Catherine C Benjamin
email: catherine.benjamin@roazhon.inra.fr

Chantal Guéguen

Magalie Houée Bigot

M Houée

World cereals markets under alternative common agricultural policy reforms

Keywords: Common Agricultural Policy, partial equilibrium model, world wheat market, simulation, trade World cereals markets under alternative Common Agricultural Policy reforms 1

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

Introduction

Previous quantitative assessments of likely impacts of recent reforms of the Common Agricultural Policy (in particular the Agenda 2000) differ across empirical studies. The empirical results are conditional on the modeling framework used. Differences are mainly due to the ways the policy instruments are taken into account (explicit modeling or implicit way i.e. using ad-valorem equivalents) ( Van tongeren et al (2001 )). The aim of this paper is to assess empirically the impacts of recent reforms of the Common Agricultural Policy (CAP) and the consequences of the mid-term proposais on world cereals markets. We develop a World Econometric Modeling of Arable Crops, which is an econometric, dynamic, multi-product, partial equilibrium commodity mode! that focuses on arable crops. For these commodities, major exporters and major importers are modeled separately, ail other countries being included in a "rest of the world" category. For the regions explicitly integrated, the mode! generates supply, demand, domestic prices and trade estimates. The mode! is able to determine endogenously the world prices of the main cereals.

The main objective of the mode! is to carry out medium term simulations of the impact of national and international agricultural polices reforms. The mode! we develop has two important features: i) the parameters estimated in the behavioral equations (supply and demand) satisfy regularity conditions and ii) the agricultural policy instruments (in particular CAP instruments) are modeled il an explicit way.

The paper is organized as follows. The second section presents the general features of the model we develop and provides an overview on the modeling framework applied to study major wheat exporters and importers behaviors. Potential effects of the Mid-Term Review proposais on European Union and world arable crops markets are discussed in section 3. The fourth section concludes.

The structure of the World Econometric Modeling of Arable Crops model

This section outlines the general structure and modeling approach used in the World Econometric Modeling of Arable Crop (WEMAC). Before presenting the behavioral equations of each regional sub-models 2 , we first describe the general features of the mode!, the current country and commodity coverage.

Model overview

The W orld Econometric Modeling of Arable Crops is a partial equilibrium commodity mode! which focuses on the arable crops world markets. The WEMAC model is an econometric, dynamic, multiproduct, non-spatiaf, mode!. The model consists of a set of country or regional sub-models with linkages established across countries and commodities. The current mode! considers 8 countries/regions. The current model allows analyzing simultaneously equilibria on the world markets for the following cereals: wheat (durwn and soft), maize, barley and other cereals.

The current country coverage is described in table 1.

(Insert Table 1)

The mode! contains five wheat-exporting countries (Argentina, Canada, the European Union, the United States, the Central and Eastern European Countries, Ukraine), two wheat-importing countries (China, North Africa and Middle East) and the Rest of the world.

An important feature of the modeling is that we do not consider the European Union as a bloc. Indeed the mode! provides country levels estimates for France, Germany, ltaly, Spain and the United-Kingdom while treating the other countries of the European Union as a group4. The mode! generates supply, demand, domestic prices and trade estimates for most of the regions/countries. Additional countries (Ukraine, Africa and Middle East) important to wheat world trade were included: for Africa, the demand side is endogenous, but the domestic production is exogenous, for Ukraine net export function has been endogenized. The rest of the world is exogenous.

The aim of the WEMAC mode! is to provide quantitative evaluations of national and international agricultural policies reforms. Hence, a notable contribution of that model is in the explicit modeling of the main policy instruments both domestic and those applied at the border mainly for the Common Agricultural Policy Instruments.

Each regional sub-model consists of the following sets of behavioral equations : production (harvested area, yield), deamnd (food use, feed use, stocks), price linkages (prices transmission mechanism between domestic and world prices)5, trade flows (import and export equations) and the market clearing.

The mode! is based on econometric estimates of behavioral equations. Most of the equations in the mode! are estimated using annual data from the period 1970-1999 ( or shorter intervals if data are unavailable). The annual series data were obtained from the "PSDView", commodity data base (USNERS) and from national agriculture departments. For the European Union data were obtained from the Cronos data bank of EUROST AT.

General behavioral specifications of each individual component in the mode! are further detailed.

Behavioral equations and model closure

The following paragraph reviews the conceptual and general description of domestic supply, demand, stocks, prices linkages and trade flows, which defines the general structure of the country sub-models.

Domestic supply

On the world market, the crops modeled (in other words the crops whose prices are endogenous) are maize, barley, soft and durum wheat. Individual models used for each country/region have however been estimated by introducing cross-linkages between other arable crops. Production in country/region is determined as the product of estimated harvested area and yield equations. In each sub-model, we assume a specific separability structure in crop production. According to that assumption land allocation decisions are taken in three stages. In a first stage, producers split the total available area between fodder crops and arable crops. In the second stage, they allocate the area under arable crops among industrial crops and cereals and oilseeds. In the third stage, the area of cereals and oilseeds is divided among the arable crops cultivated in the considered country. The allocation scheme is specific to each country studied. W e restrict to the third stage where the total area under grains and oilseeds is assumed to be fixed but allocatable across the various grains and oilseeds (Coyle 1993, Guyomard and al, 1996). Hence, we mode! a system of arable crops acreage demand as conditional on total arable crops areas. The crop acreage equations can be written as ss ;,, =ss(p'J,, l v,_i, ssgc, , Z) i, j = 1, ... , n

(1)

where ss;,, is the crop acreage in year t for the comrnodity i, P'J., is the expected crop output price j (j = J, ... n), v, _ 1 the input price in t-1, ssgc, is the total crop acreage allocated to arable crops and Z defines a vector of exogenous which could have an impact (these variables depend on the country and inc!ude for instance domestic policy variables). We assume that producers do naïve expectations on pnces, 1.e. P'},, = Pi , -I . For the estimations, symmetry conditions and adding-up6 restrictions are irnposed.

For the yields, we use the following specification

(2)
where 'i 1 is the yield per hectare in year t for the crop i, T is a linear trend. The area and yield equations are jointly estimated using the iterative Seemingly Unrelated Regression Method.

It is worth noting that in contrast to other partial world models, we do not include income per hectare in the !:pecification, this choice allows to distinguish the effect of prices and other policy instruments (for instance, in the European Union we can compare the effects of decrease of the intervention price with the increase of the area payments).

Previous general specifications may vary for some individual countries particularly for the European Union and the United States in order to take into account the respective domestic polices. For the supply modeling, in the European Union we include per hectare direct payments in area equations.

These payments have a direct effect on land demands for each crop. The land set-aside policy is taken account by introducing it in the second stage in the land allocation decisions 7

• For the United States, we incorporate the influence of commodity programs in the area and yield equations by including an additional explanatory variable, which correspond to the mean per hectare of the production flexibility contracts, the deficiency, diversion and disaster payments. Furthermore, the marketing loan is included in the definition of the producer price (both for supply equations and prices linkages equations).

Domestic demand

ln each country we estirnate only the demand for cereals

where uha;,, is the per capita non-feed demand for the crop i, pc;,, the real consumption price, pib 1 I pop 1 is per capita real income. The lagged variable uha;,1-i is included to represent the partial adjustrnent toward desired consumption.

Since feed is used as an input in livestock production the theoretical specification of feed demand follows from the theory of derived demand. Feed demand is expressed as the following relation ua;, 1 =ua(pc; 1 , pci ,,, PBkt, T)

(4)

where ua; 1 is the feed demand for the crop i, p c; 1 the real price of the commodity i, p c 1 ,1 the real price of competing feed products (cereals, oilseeds, other protein feeds), PB"' is the livestock productions (with k=poultry, beef and pork production) and Ta tirne trend.

Total domestic use is the sum of feed and non-feed uses.

Stocks

The stock level depends on the consumption price and on the beginning stock (lagged value of the stock variable).

Price transmission

A single world price is assumed to exist for each of the commodity. Since producer and consumption domestic prices are different we have transmission price equations to estimate. Except where there are set by govemment, domestic prices are linked to world prices via linkage equations including exchanges rates. The system to estimate can be written as ( 5)

PC;,, = pC(P;,,)

where P;,, is the producer price of the crop i pm; 1 the world price converted in local currency and h;,, other exogenous variables that affect prices levels (the specification allows to take into a::count domestic policies for instance, in the case of the European Union we introduce the intervention price as an additional explanatory variable)9

•

In the European Union, at the level of the individual country mode!, most prices are linked to the French market prices which are generally defined as the leading prices 10 •

Import and export equations

The WEMAC mode! distinguishes between imports and exports.

We distinguish imports on the import regime under which they enter. Hence the imports that occur under the Tariff Rate Quotas (TRQ) system are exogenous and equal to the scheduled TRQ. We defined an import equation for the out of quota imports. The import demand of each country (per capita imports) is specified as a function of the real per capita income, of the tariffs and of the world price of the cereals studied.

