + (2ba m + b 2a) 1 2 M M 1 (3) t 2 = t 1 (b + c)(2ba m + b 2a) (M 2M 1 ) 3K(2b + c) When regions have the same size ( M 1 = M 2 = 1 2 M
), the local tax rates in Nash equilibrium are the same and they increase with the size of total demand (M ), with the transport cost and with goods' substitutability, c. As in [START_REF] Baldwin | Public Policies and Economic Geography[END_REF], when regions are identical, agglomeration forces, assessed by preference for diversity and integration process, make tax competition harder: equilibrium tax rates decrease with agglomeration forces.

Since 2ba m + b 2a < 0 under the trade condition, when regions are di¤erent, the relative size of the local demand ( M i =M ) increases this optimal tax rate and the higher the trade cost, the larger this e¤ect is. It is also worth noting that the government in a larger region can tax more than the smaller region. At this stage, we therefore …nd the same results as Ottaviano and van Ypersele (forthcoming) and others before: there is an agglomeration rent for large regions and horizontal interactions between local governments depends on the size of each locality.

This results of a simple economic geography model lead to two main predictions that we will test in the following section. First of all, when jurisdictions are identical, tax competition is harder with agglomeration forces. The horizontal tax interactions between agglomerations are therefore strong. Secondly, because of the agglomeration rent, the relationship between tax rate and tax base should be positive in cities; the larger the tax base, the higher the tax rate.

3 Empirical framework, econometric procedure and data

Our main empirical purpose is to assess the existence of the taxable agglomeration rent in the French local tax setting by also taking into account the possible existence of tax interdependencies, horizontal tax interactions among municipalities but also vertical tax externalities between …rst jurisdictions and counties and second between jurisdictions and regions. We therefore have to use an appropriate econometric model taking into account spatial interactions.

The French institutional and urbanisation context

The urban employment centers where employment is at least 5,000. Note that the French de…nition of urban areas in this typology is rather broad and matches rather closely that of metropolitan areas in the US except that the threshold is much below (5,000 jobs instead of 100,000 inhabitants).

We focus on the most populated municipalities in each urban center. Thus, our sample contains 342 urban municipalities.

3.2 Econometric procedure and empirical framework

Econometric procedure

The presence of …scal externalities may imply that the tax rates set by any given local government depend upon the other-tier authorities' tax rates as well as upon the tax rates set by other horizontally related governments. However, the sign of the tax reaction functions is theoretically ambiguous (Esteller-Moré and Sollé-Ollé 2002). In the empirical literature, most of the papers have focused on the horizontal tax interdependencies (Ladd 1993;[START_REF] Case | Interstate tax competition after TRA86[END_REF]Besley and Case 1995ab;[START_REF] Feld | Le mimétisme …scal: une application aux régions françaises[END_REF][START_REF] Heyndels | Tax mimicking among belgian municipalities[END_REF][START_REF] Buettner | Local capital income taxation and competition for capital: The choice of the tax rate[END_REF][START_REF] Brueckner | Do local governments engage in strategic property-tax competition ?[END_REF][START_REF] Richard | Dynamiques des interactions …scales entre les communes belges 1984-1997[END_REF][START_REF] Leprince | Business tax interactions among levels of local governments: An empirical analysis of the French case[END_REF]. All of them have found evidence of positive interactions among tax rates of competing jurisdictions. More recent papers try to assess the existence and the magnitude of tax interdependencies among di¤erent levels of government taking into account both types of externalities, horizontal and vertical (see [START_REF] Goodspeed | Tax structure in federation[END_REF][START_REF] Goodspeed | Tax competition and tax structure in open federal economies: Evidence from OECD countries with implications for the European Union[END_REF][START_REF] Hayashi | An empirical analysis of intergovernmental tax interaction: The case of business income taxes in Canada[END_REF][START_REF] Brett | The determinants of municipal tax rates in British Columbia[END_REF][START_REF] Revelli | Spatial patterns in local taxation: tax mimicking or error mimicking?[END_REF]Esteller-Moré and Solé-Ollé 2003;Andersson, Aronsson and Wikström 2004). These papers generally con…rm the positive relationship between competing jurisdictions tax choices and provide some strong empirical support for the hypothesis of vertical tax interactions between the federal government and lower layers of government but obtain contrasting results with respect to the sign of the vertical reaction functions.

Here we aim at testing the existence of a taxable rent in the local tax setting by using a panel of 342 municipalities whose …scal choices are observed between 1993 and 2002. As we also take into account the existence of tax interactions, we estimate a model with spatial interactions using panel data. In spatial research, two problems may arise when panel data have a locational component [START_REF] Elhorst | Speci…cation and estimation of spatial panel data models[END_REF]. The …rst problem is spatial heterogeneity, which can be de…ned as parameters that are not homogeneous throughout the data set but vary with location. The second problem is that spatial dependence may exist between the observations at each point in time. The main reason that one observation associated with a location may depend on observations at other locations is that distance a¤ects economic behaviour. Each agent may change its economic decisions depending on the market conditions in the region of location compared to other regions and on the distance to these regions. This paper is related to this second issue as our model relies on spatial interaction between governments tax decisions.

To model spatial dependence between observations, the model may take the form of a spatial autoregressive process in the error term (spatial error case) or in the variable to explain (spatial lag case). The spatial econometric literature has shown that OLS estimation in models with spatial e¤ects is inappropriate. In the case of spatial error autocorrelation, the OLS estimator of the response parameters, while unbiased, loses its property of e¢ ciency. In the case of a spatially lagged dependent variable, the OLS estimator of the parameters not only loses its property of unbiasedness but also its consistency. A suggested method to overcome these problems is to estimate the model by the maximum likelihood (ML) method (see [START_REF] Anselin | Spatial econometrics: Methods and models[END_REF][START_REF] Anselin | Spatial econometrics in practice; a review f software options[END_REF].

Panel data models including either a spatially lagged dependent variable or spatial error autocorrelation are not very well documented in the spatial econometrics literature. Recently, [START_REF] Elhorst | Panel data models extended to spatial error autocorrelation or a spatially lagged dependent variable[END_REF] surveys panel data models extended to either spatial error autocorrelation or a spatially lagged dependent variable.

