André Lapidus
email: lapidus@univ-paris1.fr.

Margaret Schabas

Hume

Carl Wennerlind

David Hume'

THE POSSIBILITY OF A WELFARE POLICY IN A WORLD OF EMOTION-DRIVEN INDIVIDUALS: A HUMEAN POINT OF VIEW

Keywords: Hume, happiness, decision, pleasure, belief, emotion, violence of the passion, welfare policy. JEL classification: B11, B31, D10, D63, I38

PROBLEM

Let us leave apart some questions of utmost importance, like externalities, intertemporal inconsistencies or strategic behaviour, which all govern the reachability of an optimal state resulting from the interactions between individuals. Such an intellectual operation helps to put to the fore what has not been eliminated, a seemingly trite assumption which underlies the very idea of what is usually called "liberalism of happiness": all individuals are interested in obtaining the greatest possible happiness and, taking into account their information, cognitive ability, and constraint, they reach the best available situation.

It's not that easy to imagine that things might happen otherwise. That is, that although such individuals have a clear enough knowledge of what their greatest happiness might be, although they are clever enough, provided with relevant information and not submitted to any particular constraint, they might deliberately decide to choose an allocation which would take them away from a greater happiness. It is not that easy, because the conception of this individual would mix up two contradictory approaches: a welfarist approach, clearly involved in liberalism of happiness, and a non-welfarist approach, which is required in order to understand why an allocation which would provide a greater happiness might remain unchosen. Now, David Hume aimed at showing such individuals, in a non-contradictory way, chiefly in

Dissertation on the Passions (1757). Hume depicted them, both concerned in their own happiness, and not always matching their actions to such an objective. Broadly speaking, this is made possible because Hume had in mind emotion-driven ("passion"-driven, in the words of the XVIII th century) individuals, for whom their reason is a subordinate device which helps them to reach the ends shown by their emotions. On the one hand, such an importance granted to emotions explains that they could lead us far from our greatest pleasure, hence from our greatest happiness. But, on the other hand, it also determines our ability to happiness, which varies along with our emotional state.

Let us now assume that we are able to conceive these Humean individuals, driven by their emotions. The fact that they are interested in their happiness suggests another question:

although their emotions might move them away from their greatest happiness, is there a possibility, through public intervention, for instance, to make them reach this greatest happiness? If we only take into account the effects on happiness of the consequences of action (the effective choices), the answer might be made positive. After all, this is not that different from what Bentham called an agenda situation, in which appropriate incentives or direct intervention might lead individuals to allocations that they would not have previously chosen (section 2). But some of Hume's Essays (1777) show that these individuals are far more complex, since their happiness, instead of depending only on the direct consequences of their actions, also depends on their emotional state, typically expressed by the "violence of the passion". And according to Hume, the maximum sensitivity of happiness to the objects of pleasure is obtained when we are in a specific emotional state which he calls a "calm passion".

The policy implications of such an analysis should not be underestimated. It is obvious that my level of happiness might be increased through its consequence-dependent part: for instance, a proper modification of the set of reference on which my choices are made can increase my happiness, since it would induce me to choose elements which provide me a greater pleasure. But if I am under a violent passion, which does not allow me to draw all possible enjoyment from the objects of pleasure, what can be done? What would look like a policy aiming at modifying not only my choices, but moreover my emotions? (section 3). It is not clear that something like that would exist, so that the part of our happiness which is emotion-dependent seems non-improvable. Now, again in the Essays, Hume gives elements which allow some regulation of our emotional state, hence improving the non-improvable. This can be achieved not through a direct control, but through an indirect control on the choices performed at an initial stage, which results in tranquilizing the emotional state, so that the greatest happiness becomes reachable (section 4).

DECISION AND THE CONSEQUENCE-DEPENDENT PART OF HAPPINESS

The principle of a gap between individual decision and welfare is synthetically introduced by Hume in two well-known passages, respectively from book II of the Treatise of Human Nature and from the Enquiry Concerning the Principles of Morals (1751).

In the Treatise, Hume argues that "[m]en often act knowingly against their interest: For which reason, the view of the greatest possible good 1 does not always influence them" (Hume 1739-40, II, p. 418; see also Hume 1757, p. 162); and in the second Enquiry, he explains that "[a]ll men, it is allowed, are equally desirous of happiness; but few are successful in the pursuit" (Hume 1751, p. 239).