The export equation depends on the world price and on the domestic supply (production plus beginning stocks) ofcommodity i in t-1.

Closure of the model

In order to close each regional model a variable is not estimated but calculated as the residual to check the equilibrium on each regional market. After modeling each country, we calculate the sum of ail regional and country supplies and the sum of ail regional and country demands. Simultaneous solutions 1 1 of the models are obtained with market clearing equilibria of the different cereals. The submodels are solved 12 iteratively to obtain equilibrium world prices.

Scenarios and simulations results

This section present an analysis of the Mid-Tenn Review proposais to asses their potential effects on European Union and world arable crops markets over the period

Definition of the baseline

We first present baseline projections for world wheat markets for the period 2001-2009. The reference scenario is established under a specific set of assumptions about exogenous shifters which drives the WEMAC model.

The most important assumptions concem agricultural and trade policies. The reference scenario assumes that ail government programs and international agreements currently in effect will remain in place over the projection period. In the European Union, the reference scenario corresponds to the full implementation of the Agenda 2000 Common agricultural refonn13

•

For the forecasts of macroeconomic variables (real income per capita, rate of population growth, exchange rates ... ), the baseline is generated either by using our own time trends and constant growth rates or with forecasts coming from F APRI assumptions 14

• At last, the agricultural commodity production and prices, which are not modeled in the current version (such as livestock production, input prices, oilseeds prices), evolve as FAPRI forecasts.

A surnmary of the main findings in the reference scenario is provided in table 2 to 4. Over the medium-tenn cereals would benefit from increasing yields, and higher direct payments would on average partially outweigh the eut in cereals price support prices. Hence total cereal area in the EU is projected to exhibit a slow increase over the medium-tenn over 37.2 millions ha to 38.3 in 2009.

(Insert table 2)

The medium-tenn outlook for arable crops markets is foreseen to remain essentially supported by a rising demand driven by an improved macro-econornic environment and the continuing growth in the feed demand from livestock sector.

Since demand for wheat and maize will increase more tightly than production, european prices are projected to increase on the period 2001-2009 (+2% for the French soft wheat producer price, +0.56% for the French soft wheat market price, +6.3% for the French maize producer price, +3.3% for the French maize market price). For the same reasons, on the word market cereals, prices are estimated to reach around 120 $/t for Soft Red Win ter wheat (SRW wheat) 1 5 and 108$/t for maize. Note that world prices will increase more tightly than european prices. So, in the baseline scenario the implementation of Agenda 2000 reform leads to a decline in the gap between the european price and the world price which contributes to improve EU cereals competitiveness. Exports of maize and dururn wheat would remain broadly stagnant whereas wheat exports will increase highly. Furthermore in the baseline we found that the EU will export beyond its Uruguay Round Agreement on Agriculture limits on subsidized exports 1 6 • (Insert table 3 and4)

Mode! results

We present the results of two simulations based on different assumptions regarding the recent 'Mid Term Review' proposais over the period 2004-2009.

The first experirnent corresponds to the implementation of the proposed market measures. The 2002 'Mid Term Review' (MTR) proposais for the Cornmon Agricultural Policy contain the following elements for grains: further reduction in the cereals intervention price 1 7, compensation for the eut in cereal price by increased direct payments (from 63 euros per tonne to 66 € per tonne). The MTR proposais con tain the removal of monthly overvaluation.

The second experiment introduces the concept of decoupling with the granting of a single decoupled income payment per farm. In that scenario, we assume that the new payments will have no effect on production decisions.

Note that in each experirnent there is a mandatory system of land set aside which remains set at the l 0% reference rate.

Market measures scenario

On the supply side, compared to the current policy baseline, changes in support price and in the payments lead to a modest reduction in aggregate EU soft wheat and maize production (respectively 0.1 % and 1.5% in 2009 see table 5). More precisely, conceming the wheat market, eut in the intervention price will reduce the producer price by 8.5% which will cause a reduction of the area harvested by 0.1 %. But the final effect on production level will be weak because yields would increase on account of the decrease in low-yielding, marginal land and partially compensate the decline in area 14 The FAPRI (Food and Agricultural Research Policy Institute) forecasts corne from Standard and Poor's DRJ. 15 The SRW wheat generally quotes around 10% below the Hard Red W inter wheat (HRW). 16 That result is still holding in a context of a less fa vorable $/€ exchange rate. harvested 18 • Moreover, the decrease in production level is limited by the increasing direct payrnents even ifthey don' t overweigh the negative effects ofreducing the support price.

(Insert table 5)

On the demand side, the reduction of the support price for the cereals would lead to european lower market prices of the soft wheat on the whole period. This would cause a small increase in soft wheat consumption whereas lower availability should constrain cereal exports. Moreover the reduction in the cereal support price should affect EU border protection for the main cereals and generate additional imports. The net exports in soft wheat is reduced by 1.3% and net imports ofmaize rise by 1.8%.

Note that producer prices would drop sharply due to the reduction of the support price. In contrast to previous studies which do not distinguish market price from producer price we find stronger decrease of EU domestic prices. EU soft wheat prices are not supported by the world market prices.

(Insert table 6 to 7) W orld cereals prices are found to trend upward over the medium term. The Euro wheat price remains slightly below world market level during the simulation period and the gap between EU price and international prices narrowed down.

As noted by previous studies the estimated effects of the rnid-term scenario on EU crop prices depend on the relationship between EU and world market prices.

In our experiment, the limited impact on production level is linked to the transmission prices mechanism estimated in the Wemac mode!. Indeed, table 7 presents the prices variations for the country which is assumed to lead the domestic market (for instance for the wheat market the french price is considered as the leading price).

The decoupling scenario

The implementation of this scenario introduces the concept of decoupling with the granting of a single decoupled income payrnent. A fundamental assumption realized when we run this scenario is that we assume that the single payrnent will have no impact on production decisions of farmers. A summary of the impact for the main variables for the soft wheat and the maize in the EU is given in tables 8 to 1 O.

(insert table 8)

The overall impact of this experiment on the cereal market would have stronger effects than the projected impact of the first scenario: further decrease of the production (by 3.1 % in place of 0.1 % for the soft wheat and 5.6% in place of 1.5% for the maize market). This result partially cornes from the further oecrease in area harvested (-2. 7% in spite of -0. 1 % for the soft wheat) due to the removal of direct payments.

Lower wheat production would affect the competiveness of EU exports which would fall by approximately 12% whereas EU cereals imports would increase owing to the reduction in EU's border protection. This would lead to a further increase of the world price especially on the wheat market.

(Insert table 9 to 10) The second result is that we observe important disparities, which emerge between the United States and the European Union. lmplementation of European reforms leads a contraction of the European Union wheat production and net exports (-13.5%), offset by an expansion ofwheat production and net exports of the United States (Table 11).

(Insert table 11)

Concluding comments

An econometric, dynamic, multi-product, partial equilibriurn commodity model is developed to analyze world wheat trade under current and alternative Common Agricultural Policy reforms. Our analysis contributes to previous studies by taking into account policy instruments (and in particular CAP instruments and having some country-levels details for the European Union. An important feature is we do not consider identical effect of direct payments and prices on supply decisions for the European producers.

The paper present a market outlook for two simulations based on different assumptions regarding CAP reforms to asses their potential effects on European Union and world arable crops markets over the period 2004-2009. We run the World Econometric Modeling of Arable Crops for two experiments : i) the Mid-Term Review scenario and ii) the decoupling scenario. The starting point for the analysis, the status quo scenario is a set of baseline projections for European Union and world arable crops markets. Then the baseline projections are used as a comparison point for discussing the impacts of the evolution of the Common Agricultural Policy on the EU cereals markets and on the world wheat markets. The mode! is employed to simulate different kinds of implementation of the Mid Term Review. The estimated effects of the mid-term scenario on EU crop prices depend on the relationship between EU and world market prices.

An important result is that in both scenarios we find stronger decrease of EU domestic prices. EU soft wheat prices are not supported by the world market prices Note that producer prices would drop sharply due to the reduction of the support price. ln contrast to previous studies which do not distinguish market price from producer price. The results of the second scenarios is significant contraction of European Union wheat production and net exports offset by expansion of wheat production and net exports of United States. 18 The effect on maize production is higher because of decreasing yields.

8.

  Consumption is disaggregated into two final uses: feed and ail other uses. The theoretical specification of non-feed use is based on consumer theory. Per capita non-feed demand is deterrnined by the following equation

  2004-2009. We run the World Econometric Modeling of Arable Crops for two experiments : i) the Mid-Tenn Review scenario and ii) the decoupling scenario. The starting point for the analysis, the status quo scenario is a set of baseline projections for European Union and world arable crops markets. The section begins by a surnmary of the baseline projections. The WEMAC reference run describes what will happen on world agricultural markets, over the period 200 l to 2009, if current agricultural and trade policies (situation of 2000) are assumed to remain in place indefinitely. Then the baseline projections are used as a comparison point for discussing the impacts of the evolution of the Common Agricultural Policy on the EU cereals markets and on the world wheat markets. The model is employed to simulate different kinds ofimplementation of the Mid Tenn Review.