The aim of the present paper is to account for spatial dependence in a panel data context. In the classical …xed e¤ect panel data model 1 , spatial dependence is accounted for by including a spatially lagged term of the dependent variable so that the model assumes the following notation:

i;t = i + W i;t + X i;t + " i;t (4)
with i (i = 1; : : : ; N ) denoting jurisdictions, and t (t = 1; : : : ; T ), denoting time periods.

The dependent variable is the local tax rate set by each jurisdiction. W is the weight matrix, is the so-called spatial-autoregressive, and " i is the classical i.i.d. error. It should be noted that i are assumed to be …xed parameters and account for any jurisdictional-speci…c e¤ect not included in the regression equation.

All spatial dependence e¤ect is assumed to be captured by the spatially lagged variable term.

This model takes the name of …xed e¤ ect spatial lag model. The standard estimation method for the …xed e¤ect model is to eliminate the intercept term from the regression equation by taking the variables in deviation of their average in time, and then using OLS. Instead of estimating the demeaned equation by OLS, it can also be estimated by ML. The only di¤erence is that ML estimators do not make corrections for the degree of freedoms [START_REF] Elhorst | Speci…cation and estimation of spatial panel data models[END_REF]. A simple two-stage procedure can be used to maximize the log-likelihood function of this model [START_REF] Anselin | Spatial econometrics: Methods and models[END_REF].

The alternative way to incorporate the spatial e¤ects is called …xed e¤ ect spatial error model.

The spatial e¤ects are then incorporated in the error term, assuming that:

i;t = i + i;t + " i;t (5)
" i;t = W " i;t + i ( 6
)
where W is the spatial weight matrix, is the spatial autocorrelation coe¢ cient and the i are assumed to be i.i.d. The parameters may be also estimated by using maximum likelihood method. In this case, an iterative two-stage procedure can be used to maximize the log-likelihood function of this model [START_REF] Anselin | Spatial econometrics: Methods and models[END_REF].

1 Fixed e¤ect model is particularly indicated when the regression analysis is limited to a precise set of jurisdictions. Random e¤ect, instead, in an appropriate speci…cation when a certain number of jurisdictions is randomly drawn from a large set of jurisdictions (see [START_REF] Baltagi | Companion to Theoretical Econometrics[END_REF], for more details). [START_REF] Anselin | Spatial econometrics in practice; a review f software options[END_REF] give instructions on how to implement both procedures in routines written for spatial cross section but that can be generalized to spatial panel models. Thus, in this paper we use the routines of spatial lag model (SAR) and spatial error model (SEM) developed by Paul Elhorst and which are freely downloadable on the James P. LeSage's website www.spatial-econometrics.com.

Concerning the spatial weight matrix, there are several ways in which a jurisdiction can be neighbour to another jurisdiction. Following the empirical literature, we …rst choose arbitrarily a geographical de…nition of neighbourhood. In this case, the weighted matrix will assign higher values to jurisdictions geographically close. More precisely, we use the Euclidian distance between each jurisdiction's centroid to build our set of weights, so that:

w d ij = 1=d ij P j 1=d ij
where is the ij element of the weighted matrix W d and d ij is the Euclidian distance between the centroid of jurisdiction i and jurisdiction j. This distance decay matrix is standardized.

A second way to deal with neighbourhood is to test whether or not jurisdictions follow some leaders such as the most populated jurisdictions. In this case, a higher weight is assigned to jurisdictions with higher value of population. We also take into account the geographical proximity in this third standardized matrix where:

w P op=d ij = P op j =d ij P j P op j =d ij
An alternative way to deal with proximity is to consider a demographic criterion. We assign a higher weight to the tax choice of a jursidiction j that is similar (on a population criterion) to a jurisdiction i. In this case,

w dem ij = 1 jP op i P op j j j=342 X j=1 j6 =i 1 jP op i P op j j
A fourth way of considering weights is based on a contiguity matrix, where the value 1 is assigned if two jurisdictions share the same border and 0 otherwise. We can not use this matrix because our jurisdictions do not necessarily share a border.

Empirical framework

To assess the existence of a taxable agglomeration rent in the local tax setting, one has to test the relationship between the tax rate and the …scal base and to control for possible horizontal as well as vertical tax interdependencies. Therefore, we will use the appropriate econometric speci…cation and estimation procedure based on spatial statistics developed in the previous subsection. The empirical study of local tax setting is also conducted by controlling for speci…c socio-economic factors which might a¤ect the local tax choices. We therefore include several socio-economic characteristics of jurisdiction. Thus, the relation ( 4) can be rewritten as: Base i;t is the …scal base per capita of each municipality in year t: A signi…cant and positive sign for 3 means that there is a taxable rent in the jurisdictions.

i;t = i + W i;t + 1 t R i;t +
Density i;t and Income i;t are respectively the population density and the income per capita of juridiction i in year t. Elec i;t 1 is a dummy variable which takes the value 1 the year before the municipal election, and zero otherwise.

Elec i;t is a dummy variable which takes the value 1 for each election year, and zero otherwise.

Elec i;t+1 is a dummy variable which takes the value 1 the year after the election, and zero otherwise. An opportunistic cycle is veri…ed if 6 and/or 7 are statistically di¤erent from zero and inferior to zero while 8 is signi…cantly positive. Both variables Ad_rate i;t and S_rate i;t are dummy variables which take the value 1 when the municipality i belongs respectively to an addititional rate regime and a single rate regime in year t:This will be discussed later in the section on data set.

" i;t is a the classical i.i.d. error.

One additional problem might arise: the possible endogeneity of three variables, that is the county rate, the regional rate and the tax base. To evaluate the existence of this problem, we use a Hausman exogeneity test [START_REF] Hausman | Speci…cation tests in econometrics[END_REF], using various instruments for each variable, that is variables that are correlated with business tax rates but are uncorrelated with the regression error2 . We conclude to the exogeneity of these three variables.

Data set

In order to test the tax interdependence hypothesis, we use data the business tax rates set by the French localities, counties and regions for the period 1993-2002. These data come from the Direction Générale des Collectivités Locales (DGCL, Ministère de l'Intérieur) and from di¤erent French census. Table 1 in appendix provides some descriptive statistics for each variable used.

