Charles Figuieres

David Masclet

Marc Willinger

Weak moral motivation leads to the decline of voluntary contributions

Keywords: Conditional cooperation, voluntary contributions, moral motivation, experiments on public goods games. JEL

This paper provides a general framework that accounts for the decay of the average contribution observed in most experiments on voluntary contributions to a public good. Each player balances her material utility loss from contributing with her psychological utility loss of deviating from her moral ideal. The novel and central idea of our model is that people's moral motivation is "weak": their judgement about what is the right contribution to a public good can evolve in the course of interactions, depending partly on observed past contributions and partly on an intrinsic "moral ideal". Under the assumption of weakly morally motivated agents, average voluntary contributions can decline with repetition of the game. Our model also explains other regularities observed in experiments, in particular the phenomenon of over-contributions compared to the Nash prediction and the so-called restart e¤ect, and it is compatible with the conditional cooperation hypothesis.

Introduction

Several experimental studies have documented strong empirical regularities in linear public goods experiments including [START_REF] Goeree | A theoretical analysis of altruism and decision error in public goods games[END_REF] the fact that people contribute more than predicted by the standard theoretical prediction; and (2) that average contribution declines steadily over time when the game is repeated under a …nite horizon. 1 In contrast to the huge amount of literature concerned with the puzzling fact that subjects over-contribute with respect to their Nash contribution, the attempts made to explain the decline of the average contribution observed in most linear public goods experiments are not clear-cut. These attempts boil down to three major explanations : learning, strategic play and other regarding preferences including reciprocity (conditional cooperation).

According to the learning hypothesis over-contributions in early rounds arise because subjects are confused and make errors. As time elapses, and feedback from past rounds becomes available, they realize that they could earn more by over-contributing less, and adjust their current contribution accordingly. However, available evidence about learning suggests that it plays a limited role in the decay. Neugebauer et al. (2009a) found that repetition without feedback has no e¤ect on average contribution which seems to suggest that there is no learning by introspection. Decay arises only when information about the contribution of group members is provided. In contrast, Houser & Kurzban found a sharper decay when a subject plays against a computer program. 2 Nevertheless, the learning hypothesis seems incompatible with the "restart e¤ect" found by Andreoni (1988). 34 1 See [START_REF] Ledyard | Public goods: A survey of experimental research[END_REF] for a review of this literature published prior to 1995; See also [START_REF] Andreoni | Cooperation in Public-Goods Experiments -Kindness or Confusion?[END_REF][START_REF] Croson | Partners and strangers revisited[END_REF]Gaechter & Fehr, 1999;[START_REF] Keser | Conditional cooperation and voluntary contributions to public goods[END_REF]Fehr & Gaechter, 2000;[START_REF] Masclet | Monetary and Nonmonetary Punishment in the Voluntary Contributions Mechanism[END_REF][START_REF] Carpenter | Punishing Free-Riders: How Group Size A¤ects Mutual Monitoring and the Provision of Public Goods[END_REF][START_REF] Sefton | The E¤ect of Rewards and Sanctions in Provision of Public Goods Economic Inquiry[END_REF]; Herman, Toeni & Gaechter, 2008. 2 In their computerized treatment human subjects were told that the 3 other members of their group where computerized players, which followed a predetermined contribution path. The latter was chosen to be equal to 3 4 of the average contribution observed in the human condition, and the computers' current choice was announced at the beginning of each round. Overcontribution did not vanish even after 10 rounds. Houser & Kurzban's conclusion is that more than 50% of the overcontribution is due do confusion. 3 After having played 10 rounds of a linear public good game, Andreoni told his subjects that a new sequence of 10 rounds will be played. Surprisingly, he observed that the average contribution of the …rst restart period does not di¤er from the average …rst period contribution in the initial sequence. 4 Anderson et al. ( 2004) developed a more sophisticated theory of learning based on quantal response. Anderson et al. (2004) show that the dynamic process of individual contributions follows the well-known Fokker-Planck equation and converges to the logit equilibrium distribution of contributions. Despite its mathematical elegance, the model has two limitations : …rst, the model does not explain why contributions are sensitive to the remaining number of periods as observed in partner sessions (due to the neglect of strategic interactions across periods), and second, it assumes that subjects are able to best-respond to the stochastic distribution of other players' contributions by choosing a stochastic distribution over their strategy space, which requires a high degree of sophistication for each player to form expectations about other players' choice probabilities. While the model nicely describes the patterns observed in the data, "as if" subjects'behaviour was of the QRE type, it is not very plausible from a behavioural point of view.

1

The second candidate explanation for the decay in average contribution is reputation. The hypothesis of "strategic play" is based on the idea that players take into account future interactions when choosing their current contribution. Therefore, in early periods they have an incentive for establishing a cooperative reputation, by making a large contribution. The justi…cation of the strategic hypothesis is based on the "crazy player"assumption [START_REF] Kreps | Rational cooperation in the …nitely repeated Prisoners'Dilemma[END_REF], or equivalently on the lack of common knowledge of rationality. If (rational) players believe that there is a crazy player in the group who contributes positively in period 1, it becomes rational for them to play a trigger strategy in early periods and to mix over the strategy space as the repeated game approaches the …nal period. 5 Andreoni (1988) o¤ered the …rst test of the reputation hypothesis by comparing the average contributions of partner groups with stranger groups. Since there is no incentive to develop a cooperative reputation among strangers, one should observe higher over-contributions in partner-groups than in stranger-groups, especially in early periods of the repeated game. Surprisingly, Andreoni (1988) found that strangers contribute more than partners, that the di¤erence in average contribution increases over time, and that complete freeriding is signi…cantly more frequent in the partner treatment. These …ndings seem to undermine the reputation hypothesis as a plausible explanation of the decay in average contributions. 6 The third explanation is rooted in other-regarding preferences. Altruism 7 can account for the fact that people contribute more than their pure self-interested contribution, but cannot explain the decay in contribution. A more plausible explanation is conditional cooperation, i.e. the fact that people choose to cooperate, depending on previously observed decisions of others or on beliefs about their decisions (e.g. [START_REF] Keser | Conditional cooperation and voluntary contributions to public goods[END_REF]Fischbacher, Gaechter and Fehr, 2001;[START_REF] Croson | Theories of commitment, altruism & reciprocity: evidence from linear public goods games[END_REF]Fischbacher & Gaechter, 2009). Up to recently, reciprocity theories tended to attribute the decay to preference heterogeneity : reciprocal cooperative players are mixed with sel…sh agents who free-ride on others'contributions. In a given period, a reciprocal player who 5 Strategic play is compatible with the fact that most subjects over-contribute in early periods and switch to their Nash contribution at some later period (see e.g. [START_REF] Isaac | Group size and the voluntary provision of public goods: Experimental evidence utilizing large groups[END_REF], Laury (1997), Keser & vanWinden (2000)). In early periods they signal a desire to cooperate, but as the end of the game approaches their incentive to do so vanishes, and they switch to their Nash contribution. The evidence that the decay is slower in longer games [START_REF] Isaac | Group size and the voluntary provision of public goods: Experimental evidence utilizing large groups[END_REF]) is compatible with the strategic hypothesis. 6 Note however that there is no clear evidence that stranger contribute signi…cantly more than partners. Indeed, several studies have also found the opposite, showing that partners contribute signi…cantly more than strangers (see for example [START_REF] Croson | Partners and strangers revisited[END_REF], Fehr & Gaechter, 2000;[START_REF] Masclet | Monetary and Nonmonetary Punishment in the Voluntary Contributions Mechanism[END_REF]. However these studies also indicate that average contribution under stranger matching condition still decline over time as the game is repeated, which cannot be explained by the reputation hypothesis. 7 One potential explanation relies on the idea that people cooperate because they "take pleasure in others' pleasure" (see e.g. Dawes and Thaler,1988). Theory of altruism presented by [START_REF] Andreoni | Giving According to GARP: An Experimental Study of Rationality and Altruism[END_REF] assumes that an altruistic player's utility increases not only in his own payo¤ but also in the other players'payo¤s. Two forms of altruism are generally given in the literature: "pure altruism" (individuals care about others'payo¤s) and "warm-glow" altruism (individuals enjoy contributing per se). However, both pure and impure altruistic motives cannot adequately describe the decline of contribution observed in public goods experiments. Indeed why would altruistic motives vanish over time?

either observes that his contribution is above the average, or who expects others to contribute less, will reduce his contribution, and therefore the mean contribution declines. But heterogeneity per se is neither a necessary nor a su¢ cient condition for the decline. 8 Heterogeneity can either reinforce or attenuate the tendency for the decline, but is not the central driving force of the process. According to Fischbacher & Gaechter (2009) imperfect conditional cooperation is the main driving force behind the decay : "Many people's desire to contribute less than others, rather than changing beliefs of what others will contribute over time". There is strong experimental evidence for such imperfect reciprocity (Fischbacher & Gaechter, 2009[START_REF] Fischbacher | Are people conditionally cooperative? Evidence from a public goods experiment[END_REF] or sel…shly-biased reciprocity [START_REF] Neugebauer | Sel…sh-biased conditional cooperation: On the decline of contributions in repeated public goods experiments[END_REF]. A conclusion from this short literature review is that imperfect reciprocity is the main driving forces underlying the decay, while learning and strategic behavior reinforce this tendency.