Table 1 .

 1 Countries and regions modeled

	Country/Region	Country-level details	lmports and exports in % with respect to
			the world wheat market (2001 forures)
	Net exporters
	Argentina		14.5
	Canada		18.5
	European Union (15 countries)	France	7.9
		Germany
		ltaly
		Spain
		United-Kingdom
		Rest of the Union
	United States		28.9
	Central and Eastern European Countries	Bulgaria	4.5
		Czech Republic
		Hungary
		Poland
		Romania
		Slovakia
	Ukraine		4.6
	Net importers
	North Africa, Middle East		36.9
	China		0.6
	Rest of the world		35.3

(1) The Soft Red Winter (SRW) wheat generally quotes around 10% below the Hard Red Winter wheat (HRW).

Table 4 .

 4 Baseline Scenario: Arables crops price (expressed in euros/tonnes)

		2001 2002 2003 2004 2005 2006 2007 2008 2009
	French Soft wheat producer price	94.2	92.5	93.7	91.0 90.9 91.5 92.8 94.9 96.5
	French Soft wheat market price	125.6 125.1 125.4 124.6 124.6 124.7 125.1 125.8 126.3
	French maize producer price	94.1	90.4	90.0	90.1 90.2 90.0 92.8 96.6 100.0
	French maize market price	136.4 133.5 133.2 133.3 133.3 133.2 135.3 138.3 140.9

Table 5 .

 5 Arable crops supply and utilization results (Market measures scenario)

		2004	2004	Change	2009	2009	Change
		baseline	MTR		baseline	MTR
	Soft wheat
	Area harvested	13.8	13.8	0%	14.1	14.1	-0.1 %
	Yield	7.2	7.2	0%	7.8	7.8	0.01%
	Production (mil tones)	100.1	100.1	0%	109.8	109.7	-0.1%
	Domestic use (mil tonne) 82.5	82.8	0.4%	85.9	86.2	+0.3%
	Net exports	16.8	24.5	+ l.0%	24.5	24.2	-1.3%
	Maize
	Area harvested	4.1	4. 1	0%	4.2	4.2	-1.1%
	Yield	9.7	9.7	0%	10.7	10.7	-0.4%
	Production (mil tonne)	40.l	40.7	0%	45.6	44.9	-1.5%
	Domestic use (mil tonne) 39.3	39.2	-0.4%	45.7	45.6	-0.2%
	Net imports	0.4	0.5	+4.5%	1.5	1.6	+ l.8%
	Durum
	Area harvested	3.3	3.3	0%	3.3	3.3	0.5%
	Yield	2.6	2.6	0%	2.6	2.7	0.5%
	Production (mil tones)	8.7	8.7	0%	8.6	8.7	1%
	Domestic use (mil tonne) 9.2	9.2	0.%	10.3	10.3	+0.3%
	Net exports	0.1	0.1	+46.6%	0.2	0.2	+25.5%

Table 6 .

 6 World prices under the MTR scenario World prices ($/t) 2004 2005 2006 2007 2008 2009

	Soft wheat (SRW)
	Baseline	95.1	94.7	97.2	103.3 112.4 119.2
	MTR	94. 1	95.2	98.5	105.0 114.3 121.2
	Difference	-1.0% +0.6% +1.4% + 1.7% +1.7% + 1.7%
	Maize
	Baseline	78.6	78.7	78.3	86.6	98.0	108.1
	MTR	78.7	78.3	78.6	87.2	98.8	108.9
	Difference	+0.1% -0.5% +0.4% +0.7% +0.8% +0.7%

Table 8 .

 8 Arable crops supply and utilization results: Decoupling scenario

	2004		2004	Change	2009	2009	Change
	baseline	decoupling		baseline	decoupling
	Softwheat
	Area ha rvested	13.8	13.8	0%	14.1	13.7	-2.6%
	Yield	7.2	7.2	O"lo	7.8	7.8	-0.5%
	Production (mil tones)	100.l	100.1	O"lo	109.8	106.4	-3.1%
	Domestic use (mil tonne)	82.5	82.8	+o.4%	85.9	86.0	+o.!%
	Net exports	16.8	17.0	+I.0%	24.5	21.1	-13.7%
	Maize
	Area harvested	4.1	4.1	O"lo	4.2	4.0	-5.2%
	Yield	9.7	9.7	O"lo	10.7	10.7	-0.4%
	Production (mil tonne)	40. 1	40.1	O"lo	45.6	43.1	-5.6%
	Domestic use (mil tonne)	39.3	39.2	-0.4%	45.7	45.7	-0.1%
	Net imports	0.4	0.4	4.5%	1.5	1.7	10.3%
	Durum
	Area harvested	3.3	3.3	O"lo	3.3	3.0	-6.8%
	Yield	2.6	2.6	O"lo	2.6	2.8	+6.9%
	Production (mil tones)	8.7	8.7	O"lo	8.6	8.6	-0.4%
	Domestic use (mil tonne)	9.2	9.2	0.2%	10.3	10.3	0.3%
	Net exports	0.1	0.2	46.6%	0.2	0.2	25.5%

Table 9 .

 9 World prices under the decoupling scenario

		2009
		Baseline MTR Decoupling
	Soft wheat price (SRW) 119.2	121.2 144.2
			1.7% +20.9%
	Maize	108.1	108.9 117.3
			0.7% +8.5%

Financial support is provided by the French Ministry of Agriculture and a private partnership (Pluriagri).

In the modeling, a country represents astate and a region refers to an aggregate of different countries.

The mode! is non spatial because it does not identify trade flows between specific countries regions .

In the definition of the "Rest of the Union", we take into account European Union country enlargement over the estimation period.

For the European union this set of equations include the price transmission equation between market price and intervention price.

Adding up is implied by the restriction that the sum of the areas is equal to the total land devoted to arable land.

We try to endogenize set-aside area decis ions but we did not have enough available data for the estimations.

ln the current mode!, the demand for oilseeds is exogenous.

These price equations are estimated using Three-Least Squares to obtain consistent parameter estimates in the presence of right-hand side endogenous variables as well as contemporaneous correlation among the disturbances.1 ° For the durum wheat the Italian price is defined as the leading price.1 1 We solved simultaneously barley, durum wheat, soft wheat, maize, and other cereals world markets. 12 We use TSP 4.4.

The cereals intervention price is reduced at 103.3 EUR/t, compensation payment for oilseeds is aligned on direct payment on cereals (63 EUR/t), continuation ofmonthly increments in intervention price.

The price goes from 101.3 euros per ton to 95.35 euros per ton in 2004/05.


Carole Ropars-Collet

Louis-Pascal Mahé

Carole Ropars Collet

Louis Pascal

Mahé Aurélien Milon

Philippe Le Goffe

Adolphe Bobierre

Management strategies for invasive species : the importance of stock externalities

Keywords: JEL Classification : Q20, Q29 Invasive species, eradication, controlled invasion, re- source economics

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

MANECpMENT STRATEGIES FOR AN INVASIVE SPECIES:

THE IMPORTANCE OF STOCK EXTERNALITIES fntroduction

The spread of non indigenous invasive species raises important ecologi- cal and economical problems in many countries. They can be animal or plant, land or aquatic species. Biological invasions are responsible for the degradation of ecosystems and ecological services: modification of both biodiversity and habitats associated with competition among species, de. terioration of water quality and changes in the flow of waters in the case of aquatic species, etc. These deteriorations of ecosystems may inflict sub- stantial economic losses to the users of the invaded natural resources. In FYance, Lud,wi,gi,a spp. is one of the most intrusive aquatic plant species, threatening the environment. World-wide, it is classified among the worst plant pests. Its dynamic power of colonization is strong in France where numerous sites exhibit conditions favorable to its growth. It holds a wide ecological magnitude and presents an important potential of geographical distribution. It prefers stagnant or weak water flow environment such as still waters and wet zones. When Ludwi,gia spp. spreads over, it is responsible for important damages on ecosystems and their functionalities.

It may lower the oxygen content and alter the quality of watersheds. It also causes physical nuisances through hindrance to water flows and silting up. As a result some biotopes lose complexity and biodiversity decreases in the colonized environment. Recreational uses of natural resources such as fishing, hunting, water-based recreation, may also suffer from significant damages.

The users and managers of the afiected sites are striving to develop methods to keep Lud,wi,gi,a spp. under control. The characteristics of the species are crucial in the design of the strategy regarding management and spread risk. Some actions can have unpredicted effects on the structure of the ecosystem and its functionality. Besides, these actions tend to require costly techniques and hence large financial means. The control may consist of heavy ground works to avoid the settlement and the development of the species. Curative approaches consist of manual, mechanical or chemical techniques.