As noted above, local tax policies also re ‡ect the impact of di¤erences in economic and demographic factors grouped in the vector X in equation ( 4). Following the empirical literature, we include two sets of variables: the …rst one is an economic resource variable: the local business tax base. The expected sign is positive, due to the existence of a taxable rent.

the second data set is composed of "expenditure needs"variables, such as the density and the personal income per capita. The expected signs are positive. Indeed, one …nds that the higher this expenditure needs variables, the heavier the …scal burden, the higher the tax rates.

the third data set is linked to the political cycle 3 . We introduce three dummy variables to check the existence of an opportunistic cycle that would characterizes the budgetary choices of our jurisidictions. the …nal data set concerns the tax regime of the jurisdiction. There are three possibilities.

First, the municipality does not belong to any groups of localities and therefore alone …xes its tax rate. When municipalities belong to a group of localities with its own taxation, there are two cases; either the municipality keeps its own taxation and the jurisdictional taxation is additional (Ad_rate i;t = 1), or there is a single tax rate for all municipalities that belong to the group (S_rate i;t = 1).

Results

Our goal is to test the presence of …scal externalities which may imply that the tax rates set by any given local government depend upon the tax rates set by other horizontally related business tax rates for the county (resp. region) to explain the cross-sectional variation in the county's (resp. regional) tax rates. For the tax base, we use the share of old people (more than sixty years old) and the share of scholars in the municipality.

3 French municipal elections hold each 6 years and permit to design a political assembly formed by elected members (named "conseil municipal") whose number depends on the size of population. The ballot is a proportional representation list system with two rounds. The election years on the period 1993-2002 are 1995 and 2001. governments, that is the equation ( 7), which represents the reaction function of one jurisdiction's tax choice to other jurisdictions decisions. Therefore, we never tested the spatial lag model against the spatial error model. Column 1 shows the estimation results of the model without …xed e¤ects and without spatial lag. We then run spatial tests that indicate the presence of spatial correlation. We thus tested the …xed e¤ects spatial lag model against the spatial lag model without …xed e¤ects (column 2). We have rejected the latter as the spatial lag model with spatial (or jurisdiction) …xed e¤ects gives the better results. The results of the spatial lag model with time period …xed e¤ects are not presented as they did not give better results than the spatial lag model without …xed e¤ects. Columns 3 to 5 report the regression results of the model with spatially lagged dependent variable with spatial (or jurisdiction) …xed e¤ets using ML method with respect to three weight matrices based respectively on demographic proximity W dem , on distance W d and on population and distance W P op=d . Columns 3 to 5 show the estimation results of the model with spatially lagged dependent variable and with spatial …xed e¤ects respectively for each weight matrix. Finally, table 3 in appendix shows the estimation results of the model with spatially lagged dependent variable but without spatial …xed e¤ects using the two other weight matrices. These results suggest that jurisdictions can tax more as their local tax base increases and that there is a taxable rent in the urban jurisdictions in France.

Let us turn to the estimates of the three tax parameters: the horizontal tax interaction parameter, the vertical tax interaction parameter between counties and municipalities and the vertical tax interaction parameter between municipalities and regions.

First, for both matrices based on distance, we …nd that the coe¢ cient of the local business tax rate of the jurisdictions is signi…cant and positive. On the other hand, there is no interaction using the demographic matrix4 . The results show that horizontal …scal interactions between neighbouring jurisdictions are quite strong. With both weight matrices based on distance (columns 4 and 5), the estimate takes a value of about 0; 285. This implies that an average business tax increase of 10% in the neighbouring municipalities induces an increase of around 3% in the jurisdictional business tax rate. This result suggests that jurisdictions mainly look at their geographical neighbours to set their tax choices. This result can be explained by a standard tax competition argument. Indeed, French jurisdictions tend to develop strong local economic programs to maintain or attract some new …rms. Municipalities might thus want to remain attractive with respect to their competing neighbours and engage themselves in a strategy of 'copy cat'in the business tax rates. One can note that this result of horizontal tax interactions in the French jurisdictional case is close to those obtained in previous tests in di¤erent countries.

In the USA, [START_REF] Ladd | Mimicking of local tax burdens among neighboring countries[END_REF] obtains estimates of the spatial correlation coe¢ cient between counties' tax burdens that range form 0; 45 to 0; 8 while in Europe Heyndels and Vuchelen (1998) using a cross-section of 589 Belgian municipalities conclude to a mimicking behaviour amongst these local jurisdictions, the estimates of the spatial correlation coe¢ cient ranging form 0; 5 to 0; 7. In the French case, our result at the jurisdictional level of local government is also consistent with those obtained by Jayet, Paty and Pentel (2002) using a sample of northern France municipalities.

Second, the tax parameter 1 associated to the regional rate is indeed never signi…cant in any speci…cation. Thus the estimation of the spatial tax model with two overlapping levels of local government leads to reject the hypothesis of business tax interactions between French counties and regions. This result might be explained by the vertical structure of the aggregate tax rates paid by French business taxpayers. Indeed, regional tax rates account for a small part (around 10%) of the sum of the municipal, county and regional rates, whereas the …rst two rates respectively account for 60% and 30% of the sum. Regional tax rates might thus have no e¤ect on the tax behaviour of jurisdisctions.

Furthermore, the county tax rate is statistically signi…cant and the estimate of its parameter has a positive sign in the three colums. The estimate of parameter 2 takes a value of about 0; 034 using both weight matrices based on distance. This result suggests that for the business tax, county tax rates and municipal tax rates are strategic complements. More precisely, this means that a tax increase of 10% in the county tax rates induces an increase of around 0,3 % in the jurisdictional business tax rate. Studies in the existing literature often conclude to a signi…cant positive interdependence between di¤erent layers of governments in a federal system. [START_REF] Goodspeed | Tax structure in federation[END_REF][START_REF] Goodspeed | Tax competition and tax structure in open federal economies: Evidence from OECD countries with implications for the European Union[END_REF] con…rms the existence of vertical income tax externalities in the OECD countries. Esteller-Moré and Solé-Ollé ( 2001) show a positive response of state tax rates to changes in the federal income tax rate in the USA. They also provide evidence of a signi…cant and positive response of provincial tax rates to changes in the federal income tax rate in Canada (Esteller-Moré and Solé-Ollé, 2002). [START_REF] Brett | The determinants of municipal tax rates in British Columbia[END_REF] demonstrate some evidence that municipal tax rates are sensitive to taxes set on the same base by super-municipal bodies in the province of British Columbia. However, [START_REF] Revelli | Spatial patterns in local taxation: tax mimicking or error mimicking?[END_REF] shows the absence of correlation in property tax rates between lower tier (district) authorities and upper tier (county) authorities in UK In the French case, this result can be explained by the complementarity of public services provided by municipalities and counties. Major public infrastructures and capital spending in primary schools provided by municipalities might indeed increase the marginal utility of social services and capital spending in secondary schools provided by counties.