In this paper, we propose a new model of behavior, compatible with the imperfect conditional cooperation hypothesis, that accounts for the decline of average contribution. Precisely, it is based on the idea that agents set their moral target by relying on two dimensions : a "morally ideal contribution" (see [START_REF] Brekke | An economic model of moral motivation[END_REF][START_REF] Nyborg | Homo economicus and homo politicus: Interpretation and aggregation of environmental values[END_REF] and the observed contributions of others. The assumption that people rely on a morally ideal contribution is defended by commitment theories (see e.g. [START_REF] Croson | Theories of commitment, altruism & reciprocity: evidence from linear public goods games[END_REF]). Based on Kantian reasoning, these theories assume that individuals make "unconditional" commitments to contribute to the public good. Our originality is to assume that for most people such commitments are weak in the sense that they are sensitive to the observation of others'actions. In a contribution context, individuals might therefore be tempted to revise their preferred contribution after observing others'contributions. The extent of such a revision typically varies across individuals : strongly morally motivated agents will closely stick to their ideal contribution, while weakly motivated agents are prone to revise their morally ideal contribution whenever they observe a gap between their own and others'contributions. Our idea of weakly morally motivated agents captures a large spectrum of contribution behaviors : at one extreme, unconditional contributors, who always stick to their ideal contribution whatsoever, and at the other extreme pure reciprocators who always match the observed group contribution. Free-riding behavior is a particular case of unconditional behavior : always contributing zero in a linear public good game whatever the other group members do. Our idea, is that most people are of the "mixed" type, i.e. their actual contribution is the outcome of a deliberative process through which their preferred contribution is balanced against others'observed average contribution. The assumption of weakly morally motivated agents o¤ers a possible justi…cation for imperfect reciprocal behavior that we call action-based reciprocity : individuals'ideal contribution is sensitive to others'observed contributions. Alternatively, individuals might also decide about their contributions by relying on their expectations about others' contributions (belief-based reciprocity). However, such beliefs are themselves revised according to observed contributions.

The model is primarily designed to explain the decline of average contributions in linear public goods experiments. However, it is also compatible with several other stylized facts observed in experiments on voluntary contributions to a public good. For linear public goods experiments these facts may be summarized as follows : a) subjects contribute half of their endowment in the …rst period, b) the average contribution tends to decline as the game is repeated, c) there is signi…cant over-contribution in the …nal period, d) there is high variance of individual contributions, e) most subjects adjust their contribution from one period to the next. Similar observations have been made for interior Nash equilibria and for interior dominant strategy equilibria, except that stylized fact a) should be understood as "subjects contribute mid way between the equilibrium contribution and the socially optimum contribution" (see [START_REF] Sefton | Reward structures in public good experiments[END_REF], Laury & Holt, 1998). Although we are mainly concerned with facts b) and e), our model is also compatible with facts a), c) and d).

Section 2 introduces the concept of weak moral motivation and shows its implications for the dynamics of average contributions in a simple linear public good model with myopic agents. Section 3 extends the results to non-myopic agents. Our assumptions and results are discussed in section 5 and contrasted with other models, with a particular attention to [START_REF] Kandori | The erosion and sustainability of norms and morale[END_REF], Klumpp (2005) and Ambrus & Pathak (2007) that are closely linked to our idea. Section 6 concludes.

Weak moral motivation and voluntary contributions

Consider n agents, indexed i = 1; :::; n; who can contribute voluntarily to a public good. Each of them has an endowment w i , which he can split between his contribution to the public good, x i , and the consumption of private goods, w i x i . Using the notation x i = P j6 =i x j , the cardinal representation of agents'preferences with moral motivation is :

U i (x i ; x i ; b x i ) = w i x i + i (x i + x i ) v i (x i b x i ) : i = 1; :::; n; (1)
where i 2 ]0; 1[ is the marginal utility from consuming G = x i + x i ; the public good 9 . Agent i's moral motivation is embodied in the function v i (:), where b x i stands for his moral obligation. Her loss of utility attached to any deviation from her moral obligation is v i (x i b

x i ). This function is assumed to be convex. In addition two natural assumptions about v i (:) are as follows:

Assumption 1 v i (0) = 0; v i (x i b x i ) > 0 i¤ x i 6 = b x i : Assumption 2 v 0 i (:) R 0 , x i b x i R 0
The …rst assumption is obvious: a departure from one's moral obligation entails a loss of utility. The second assumption means that, starting from a situation where agent i contributes less (more) than her moral obligation, a marginal increase of x i reduces (increases) her loss of utility.

We shall conceptualize the weak moral motivation of each agent as a combination of two logics : an autonomous logic and the logic of social in ‡uence. The autonomous logic is captured by an ideal, or "ethical", level of contribution noted x i 0. For instance, it could correspond to a Pareto optimal level of contributions, i.e. contributing w i for each i. Such autonomous logic can be grounded on a Kantian Categorical Imperative, or on an unconditional commitment to a contribution [START_REF] La¤ont | Macroeconomic Constraints, Economic E¢ ciency and Ethics : An Introduction to Kantian Economics[END_REF][START_REF] Harsanyi | Rule Utilitarianism, Rights, Obligations and the Theory of Rational Behavior[END_REF]). The second logic, our originality, captures social in ‡uences via the average contribution observed in the immediate past, x t 1 0. The group contribution is publicly observed after each period. Each player can therefore compare his contribution to the average group contribution. Discovering that her own contribution di¤ers from the group contribution eventually leads her to judge that the society is less (or more) deserving than she initially though, and consequently to revise her moral obligation b x i . For example a player who discovers that he has contributed more (less) than the average might decrease (increase) his current moral obligation. This "weakness" in moral motivations echoes popular and well-documented ideas among moral philosophers and moral psychologists. Those scholars will see some bearings with the internalist versus externalist moral motivation debate that discusses the interactions between individual motivations and moral judgments (see for instance [START_REF] Zangwill | Externalist moral motivation[END_REF]. Do moral ideals motivate people's decisions or are moral opinions an ex-post rationalization largely dictated by social in ‡uences and circumstances? Our concept is also at takes with their discussion about the weakness of will (which they refer to as akrasia, see Holton 2007), an over-readiness to abandon or revise one's moral resolution. Do people change their mind in the course of interactions with others or is their will insu¢ ciently strong to overcome the cost of respecting their moral judgement? The standard decision theory used in economics typically ‡attens those aspects. The goal of the so-called behavioral economics program is to bring such aspects into economics. We will get back brie ‡y to those subtleties in the conclusion of the paper.

Overall, the quali…ed moral obligation, b x it , is de…ned as a function of the aforementioned variables:

b x it = (
x i ; t = 0; M i (x i ; x t 1 ) ; t = 1; 2; ::: where function M i (:; :) is discontinuous at t = 0, for there is no previous observations at that date that could be used to qualify the autonomous ethical level.

The moral obligation function satis…es the intuitive properties:

Assumption 3 @M i @x i = M i 1 0; @M i @x t 1 = M i 2 0; Assumption 4 x min it = min fx i ; x t 1 g M i (x i ; x t 1 ) x max it = max fx i ; x t 1 g :
Also, it is assumed that the aggregate quali…ed moral obligation is bounded above by the aggregate autonomous moral obligation:

Assumption 5 P i M i (x i ; a) P i x i = G ; 8a 0:
Assumption 5 plays a key role for the dynamics of contributions in the linear public good's game. According to this assumption aggregate contributions cannot exceed the aggregate initial moral motivation. For instance, if x i = w i for all i, actual contributions are necessarily bounded by aggregate endowment. In a more general sense, Assumption 5 means that players' moral motivation is not grounded on utopia but on realism and feasibility. However, while Assumption 5 holds in aggregate, it needs not be true at individual levels, i:e: M i (x i ; a) > x i for some i and some a is a possibility.