According to the managers, it seems that the complete eradication is not feasible once the colonization has started. Depending on the sites and the degree of colonization, the management objectives are either to keep the invasion at very low levels or simply to minimize the nuisances and the dispersion. However, the objective of controlling the invasion to a given physical target may not always be optimal from an economic point of view. The management level should be given by a trade off between costs and benefits.

The control of invasive species has features similar to the problems of pollution management. In both cases the spread entails damages to the society. However, unlike pollution, biological invasions face limiting factors to a species spread on a given site, due to ecological and biological conditions. In this respect they are similar to renewable resources such as fisheries stocks. But the main difference is that in the case of renew- able resources extraction provides a valuable output, and the problem is to maximize the present value of the profit generated by catches. While in the case of invasive species the problem is to minimize the present value of the sum of the cost of control and of the current flow of damages generated by the stock. Eiswerth and Johnson (2002) stress that very few economic studies have been conducted on the biological invasions management. To our knowledge, (Junqueira Lopez, Michel, and Rotillon 1993) , Knowler and Barbier (2000), and Eiswerth and Johnson (2002) developed dynamic models that we can compare with those used for renewable resources.

Junqueira Lopes and al (1993), have studied a population of scrawfishes deteriorating irrigation channels. Eiswerth and Johnson (2002) have modeled an invasive plant which slows down the productivity of pasture. They derive solutions for stationary stocks of invasive species and to optimal levels of control. We note that these studies are limited to theoretical modelization and do not include fully empirical applications. Eiswerth and Johnson (2002) developed a dynamic model of optimal control about an invasive species management. The model is close to bioeconomic models applied to fisheries and is followed by a numerical illustration. They derive optimal solutions for steady state level of invasion.

The comparative statics shows that the impact of ecological, biological and technical factors on the optimal control is ambiguous and strongly depends on the species characteristics and on the colonized site. However, they do not examine the impact of economic parameters on the solution. The damage function they use depends on the invasion level, whereas the costs only are a function of the quantity withdrawn from the biomass.

The problem of controlling invasive species with a dynamic model including externalities has already been considered (Olson and Roy undated).

Their contribution is to give the implications of non classical assumptions on the cost functions, the growth function and on the optimal management policy. They determine the economic and biologic conditions under which the optimal policy leads either to eradication, to inaction or to partial withdrawal. The implications in terms of optimal management are ambiguous; they can lead to complex and cyclical dynamics of control. Simulations are realized. Eiswerth and Van Kooten (2002) study the stochastic case, using probabilities from surveys of experts in the field.

The aim of this study is to identify and quantify optimal control strategies for various French sites invaded by Lud,wi,gia spp. Unlike Eiswerth and Johnson, we allow for a stock externality to exist. Under reasonable circumstances, this assumption seems to be a necessary condition for the existence of a non zero.solution, hence different from eradication. A static approach is first used to identify and simulate mânagement solutions. A dynamic model is also developed, and leads to formal steady solutions. We also examine existence and stability conditions. Although we have no gen- eral conditions on the technology and the biological characteristics which ensure that a non corner solution exists and is stable, we find that stock externalities appear to make these conditions easier to fulfill.

1 Static model : the importance of stock exter- nalities

We consider a site invaded by species such as Ludwigi,a spp. . Their spread is responsible for nuisances or negative impacts on recreational and other uses. In order to cope with economic damage, the manager of such a site would like to control the species proliferation. He has to bear the mânagement cost of the invaded site. We assume that the cost function depends not only on the amount of biomass retrieved but also on the invasive species stock. In the static case, the sole owner is indifferent between present and future. The manager aims at finding an efficient trade off between the current costs of control and future damages generated by the stock. The optimal management of the affected site requires to minimize the sum of control costs and damages induced by the biological invasion subject to the growth function.

Let Y be the control i.e. the amount of the invasive species extracted, and ,S the stock of biomass. Total and marginal economic damages are assumed to be increasing with the biomass stock. They are both zero before the invasion i.e. when the stock is nul. The damage function represented by F(S) is assumed to be continuous and twice differentiable, increasing and strictly convex in ^9. Hence, except for specified cases, the following assumptions are made on the damage function (where indices denote partial derivatives): Fs > 0; Fss > 0; F'(S) > 0; F(0) : trb,(O) : 0

(1) Managing the invaded species incurs a cost wich in general will depend on both the 'ouput' Y and of the stock of biomass ,5. The latter assumption expresses the possibility of a stock externality. The assumptions on the control cost function are summarised in the following expressions: C7(Y,S) >0; Cvv(Y,S) >0

(2) Cs(Y,S) < 0; Cvs(Y,S) < 0; Css(Y,S) > 0

(3) CvvCss-C?s>o (4) When stock externalities do not exist relations 3 are strict equalities. In the presence of externalities they are strict inequalities and we add the following realistic assumptions for extreme points: C(O'S) : 0,'S > 0; CY(0,'5) > 0, S > 0 (5) C(Y,0) -oo; C7(Y,O): *; Cv(0,0): -;Cs(Q,0): --; Cvs(0,0): -oo (6) Expression 2 implies that total and marginal costs of managing the invasive species axe non decreasing in Y. Expressions 3 mean that the stock externality is weakly negative and decreasing in magnitude: total and marginal costs are non increasing in the biomass stock. The cost function is also assumed to be continuous and twice differentiable, strictly convex in Y, in S and jointly convex in ,S and Y, according to expression 4. Expressions 3 reflect the increasing difficulty to eradicate the species from its environment as the amount of biomass becomes scarce and, conversely, the relative easiness to remove a unit when the stock is large. We also assume in general that the cost is zero for a no control strategy and that marginal cost is a non negative number when the stock is strictly positive.

We assume a logistic growth function. Then, as the species is spreading, competition between species increases and pests and biological interactions appear. The biomass proliferates at a diminishing rate from some level and then stabilizes. The natural growth function of the species, represented by G(S), is then assumed to be strictly concave with a maximum at Spr which is the maximum sustainable yield of the species. It is increasing when the stock is below Sv and decreasing otherwise. We make the usual and classical assumptions, of renewable resources management models such as fisheries, where a quadratic form is ofben assumed for G: Gs(S) )0, 0 <,S< Su ; Gs(S) S0, S > SutGss(S) <0; G(0) :G(K):0 (7) When management is implemented, the natural growth of the stock is cut down by the biomass extracted, hence the following usual assumption for the net growth when the control is set at level Y:

dsldt: G(st) -Yt (8)
The optimal management of the biological invasion is defined as the social planner problem. In a static approach he tends to minimize V(S), the sum of damages and management costs, subject to a stationary stock biomass, i.e. to equation 8 set to zero. Then, the static optimal stock, uniquely determines the amount Y to be extracted in order to maintain the stock and keep the entailing damage under control in an efficient manner.

Replacing Y by G(S) in the cost function, the problem is then reduced to find an optimum without constraint excepted for the non negativity of the stock ,S and the condition that the stock cannot be larger than K, as minV(S) : r'(,9) +C(G(S),S) ; S > 0; (l(-S) >0 ( 9) s'

The first order necessary condition for a solution is the following: Vs : Fs -f Cv 'Gs * Cs > 0;,S 'Vs :0 (10) -Vs ) 0; (K -S) ' Vs :0 (11)

Lf. Vg > 0 for all ,S, then ,S* is zero and the optimal solution is eradi- cation, 1f Vs < 0 for all ,S, then K -S* : 0 and the optimal solution is laisser fa,ire, 1f Vs :0 for some S and Iz(S) is strictly convex, then 0 < ,S* < K and the optimal solution is controlled invasion.

The sufficient condition for an interior solution to be a true minimum 1S:

Vss: Fss* Cvv'Gb+Cssi2Cys 'Gs+ Cy'Gss)0 (12) Assumptions2 to 4 do not ensure that this condition is always met. The value function V(S) could in principle be increasing for the whole range of stock levels. In order to minimize the total loss, the condition 1-0 requires the stock to be zero if. the value function V(S) is strictly increasing in ^9. There is no interior solution. Indeed, it turns out that it is the most likely case when the damage function is strictly increasing and when the stock externality is either zero or small in comparison with the marginal damage. As a result, the planner should either prevent the species from proliferation at the outset or completely eradicate the biomass on the site subject to invasion. The absence of an externality does not guarantee that the function V(S) is strictly increasing because when ^9 ) Sm, the natural production function is decreasing (Gs < 0). Nevertheless, even in that case, it turns out that a weaker condition justifies eradication under our realistic assumptions. Let's examine different cases leading to several types of control strategies.