Concerning the other control variables, another interesting result concerns the political dummies which con…rm the existence of an apportunistic cycle in the tax choices. Jurisdictions tend to decrease their tax before and during the year of election while they increase their tax rate the year after the election. The density exhibits a negative sign (in the model with …xed e¤ects) which means that there is probably some economies of scale in the supply of local public goods.

The parameter associated to the income per capita is positive (also in the model with …xed e¤ects). This result captures the positive e¤ect of income per capita on the demand in local public services, hence on business tax rates. Finally, concerning the tax regime, we observe the expected results: the choice of an additional tax regime has no e¤ect on jurisdictional tax rates while municipalities that have chosen a single tax rate tend to set higher tax rates than the others.

Conclusion

The main purpose of this paper is to test the existence of a taxable rent in the French local tax setting by taking account the tax interactions among the jurisdictions. First we build a simple economic geography model with …scal interactions. We estimate a model of tax setting for the local business tax using the econometrics techniques on panel data for 1993 to 2002. We observe that the relationship between tax rate and …scal base gives presumption of the existence of a "taxable agglomeration rent" in the local French setting.

  are the numbers of consumers in each region and t 1 is the local government tax rate. The clearing condition on capital market requires:

  French local institutional context is characterized by three tiers of overlapping local governments. The lowest tier is made up of 36,000 local jurisdictions or localities. The middle-tier consists of 96 counties. Finally, 22 regions are at the highest level of local government. Municipalities are responsible for local urban services, building, and maintaining nursery and primary schools and sport facilities, municipal roads and urban public transport. Counties are in charge of administering social assistance, county roads and maintaining middle schools. Regions are responsible for vocational training, economic development and building and maintaining high schools. Local revenues mainly come from taxation (54%) and grants (23%). The local business tax or 'taxe professionnelle' accounts for approximately 45% of revenues from local taxation.

Its base is the same for the three layers of local governments and is mainly made up of capital goods. Furthermore, regions, counties and municipalities have a large autonomy to set their tax rate on that tax base. Even though the local business tax reaches a maximum and a lot of …rms are exempted for this taxation .

Municipalities are distributed among rural and urban employment centers, de…ned by the French National Statistics Institution (INSEE). In 1999, metropolitan France contained 360

  2 t D i;t + 3 Base i;t + 4 Density + 5 Income i;t (7) + 6 Elec i;t 1 + 7 Elec i;t + 8 Elec i;t+1 + 9 Ad_rate i;t + 10 S_rate i;t + " i;t

with:

i;t represents local business tax rate of the municipality i in year t: t R i;t is the regional tax rate and t D i;t represents the tax rate of the county to which jurisdiction i belongs.

Table 2 :

 2 Estimation results of the model with spatial …xed e¤ectsThe most important results in table 2 are the estimates of the parameter for the local tax base. We …nd a positive and signi…cant sign for the local tax base in the model with …xed e¤ects.

		(1)	(2)	(3)	(4)	(5)
	Weight matrix	-	W d	W dem	W d	W P op=d
	Estimation method	OLS	ML	ML	ML	ML
			0.591**	0.045	0.289**	0.282**
		-
			(0.000)	(0.291)	(0.000)	(0.000)
	Regional rate	0.076**	0.065**	0.032*	0.020	0.020
		(0.001)	(0.005)	( 0.073)	(0.262)	(0.258)
	County rate	0.286**	0.236**	0.041*	0.034*	0.033*
		(<.000)	(0.000)	(0.016)	(0.044)	(0.046)
	Fiscal base p.c.	-0.072	-0.052**	0.056**	0.055**	0.055**
		(<.000)	(0.000)	(0.000)	(0.000)	(0.000)
	Density	0.072	0.074**	-0.166*	-0.144*	-0.144*
		(<.000)	(0.000)	(0.013)	(0.031)	(0.031)
	Income p.c.	-0.050*	-0.139**	0.338**	0.265**	0.266**
		(0.087)	(0.000)	(0.000)	(0.000)	(0.000)
	Election year (t-1)	-0.013	-0.004	-0.009*	-0.006	-0.007
		(0.234)	(0.664)	(0.010)	(0.075)	(0.052)
	Election year (t)	-0.017	0.004	-0.012**	-0.008*	-0.008*
		(0.125)	(0.708)	(0.000)	(0.030)	(0.029)
	Election year (t+1)	-0.009	-0.006	0.011**	0.010**	0.010**
		(0.428)	(0.562)	(0.002)	(0.003)	(0.005)
	Additional rate regime	0.002	0.003	-0.001	-0.002	-0.002
		(0.757)	(0.671)	(0.968)	(0.622)	(0.622)
	Single rate regime	0.017	0.007	-0.018*	-0.019**	-0.019**
		(0.223)	(0.580)	(0.003)	(0.001)	(0.002)
	Intercept	2.646**	1.737**	-	-	-
		(<.000)	(0.000)
	Jurisdiction …xed e¤ects	no	no	yes	yes	yes
	R 2	0.19	0.25	0.92	0.92	0.92
	Log-likelihood	-	92.312	4112.48	4138.39	4137.16
	Observations	342	342	342	342	342
	Note: all variables are log-transformed. Probability values are given into brackets. **:
	signi…cant at 5%. *: signi…cant at 10%.