Example 1 An illustration of a weak moral motivation function is the following:

b x it = (1 i ) x i + i x t 1 ; i 2 [0; 1] ; = x i i (x i x t 1 ) :
The weight 1

i may be interpreted as the "strength" of agent i's moral motivation. If i = 0 agent i has as strong moral motivation : he never deviates from his ideal contribution, whatever the observed average contribution by other members of his group. On the other hand, an agent for whom i is close to 1 will strongly revise her initial moral ideal, whenever her current contribution di¤ ers from the average group contribution. Assuming the above revision rule, a purely reciprocal player can be de…ned as a player for whom i = 1, while a unconditional free-rider is de…ned by i = 0 and x i = 0:

If the contribution game is played only once, player i has a dominant strategy to contribute less than his moral motivation. He chooses x i to solve :

max x i w i x i + i (x i + x i ) v i (x i x i ) :
The …rst order condition gives :

1 + i = v 0 i (x i x i )
At equilibrium the agent equalizes the marginal material cost of a contribution ( i 1) to the marginal moral cost of a deviation from her moral ideal (v 0 i (x i x i )), which implies that her actual contribution is less than her moral ideal :

x i = x i + v 0 i 1 ( i 1) < x i ; since i < 1, (v 0 i ) 1 ( i 1) < 0.
While our de…nition of weak moral motivation is related to a player's sensitivity to social in ‡uence, the above result shows that there is also a "private component" that drives agents' decisions. The latter can be thought as the temptation to deviate from the moral ideal, in order to increase one's material utility. Indeed the individual chooses her optimum level of contribution by equalizing the marginal material cost of a contribution to the marginal moral cost of deviating from the moral ideal. As we shall see below, this sel…sh bias towards the material payo¤ plays also a role in the decay of average contributions.

Repeated play with myopic contributors

Assume now that the contribution game is played a …nite number of periods. We assume that in each period players rely on their current updated moral motivation, which is determined by the observed average contribution of the previous period. A key assumption for this section, which is relaxed later in the paper, is that players do not take into account their in ‡uence on other players'future moral motivation when choosing their contribution. We de…ne therefore, for each period of time, a Myopic Nash Equilibrium (MNE) 10 as a pro…le of contributions such that each agent's contribution maximizes his own current utility, given the other agents'contributions:

max x it w i x it + i (x it + x it ) v i (x it b
x it ) :

From the …rst order conditions, interior decisions solve:

1 + i = v 0 i (x it b x it ) ; 8i; 8t;
thus individual equilibrium contributions at period t are:

x it = M i (x i ; x t 1 ) + v 0 i 1 ( i 1) ; 8i :
The revision rule for the moral motivation naturally leads to an interpretation of action-based reciprocity: current period contributions are partly determined by past observed contributions (and partly by individuals'moral motivation). The revision rule can be easily adapted to capture belief-based reciprocity. If we substitute "others'average contribution in the previous period" by the "expectation about others'contributions". The revision rule becomes b

x it = M i (x i ; x e it ) ;where x e it is agent i's expectation of the average contribution of other players for period t. The interpretation is now that agent i determines her current contribution by taking into account her expectation about the (current) contribution of other players and her initial moral motivation. The two formulations do not fundamentally di¤er if we assume that individuals'expectations are positively related to their observed contributions of other group members, i.e. if x e it = f (x it 1 ), with f 0 (:) > 0. With this assumption we restrict our interpretation to action-based reciprocity.

Proposition 1 At a MNE, the level of public good is non increasing over time. If Assumption 5 is veri…ed with a strict inequality, then the level of public good is strictly decreasing over time.

Proof. The proof is established recursively. Note …rst that G 1 = P

i x i + P i (v 0 i ) 1 ( i 1) P i x i because P i (v 0 i ) 1 ( i 1) 0: Then observe that G 2 = P i M i x i ; G 1 n + P i (v 0 i ) 1 ( i 1) G 1 ; because P i M i x i ; G 1 n P i x i by
= P i M i x i ; G k n + P i (v 0 i ) 1 ( i 1) is not larger than G k = P i M i x i ; G k 1 n + P i (v 0 i ) 1 ( i 1)
; because each M i (:; :) is an increasing function of its second argument and this argument has fallen, G k G k 1 .

To obtain the second claim of the proposition, repeat the same logic using strict instead of large inequalities. Assumption 5 turns out to be crucial in explaining the decay of aggregate contributions. It can receive two justi…cations. First, the assumption is necessarily satis…ed in period 1, since the sel…sh bias curbs downwards each individual's contribution with respect to her initial ideal contribution. Of course, this fact does not preclude that some players adjust their moral ideal upwards. Assumption 5 can therefore be thought in the following way : downwards adjustments by high-motivated agents always loom larger than upwards adjustment by low-motivated agents. Second, and more generally, it is reasonable to set as an upper limit to the aggregate moral ideal. Budget constraints are on obvious reason. But more importantly, the fact that group interactions occurs only over a …nite number of periods, sets a natural upper boundary on individual revised moral ideals, whenever these are in ‡uenced by social interactions.

We now turn to another important regularity in public good experiments, namely that even at the end of the interactions subjects over-contribute signi…cantly compared to the Nash prediction. The dynamics of aggregate equilibrium contributions G t = P i x it are:

G t = X i M i x i ; G t 1 n + X i v 0 i 1 ( i 1) : (2)
The dynamic process in (2) can eventually reach a level of contribution equal to zero, the free-riding equilibrium in standard linear public good's games. To account for over-contributions in our framework, two additional assumptions on the moral motivation function are required : the …rst one stipulates that an increase of the previous level of public good has a less than proportional positive e¤ect on the levels of weak moral motivations:

Assumption 6 M i 2 1:
The second requires the moral motivation to be strong enough to induce a positive level of public good at a MNE even if the previous observable level was zero, i.e. even with an extremely adverse social in ‡uence.

Assumption 7 P i M i (x i ; 0) P i (v 0 i ) 1 ( i 1) :
Theorem 2 Under Assumptions 5, 6 and 7, the sequence of public good levels converges to a unique positive interior level G 1 2 ]0;

P i x i [.
Proof. Under Assumption 6, the right hand side of the dynamics (2) is a contraction. Therefore, according to Banach's …xed point theorem : i) the dynamics (2) has a unique steady state, ii) the sequence converges towards this steady state. Assumptions 5 and 6 respectively discard the zero and full contributions corner stationary points.

Proposition 2 Under Assumption 6, the higher the autonomous ethical level x i , the higher the long run level of public good G 1 .

Proof. The long run level of public good solves

G 1 = X i M i x i ; G 1 I + X i v 0 i 1 ( i 1) : (3)
Using the implicit function theorem:

dG 1 dx i = M i 1 1 P h M h 2 I > 0
under Assumption 6.

Proposition 3 Under Assumption 6, the higher the marginal utility of the public good i , the higher the long run level of public good G 1 .

Proof. Using (3) and the implicit function theorem again, one …nds:

dG 1 d i = 1 1 P h M h 2 I v 00 i > 0;
since in the denominator the …rst term between bracket is positive under Assumption 6 and the second term is also positive, for v i (:) is a convex function.

Forward-looking contributors

In this section we relax the assumption of myopic behavior in order to investigate how forward looking behavior a¤ects the dynamics of average contribution. Forward looking players take into account the impact of their current contribution on other players'revised moral motivation in future periods, and are aware that other players try to in ‡uence their own future moral motivation. Such mutual in ‡uence, might eventually lead to an increase in average contributions. We show however that, under reasonable assumptions, the average contribution still declines over time.

Let T be the number periods during which agents interacts and 0 < 1 their common discount factor. We de…ne players'intertemporal utility as :

T X t=0 t U i (x it ; x it ; b
x it ) ; i = 1; :::; n;

where

U i (x it ; x it ; b x it ) = w i x it + (x it + x it ) v i 2 (x it b x it ) 2 ; v i a positive scalar, b x it = (1 i ) x i + i x t 1 = M i (x i ; x t 1 ) ; i 2 [0; 1] :
We will consider a Markov perfect equilibrium (MPE) for this dynamic public good game. Reasoning backward, in the last period agent i takes as given x iT and solves:

max x iT w i x iT + i (x iT + x iT ) v i 2 x iT M i (x i ; x T 1 ) 2 :
He has a dominant strategy, con…gured by the average contribution inherited from the previous period:

x iT = (1 ) v i + M i (x i ; x T 1 ) g iT (x T 1 ) : It is worth noting that g 0 iT = M i 2 (:; :) = i : (4)
Those equilibrium strategies can be plugged back into the last period utility, giving each agent's value function for the last period:

V i T (x T 1 ) U i 0 @ g iT (x T 1 ) ; X j6 =i g jT (x T 1 ) ; M i (x i ; x T 1 ) 1
A :

Moving backward to the before last period, each agent solves:

max x iT 1 ( w i x iT 1 + i (x iT 1 + x iT 1 ) v i x iT 1 M i (x i ; x T 2 ) + V i T x iT 1 +x iT 1 n
)

The optimal decision x iT 1 cancels out the addition of several marginal e¤ects:

i) as when agents are myopic, in the current period:

1 + i v 0 i x iT 1 M i (x i ; x T 2 ) ;
ii) but unlike the case of myopic agents, there is also a marginal e¤ect on the next period @

x iT 1 V i T (x T 1 ) : This expression can be developed as follows:

@ x iT 1 V i T (x T 1 ) = " g 0 iT + i g 0 iT + P j6 =i g 0 jT v 0 i x iT M i (x i ; x T 1 ) g 0 iT M i 2 (x i ; x T 1 ) # @x T 1 @x iT 1 ; = 2 4 g 0 iT + i 0 @ g 0 iT + X j6 =i g 0 jT 1 A 3 5 1 n ; = n 2 4 ( 1 + ) i + X j6 =i j 3 5 :
This second marginal e¤ect explains the di¤erence between the myopic and farsighted behaviors. Note that this di¤erence owes nothing to the next period deviation from the moral motivation. Indeed, a marginal increase of x iT 1 has an impact on the next period moral motivation equal to i dx iT 1 but this increase is exactly o¤set by the next period optimal contribution, as noticed from (4), leaving the gap x iT M i (x i ; x T 1 ) unchanged. The difference only goes through the e¤ect on the last period self-centered part w i g iT (x T 1 ) + i g iT (x T 1 ) + P j6 =i g iT (x T 1 ) : Overall, the …rst order conditions are:

1 + v 0 i x iT 1 M i (x i ; x T 2 ) + n 2 4 ( 1 + ) i + X j6 =i j 3 5 = 0 ; 8i:
Hence, the best (dominant) response for each agent is:

x iT 1 = (1 ) v i + v i n 2 4 ( 1 + ) i + X j6 =i j 3 5 + M i (x i ; x T 2 ) ; (5)
g iT 1 (x T 2 ) :
Observe again that: g 0 iT 1 = M i 2 (:; :) = i : Each agent's value function for the before last period is then:

V i T 1 (x T 2 ) U i 0 @ g iT 1 (x T 2 ) ; X j6 =i g jT 1 (x T 2 ) ; M i (x i ; x T 2 ) 1 A + V i T 0 B B B B @ n X h=1 g hT 1 (x T 2 ) n 1 C C C C A
Recursively it is possible to construct the agents'value functions for each date. There is no conceptual di¢ culty in this exercise but it is tedious and relegated to the Appendix. The important piece of information is that the individual problems at date t generically read as:

max x iT t ( w i x iT t + i (x iT t + x iT t ) v i x iT t M i (x i ; x T t 1 ) + V i T t+1
x iT t +x iT t n

) :

And, using the notation = n P n h=1 h = < 1; the dominant strategy t periods before the last can be written generically:

x iT t = (1 ) v i + v i n 2 4 ( 1 + ) i + X j6 =i j 3 5 t 1 X h=0 h + M i (x i ; x T t 1 ) ; (6)
g iT t (x T t 1 ) :
In particular, at the …rst period equilibrium decisions are:

x i0 = (1 ) v i + v i n 2 4 ( 1 + ) i + X j6 =i j 3 5 T 1 X h=0 h + x i ; (7) = g i0 (x i ) :
We are now in a position to investigate whether those contributions could decline over time.

Assumption 8 Assume that:

(1

) v i + v i n 2 4 ( 1 + ) i + X j6 =i j 3 5 T 1 X h=0 h 0; ( 1 + ) i + X j6 =i j 0:
Those two conditions on parameters are met for instance when agents value su¢ ciently the public good ( is large enough) and discount heavily the future ( small enough). It can then be established: Theorem 3 Under assumption 8, the MPE is characterized by non increasing contributions over time.

Proof. Observe …rst that x i0 x i 8i; by the …rst inequality in Assumption A 8 , hence M i (x i ; x 0 ) x i 8i: Then, we also have:

x i0 x i1 = v i n 2 4 ( 1 + ) i + X j6 =i j 3 5 T 1 + x i M i (x i ; x 0 ) 0; 8i;
since, by the second inequality in 8 the …rst term in the right hand side of the above expression is positive and, as seen above x i M i (x i ; x 0 ) 0: Repeating the comparison of successive contributions, one immediately sees that x it is non increasing over time.

From [START_REF] Andreoni | Giving According to GARP: An Experimental Study of Rationality and Altruism[END_REF], when the horizon growths large (T ! 1), this …rst equilibrium decisions tend to:

x i0 = (1 ) v i + v i n 2 4 ( 1 + ) i + X j6 =i j 3 5 1 1 + x i :
Similarly, considering that period t is the …rst one, and letting the time horizon go to in…nity, it is easy to see that the dominant strategies become stationary feedback rules:

x it = (1 ) v i + v i n 2 4 ( 1 + ) i + X j6 =i j 3 5 1 1 + M i (x i ; x t 1 ) ; (8)
g i (x t 1 ) ; 8i:

Clearly, under Assumption 8; the property of non increasing contributions carries over to the case of an in…nite horizon.

A last question is in order: could this logic of behaviors explains the so-called restart e¤ect? The restart e¤ect can be understood in two related yet distinct ways. In the formalism of our model, when the condition of declining contributions is met, one would speak of a restart e¤ect in either of the two following situations:

1. say that the duration of the game is …rst announced to be of T =2 periods, then at date T =2 1 there is a surprise restart announcement, according to which agents will play a further T =2 periods after date T =2. there is a restart e¤ect if the the contributions at date T =2 with the restart announcement, x 0 i T

2

; are larger than the contributions at the same date without the announcement, x i T 2 .

2. imagine now that the announcement is made at date T =2; there is a restart e¤ect if the the contributions at date T =2 + 1 with the restart announcement, x 0 i T 2 +1 ; are larger than the contributions at date T =2 without the announcement,

x i T 2 .
Let us investigate each possibility in turn. Without the surprise restart announcement, according to (6) or ( 5) at date T =2 agents would contribute:

x i T 2 = (1 ) v i + v i n 2 4 ( 1 + ) i + X j6 =i j 3 5 + M i x i ; x T 2 1
:

With the restart announcement made at date T =2 1, agents treat the problem as if they were engaged in a new T 2 + 1 period game, with an initial moral motivation M i x i ; x T 2 1 ; so their contribution in the next period of this new sequence (at date T =2) is going to be:

x 0 i T 2 = (1 ) v i + v i n 2 4 ( 1 + ) i + X j6 =i j 3 5 T 2 X h=0 h + M i x i ; x T 2 1 :
Comparing the contributions of the two scenarios at period T =2; one …nds:

x 0 i T 2 x i T 2 = v i n 2 4 ( 1 + ) i + X j6 =i j 3 5 T 2 X h=1 h 0;
where the positive sign of the right-hand side is guaranteed from the second inequality in Assumption A 8 : So, Proposition 4 A restart e¤ ect of the …rst kind occurs under Assumption 8.

As for the second kind of restart e¤ect, notice that the contributions in period T =2 + 1, after the announcement at date T =2, are going to be:

x 0 i T 2 +1 = (1 ) v i + v i n 2 4 ( 1 + ) i + X j6 =i j 3 5 T 2 1 X h=0 h + M i x i ; x T 2 :
Next consider the di¤erence:

x 0 i T 2 +1 x i T 2 = v i n 2 4 ( 1 + ) i + X j6 =i j 3 5 T 2 1 X h=1 h +M i x i ; x T 2 h +M i x i ; x T 2 1 i ; = v i n 2 4 ( 1 + ) i + X j6 =i j 3 5 T 2 1 X h=1 h + i h x T 2 x T 1 i : Hence x 0 i T 2 +1 > x i T 2 , i v i n 2 4 ( 1 + ) i + X j6 =i j 3 5 T 2 1 X h=1 h > x T 2 1
x T

:

Observe that, under Assumption 8; the right hand side of the above inequality is positive (because contributions are decreasing) and bounded. Indeed, the average contribution necessarily falls in the interval [0; w i ] ; therefore 0 x T 2 1

x T 2 w i : By contrast, if v i approaches zero, the left hand side of the inequality tends to in…nity. Thus: Proposition 5 Under Assumption 8; there exists values of parameters v i of the weak moral motivation functions such that a restart e¤ ect of the second kind occurs.

Discussion

Three attempts to explain the decline in contributions to public goods are closer to ours than any others. These are [START_REF] Kandori | The erosion and sustainability of norms and morale[END_REF], Klumpp (2005) and Ambrus & Pathak (2007).

The model proposed by [START_REF] Kandori | The erosion and sustainability of norms and morale[END_REF] is based on the general idea that the decline is generated by the erosion of norm and morale. This idea is very close to our concept of weak moral motivation , although the author takes a radically di¤erent modeling approach. As in other models, including our own, Kandori assumes that an individual's utility has two components: a material and a psychological one. The psychological component depends on the di¤erence between his own e¤ort (or contribution) and the median e¤ort in the population. The dynamics is introduced in two ways. First, individuals revise their current e¤ort with respect to the previous period median, which determines therefore a new current median. Second, in each period there is a small probability (the mutation rate) for each player to change his behavior. He ends up choosing randomly, i.e. each level of e¤ort is chosen with equal probability. The author shows that the evolutionary stable equilibria are characterized by declining median e¤ort. With respect to the experimental …ndings about the decay, this model does not account for variability in individual contributions since only the symmetric case is discussed. Furthermore, the model does not account for belief-based reciprocity , since players are assumed to behave myopically. Finally, the hypothesis that players adjust their e¤ort with respect to the median e¤ort, requires that each player observes all other players'individual e¤orts, a context that does not …t most of the available experimental data on voluntary contributions.