No stock externality

Without stock externalities, the necessary condition for a minimum is : Vs: Fs*Cv' Gs > 0 i S'Vs:Q

(13)
For ,S 1 Su, Gs is strictly positive and the value function is increasing. Then, an optimal solution is not possible in this interval. When S > Su, I/g is likely to have à zero value. However, it is not a minimum even if we can not conclude from the simplified second order condition:

Vss: Fss * Cvy'G7+Cv 'Gss ) 0 (14) This condition is not guaranteed because in theory, the concavity of. G can offset the other two positive terms and the value function I/(S) can either keep on increasing after a turning point or be decreasing after a maximum. This will be clearly the case if marginal damages and marginal costs are constant.

Nevertheless, \Me can check that, in the absence of stock externalities, the loss function V has a global minimum at a zero stock level if damage function is non decreasing as assumed : v(s) : F(s) + c(G(s),s) > v(0):.F(0) +c(0,0):0 (15) Result 1-: In a stati,c approach, wheneuer stocle erter"naliti,es are absent and the damage functi,on is non decreas'ing, the opti,mal soluti,on i,s to driae the stock to zero i,.e. to eradicate completely the i,naas'i,ue species from the enuironment.

If for low levels of the invasion damages are decreasing over some range and then increasing, as the weeds may provide shelter to fish for spawning, we may still have an interior solution. Expressions l-3 can then be zero for some non zero S and be a minimum of V(S) as the second order condition L4 is negative. Such a case, which violates the more relevant assumptions stated in 1, will occur for some species which first provide benefits so that damages are negative and decreasing for small values of the stock biomass, then increasing after a minimum and then positive. As a result, a non zero stock can be optimal and the optimal policy will not be eradication. I Result 2: In a stati,c approach, uheneuer stock erternali,ties are absent, it 'i,s necessary for the opti,mal solution to occur at a (stri,ctly) posi,ti,ue stock leuel that the d,amage functi,on be decreasing oaer sonxe r&nge.

With no stock externalities and an increasing damage function the first order conditions do no provide the global minimum but a maximum, or a turning point. Eiswerth and Johnson (200a) used cost functions which are independent of the colonization size, hence they can not ensure that their solution is a true minimum even if the model is dynamic.

L.2 Stock externalities

When it is hardly feasible or impossible to eliminate the last individuals, eradication costs become prohibitive as the stock becomes very low. The optimal management may consist of maintaining the stock at the positive level derived from expression 1"0, which means that the optimal stock is such that the marginal savings on costs due to an extra unit of stock should offset the corresponding increase in damage.

(16)

This condition can also be written as Gs : -[Fs + Cs]lCv which requires the marginal productivity of the stock (the slope of the growth function) to be the opposite of ratio of the marginal damage net of the stock externality to the marginal cost of extraction. Depending on the relative importance of externalities and marginal damages, Gg is positive or negative, hence the optimal solution can then be on the left or on the right of ,Sy.

This condition leads to a non zero solution for ,S, as long as the second order condition 11 is also met for all positive,9. We cannot conclude about the convexity of V(S) under the weak assumptions made in 1 to 4. Given these assumptions on cost and damage functions, the first three terms are positive. The fourth is negative if S < ,S71a and positive otherwise. The last term is always negative. The sign of Vss is thus ambiguous. Consequently, the conditions to get a non zero optimal solution ,S* are fairly restrictive.

\Me may add that strongly increasing damage function (large ,Fss ) and rapidly decreasing externalities in absolute value (large Css) make an interior solution more likely. The nature of the solution, eradication, controlled invasion, or la'isser faire seems very sensitive to parameters and to the functional forms for costs, damages and growth. Regulation and action levels are different and strongly depend on the characteristics of the colonized sites. As a matter of illustration in figure 1 and 2 we provide typical forms Figure L corresponds to the case of no externalities (z : 0). A mono- tonic damage function (r : 0) gives curves Iz1(S) and V12(S) which are two cases for eradiction. A damage function, decreasing for low stock lev- els and increasing after (curve y11(S)), may lead to an interior solution. Figure 2 synthetises the main cases with a strictly monotonic damage func- tion. Curves Vl(S)and y11(S) are just the previous ones with no externalities. Curves Vz(S) and Iz4(S) correspond to stock externalities. Iz2(S) illustrates the corner solution of. laisser fai,re S* : I( (damages are small compared to costs, and (d,C I d,S + .F's is always negative). V 4(S) is a com- bination of strong externalities and large and increasing damages. and a case of positive solution (-Fg negative for small ,9 )

A few empirical results

To complete the empirical application to Ludwigi,a spp. we need to estimate the cost, damages and growth functions. To that purpose, managers who are in charge of controlling the spread v/ere surveyed to collect data, identify strategies and assess the benefit cost efficiency of the actions. 3). This heterogeneity is due to differences between sites characteristics and degree of invasion.

L.4 Comparative statics

We examine two schocks on the optimal solution: an increase in the cost C(Y,S,a) due to an input price change da and a shift dd in the damage function ,F'(S, ô) . These two schocks relate to economic variables and are relevant to an interior solution, where I/5s is strictly positive. We note that Eiswerth and Johnson (2004) The partial effect of an input price on optimal stock is then positive under usual assumption Cy. ) 0 et Cs. : C-s I 0, with no doubt if ,S* > 57,4 or when the the stock externality effect on input demand is strong. This is consistent with a negative effect on the control effort Y.

When the valuation of damages increase, the optimal stocks should also be cut down. Our comparative statics of exogenous economic shocks are therefore consistent with economic intuition.

2 Solutions for the dynamic model

In the dynamic approach the manager has a preference for the present and faces the trade off between current and future value of damages and costs.

A typical formulation of the problem in renewable resource is to minimize the discounted value of the losses subject to the dynamics of the growth function. Our model is similar to that of Eiswerth and Johnson (2002) except that we allow for stock externalities, which seems to be relevant to our case study. The problem is written as subject to the non negativity of the control variable Y, to an initial value of the stock ,56 and to the growth function 8. The general conditions 1 to 6 on the damage and cost functions are also assumed. To solve this classical optimal control problem with an infinite time horizon we construct the current value Hamiltonian (where time subscript is deleted).

fr : -F(s) -c(Y,s) + p(c(s) -y)

(24

)
Where p is the current value of the costate variable, i.e. the shadow value of the stock which should be negative on the optimal trajectory. pr and the present value costate variable, called À, are related through À -prr-'t. An optimal trajectory must satisfy the following conditions for a maximum:

The necessary condition 25 says that the marginal cost of effort should be equal to the (negative of the) shadow cost of the biomass stock for the optimal control to be non zero .

(")Cv) > -p lY :0

(30) (u)Cv0--tt+Y>o (31)
If the cost function is strictly convex in Y, the optimal value of Y will be unique and betweerl zero and the maximum admissible for Y (no bangbang solution). Under strictly increasing marginal costs, expression 31 can be inverted to give ;ï,;îi "::;":î,ïjï""nof p' and 's (32) This function is the (restricted) supply function of control effort Y in terms of the shadow price pr and the stock. FYom difierentiation of SL and the assumption of diminishing returns, Y appears to be increasing in -p and increasing in ,S. >0 Another necessary condition for a unique (interior) solution to be a maximum of problem 2l-is that the Hamiltonian is strictly concave with respect to the state variable ,9 along the optimal trajectory (p, * 0;Y : G(S)) , i.e.

frr, :-(Fss *Cvv' G'sl Css *2Cvs' Gs +Cv'Gss) <0 (35) A stationary steady state solution should verify this condition which is formaly the same as the second order condition of the static case (Vss > 0).

Again, our general assumptions 1 to 7 on the functions do not ensure it is fulfilled. It will be more likely satisfied if the damage and cost functions are strongly convex in ,5 and Y and if the solution occurs when Gg is negative. Strong stock externalities help satisfy this condition. We now study the existence and stability of a stationary solution under the general assumptions.

A solution should verify both differential equations 27 and 28, with Y defined in 32 by the necessary condition 26. A stationary interior solution, if it exists, corresponds to ,S : 0 and lt : 0, and should satisfy: tt: (r -Gs)p+Cs(Y(p,,S),S) +r's:0 If a non zero stationary solution (Lt*,Y*,,S*) exists, it will therefore be such that u: -c,'Ê^* ", --cy (g8) r (Gs -') Expressions 36 and 37 define two relations between p and ,S in the (p,, S) space. We call them pa(^9) and pls(S) respectively to trace their origin. We first study the corresponding curves on the basis of slopes. dtts _ (. ;S : -SslSp: -(CyyGs + Cys) (39) d[rp .: t.

-CvvCyGss -FssCvv - (CvvCss -CTù_ (40) d,S

: -ILsl tLtL:

ç, _ Cr1ç", _ grs

The slopes of both curves are not clear cut under general conditions. We have to consider subcases related to externalities and extreme points when S : 0 and S : K, in order to identiS' likely solutions.