Table 1

 1

	: summary statitics
	Variable	Mean	Maximum Minimum Standard dev.
	Population	45866	2143364	4845	131597
	Local business tax rate (%)	16.15	29.53	5.54	4.09
	County's business tax rate (%)	7.06	12.36	0	1.81
	Regional business tax rate (%)	2.17	3.33	0	0.42
	Fiscal base (euros/inhabitant)	1888.27 9435.16	189.94	1003.18
	Density (inhabitants/km 2 )	1354.56 20335.52	35.11	1684.44
	Income per capita (euros/inhabitant) 7081.71 18384.49	3701.27	1075.60

Table 3 :

 3 Estimation results of the model without …xed e¤ets

		(1)	(2)
	Weight matrix	W dem	W P op=d
	Estimation method	ML	ML
		0.156**	0.588**
		(0.000)	(0.000)
	Regional rate	0.075**	0.067**
		(0.002)	(0.004)
	County rate	0.283**	0.235**
		(0.000)	(0.000)
	Fiscal base p.c.	-0.059**	-0.052**
		(0.000)	(0.000)
	Density	0.063**	0.075**
		(0.000)	(0.000)
	Income p.c.	-0.097**	-0.140**
		(0.001)	(0.000)
	Election year (t-1)	-0.009	-0.005
		(0.429)	(0.594)
	Election year (t)	-0.009	-0.004
		(0.404)	(0.712)
	Election year (t+1)	-0.004	-0.007
		(0.705)	(0.511)
	Additional rate regime	0.002	0.003
		(0.760)	(0.689)
	Single rate regime	0.014	0.007
		(0.306)	(0.565)
	cst	2.591**	1.749**
		(0.000)	(0.000)
	Jurisdiction …xed e¤ects	no	no
	R 2	0.20	0.25
	Log-likelihood	-7.47	91.84
	6 References

To test the possible endogeneity of the county's and the regional tax rates, we use as instruments some lagged

Another possible explanation of tax interactions among jurisdictions could be related to a common "intellectual" trend, as suggested by[START_REF] Manski | Identi…cation of endogenous social e¤ects: The re ‡ection problem[END_REF]. If this was the case, we should observe the same level of interactions for all matrices.


domain: math info sdv

text:
Anne Goelzer

Bekkal Fadia

Vincent Brikci

A first analysis of the central carbon pathway of Bacillus subtilis: Integration of both genetic and enzymatic levels in regulations

A first analysis of the central carbon pathway of Bacillus subtilis

Integration of both genetic and enzymatic levels in regulations

Anne GOELZER, Fadia BEKKAL BRIKCI, and Vincent FROMION INRA, Unité Mathématique Informatique et Génome, Jouy-en-Josas, France A challenging problem in systems biology consists in developing tools and methods to apprehend high-dimension dynamic systems in order to understand the global coordination of metabolic pathways in response to environmental changes. The recent module definition proposed by [1] combining both the genetic and metabolic levels allows to break down the metabolic network into subsystems with a simplified behavior in steadystate [START_REF] Bekkal-Brikci | preparation. This work was supported by ANR Dynamocell (NT05-2-44860) and by the BaSysBio european project[END_REF]. We illustrate this definition through the mathematical analysis of the central carbon pathway of Bacillus subtilis. The main players of this regulation structure are identified and we explain the global coordination of this pathway. Contact : anne.goelzer@jouy.inra.fr A first dynamic model combining both the metabolic and genetic levels can be built : Genetic level, 38 ODEs such as

Modular representation of the central carbon pathway

• E i (t) = g E (T F i (t)) -µE i (t)
Metabolic level, 43 ODEs such as

• x(t) = f i (x i-1 , x i )E i (t) -f i+1 (x i , x i+1 )E i+1 (t)
with µ, the growth rate ; E i , the concentration of the enzyme E i ; T F i , the concentration of the i-th transcription factor bound to DNA ; g E , modulation of the enzyme synthesis ; x i , the concentration of the metabolite X i ; f i , the reaction rate of the enzyme E i .

=⇒ High dimensional model (Total : 81 ODEs !) : currently unsolvable.

=⇒ Break down the system into modules to reduce the complexity.

The mathematical analysis of this model allows to determine (i) if the known regulation structure is compatible with anabolism requirements ; (ii) the role of each regulation loop ; (iii) the main players/steps which determine the steady-state behavior.

Mathematical analysis of the dynamic model

Simplification of the dynamic model

Elementary modules are identified according to the definition in [1].

Conditions of existence of the steady-state

for each module and for their interconnection : enzymes should not saturate ; key role of irreversible enzymes ; unicity of the steady-state.

=⇒ determination of key steps/metabolites.

Sensitivity analysis

with respect to small flux perturbations in anabolism requirements :

• on each module : behavior prediction of each module component (metabolites and enzymes concentration, fluxes) ;

• on the interconnection between modules : identification of the sensing signals (metabolite pools) responsible for the general coordination, and the nature of the information carried by these signals.

Systemic interpretation of the regulation structure

Identification of the four key metabolites essential for the modules coordination

• fructose-1,6-biphosphate (FBP) : modulates (i) the glucose uptake, (ii) the flux of the lower part of glycolysis through CggR, (iii) the fluxes repartition between the TCA cycle and the acetate excretion through CcpA ; =⇒ global coordinator of the central carbon pathway ;

• pyruvate (PYR) : reflects the needs in branched-chain and aromatic amino-acids, serine derivatives ;

• oxaloacetate (OAA) : reflects the needs in aspartate derivatives ; • 2-oxoglutarate (AKG) : reflects the needs in glutamate derivatives.

Complementary roles of the genetic and metabolic regulations

Only the integration of both regulation loops levels reveals the control structure behavior.

Genetic regulations :

• CggR : modulates the flux through the lower part of glycolysis according to the state of the FBP pool ;

• CcpA : controls the flux repartition between the TCA cycle and the acetate excretion according to the state of PTS glucose transporter ;

• CcpC : induces the TCA cycle if the citrate pool (toxic) is increasing.

Enzymatic regulations :

• HPr kinase/phosphorylase : the glucose input flux is modulated with respect to the state of the FBP pool ;

• fructose-1,6-biphosphate aldolase : the FBP pool is adjusted according to the state of anabolism requirements reflected by the PYR, OAA and AKG pools.


Maxime Cailleret
email: maxime.cailleret@avignon.inra.fr

Hendrik Davi

LIKELY EFFECTS OF CLIMATE CHANGE ON GROWTH OF FAGUS SYLVATICA: STUDY ALONG ALTITUDINAL GRADIENTS AND COMPARISON WITH THE CO-OCCURRING SPECIES ABIES ALBA

Introduction

Forest growth in Mediterranean mountains is limited by two major factors: summer drought at low elevation and low temperatures at high altitude (Korner 2007). As a consequence of climate change, observed trends would be the consequence of the contradictory effects of reduced frost and increased drought (IPCC 2007). On the one hand, an increase of tree growth is expected at higher elevations resulting of warming temperatures, lengthening of growing season (Badeck et al. 2004), and rising atmospheric CO 2 concentrations. On the other hand, late frost damages might not decrease (Hanninen et al. 2006). At the same time, tree growth should be reduced as a consequence of summer drought increase in sites at lower elevations (Jump et al. 2006). The aim of this study was to analyze the effects of altitude and climate change on the growth of European beech (Fagus sylvatica L.) in a Mediterranean mountain. A comparative dendroclimatological study of climate-growth relationships was done. Then, the difference of growth between the North and the South faces and along elevational gradients was assessed. Effects on radial growth of recent climate change since the beginning of the twenty first century were further studied by analyzing global trends and shifts of growth optima. Finally, a comparison with a co-occurring species was done and according to these results, a prediction of their future potential growth and distribution range in the study site was made.