Ambrus & Pathak (2007) consider a mixed population of players, which consists of sel…sh and reciprocal types. While the sel…sh players have homogenous preferences, there is heterogeneity among reciprocal types, which is captured by reciprocity functions. The dynamics of the model is generated by the behavior of sel…sh players who have an incentive to contribute large amounts in early periods because of their in ‡uence on future contributions of reciprocal types. The incentive to cooperate of sel…sh players depends on the number of remaining periods in the repeated game. As the end of the game approaches, the sel…sh players switch to their Nash contribution of the one-shot game, i.e. zero contribution. The authors assume a continuous strategy space (players can contribute any real number between 0 and 1). The key assumption for the decline is common knowledge of preferences of all players, in particular reciprocity functions are common knowledge. Although such an assumption can have some realism in a population of players who know each other well and have experienced frequent interactions over a long period, it does not apply to most experimental data, where subjects are anonymous and interact only for a few periods. Furthermore, the decay in average contribution is obtained by a decline in individual contributions for both types. This requirement seems unnecessarily strong, and does not match individual behavior in voluntary contribution experiments. The experimental data reveals a high variability of individual contributions from period to period (see e.g. [START_REF] Keser | Conditional cooperation and voluntary contributions to public goods[END_REF], which is typically not captured in their model. In contrast, our model does not require common knowledge and allows both for increasing and decreasing individual contributions, with the weaker requirement that aggregate contributions cannot be larger than the initial aggregate moral motivation.

In Klumpp (2005) players are endowed with social preferences. Their utility representation has two additively separable components : material utility and psychological utility. The stage game admits two symmetric Nash equilibria : one where no player contributes to the public good, and one where each player contributes a strictly positive amount. While this dynamic game admits multiple Nash equilibria, the author shows that there is a unique maximal symmetric equilibrium path in pure strategies , for which individual contributions decline. As in Ambrus & Pathak (2007) restricting attention to this particular path is too strong for generating a decline in average contributions, and does not correspond to most available data. More important however, is that the temporal pro…le of the maximal equilibrium path is not compatible with the pattern typically observed in most experiments on voluntary contributions to a linear public good. In Klumpp's model, the maximal equilibrium path is one where all players contribute all of their endowement up to some date, after which they start lowering their contribution down to a level that is approximately equal to zero. In contrast, average contributions in linear public goods start at a level that is in between half the endowment and the Nash contribution (see [START_REF] Laury | Voluntary Provision of Public Goods : Experimental Results with Interior Nash Equilibria[END_REF] and then declines slowly to reach a positive level that is signi…cantly larger than the Nash contribution of the constituent game. In Klumpp's model the average contribution falls very sharply from 100% contribution to nearly 0% contribution over a few periods.

The conclusion of this discussion is that the models proposed by [START_REF] Kandori | The erosion and sustainability of norms and morale[END_REF], Klumpp (2005) and Ambrus & Pathak (2007) have the clear merit to indicate research directions that are worthwhile exploring. But like many pioneering contributions, they rely on unnecessarily strong assumptions to generate the decay of the average contribution and/or their outcomes …t only very roughly with observed data. By contrast, our explanation does not rest on the assumption of common knowledge; it does not depend either on an equilibrium selection argument or on a evolutionary game concept. And the generated outcome accounts for most, if not all, of the empirical regularities observed in the experimental literature.

Conclusion

Our aim in this paper was to provide a general framework that accounts for the decay of the average contribution observed in most experiments on voluntary contributions to a public good. Each player balances her material utility loss from contributing with her psychological utility loss of deviating from her moral ideal. The central idea of our model is that people's moral motivation is "weak": their judgement about what is the right contribution to a public good can evolve in the course of interactions, depending partly on observed contributions and partly on an intrinsic "moral ideal". The decline of the average contribution is generated by two e¤ects, that presumably can be in con ‡ict. The …rst one is a downward or sel…sh-bias due to the presence of material payo¤s in agents'preferences. The unambiguous outcome is that each player contributes a little less than her moral ideal. The second -and novel -e¤ect is that, because individuals' moral ideals are weak, in the sense de…ned above, the upward biais induced by moral motivations can become less stringent from one period to the other.

We started by showing that if players behave myopically, i:e: they do not take into account the in ‡uence of their contribution on others'future moral motivations, under natural conditions the average contribution is non-increasing as the contribution game is repeated.

The hypothesis of myopic behavior seems to us the most appealing one with respect to the experimental data about subjects' behavior. However, we cannot preclude the fact that some subjects act as farsighted players and try to manipulate others'moral motivation. Therefore, we provided an extension of our basic model, to account for the more general case of farsighted players. Assuming farsighted behavior, we showed that the decline arises if agents value su¢ ciently the public good ( is large enough) and discount su¢ ciently the future ( small enough). The requirement, that under farsighted behavior the discount rate must be small with respect to the value of the public good, justi…es our preference for the simpler assumption of myopic behavior for accounting for the decline.

The proposed framework allows for heterogeneity in players' endowment, preferences, and moral ideal. It therefore encompasses a huge variety of individual behaviors. It predicts many observed experimental regularities 11 : over-contributions, heterogeneity of contributions, declining average contributions, …nal over-contributions and the restart e¤ect.

The proposed model can be interpreted from two, apparently di¤erent, behavioral angles: reciprocity and moral motivation. While the reciprocity motive has been widely documented in the recent theoretical and empirical economic literature, the moral motivation hypothesis has not retained much attention. There is a large historical trend in the philosophical literature concerned with moral motivation and the strength of will, that is relevant with respect to our assumptions. In our model there is a strong link between these two dimensions. The reason is that reciprocal behavior is somehow grounded on an internal deliberation process, through which individuals combine their intrinsic motivation to contribute with external pressures in their environment. The hypothesis of weak moral moral can therefore be thought as a means to rationalize reciprocal behavior. We believe that such hypothesis can be tested with a carefully designed experiment.

Appendix

A Derivation of the Markov Perfect Equilibrium

In the text, equilibrium decisions for periods T and T 1 have been given. Moving backward to period T 2, each agent's decision solves:

max x iT 2 ( w i x iT 2 + i (x iT 2 + x iT 2 ) v i x iT 2 M i (x i ; x T 3 ) + V i T 1 x iT 2 +x iT 2 n ) :
The marginal e¤ects of changing x iT 2 are now as follows:

i) As before there are e¤ects on the current utility:

1 + i v 0 i x iT 2 M i (x i ; x T 3 ) ;
ii) there are also marginal e¤ects on the discounted indirect utility of period T 1 :

" g 0 iT 1 + i g 0 iT 1 + P j6 =i g 0 jT 1 v 0 i x iT 1 M i (x i ; x T 2 ) g 0 iT 1 M i 2 (x i ; x T 2 )
# @x T 2 @x iT 2 ;

= n iii) and …nally, there are marginal e¤ects on discounted indirect utility of period T : The …rst order condition is therefore: The marginal e¤ects of changing x iT 3 are now as follows:

2 " g 0 iT + i g 0 iT + P j6 =i g 0 jT v 0 i x iT M i (x i ; x T 2 ) g 0 iT M i 2 (x i ; x T 1 ) # @x T 1 @x iT 2
1 + i v 0 i x iT 2 M i (x i ; x T 3 ) + n
i) the e¤ects on the current utility are:

1 + i v 0 i x iT 3 M i (x i ; x T 4 ) ;
ii) there are also marginal e¤ects on the discounted indirect utility of period T 2 : " g 0 iT 2 + i g 0 iT 2 + P j6 =i g 0 jT 2

v 0 i x iT 2 M i (x i ; x T 3 ) g 0 iT 2 M i 2 (x i ; x T 3 ) # @x T 3 @x iT 3 ;

= n iii) and also, there are marginal e¤ects on discounted indirect utility of period T 1:

2 " g 0 iT 1 + i g 0 iT 1 + P j6 =i g 0 jT 1 v 0 i x iT 1 M i (x i ; x T 2 ) g 0 iT 1 M i 2 (x i ; x T 2 )
# @x T 2 @x iT 3 The …rst order condition is therefore: And the dominant response can be expressed again as: Repeating the logic, and using the notation = n P n h=1 h ; the dominant strategy t periods before the last can be written generically:

1+ i v 0 i x
x iT 3 = (1 ) v i + v i n 2
x iT t = (1 ) v i + v i n 2

+

  And the dominant response can be expressed again as: M i (x i ; x T 3 ) ; g iT 2 (x T 3 ) :

  and …nally, there are marginal e¤ects on discounted indirect utility of period T :3 " g 0 iT + i g 0 iT + P j6 =i g 0 jT v 0 i x iT M i (x i ; x T 1 ) g 0 iT M i 2 (x i ; x T )