2.L No stock externality

Without stock externality 39 simplifies and the slope of ps is the opposite of that of the growth function of which it has a symmetrical shape. For ^9 : 0, Y also has to be zero, hence we must by 30 also have p > -Cv(O) which is a finite negative number, say -a, in regards to the particular case described in functions 1,7. Because we have no externality, tts takes the same value for ,S : -I(. Hence the shape of the ,us currre in figure 4. The slope of the pp function also simplifies to (-CyGss-fss)/(r-Gs).

The sign of the numerator is ambiguous. The denominator is negative (and positive otherwise) when ,9 is below a critical level where the pu will have an asymptote. This critical level ,5 is defined by: cs(S) -r:0 (41) Consider first the domain where 0 < S < ,9. Fot S : 0, p& is positive (or zero if Fs(O) : 0). When ,S --,f-, pp -+ae. In this domain we have apossible solution at,S*:0 since pt"(0)> 0 > -Cy(0): -o. The other segment of the pp-curve will start from the asymptote at ,5 where Fp ---oo when,9 --+ S+. By 38, l.rp will have afinite negative value for S : K, namely Fs(K)l(Gs6) -r) i.e., -2pKl0 *r) in our example.

For this curve to cross the ps-curve, this will have to be greater than -Cy(0) : -(t. If this is the case, the two curves intersect in this domain, say at ,9'. However for this to be a true maximum, the concavity of the simplified Hamiltonian in 42 should be verified. This condition is in general ambiguous and depends on functions and pa- rameters. In the simulation which has generated figure 4, this virtual solu- tion turned out to violate the concavity condition and was not an optimum.

When S : K, the necessary condition 30 is also satisfied, it is therefore a solution candidate. We seem to have at first glance three possible solutions.

Can we still have a strong conclusion as in the static case which led to eradication? Yes, since the steady state current value (and present value as well) function at ,S' > 0 is necessarily a larger negative number than at,9 : 0 and y : 0 since -f'(,s') -c(y') < -r(0) -c(0), hence any intersection between the p-curves at an interior stock level does not give an optimum. K is not an acceptable solution either since -F(1() -C(0) < -.F' (0)-C(0). Therefore the only optimal solution in the dynamic approach without externality and with an increasing damage function is also ,S* : 0. This no externality solution is consistent with the static case and implies eradication. Again, if we had a decreasing damage function over some low stock level, the critical value of prp(O) might be negative so that the two p4-curve start from a negative intercept and therefore might intersect (but .F'ss < 0 makes the concavity condition 42 harder to fullfil).

Negative stock externality

The shape of the p-curves will be different when stock externalities prevail. The slope of the ps-currre in 39 does not have an obvious sign throughout, unless reasonable assumptions are made on the externality. However as- sumptions made in 6, ensure that as ,S approaches zero F: -Cv(O,0) r -oo and the slope of the ps-currre is positive and large (Cys(O,0) -+ -oo).

When S : K, F: -Cv(O,K) which is a finite negative number. When S > Snr, the slope is positive. When S 1Sm, this will also be positive if externalities are large so as to offset the first term. Hence the ps-curve in figure 5.

The slope of the pp-atrve was given in 40. The sign of the numerator is ambiguous. The denominator is clearly positive when ,5 > ,3, bnt th" slopes keeps its ambiguity. By 38 there is an asymptote at S > S. If the externality dominates the marginal damage i.e. lCsl > lFsl, Itp + *oo when ,S --,9+ and ptt ---+ -oo when ,9 --3-. It is the converse in the opposite case. When,9:0, ttp -(Cs(0,0) +f's(0))/(Gs(O) -r) :

-oo, under assumptions 1 L and 6 corresponding to our functions used for numerical simulations and the graphic illustration in figure 5.

With our functionnal forms in 17 to 19, we have obtained a non zero solution corresponding to both strong externalities and rapidly increasing tothe. forms could sensibly imply that this limit is zero. This does not preclude our solution to satisfy existence and stability) damages. These are conditions which favor the prevalence of controlled invasion strategies. The non zero solution produced in figure 5 has proved to satisfy both the condition of concavity of the Hamiltonian and also the local stability condition for a saddle point described in the appendix. It is easy to produce a subcase with externality where eradication is recommanded as it was the case in figure 4. We can also easily produce a case where costs dominate damages and la'isser faire at S : K is the most sensible policy.

Conclusion

The modelling of invasive species manâgement seems to have made little use of externalities. The first order conditions for discovering the optimal management strategy of an invasive species are to be used with caution. In the absence of such externalities, non zero optimal solutions in steady state are unlikely to fulfil second order conditions and to be stable. We have established the conditions for different strategies in the static approach and sketched the likely structure of the solutions in the dynamic case. An empirical application to Ludwi,gi,a spp. is in progress.

From an empirical view point, the analysis shows that eradication will always be the best policy if no stock externality exists and if damages are non decreasing. It does make sense, when it is easy to catch and destroy the ultimate individuals of an invasive species, to opt for preventive policy which consists of eradication. This case seems to be fairly rare. If however, the costs of catching these last individuals tend to sharply raise, i.e. in the presence of severe stock externalities, the best policy is likely to be a population control at a positive level and to regularly destroy a certain amount of the biomass to keep the population stable. If damages are small and weakly increasing and if externalities are significant, a lai,sser faire policy is more likely to prevail. The existence of stock externalities are in reality nearly necessary conditions to encounter a non corner solution.

A Stability of the steady state interior solution

The optimal control problem is autonomous with a positive discount rate.

The solution can only be locally stable along a defined time path and be, at best, a saddle point. Assuming a steady state exists, the local stability is studied by linearising the differential equations system around equilibrium.

Taking a first order linear approximation around the steady state, we get:

(; ): (;;[;] i;[r] ) (n-;îi ). (rl:i:fi] ) where e (^9x, px) ---+ 0 and e'(,9x, p*) -t 0. If the characteristic roots of the matrix are real and of opposite sign, then the equilibrium is a saddle point. The correponding determinant has to be negative, i.e.:

Gs(r -Gs) -(Cv 'Gss r Fss)lCvv * (Cvs(r -Gs) iCvs -Cvv 'Css)lCyy <0 (43) A sufficient condition is that, at steady state, the current Hamiltonian is concave and also that either the stock is larger than ^9y, or the discount rate is low. The concavity of the Hamiltonian v/as seen to be uncertain. However, as for existence of an interior solution, the presence of stock externalities strengthens the negativity of the determinant.

-

  asQ : -[cv .Gs * cs]: Fs of the V(,S) curve under different parameters of the following functionnal forms:c(Y, s) : (aY +0.5pY2)l@lK)"

  Figure L: No stock externalities: two corner solutions (^9x : 0: Eradication)

  -f Fsçdg * GsCy.d,w * Cs-d,w :0 Hence the impacts of the shocks on the optimal stock: No .Extemalitv-and small / mùqnil damases ,,/ v2(s) -

Figure 2 :

 2 Figure 2: Four Strategies for selected cases: two with and two w/o externalities

  studied shocks on the technology only. Total differentiation of L0 gives :

Figure 3 :

 3 Figure 3: Some empirical evidence on total costs of control

F^pIr^FFigure 4 :

 4 Figure 4: Corner solution (,S* : 0: Eradication, no stock externalities, u: 0)

Figure 5 :

 5 Figure 5: Interior solution (Stock externalities, u:1-.2)


M R Bellon

J Berthaud

M Halewood

J M M Engels

V Henson-Apollonio

M Broggio

S C González-Martínez

J J Robledo-Arnuncio

P E Smouse

The consequences and implications of introgression in the conservation of forest trees

The International Plant Genetic Resources Institute (IPGRI) is an independent international scientific organization that seeks to improve the well-being of present and future generations of people by enhancing conservation and the deployment of agricultural biodiversity

Introduction

'Introgression' is defined as "...the permanent incorporation of genes from one differentiated population into another" [START_REF]Introgressive hybridization[END_REF][START_REF] Rhymer | Extinction by hybridization and introgression[END_REF]. It is an important evolutionary process in plants [START_REF] Rieseberg | Introgression and its consequences in plants[END_REF] that may operate at either the species or subspecific (population) level. Its potential effects include changes of genetic variation and the appearance of novel adaptations [START_REF] Abbott | Plant introductions, hybridization and gene flow[END_REF].

Introgression is a long process, involving many steps and several generations of genetic segregation [START_REF] Stewart | Transgene introgression from genetically modified crops to their wild relatives[END_REF]. Evaluation of the precise biological significance of natural introgression is difficult because, for example, the relationship between spontaneous hybridization (a first step for natural introgression) and long-term local adaptation is still largely unknown [START_REF] Barton | The evolutionary consequences of gene flow and local adaptation: future approaches[END_REF]. Compounding the difficulties are the consequences of introgression derived from planting exotic seed sources or species (i.e. human-mediated introgression), including those from genetically modified organisms (GMOs). These consequences require additional economic, aesthetic, philosophical and political considerations.