In a previous paper (A. Lapidus 2010), I had shown that such a distinction, typical to Hume, might be addressed through alternative kinds of evaluation of an individual position, which contrast decision and happiness. These alternative evaluations rest on the fact that although pleasure and pain play a non-disputable part in the decision process, (1) this latter does not lead toward the maximum of pleasure available in a given emotional state; and (2) does not lead any more toward the emotional state in which the greatest pleasure is available. These two gaps, between the pleasure proceeding from a decision and the ones which might have been appropriate targets, are obviously the effects on decision of our emotional state. This means that they both can be considered as a characteristic of an emotion-driven individual. However, they also allow a distinction, in the determination of happiness, between its consequence-dependent part (our choices, which can move us away from our greatest emotionally available pleasure), and its emotion-dependent part (our emotional ability to feel pleasure). The consequence-dependent part and the emotion-dependent part of happiness will be successively dealt with in this section and in the following one.

Their common foundation is the respective roles of what Hume called "impressions of sensation" (pleasure and pain) and "impressions of reflexion" (the emotions, or passions) in the decision process. This latter is an outcome of Hume's theory of passions 2 . In book II of the Treatise, like in his later published Dissertation, Hume distinguishes direct passions such as joy and grief, desire and aversion, volition, which "arise immediately from good or evil, from pain or pleasure" (Hume 1739-40, II, p. 276.), and indirect passions (pride and humility, love and hatred) for 1 "Good" and "evil" are explicitly presented by Hume as synonyms for "pleasure" and "pain"; see Hume 1739-40, II,, p. 439. 2 The canonical contribution on Hume's theory of passions remains Páll Árdal (1966), especially chap. 1, 2, and 5.

which, although they "proceed from the same principles" (Ibid.), pleasure and pain appear as their outcomes. A central place is devoted to the explanation of a dynamic of passions which transforms our emotional state and in which, as it is well known by each Hume scholar, reason only has a subordinate role 1 . And what we to-day consider as decision is only viewed as the last step, before action, of this wider process describing the transformations of our emotional state 2 .

In this last step, the above-mentioned direct passions play a crucial part. They all converge, like in a funnel, to desire and aversion, and end with volition or will which immediately precedes action: desire and aversion both represent the emotional state of the mind which constitutes comparable objects according to the sensations of pleasure and pain; and finally, the will, in Hume's own words, is "nothing but the internal impression we feel, and are conscious of, when we knowingly give rise to any new motion of our body, or new perception of our mind" (Hume 1739-40, II, p. 399). In spite of a vocabulary unfamiliar to most contemporary economists, we can recognize the usual features of a decision process, in which desire and aversion on the one hand, volition on the other, respectively stand for preferences and choice 3 .

The place of pleasure and pain in the Humean decision process deserves special attention.

Pleasure is determining in the formation of our desire and our will -our preferences and our choices. It would therefore be tempting to conclude that the resulting relation between the sensation of pleasure and the passion of desire is somehow similar to the one we are used to, between utility and preference: the former would be a numerical representation of the preorder involved in the latter. However, such is not the case. What we desire the most is not necessarily what pleases us the most. Or, to put it in Hume's words, a "trivial good [that is, a lesser pleasure; A.L.] may, from certain circumstances, produce a desire superior to what arises from the greatest and most valuable enjoyment" (Hume 1739-40, II, p. 416). This is clearly counter-intuitive, both from a Benthamian and from a standard decision theory point of view.

The reason for such a divergence between sensations (pleasure) and decisions governed by emotions (desire) rests on something specific to Hume, which he does not share with his 1 "Reason is, and ought only to be the slave of the passions, and can never pretend to any other office than to serve and obey them" (Hume 1739-40, II, p. 415) 2 For a formal account, see M.-A. [START_REF] Diaye | A Humean Theory of Choice of which Rationality May Be one Consequence[END_REF]A. Lapidus 2005a and[START_REF]Pleasure and Belief in Hume's Decision Process[END_REF] 3 For a discussion of the assimilation made here between desire, aversion and preferences on the one hand, and will and choice on the other, see [START_REF] Diaye | A Humean Theory of Choice of which Rationality May Be one Consequence[END_REF]Lapidus 2005a, pp.94-5 and98-9 and2005b, pp. 120-1. followers: the double meaning of "pleasure". On one hand, it is an impression of sensation; on the other hand, it is an idea, derived from this impression:

But pain and pleasure have two ways of making their appearance in the mind; of which the one has effects very different from the other. They may either appear in impression to the actual feeling, or only in idea, as at present when I mention them (Hume 1739-40, I, p. 118).