Materials and Methods

The study was conducted on Mont Ventoux, a calcareous mountain in south-eastern France, where beech is located in the mountain vegetation area on the north and south face. On the North face, beech is generally associated with fir. On the north face, 73 firs and 77 beeches were sampled along a continuous elevational transect with the same slope orientation for both species from 970 to 1530 m and were cored in autumn 2006 and 2007. On the south face, 80 beeches in 4 different plots (890m, 1115m, 1410m, and 1525m) were cored in autumn 2007. Dendrochronological analyses were made using the software CooRecorder & CDendro v5.3 (Larsson L.A. et al. 2006, Cybis Elektronik & Data AB. Sweden). To get free from age and date effect, and to compare growth of both species, a polynomial curve was fitted against regional age mean curve of cumulative basal area. Using this function, we projected the cumulative ring area (RA) for all trees at a same age (90 years), which gave theoretical mean of annual area increase at 90 years (RA90). The same methodology was applied to study mean annual growth for the period 2000-2006.

Results and Discussion

Only results on the North face and dealing with the comparison with silver fir were presented here.

Comparison of Beech Ecology with silver fir: two co-occurring species

Climate-growth relationships: Even if these late-successional species are associated on the North face, radial growth-climate relationships were divergent. A positive correlation was found between April temperatures and fir growth. Indeed, it causes earlier budburst and cambium activation that lengthen the growing season and increase the carbon assimilation. Inversely, a significant negative effect of maximal temperatures in April was observed for beech. An earlier budburst increases the risk of late frost damages on open buds and leaves, which can provoke a decrease of radial growth (Dittmar et al. 2006). Drought during the first half of summer (May-July) influenced negatively ring-width of fir. In contrast, beech growth index were not related to summer rainfalls, and a positive role of May temperatures was found. Altitude: Until the end of the 20 th century, fir growth optimum was at intermediate altitude (figure 1b; S3: 1140 to 1240 m) whereas for beech it was at lower elevation (figure 1a; B1 and B2: 950 to 1230 m). Its weak presence below 950 m should probably be due to low recolonization rates from upper sites. Possible presence from about 800 to 1600 m was expected (figure 2a). This concept of optimum of growth potentialities is connected with the existence of two major limiting factors depending on altitude whose impact growth intensity : i) late frost damage and the time of growing period at high elevation and ii) summer drought in the bottom of the gradient.

Climate change effects

Global trend: In South-eastern France, temperatures increase (0.6°C to 0.7°C by decade since 1960) was not matched by rainfalls increase. Our results show that it has provoked a shift of growth optimum to higher altitudes. Since beginning of twenty-first century, most of firs showed a growth decline (52%), with mortality, whereas for beech no significant trend was shown up. In the study area, rising temperatures and decreasing rainfalls (4-27%) are predicted (IPCC 2007). These growth trends would logically go on. Effects on climate events: An earlier budburst results in an increase of damage probabilities due to late frosts (Hanninen et al. 2006). As a consequence, growth of beech at high altitude might be not as much favored as it could be by the temperature increase. 2003 summer was exceptional for the intensity and the length of the heat-wave but it occurred at the end of growing season (most in August). No significant growth decrease was observed during this year because most of the growth rings were produced earlier (Bouriaud 2004). A significant growth decrease took place in 2004 due to the reduction of carbohydrate storage and to the reduced rainfalls during June and July 2004. We found a higher negative response for beech than for fir. The higher sensitivity of beech growth to climate events may be due to the non persistence of its leaves.

Likely modification of species' range

The elevational gradient can be schematized as a curve where the two majors limiting factors progress exponentially with the altitude (figure 2a,2b). The number of frost days and their intensity increase exponentially with the upward shift in altitude. Toward lower altitudes, the frequency, intensity and duration of summer drought increase exponentially owing to the mix of rising of temperatures and decline of rainfalls. In lowest altitudes fir would disappear (figure 2b), but the expected increase of heat-waves (Meehl and Tebaldi 2004) will affect also beech vitality. At high elevation, the upward shift of beech may probably be limited by late frost damages. Silver fir will completely take advantage of the temperature rising and the lengthening of growing season. Distribution range would be reduced since their upward progression thanks to dispersion which will be probably lower than the rising of temperatures.

If extreme events were not taken in account, Abies alba is predicted to face higher risk of extinction than Fagus sylvatica (Ohlemüller et al. 2006). But the probably increase of late frosts, heat-waves frequency and intensity would put beech in a disadvantageous situation.

Figure 1 :

 1 Figure 1: Altitude effect on mean annual ring-area increment (mm²) of Fagus sylvatica (a) and Abies alba (b) for all the period studied (black histogram) and for the period 2000-2006 (grey histogram). Elevational levels are the altitudinal classes (B1 and S1: low altitude to B5 and S5: high altitude). Different letters indicate significant differences between means for the same period (P<0.1, t.test).

Figure 2 :

 2 Figure 2: Actual (a) and likely future (b) distribution range of silver fir (black) and common beech (grey). The two major limiting factors are late frost (number and/or intensity), and summer drought (frequency, intensity and/or duration). The curve is the elevational gradient of the North face of the Mont Ventoux.


text:
Anne Goelzer

Bekkal Fadia

Vincent Brikci

published or not. The documents may come

Integration of genetic and enzymatic controls in metabolic pathways

Fadia BEKKAL-BRIKCI, Anne GOELZER and Vincent FROMION

INRA unité Mathématique Informatique et Génome, France

The bacterial metabolic machinery and its regulation are a complex system and involve many components: metabolites and enzymes. The reconstruction of the regulatory networks of B. subtilis including the enzymatic reactions, the control of enzymatic activities and the genetic regulations (see [START_REF] Goelzer | Reconstruction and analysis of the genetic and metabolic regulatory networks of the central metabolism of Bacillus subtilis[END_REF]) allowed us to identify the main regulation structures of metabolic pathways. We noticed a strong interplay between the metabolic pathways and the genetic regulations. Then, in order to break the intrinsic complexity of such huge system and to reveal somewhat an order, we propose a new suitable notion of subsystems (modules) using mathematical dynamic models associated to these structures. Contact: fbekkalb@jouy.inra.fr