A broad spectrum of opinion exists on introgression, ranging from the view that it poses a serious threat to the genetic integrity of plant genetic resources (e.g. [START_REF] Rhymer | Extinction by hybridization and introgression[END_REF] to the viewpoint that genetic engineering could be part of the conservation effort itself by introducing new genes into native plant populations (e.g. [START_REF] Adams | The case for genetic engineering of native and landscape trees against introduced pests and diseases[END_REF].

Generalizations are difficult, and any objective appraisal of the implications of introgression requires a case-by-case analysis. We intend to provide a comprehensive general overview of the role of human-mediated introgression in the particular context of the conservation of forest tree species.

Trees: how do they differ from crops?

Trees are long-lived organisms, generally spread in continuous stretches (forests) that can cover hundreds or thousands of hectares. They represent the dominant life form in many ecosystems. Forests, even those that are periodically harvested, are best viewed as multi-purpose ecosystems and not only as crops. Societal perception of the natural aesthetic value of 'the forest' highlights the list of non-economic ecological values attributed to large forested expanses; however, the overriding ecological imperative is to simultaneously preserve local adaptation to the environment and the evolutionary potential, i.e. the genetic variability, of the resident native species.

As yet, most forest-tree species have not been subjected to consistent domestication or plant breeding efforts. Any serious efforts have been restricted to only a few fast-growing and easy-topropagate species (Campbell et al. 2003, Appendix). Until about 50 years ago, most domestication efforts focused on choosing the right seed source for different localities. For a few heavily used species, breeding concentrated on the selection and establishment of superior trees in seed orchards. The use of tools from biotechnology is expected to accelerate the domestication of forest trees in the near future [START_REF] Campbell | Forestry's fertile crescent: the application of biotechnology to forest trees[END_REF], thus heightening our interest in conserving native germplasm and the adaptive variation it carries.

The characteristics of the life history and reproductive system can play major roles in determining specific patterns of introgression in trees. First, trees have a long life span and many woody perennials are able to propagate vegetatively. These factors extend the time scale over which any potential introgression can be expected to operate in tree populations, making the assessment of its long-term effects difficult. Recurrent gene flow over several reproductive cycles, from the crop into the native species, may be sufficient to overwhelm any slight fitness disadvantages of the hybrid or exotic seed [START_REF] Haldane | A mathematical theory of natural selection, VI: Isolation[END_REF].

Second, trees outcross considerably more than annual crops [START_REF] Barrett | The evolution of mating strategies in flowering plants[END_REF]). Many plant taxa with higher frequencies of interspecific introgression are outcrossing perennials [START_REF] Ellstrand | Distribution of spontaneous plant hybrids[END_REF]. In plants, gene flow is a complex process; it involves propagule dispersal and subsequent interbreeding with individuals in the recipient population. In general, successful gene flow into native populations via pollen from gardens and roadside ornamentals, from restoration and commercial plantations or even from transgenic tree plantations into native forests is likely to initiate introgression. Because tree plantations of exotic or 'improved material' are often located in close proximity to native stocks, opportunities for introgression involving forest trees are frequent.

Forest-tree genera include major crop species such as pine (Pinus L.), spruce (Picea A. Dietrich), fir (Abies Miller), oak (Quercus L.), eucalyptus (Eucalyptus L'Hérit.) and poplar (Populus L.); widespread horticultural genera that include major crop species are junipers (Juniperus L.) and cypresses (Cupressus L.) and fruit crops. Most of these genera hybridize naturally with wild congeners, creating a steady supply of genetic novelty on which evolutionary processes can operate. Also, over the last 50 years tree breeders have developed highly successful artificial hybrids, for example, Pinus caribaea var. hondurensis (Sénécl) Barrett et Golfari × P. elliottii Engelm. var. elliottii, P. rigida Mill. × P. taeda L., Castanea crenata Siebold & Zucc.× C. sativa L. These hybrids frequently involved allopatric species, as in the example of Populus × euramericana, using North American P. deltoides Bartram ex Marshall and European P. nigra L.

New knowledge on tree genomes is expected to promote, in the decades ahead, the domestication of forest trees to the level of herbaceous crops, for instance, through the commercial use of transgenic trees [START_REF] Campbell | Forestry's fertile crescent: the application of biotechnology to forest trees[END_REF]). This will increase interest in conserving native germplasm and the adaptive variation it harbours.

Human-mediated introgression: risks and consequences

The occurrence of introgression into native forests may have ecosystem-wide effects. For example, hybridization in eucalypts affects the abundance of associated herbivorous insects and pathogenic fungi [START_REF] Whitham | Plant hybrid zones as centers of biodiversity: the herbivore community of two endemic Tasmanian eucalypts[END_REF], potentially affecting higher trophic levels.

Global changes in genetic diversity can also take place, depending on the levels of allelic diversity in the exotic plantations and the native populations.

Introgression may also have important adaptive consequences for single local populations. On the one hand, reduced adaptation to local conditions can arise because of gene immigration from distant populations (i.e. 'migrational load'). On the other hand, introgression can both increase the genetic variability available for the evolution of adaptation in marginal populations (the 'rescue effect') and reduce the deleterious effects of inbreeding in small populations [START_REF] Lenormand | Gene flow and the limits to natural selection[END_REF].

Interspecific hybridization

One type of human-mediated introgression derives from the possibility of hybridization with related species that have been planted beyond the range of their original distribution. Simulation analysis has shown that, for high levels of introgression to occur between two hybridizing populations, there must be high levels of interfertility and limited immigration of pure individuals from nearby populations of one or the other parent species into the hybrid zone [START_REF] Ferdy | Extinction and introgression in a community of partially crossfertile plant species[END_REF]. The same study suggests that when interfertility is moderate, relative to immigration from the monospecific, an initial population size difference between the two species will ultimately result in the probable extinction of the rarer species. It can be expected, however, that when selection pressure against (or in favour of) the hybrids is strong, the process of introgression will be delayed (or enhanced) substantially.

The risk of hybridization and rate of introgression with exotic species also depend on the taxonomic distance between the species involved. In Eucalyptus, for instance, [START_REF] Potts | Genetic pollution of native eucalypt gene pools-identifying the risks[END_REF] found 0.03% to 3.90% of native forests were first generation (F 1 ) hybrids. The potential for hybridization and the viability of F 1 hybrids was higher among species belonging to the same section of the genus. However, despite the scarcity of crosses between species of greater taxonomic divergence, their impact on native genepools is potentially greater than that produced by crosses between less divergent species. For example, introgression of genes from the exotic Populus deltoides into the European black poplar (P. nigra), caused by gene flow from cultivated hybrid poplars (Populus × euramericana), is considered a major threat to the native species, even though estimates of introgression levels are low (<5%) (van Dam and Bordács 2002; Storme et al. 2004).

Other concerns regarding tree species artificially moved beyond their original locations are (1) the fact that allopatric species may lack barriers to hybridization, which would make crossfertilization easier when the two species are artificially brought together [START_REF] Potts | The risk of genetic pollution from farm forestry using eucalypt species and hybrids[END_REF]; and

(2) the fact that hybrids produced via advanced reproductive technology (e.g. the use of pollen solvents for pollen extraction) can circumvent natural barriers to interbreeding, allowing backcrosses to the parental species. Thus, widespread planting of exotic species or artificial hybrids might, when they hybridize with local stocks, deeply affect native populations and, in some cases, lead to the assimilation of the native stock by the exotic.

Exchange among seed sources or provenances

At the intraspecific scale, reproductive barriers with local conspecific populations are not expected and, as a consequence, a high level of genetic exchange exists. The global impact of seed transfer varies according to the origin of the material transplanted, the destination environment and the local population size (Figure 2 in [START_REF] Lefèvre | Human impacts on forest genetic resources in the temperate zone: an updated review[END_REF].

Lack of domestication in many tree species implies that the only possible breeding of these trees is done by selection among available seed sources, which, in some cases, involves the movement of plant material over large geographic distances. Long-distance transplantations may be significant because variation in adaptive traits among seed sources may be substantial, as in the example of the Mediterranean pine [START_REF] Alía | Mejora genética y masas productoras de semilla de los pinares españoles[END_REF]. Consequently, valuable adaptive traits and/or gene complexes developed in a particular local environment may become diluted or eventually lost through admixture with commercial exotic seed sources.

An interesting case is provided by the Scots pine. Pinus sylvestris var. nevadensis H. Christ is a relict variety of this widespread species. It is found only in the Sierra Nevada National Park (Spain), which lies at the southernmost extremity of the pine's range. The entire population of the relict variety is found as scattered stands over an area of about 120 hectares. This area is surrounded by plantations of Scots pine of unknown origin (about 18 000 ha) that show clear divergence from the native local stock, according to molecular marker studies by J.J. Robledo-Arnuncio (unpublished data).