2 4

 2 iT 3 M i (x i ; x T 4 ) + n

4 ( 1 5 +

 15 M i (x i ; x T 4 ) ; g iT 2 (x T 3 ) :

  Assumption A 5 . Assume the property G t G t 1 holds for t = 3; :::; k; for some k. To complete the proof, it must be established that G k+1 G k This is straightforward, for if the property is true until t k; it follows that G k+1

  + :::+ t 1 + M i (x i ; x T t 1 ) ;

	3
	4 ( 1 + ) i + 5 1 + + 2 = X j6 =i j (1 ) v i j6 =i h=0 + v i n 2 4 ( 1 + ) i + X j 3 5 t 1 X h + M

i (x i ; x T t 1 ) ; g iT t (x T t 1 ) :

It is not necessary because if reciprocators contribute a little less than the observed (or expected) average contribution, decay can arise even in a population composed exclusively of non-sel…sh agents. A population of identical non-sel…sh agents, but slightly sel…shly oriented, is enough to provoke the decline. .To see why it is not su¢ cient, let us de…ne a perfect reciprocator as a player who matches the average group contribution of the previous period. Consider a case involving only two players : a perfectly reciprocal player and an unconditional player who contributes a …xed amount in each period. As the game is repeated the contribution of the reciprocal player converges to the …xed contribution of the unconditional player, with a slope that depends on the initial contribution of the reciprocator. Hence the average contribution could increase! The example can be easily extended to any mixed population of any …nite size composed of perfect reciprocators and unconditional players. Adding noisy players who contribute a random amount does not prevent that the mean contribution either decays or increases.

The results of the present paper also hold when preferences are captured by quadratic utility functions:U i (xi; x i; b xi) = i (w xi) (wi xi) 2 + i (xi + x i) vi 2 (xi b xi) 2 :This family of functions, which allows for a dominant strategy equilibrium with strictly positive contributions, has been documented in the experimental literature by relatively few papers[START_REF] Keser | Voluntary contributions to a public good when partial contribution is a dominant strategy[END_REF], Bracht et alii, 2008).

0 This concept is not ours. In particular it has been used extensively in the literature on processes (see Drèze and De la Vallée Poussin, 1977, for instance).

[START_REF] Goeree | A theoretical analysis of altruism and decision error in public goods games[END_REF] Actually we are aware of no such regularities that the model does not predict.

Documents de Recherche parus en 2009

Contact :

Stéphane MUSSARD : mussard@lameta.univ-montp1.fr


In order to analyze root proteins involved in drought tolerance in poplar, a proteomic study was conducted on the roots of two Populus deltoïdes × Populus nigra cultivars, Carpaccio and Soligo. These cultivars were selected based on contrasted physiological responses under water stress. Plants were exposed to different water stress levels (Control, Early, Medium and Severe), and root tips collected. Technical optimization included protein extraction and resolubilization, as well as the finetuning of electrophoretic conditions. The best results were obtained upon using phenol extraction, a resolubilization solution containing two reduction reagents, DTT and 2-ME, and 100 µg protein load on both acidic (pH 4-7) and basic (pH 7-11NL) IPG strips. A total of 48 2-D gels were then produced and quantitatively analyzed using SameSpot Progenesis software. Statistical analyses were completed using normalized spot volumes. Multivariate analyses (correlation matrix, PCA and HCA) and twoway ANOVAs showed that protein expression was first regulated by genotype effect and second by treatment effect. Differentially regulated proteins are being identified based on tandem mass spectrometry. This functional information should shed some lights on the molecular players involved in drought-stress response and potentially underlying adaptation to this abiotic constraint.

1/ INTRODUCTION

Drought is one of the most important constraints limiting the growth of plants and ecosystem productivity around the world. Several recent studies have dealt with molecular responses to water shortage, however they have focused mainly on short-term responses to acute stress rather than on long-term acclimation processes to moderate and gradually increasing water deficits. While short-term studies provide useful information about water deficit sensing and signaling pathways, long-term studies may shed light on proteins involved in long-term responses to water deficit and in potential acclimation to low water availability. Poplars are known to be drought sensitive so their natural distribution area is mainly restricted to riparian zones. However, some diversity occurs among species and clones with respect to water use efficiency and drought tolerance. The genus Populus is an obvious choice for analyzing the responses and acclimation processes occurring during soil water depletion in a tree species, due to the recent sequencing of its genome (Tuskan et al., 2004). Only two studies have been published so far on poplar responses to water stress at the proteomic level (Plomion et al., 2006;Bogeat-Triboulot et al., 2007). In this follow-up study, two poplar cultivars displaying contrasting drought tolerance were subjected to several water deficit stresses varying in intensity and duration. Expression profiles from both acidic and alkaline proteins were obtained from roots, the organs initially sensing the water constraint and triggering adaptative responses.

2/ MATERIALS & METHODS

Experimental design -2 poplar cultivars: Populus deltoïdes × Populus nigra cv. Carpaccio (C) and Soligo (S) grown into potted soil under greenhouse monitored conditions. -4 treatments: Con. Full watering for the whole duration of the experiment, Ear. Short mild water deficit (watering was stopped 30h before harvest and soil relative extractable water (REW) was reduced to 20-35% of field capacity ), Med. Extended mild water deficit (soil relative extractable water (REW) was reduced and maintained in the range 20-30 % of field capacity for 12 days ) and Sev. Extended moderate water deficit (soil relative extractable water (REW) was reduced and maintained in the range 10-20 % of field capacity for 12 days ). Plant materials -Young roots visible at the soil/pot interface from both Carpaccio and Soligo cultivars (16 samples including 3 biological replicates). Proteomic analysis -Protein extraction using phenol/ammonium acetate method. -Protein assay using 2-D Quant Kit (GE Healthcare).

-Protein separation (100µg) using two-dimensional electrophoresis (2-DE) along 4-7 and 7-11NL pH ranges during immobilized pH gradient-isoelectric focusing (IPG-IEF) and 11% acrylamide SDS-PAGE (2 technical replicates).

-Protein staining using silver nitrate protocol. -Image analysis using SameSpot Progenesis (NonLinear) Statistical analyses -Multivariate analyses: Principal Component Analyses using R software were performed to unravel the main sources of protein quantity variation.

-Univariate analyses: a two-way Analyses of Variance (ANOVA) model with FDR multiple testing adjustment was used to isolate water deficit-responsive proteins.

4/ CONCLUSIONS & PERSPECTIVES

Alkaline proteins are seldom considered in plant proteomic analyses. In this study, we were able to detect 1500 acidic proteins and 900 alkaline proteins on 2-D patterns from poplar roots. Genotype is the main source of variation of protein abundances. Protein expression profiles varied under the increasing water deficit intensity as well. The identification of water stress responsive proteins by mass spectrometry will highlight the metabolic processes involved in poplar drought adaptation. Two-way ANOVA isolated 88 acidic proteins whose expression profiles varied significantly (5%) under water deficit treatments.

  REFERENCES-Tuskan GA, DiFazio SP, Teichmann T (2004) Poplar genomics is getting popular: the impact of the poplar genome project on tree research. Plant Biol. 6: 2-4 -Plomion C, Lalanne C, Claverol S, Meddour H, Kohler A, Bogeat-Triboulot MB, Barre A, Le Provost G, Dumazet H, Jacob D, et al (2006) Mapping the proteome of poplar and application to the discovery of drought-stress responsive proteins. Proteomics 6: 6509-6527 -Bogeat-Triboulot MB, Brosche M, Renaut J, Jouve L, Le Thiec D, Fayyaz P, Vinocur B, Witters E, Laukens K, Teichmann T et al (2006) Gradual Soil Water Depletion Results in Reversible Changes of Gene Expression, Protein Profiles, Ecophysiology, and Growth Performance in Populus euphratica, a Poplar Growing in Arid Regions. Plant Physiol. 143: 876-892.

Figure 2 .

 2 Figure 2. The number of spots and their resolution on 2-D profiles is greatly improved upon using narrow pH ranges. Acidic proteins are twice more numerous than alkaline ones.

Figure 3 .

 3 Figure 3. PCA indicates that protein quantities are mainly affected by genotype effect, then by treatment effect, with Ear-Med opposing Con-Sev.

Figure 4 .

 4 Figure 4. The 12 main expression profiles confirm PCA results for both acidic and alkaline proteins.

Figure 5 .

 5 Figure 5. The expression profiles of acidic and alkaline proteins responding to water deficit follow different trends.


A S Walker

B Hommel

J Inra

INRA J F Weber

; Picard

B Jki

Hommel

Tomato in European agriculture

Tomatoes are one of the most popular and widely grown vegetables in the world and can be grown either in the field or under greenhouse conditions. Greenhouse production in Europe is extremely intensive and can produce very high yields (up to 700 tonnes/ha). Field production is much less intensive.