As a result, the pleasure which I enjoy from such or such allocation is substantially different from the one which leads me to choose this allocation: the first is a sensation, the second is an idea. Now, Hume's theory of knowledge developed in Book I of the Treatise argues that an idea as such (that is, as a mere conception) cannot cause any action even if its correlate is a very intense sensation (Hume 1739-40, I, p. 118). This means that as such, the idea of a great pleasure cannot give rise to any kind of decision: it would remain what Hume identified as a "loose reverie" (Hume 1739-40, I, p. 97). The solution to this difficulty is technical. It consists in adding something to the idea as such, so that it could give rise to action. Hume called this a "belief" 1 .

A "belief" is a "LIVELY IDEA RELATED TO OR ASSOCIATED WITH A PRESENT IMPRESSION" (Hume 1739-40, I, p. 96). It transfers to a simple idea a share of the force and vivacity from the original impression of sensation in order to cause action (Hume 1739-40, I, p. 98). This meaning of "belief" is far from familiar uses of the word, either in standard language, or in decision theory. It might be reached by focusing on the way it is built up, when the force and vivacity of an impression are transferred to an idea: this is the task of the "natural relations", resemblance, contiguity, and causality (see Hume 1739-40, I, pp. 10-3;1748, pp. 23-4). A distinctive feature of these natural relations 2 is that they associate ideas (in contrast to philosophical relations which compare them) without any deliberate effort. Through the natural relations and the belief that they built, the mind slides from an original impression to a correlated idea, to which a part of the force and vivacity of the impression is given. This can explain the disturbing conclusion of the most commented passage of the Treatise, in which Hume argued that one might prefer the destruction of the world to a scratching to his finger: 'Tis as little contrary to reason to prefer even my own acknowledg'd lesser good to my greater, and have a more ardent affection for the former than the latter. A trivial good may, from certain circumstances, produce a desire superior to what arises from the greatest and most valuable enjoyment (Hume 1739-40, II, p. 416).

The source of the divergence between what pleases the most and what is desired the most lies here, in the distortion introduced by belief when it weights differently the ideas of pleasure which govern the desires. Each natural relation might be viewed as generating a particular 1 For an interpretation and a discussion of the role of belief relatively to Hume's decision process, see Diaye and Lapidus 2012, § 3. 2 The natural relations are so fundamental to the operations of our minds that, commenting on his own previous work, Hume referred to them as "the cement of the universe" (Hume 1740, p. 662).

topic in the analysis of decision (Diaye and Lapidus 2012, § 3.3). Though causality, Hume argues, is always present 1 , it gives rise to decision under risk or uncertainty when considered in isolation (Hume 1739-40, II, pp. 439 sqq;1757, pp. 139 sqq.); resemblance corresponds to decision when indiscrimination occurs (Hume 1739-40, I, pp. 141-2); and contiguity is linked to intertemporal and spatial decision (Hume 1739-40, II, pp. 418-22, 427-38;1751, pp. 239-40;1757, pp. 161-2).

Contiguity, in relation to intertemporal decision, is a good example of the working of belief 2 .

From a Humean point of view, according to contiguity, the force of the idea of a pleasure is all the more low that the correlate impression of pleasure is remote. As Hume explains in book 2 of the Treatise, [t]he fewer steps we make to arrive at the object, and the smoother the road is, this diminution of vivacity is less sensibly felt, but still may be observed more or less in proportion to the degrees of distance and difficulty. Here then we are to consider two kinds of objects, the contiguous and remote; of which the former, by means of their relation to ourselves, approach an impression in force and vivacity; the latter by reason of the interruption in our manner of conceiving them, appear in a weaker and more imperfect light. This is their effect on the imagination. If my reasoning be just, they must have a proportionable effect on the will and passions. Contiguous objects must have an influence much superior to the distant and remote. (Hume 1739-40, II, p. 428) 3

The evocative image of the "steps" makes it obvious that through its action on belief, the natural relation of contiguity is at the origin of the preference for present. However, this is not sufficient to understand the extent to which a future allocation is discounted. It is to allow this, that Hume introduced a property of the emotional state, which he called the "degree of violence" of the passions.