End-product control structure

                 • x 1 = ν 1 -E 1 f 1 (x 1 , x n , p) -E * 1 f * 1 (x 1 ) • x 2 = E 1 f 1 (x 1 , x n ) + E * 1 f * 1 (x 1 ) -E 2 f 2 (x 2 , p) . . . • x n = E n-1 f n-1 (x n-1 , p) -E n f n (x n ) • E 1 = g(x n , q) -µE 1 x i : the concentration of the metabolite X i , E i : the concentration of the enzyme E i ν 1 : the input flux (the flux supply) E n f n (x n ) :
represents the output flux (the flux demand) f i : the reaction rate of the enzyme E i g : the genetic control of E 1 p : a vector of external factors (cofactors) q : a vector of global regulators µ : the growth rate. (i.e V (t) = µV (t))

The study of the equilibrium regime in exponential phase allows us to deduce some biological properties, and the ability to breakdown the huge metabolic network on subsystems(modules).

Equilibrium regime

       Ē1 = g( xn ) µ , f 1 ( x1 , xn )g( xn ) = µE n f n ( xn ), ν 1 = E n f n ( xn ) and for any i = {2, . . . , n -1}, xi = f -1 i E n f n ( xn ) E i . Saturation condition: E i M i = E i lim x i →+∞ f i (x i ) > E n f n ( xn ).

Biological properties of the equilibrium regime

The prediction of the equilibrium behavior of such linear metabolic pathway in the exponential phase can be simple even though it is composed of many reactions

• The end product depends only on the genetic and allosteric controls of the first enzyme E 1 .

• The nature of the intermediate enzymes E 2 , . . . , E n-1 has no impact on the equilibrium regime of the end product concentration and only impact the equilibrium of the intermediate metabolite concentrations.

• The way to increase the output flux is to decrease the end product concentration xn .

• The equilibrium of the intermediate metabolites are increasing when the output flux are increasing.

• The presence of the isoenzyme can allow the metabolic pathway to have a larger flux increasing the concentration of the isoenzyme.

• Cofactors act on (i) the first enzyme E1 (ii) the last enzyme En (iii) the intermediate enzymes.

(i) and (ii)⇒ a direct impact on the equilibrium of the end product, (iii)⇒ no impact on the equilibrium only if it leads to saturate an intermediate step.

• Global regulation is able to modify the enzymes production of many pathways (pleiotropic factors (CcpA,TnrA) [START_REF] Goelzer | Reconstruction and analysis of the genetic and metabolic regulatory networks of the central metabolism of Bacillus subtilis[END_REF]) ⇒ modifies the relation between the end product concentration, the flux demand and the enzyme concentration. For the operon case, it modifies all the concentrations of the pathway.

Although this study concerns the particular end product structure, the obtained results could be extended to other control structures [START_REF] Bekkal-Brikci | Fromion: Integrated enzyme controls in metabolic network analysis[END_REF].

How to break down the huge metabolic network into modules

To reveal an order in such a huge system, we introduce a suitable notion of subsystems (modules).

• The key role of irreversible steps, • The key role of the regulated enzymes and the metabolite associated to their regulations,

• The coordination between different modules: compatibility of the fluxes through key metabolites, coordination with a global regulator.

  Regulation of genes involved in theThreonine module ilvL Also repression by the global IHF regulator Lrp IlvL: peptide leader Ile (5), Val (6) and Leu (4) rich (15 amino acids on 32) Leucine inhibits (but not prevent) Lrp binding Regulation of genes involved in the Isoleucine module Constitutive transcription of: asd


Cédric Tentelier

Cyril Piou

Weirs cause aggregation of Atlantic salmon redds

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction Introduction Introduction

In most populations, competition for resources is local, so aggregation in suboptimal sites curtails population growth rate 1 . If aggregation in suboptimal sites increases at low density (non-ideal despotic distribution), small populations may suffer Allee effects 2 .

Atlantic salmon juveniles undergo local competition for food and shelter. Juvenile distribution is greatly determined by the choice of spawning site, made by mothers 3,[START_REF] Einum | 5 Garcia de Leaniz[END_REF] . This choice may in turn be constrained by obstacles to upstream migration.

Is the distribution of Atlantic salmon redds influenced by obstacles?

Does the density of spawners modulate this influence? Study site: Nivelle river main stream + Lurgorrieta (main tributary), 27.4 km accessible to salmon, 5 weirs > 1.5 m.

Database: map of hydromorphic units suitable for spawning, number of spawning females (estimated from captures at fishways) and location of redds between 1992 and 2006 (weekly census during spawning season).

Analysis: Bivariate point pattern analysis: density of redds within r suitable hydromorphic units downstream from weirs.

Cédric Tentelier & Cyril Piou

Methods

Methods Methods

Results

Results

Results

Discussion

Discussion Discussion

Redds usually aggregated in the first 15 suitable hydromorphic units below weirs.

Aggregation occurred almost every year, at all densities of spawning females in the river.

Redds usually aggregated in the first 15 suitable hydromorphic units below weirs.

Aggregation occurred almost every year, at all densities of spawning females in the river.

  UMR INRA-UPPA Fish behavioural ecology and population biologySt Pée / Nivelle, France cedric.tentelier@univ-pau.fr th centile of 999 random distributions within suitable habitat

Implications for population dynamics: fish accumulation below obstacles is known 5 , but the aggregation of redds below weirs is a new result. This aggregation may lead to high local densities of juveniles, thereby increasing density-dependent effects on population growth. Habitat restoration: if fish prefer to spawn just below obstacles, habitat improvement should be directed to these zones. Also, opening access to a long stretch of river at one go may lead to aggregation at the new upstream limit and underuse of intermediate zones.

N iv e ll e L u r g o r r ie t a France

Spain

The Nivelle river and its weirs


Raffaella Goglia

Marine Spiteri

Marion Henini

Pierre Combris

Louis Georges Soler

Scenario S0: current situation

To what extent can food nutritional quality improvement allow public health goals to be reached?