In 2008 the European Union (EU) was the third largest tomato producer with an annual production of 20 million tonnes (China was the leading producer with 33 million tonnes) (FAOSTAT, 2008). The main European producing countries are: Italy (6 million tonnes) followed by Spain (3.8 million tonnes), Russian Federation (1.8 million tonnes), Greece (1.3 million tonnes) and Portugal (1.1 million tonnes). Between them, Southern European countries contribute a total production of 13 million tonnes, which corresponds to 70% of the total production. But in terms of yield (Hg/Ha), Western Europe and Northern Europe have the best performances (see Figure 1 below).

During the past eight years there has been a positive trend in tomato yields, while the production and harvested area remained essentially the same (see Figure 2 below).

Pesticides are widely used by tomato growers. More sustainable production methods are readily available but, unfortunately, not widely disseminated. We strongly believe that biological control methods and improved cultural practices can reduce pesticide use dramatically. > Bacterial canker: caused by the bacterium Clavibacter michiganensis subsp. michiganensis, can cause serious losses in some tomato plantings. Spots on fruit are quite distinctive: white and slightly raised at first, then raised, dark-colored centres with white halos. These spots are sometimes termed 'bird's-eye' lesions. The white halo turns brown as the spot becomes older.

Biocontrol in Selected Crops

Number 2: Tomato > Bacterial wilt: caused by Ralstonia solanacearum, a soil borne bacterium that spreads most quickly in warm, wet climates. The infection disrupts water intake. Younger plants wilt in heat but recover, while the wilting is permanent in older plants.

> Viral diseases: a number of viruses cause mottling or mosaic symptoms on the leaves. Tomato mosaic virus (TMV) and pepino mosaic virus (PepMV) can be transmitted mechanically, while others are transmitted mainly by aphids, thrips and whiteflies.

Diseases more frequently found in greenhouse production

High humidity and warm temperatures in greenhouses provide a favorable environment for the development of certain diseases. The diseases listed below are much more likely to occur inside greenhouses than outdoors.

> Gray mould: caused by the fungus Botrytis cinerea. This is a common disease of greenhouse-grown tomatoes. This disease is characterised by a light-gray fuzzy growth that appears on stems and leaves. Soft rot of the stem end of the fruit can also occur. Botrytis infections are most severe in greenhouses with moderate temperatures, high humidity and stagnant air.

> Leaf mould: caused by the fungus Fulvia fulva and can cause problems in humid greenhouses with poor air circulation. This fungal disease appears on lower leaves as yellow spots on the upper surface and fuzzy masses of buff-colored spores on the underside.

> Powdery mildew: caused by the fungus Oidium neolycopersici and is common in all types of greenhouses. Characterised in the early stages by white patches on the upper surface of leaves, this disease can cause defoliation as the spots develop into brown lesions. A type of powdery mildew, caused by Leveillula taurica, is mostly found in unheated tunnels. Aphids extract nutrients from the plant and secrete a large amount of honeydew that promotes the development of sooty mould on leaves and fruits, and can introduce toxic substances in the plant. High populations can reduce plant growth and distort leaves and stems, delay fruit maturity, and reduce yield quantity and quality. More importantly, they transmit virus diseases (i.e. cucumber mosaic virus (CMV) and alfalfa mosaic virus (AMV)).

> Thrips (Thysanoptera: Thripidae): western flower thrips (Frankliniella occidentalis, Frankliniella spp.), onion thrips (Thrips tabaci).

Thrips feed on plant cell fluids. During early development, nymphs eat pollen inside the flowers and then feed on the new fruits. The plant is wounded by feeding, and the empty cells fill with air and appear silvery. Plant tissue is also wounded by the adults during oviposition. Thrips are vectors of the tomato spotted wilt virus (TSWV) and other Tospoviruses.

Biocontrol in Selected Crops

Number 2: Tomato > Stink bugs (Rhynchota: Pentatomidae): southern green stink bug (Nezara viridula) and other species.

Stems, leaves, blossoms and fruits are attacked but the latter are preferred. On green fruit, damage appears as dark pinpricks, surrounded by a light discoloured area that turns yellow or remains light green on ripe fruit. As the feeding site heals it become hard and darkened. Stink bugs may also carry bacteria and yeast that may cause decay when introduced into fruit on the bugs' mouth parts.

> Whiteflies (Hemiptera: Aleyrodidae): sweet potato whitefly (Bemisia tabaci, biotypes B and Q), greenhouse whitefly (Trialeurodes vaporariorum).

Both species of insects cause large economic losses, as a consequence of whiteflies feeding on phloem, deposition of honeydew and the development of sooty mould. Fruits cannot be sold and the sooty mould inhibits photosynthesis and respiration of the plant. Cutworms chop off seedlings or recently transplanted tomato plants at the soil plane. Subsequently, worms can also injure fruits by eating the surface, especially of the fruits next to the ground.

> Armyworms (Lepidoptera: Noctuidae): cotton bollworm (Helicoverpa armigera), beet armyworm (Spodoptera exigua), African cotton leafworm (Spodoptera littoralis), other noctuid moths.

Worms eat leaves and fruits and can complete larval development inside fruits. The young larvae enter a fruit at the stem end and during development can emerge from one fruit and enter another. Damaged fruits show superficial wounds or are chewed internally and filled with faeces; they ripen prematurely and will be subject to rot. Young larvae are difficult to detect and are a serious problem for canned tomatoes.

> Tomato leafminer (Lepidoptera: Gelechiidae, Tuta absoluta).

Tuta absoluta is a devastating invasive pest which originated in South America, was recently introduced to the Mediterranean region and is now widespread in other European countries. Larvae feed on mesophyll tissues and make irregular large mines on the leaf surface. Larve also penetrate into the fruits, which become unsellable, and stems. Bored seedlings may stunt and die. Damage can reach 100% in protected as well as open field crops.

> Leafminer flies (Diptera: Agromyzidae): American serpentine leafminer (Liriomyza trifolii), South American leafminer (L. huidobrensis), L. bryoniae.

Leafminer feeding results in serpentine mines. Injured leaves drop prematurely and heavily infested plants may lose most of their leaves. Photosynthesis can be reduced enormously. Consequently, yield, fruit size and quality (fruits exposed to sunburn) decrease.

> Wireworms (Coleoptera: Elateridae): Agriotes brevis, A. lineatus, A. litigiusus, A. obscurus, A. sputator, A. ustulatus.

Biocontrol in Selected Crops Number 2: Tomato

Early in the season cutworms may cause stand loss by cutting off seedlings or recently transplanted tomato plants at the soil line. Later in the season these pests can also injure tomatoes by eating irregular holes in the surface of fruits. Fruits close to the soil plane are generally the most seriously injured.

> Two-spotted spider mite (Tetranychus urticae, Acari: Tetranychidae).

Mites suck cell contents from the leaves. Plant cells turn yellow, which can be seen on the upper surface of the leaf as small yellow spots. This reduces the photosynthetic area of the leaf and causes physiological disorders. A high density of mites can kill the plants. Yield is reduced and fruits bearing feeding spots are unsellable.

> Broad mite (Polyphagotarsonemus latus, Acari: Tarsonemidae).

Mites cause apical leaves and flower buds to become malformed. The mite's toxic saliva causes twisted, hardened and distorted growth in the terminal of the plant. Leaves turn downward and turn coppery or purplish. Internodes shorten and the lateral buds break more than normal. The blooms abort and plant growth is stunted when large populations are present.

> Tomato russet mite (Aculops lycopersici, Acari: Eryophyidae).

Mites remove cell contents from leaves, stems and fruits. The colour of the stems and leaves frequently becomes bronze or russet coloured. Leaves dry and heavily infested plants can die. Not all natural products meet the expectation of low non-target toxicity and low environmental impact. The spraying of natural insecticides and acaricides is in general incompatible with contemporary use of biocontrol agents due to the toxic effects to predators and parasitoids. Introduction of biocontrol agents in a cultivation previously treated with a natural product is possible only after waiting for the time necessary to make pesticide residues safe to beneficials. The persistence of natural products varies (0-15 days) according to the compound and beneficial. Milbemectin and abamectin are not authorised in organic crop protection.

Main available biocontrol solutions (OF and GH

Nematodes

Small, worm-like plant parasitic nematodes mainly attack roots. The most significant for tomato are from the Meloidogyne family. Infected plants are less vigorous with fewer fruits. Root-knot nematodes interact with bacterial and fungal wilts, increasing the damage.

Weeds

Weeds reduce yields by competing for space, light, water and nutrients, weakening the crop stand, and by reducing harvest efficiency. Some weeds can also increase pest problems by serving as alternate hosts for insects, diseases or nematodes. Weeds are most competitive if they emerge from planting until about six to eight weeks after crop emergence. After six to eight weeks, tomatoes become more competitive and they are usually less affected by late germinating weeds. However, even late germinating weeds can produce seed and, in some instances, interfere with harvest.

SWOT analysis

> Strengths: biocontrol products are usually user and environment friendly. > Weaknesses: however, used alone, their efficacy is considered lower than competitive chemicals. They need to be used at a lower level of infestation (threshold). > Opportunities: easier registration. > Threats: high cost and complicated to use.