Because both mtDNA [START_REF] Sinclair | The postglacial history of Scots pine (Pinus sylvestris L.) in western Europe: evidence from mitochondrial DNA variation[END_REF]) and quantitative growth studies [START_REF] Alía | Genetic variability of Spanish provenances of Scots pine (Pinus sylvestris L.): growth traits and survival[END_REF]) have shown the uniqueness of P. sylvestris var. nevadensis, introgression from the exotic conspecifics may result in the loss of genetic variation of potentially high local ecological value. We are currently assessing the actual risk of introgression, testing whether effective pollen migration from the plantations into the relict population is taking place and whether the resulting progeny are successfully establishing and backcrossing with the local trees.

Transgenic movements

In the last decade, serious concerns have arisen regarding the use of biotechnological tools. These tools could lead to the production of genetically modified trees for a wide range of traits such as insect and herbicide resistance, lignin composition and content, salinity and drought tolerance and reproductive sterility [START_REF] Coventry | Forest certification and genetic engineered trees: will the two ever be compatible? Occasional Paper[END_REF][START_REF] Campbell | Forestry's fertile crescent: the application of biotechnology to forest trees[END_REF]. Introgression of neutral transgenes into native populations is probably not important, but major risk is associated with introducing transgenes with significant fitness effects such as insect resistance (e.g. poplar or spruce engineered to produce Bt toxins) or herbicide tolerance (e.g. reduced sensitivity to glyphosate).

Risk assessment studies of the impact of gene flow from transgenic trees into native poplar stands, using the Simulation of Transgene Effects in a Variable Environment (STEVE) model [START_REF] Difazio | Measuring and modelling gene flow from hybrid poplar plantations: implications for transgenic risk assessment[END_REF], showed low neutral transgene flow (about 1.4%) over 25 years. The flow, however, became significant over 100 years (9.50%), with continuous increase over time for an insect-resistance transgene conferring growth benefits in the wild.

Because of the potential for widespread escape of transgenes into natural forests and the difficulty of assessing their long-term evolutionary consequences, several authors have suggested the development of male sterility in transgenic trees as an advisable prerequisite for their commercial use [START_REF] Potts | The risk of genetic pollution from farm forestry using eucalypt species and hybrids[END_REF] and references cited therein). Male sterility is not sufficient, however, because transgenic plants can serve as seed parents, receiving pollen from the natural population and subsequently dispersing hybrid seeds (carrying both the transgene and the male-sterility gene) into wild populations. Moreover, male sterility would not remove the other risks associated with transgenic releases. For example, in trees engineered for pest resistance, strong selective pressures may be exerted on pest populations, thus fostering the evolution of genetic resistance in the pest to those same chemicals in the transgenic tree.

Introgression and management strategies for the genetic reserves of forest trees

The conservation of local adaptive variation and interest in the preservation of local genetic identity of forest tree populations (frequently through the establishment of genetic reserves) are recent developments, dating back only a few decades. In contrast, germplasm movements and tree breeding have been documented from much earlier times; examples are the massive propagation across western Europe of an English elm clone by the Romans [START_REF] Gil | English elm is a 2,000-year-old Roman clone[END_REF]) and the successful introduction of Pinus radiata D. Don into Australia in the 1850s. For most forest trees, however, a complex mosaic of native populations is commonly found, including forests proposed as in situ conservation areas, and plantations of exotic seed sources (often of unknown origin) or even exotic species.

Although our knowledge of the ultimate evolutionary consequences of introgression in the wild is limited, preventing introgression of exotic genes into genetic reserves may well be an appropriate measure to fulfil a customary objective, which is to preserve the natural evolutionary processes in the local ecosystem. In particular cases, however, the introduction of novel genes into genetic reserves, in the form of individuals from other locations, may be required to preserve the viability of small inbred populations. Empirical evidence exists to support the assertion that this action may increase the fitness of endangered plant populations [START_REF] Heschel | Inbreeding depression, environmental stress, and population size variation in scarlet gilia (Ipomopsis aggregata)[END_REF][START_REF] Richards | Inbreeding depression and genetic rescue in a plant metapopulation[END_REF].

In other cases, the viability of the endemic species may be severely threatened by introgression. A classic example, reported by [START_REF] Frankham | Introduction to conservation genetics[END_REF], is the Catalina Island mountainmahogany (Cercocarpus traskiae Eastw.), a small endangered tree from Catalina Island (California, USA). Hybridization with a closely related species (C. betuloides Nutt.) affected about 40% of the remaining trees so that, by 1996, only 11 mature individuals existed from a population of 40.

Management strategies to limit gene flow into genetic reserves of forest trees involve one or more of the following actions [START_REF] Adams | Magnitude and implications of gene flow in conservation reserves[END_REF]: (1) controlling the location, size and isolation of the reserves; (2) maximizing pollen production within reserves, relative to surrounding stands; and (3) controlling mating within the reserve. Particular attention is needed to design conservation units sufficiently large and isolated from genetic pollution sources.

Most authors suggest isolation distances from exotic sources of pollen of about 1000 m [START_REF] Potts | The risk of genetic pollution from farm forestry using eucalypt species and hybrids[END_REF] and references cited therein). Geographic isolation is probably insufficient for many cases, and the use of guard rows of inert genotypes or nonhybridizing species is advisable. For example, for the European black poplar large differences in introgression levels exist, depending on the presence of P. nigra males competing as pollen donors with the exotic hybrid Populus × euramericana (van Dam and Bordács 2002;[START_REF] Broeck | Gene flow between cultivated poplars and native black poplar (Populus nigra L.): a case study along the river Meuse on the Dutch-Belgian border[END_REF]). Establishing rows of male P. nigra trees surrounding hybrid poplar plantations might reduce the impact of the hybrids on native stands.

A very effective and feasible strategy to preserve the long-term genetic integrity of a population from undesirable introgression is to reinforce recruitment from the local (pure) forest, for example by planting offspring obtained by artificial crossing of pure individuals. This strategy can be more easily accomplished than removing hybrids or preventing hybridization [START_REF] Ferdy | Extinction and introgression in a community of partially crossfertile plant species[END_REF].

Phenological differences among seed sources can also constitute a significant barrier to gene interchange. In fact, [START_REF] Burczyk | Complex patterns of mating revealed in a Eucalyptus regnans seed orchard using allozyme markers and the neighborhood model[END_REF], examining a Eucalyptus regnans F. Muell. seed orchard that included two different seed sources (Tasmania and Victoria, Australia), found crosses between trees from the same origin to be three times more frequent than between trees with different origins, primarily because of phenological differences (but see [START_REF] Chuine | A modeling analysis of the genetic variation of phenology between tree populations[END_REF]. Because timing and intensity of flowering seem to be under genetic control [START_REF] El-Kassaby | Genetic variation and correlation in growth, biomass and phenology of Douglas-fir diallel progeny at different spacings[END_REF][START_REF] Farmer | Latitudinal variation in height and phenology of balsam poplar[END_REF], deployment of plant material secondarily selected for delayed onset, different phenology, low flowering rate or even sterility may also help reduce genetic pollution of genetic reserves by commercial plantations.

Conclusions

Forest trees are long-lived, largely undomesticated organisms that generally grow in wild multipurpose ecosystems. Introgression is a natural process of great importance to plant species for creating novel and valuable variation. However, many effects are also potentially negative, especially when exotic species or transgenics are involved. A case-by-case analysis is therefore necessary. Introgression in forest trees can be assessed at different levels of increasing potential impact: gene transfer among seed sources, interspecific hybridization and, most relevant, transfer from transgenic tree plantations.

We identified two major risks: (1) that associated with the introduction of transgenes with significant fitness effects; and (2) hybridization with exotic species or with exotic conspecifics when native local stocks have low effective population sizes. We also described methods to prevent introgression in genetic reserves.

Notwithstanding the available knowledge, the process of introgression in forest trees is still poorly understood and further research is urgently needed. Research priorities should include (1) the study of the precise spatial extent of pollen and seed flow, particularly the role of long-distance dispersal events in the dynamics of introgression; (2) differences in fitness of native and introgressed stocks, under both controlled and field experimental conditions; (3) risks of introgression into native populations of major tree crops, including those targeted for gene modification; and (4) the impact of human-mediated introgression on biodiversity at the ecosystem level.

Harvest Centres supported by the Consultative Group on International Agricultural Research (CGIAR), an association of public and private members who support efforts to mobilize cutting-edge science to reduce hunger and poverty, improve human nutrition and health, and protect the environment. IPGRI has its headquarters in Maccarese, near Rome, Italy, with offices in more than 20 other countries worldwide. The Institute operates through four programmes: Diversity for Livelihoods, Understanding and Managing Biodiversity, Global Partnerships, and Improving Livelihoods in Commodity-based Systems.

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ISBN-10: 92-9043-693-X