Conclusions and perspectives

The results give useful insights and show to what extent food modifications can contribute to public health goals. Nevertheless, it would be necessary to take into account the interactions between nutrients. For instance, a decrease in fat may in some cases imply an increase in the sugar content (for technological or sensorial reasons).

The food modifications simulated in the study can be interpreted as the improvement of the Minimum Quality Standard (MQS) -i.e. the enhancement of the lowest nutritional quality itemswithin each food category. The potential magnitude of the effects suggests that such a strategy can constitute a relevant target for the public authorities, which radically differs from the one which would promote quality improvement through differentiated product claims.

To test the significance of nutrient individual consumption evolution, two-sample t statistic tests were performed (α=5%) which allow to compare the current situation with the various scenarios.

Introduction

To face the burden of chronic diseases linked to food consumption, improving nutritional quality of processed foods becomes a crucial issue for health policy makers. This issue raises two questions: to what extent modifications of food composition are feasible and what can be their impacts on health, and what means can be used by policy makers to favor food quality improvement.

The purpose of the study is to contribute to these debates by assessing what can be the potential contribution of food quality modification from a public health point of view. More precisely, we assume that consumers continue to consume the same food products but that the nutritional characteristics of each one of these food products have been improved in a realistic way, i.e. acceptable from technological and sensorial points of view. Then, what could be the impacts on the individual nutritional intakes?

To address this question, detailed data on nutritional characteristics of food items and on individual consumption among representative samples of population are clearly required.

Methods

Food Quality database

In France, Ministries in charge of Food and Agriculture, Health, and Consumption decided to fund the creation of an Observatory of Food Quality (Oqali) in 2008. The goal was to set up an independent system of observation in order to assess the nutritional composition of food items marketed by all the brands present in the French market. In 2010, the Oqali database contains about 15,000 items, representing around 30% of the processed food marketed in France.

We used these data to assess the nutrient composition of individual branded food items among three groups: breakfast cereals (355 items available divided into 29 food categories, covering 75% of the market in 2008), biscuits/pastries (1805 items, 51 food categories, 72% of the market shares in 2008) and bread-based products (620 items, 31 food categories, 57% of the market shares in 2009).

Consumption databases

For each food item, we matched the food quality database with two consumption databases: TNS Kantar Worldpanel (to assess the market shares of each food item delivered to the market) and INCA2 (an individual consumption survey). On this basis, we considered mean consumers of the 3 groups studied for children and adult sub-populations.

Scenario analysis

First, we determined the nutrient composition variability among each product category of breakfast cereals, biscuits/pastries and bread-based products.

Second, we considered several scenarios of food composition modification within each product category, by assuming that the lowest nutritional quality food items were modified in order to reach better quality levels already observed in the food category. Then, for each scenario, we calculated the variation of total quantities of sugars, fat, fiber and sodium delivered to the market. Finally, we determined the variation induced at the individual consumption level by each scenario and assessed the modification of the individual consumption distribution of each of these nutrients among adults and children.

French Observatory of Food Quality The impacts of scenarios on individual consumption for adults and children subpopulations are up to 4.2% for S1, to 8.4% for S2 and to 18.8% for S3, depending on the sector and the nutrient considered. For adults, the greatest impact is observed for each scenario on sugars intakes provided by bread-based products (respectively -2.8%, -5.7% and -13.9%). For children, the strongest impact depends on the scenario considered: for S1 it concerns fat intakes provided by breakfast cereals (-4.2%), for S2 it concerns sodium intakes provided by breakfast cereals (-8.4%) and for S3 it concerns fiber intakes provided by bread-based products (+18.8%).

*significant difference compared with the current situation (α=5%)

-4.2%* 18,8%* -8.4%*

The impacts of scenarios on the total amounts of nutrients delivered to the market are between 1% and 5% for S1, 2% and 9% for S2 and 6% and 22% for S3 depending on the food sector and the nutrient considered. For each scenario, the strongest impact concerns quantities of sugars delivered by bread-based products (-5%, -9% and -22%). For S2, we also observe a great impact on the amount of sodium delivered by breakfast cereals (-9%). Statistical tests show that nutrient individual consumption evolution is significant, for all scenarios and nutrients tested except for fat and fiber adults individual consumption within scenario S1 for breakfast cereals.

Table 1 :

 1

	Results
				Relative
	Food categories	Number of items	Nutrient	interquartile range
				(q3-q1)/q2
			fat	73%
	Honey puffed wheat	13	fiber	36%
			sodium	> 100%
			sugars	31%
	Unflavoured fiber-rich cereals	10	fat fiber	58% 83%
			sodium	52%
			fat	28%
	Fruit fiber-rich cereals	17	fiber	31%
			sodium	29%
			sugars	67%
	Unflavoured corn flakes	12	fat fiber	39% 35%
			sodium	29%
			fat	43%
	Chocolate wheat flakes	23	fiber	42%
			sodium	> 100%
	Chocolate filled cereals	27	fiber sodium	54% 50%
	Unflavoured light cereals	23	fat sodium	33% 38%
	Chocolate light cereals	16	sodium	44%
	Fruit light cereals	24	sodium	43%
			sugars	39%
	Traditional muesli flakes	11	fat fiber	> 100% 25%
			sodium	> 100%
	Fruit crunchy muesli	23	fiber sodium	36% 70%
	Chocolate crunchy muesli	20	fiber sodium	28% > 100%
			fat	69%
	Traditional muesli flakes no added sugars	12	fiber	33%
			sodium	> 100%
			sugars	39%
	Honey frosty wheat flakes	11	fat	83%
			fiber	50%
	Chocolate puffed rice	15	fat	48%
	Honey corn balls		fiber sodium	71% 78%
			fat	50%
	Chocolate puffed cereals	17	fiber	33%
			sodium	60%

Relative interquartile ranges (RIR) greater than 25% for sugars, fat, fiber and sodium content within the categories of breakfast cereals having at least 10 items

We observe a large variability of nutritional composition within food categories: RIR are greater than 50% for 21 cases out of 68, and greater than 25% for 43 cases out of 68. For the other groups, we also have a large variability within food categories: in bread-based products RIR are greater than 25% for 39 cases out of 60 and in biscuits and pastries for 46 cases out of 88.

Table 3 :

 3 Impacts of scenarios on individual consumption for adults and children subpopulations

Table 2 :

 2 Impacts of scenarios on the total amounts of nutrients delivered to the market

	-9%