Biocontrol in Selected Crops Number 2: Tomato

Recommendations for biocontrol in tomato

Research and development

Technical institutes should look deeper into integrating biological and chemical control. > Weed control is a big gap to be explored, both on the plantation row and in the control of invasive weeds. > Develop the concept of integrating pheromones and insecticides in order to protect tomato when heavy pest infestations occur. > Develop the concept of integrating prevention methods with bacterial antagonists associated later with curative fungicide treatments.

> Reinforce research on alternatives to copper and sulphur. > Set up 'new application thresholds' adapted to the use of biologicals. > There is a need to identify native natural enemies for new invasive pests such as Tuta absoluta.

> There is a need to develop biocontrol solutions for pests such as russet mite.

> For more information on gaps and needs, download the booklet produced by ENDURE's tomato case study team, in particular pages 8 and 36-38.

Policy makers and regulation

> Reinforce the trend towards zero pesticide residues.

Education, training, communication

> Involve farmers' organisations in the promotion of alternative protection systems.

> Demonstration plots, especially on reputable tomato farms.

> Training courses.

Industry and distribution

> Development of more user friendly biological products. > Make available application 'kits', including decision support tools. > Active promotion (demonstrations, lectures, training etc).

For further information please contact:

  Figure 2: European tomato production during the last 8 years

  refer to the use in open field and greenhouse cultivations respectively)

Tomato production in Europe

  Many diseases and pests can affect tomatoes during the growing season: >Septoria leaf spot: caused by the fungus Septoria lycopersici appears as small, water-soaked spots that soon become circular spots. Infection can occur at any stage of plant development but appears most frequently after plants have begun to set fruit. The fungus survives the winter in tomato debris.> Early blight: caused by the fungus Alternaria solani, and is also known as Alternaria leaf spot or target spot. Brown to black spots appear on lower leaves Spots frequently merge, forming irregular blotches. Dark, concentric rings often appear in leaf spots, resulting in the 'target' appearance suggested by the common name. The fungus occasionally attacks fruit at the stem end, causing large, sunken areas with concentric rings and a black, velvety appearance. Warm, wet weather favours the rapid spread of early blight.> Anthracnose: caused by the fungus Colletotrichum coccodes. Symptoms first become visibile on ripe or ripening fruit as small, circular, indented spots in the skin. As these spots expand, they develop dark centres or concentric rings of dark specks, which are the spore-producing bodies of the fungus.

	Biocontrol in Selected Crops
	Number 2: Tomato
	Diseases more frequently found in open field production
	Figure 1: Western Europe
	100%	Southern Europe
	80%	Northern Europe
	60%	Eastern Europe
	40%
	20%
	0%
	> Late blight: caused by the fungus Phytophthora infestans. It can devastate tomato plantings during
	periods of cool, rainy weather. Late blight may infect either young (upper) or old (lower) leaves. It
	first appears as water-soaked areas that enlarge rapidly, forming irregular, greenish black blotches, giv-
	ing the plant a frost-damaged appearance. The undersides of the leaves often show a downy white
	growth in moist weather.
	> Southern blight: a fungal disease caused by Sclerotium rolfsii, which mainly attacks mature plants,
	attacking roots, leaves and fruit. It can survive in the soil for many years.
	> Damping-off diseases: can be caused by several soil-borne pathogens, including Rhizoctonia solani,
	Pythium spp. and Fusarium oxysporum fungi, and will kill seedlings.
	> Bacterial spot: caused by the bacterium Xanthomonas campestris pv. vesicatoria. It appears as small
	circular to irregular spots on leaves and stems. The bacterium overwinters on the surface of seeds, in
	infected debris and in soil. It is commonly brought into fields on infected transplants. Warm, rainy
	weather favours rapid spread of bacterial spot.
	> Bacterial speck: caused by the bacterium Pseudomonas syringae pv. tomato. Although bacterial
	speck seldom reduces yields greatly, it can harm fruit quality. Tiny, dark spots appear on leaves, sur-
	rounded by yellow halos. However, as with bacterial spot and bacterial canker, the fruit symptoms are
	most characteristic. The specks are considerably smaller than the spots caused by bacterial spot, do not
	penetrate the fruit deeply, and can be scraped off with a fingernail. Infection is favoured by cool (less
	than 20°C), wet conditions. Epidemics often follow rainstorms that cause abrasion of leaves and splash
	soil onto the foliage.

> Fusarium wilt: caused by the fungus Fusarium oxysporum f. sp. lycopersici. The fungus attacks only certain tomato cultivars Plants infected by this soil-dwelling fungus show leaf yellowing and wilting that progress upward from the base of the stem. Initially, only one side of a leaf midrib, one branch, or one side of a plant will be affected. The symptoms soon spread to the remainder of the plant.

> Verticillium wilt: caused by Verticillium albo-atrum and Verticillium dahliae. Like Fusarium wilt, this disease appears first on the lower leaves and progresses upward. Unlike Fusarium wilt, symptoms of Verticillium wilt do not progress along one side of a leaflet, branch, or plant.

Alternaria solani Botrytis cinerea Trichoderma harzianum; Bacillus subtillis Clavibacter michiganensis subsp. michiganensis Colletotrichum coccodes Fulvia fulva Fusarium oxysporum f. sp. lycopersici

	Biocontrol in Selected Crops
	Number 2: Tomato
					extracts from
					Fallopia sa-
					chalinensis (Mil-
					sana in Ger-
					many)
	Phytophthora
	infestans
	Pseudomonas syringae
	pv. tomato
	Pythium spp.	Trichoderma
		harzianum;
		Streptomyces
		griseoviridis
		Strain K61
	Ralstonia
	solanacearum
	Rhizoctonia solani	Trichoderma
		harzianum;
		Streptomyces
		griseoviridis
		Strain K61
	Sclerotium rolfsii	Trichoderma
		harzianum;
		Coniothyrium
		minitans
	Septoria lycopersici	Trichoderma
	harzianum Available biocontrol solutions Verticillium spp. Streptomyces
	Pathogen/Biocontrol	Micro-BCA griseoviridis Strain K61	Macro-BCA	Semiochemicals	Natural
	agent Viral Diseases				products
	Xanthomonas
	campestris pv.
	vesicatoria
	Insect and mite pests frequently found in open field and
	greenhouse production
		Trichoderma
		harzianum;
		Streptomyces
		griseoviridis
		Strain K61
	Oidium spp.	Ampelomyces			Potassium io-
		quisqualis strain			dide and potas-
		AQ10			sium thiocy-
					anate lacto-
					peroxidase; en-
					zyme extracted
					from milk (Kop-
					pert's Enzy-
					cure),

> Aphids (Hemiptera: Aphididae): green peach aphid (Myzus persicae), potato aphid (Macrosiphum euphorbiae), glasshouse and potato aphid (Aulacorthum solani), cotton aphid (Aphis gossypii), black bean aphid (Aphis fabae).

  Also, biotype B of B. tabaci injects toxic saliva inducing plant physiological disorders. Moreover, they are vectors of plant viruses. Whiteflytransmitted viruses are among the most severe diseases in several European tomato growing areas. B. tabaci transmits Geminivirus causing epidemic diseases, like tomato yellow leaf curl caused by TYLCV and TYLCSV viruses. T. vaporariorum transmits tomato infectious chlorosis virus (TICV). Both species transmit Crinivirus, like the tomato chlorosis virus (ToCV). Furthermore, both species of whitefly have been implicated in transmission of an emergent quarantine picorna-like virus, the tomato torrado virus (ToTV). Further information on relationships between tomato and whiteflies, and control methods are available from the ENDURE website: Deliverable DR1.10 Map of EU tomato growing areas and Tomato Case Study Guide Number 1: Evaluation of tools to manage whiteflies in Europe.

> Cut worms (Lepidoptera: Noctuidae): turnip moth (Agrotis segetum), black cutworm (Agrotis ipsilon) and Agrotis spp.

  ENDURE is the European Network for the Durable Exploitation of Crop Protection Strategies. ENDURE is a Network of Excellence (NoE) with two key objectives: restructuring European research and development on the use of plant protection products, and establishing ENDURE as a world leader in the development and implementation of sustainable pest control strategies through: > Building a lasting crop protection research community > Providing end-users with a broader range of short-term solutions > Developing a holistic approach to sustainable pest management > Taking stock of and informing plant protection policy changes. Eighteen organisations in 10 European countries are committed to ENDURE for four years(2007)(2008)(2009)(2010), with financial support from the European Commission's Sixth Framework Programme, priority 5: Food Quality and Security.

Michelina Ruocco, Italian National Research Council (CNR), Italy Telephone: +39 081 25 39 337. Email: miruocco@unina.it About ENDURE

This publication was funded by EU grant (Project number: 031499), under the Sixth Framework Programme, and is catalogued as Biocontrol in Selected Crops Number 2: Tomato, published