Initially, the degree of violence of a passion might be viewed as an expression of its emotional intensity. Contrary to a "calm" passion, a "violent" passion, which is commonly regarded as "passion" in the proper sense, is according to Hume "a violent and sensible emotion of the mind" (Hume 1739-40, II, p. 437). However, this degree of violence might alternatively be considered as the emotional sensitivity to the action of the relation of contiguity. So that the belief in a near pleasure is greater if the desire which constitutes its object is violent (see ibid., 1 In section 9 of book 1, part 3 of the Treatise Hume argued that causality establishes a sort of conduit that allows the vivacity of a present impression to be transferred to an idea. 2 On Hume's treatment of intertemporal decision, see [START_REF] Lapidus | La Rationalité du Choix passionnel : En Quête de l'Héritage de David Hume[END_REF], pp. 45-9, Davis 2003[START_REF] Palacios-Huerta | Time-Inconsistent Preferences in Adam Smith and David Hume[END_REF], Lapidus 2010, pp. 10-5. 3 This idea is applied in Book III of the Treatise to the analysis of the origin of justice. It makes possible an understanding that preference for the present is a consequence (and not always a very happy one, according to Hume) of the natural functioning of imagination, which always lends more force to the idea -even if the sensation is identical -of a present pleasure (Hume 1739-40, III, p. 535). One encounters the same thesis in the Enquiry concerning the Principles of Morals (Hume 1751, p. 205) All this is not that unfamiliar. It sounds like the difference initiated by D. [START_REF] Kahneman | New Challenges to the Rationality Assumption[END_REF] between what he called "decision utility" and "experienced utility", which respectively reflect the attractiveness of an object and its welfare content. Like in Kahneman, to which the Humean approach could give philosophical foundations, the Humean individual is aware of the effects of his or her actions on his or her happiness (at least, on its consequence-dependent part). And it is "knowingly" that he or she decides not to reach his or her maximum of happiness.

Such an individual seems not to leave any room to a self happiness improvement. But there is some room for an external improvement. From a public policy point of view, taking only into account the consequence-dependent part of happiness, a goal consisting in increasing individual happiness does not seem definitely out of reach. Its purpose would be to obtain that each individual matches his decisions on the ones he would have taken, had he been under the influence of a calm passion. This is presumably difficult, but it is not that remote from a standard asymmetric information problem (or, from a more historical point view, from a Benthamian agenda problem), that we cannot conceive that there should be a solution.

But a new difficulty comes from the fact that happiness cannot be reduced to its consequencedependent part.

WELFARE POLICY IN PRESENCE OF AN EMOTION-DEPENDENT PART OF HAPPINESS

In the Treatise, there is no place where Hume wrote something like "well, let's now talk about happiness: in my opinion, happiness consists in so and so...". Up to my knowledge, such an issue is addressed only in some of the Essays that Hume published and continuously revised and republished as from 1742 till the posthumous edition of 1777, in reaction against the poor reception of his Treatise. The main features of the analysis can be found in the essay on "Refinement in the Arts", first published in 1752 under the title "Of Luxury". It clearly shows that for Hume, happiness, in a certain way, did consist in pleasure (that is, happiness was an increasing function of the impression of pleasure), but that this latter was not the end of the story:

Human happiness […] seems to consist in three ingredients; action, pleasure, and indolence: And though these ingredients ought to be mixed in different proportions, according to the particular disposition of the person; yet no one ingredient can be entirely wanting, without destroying, in some measure, the relish of the whole composition. (Hume 1777, Of It would be a misunderstanding to conclude that the three ingredients should be regarded at the same level, that Hume, like John Stuart Mill, favoured some kind of eudemonism, so that happiness would properly speaking consist in pleasure, action, and indolence. Hume rather considered happiness as a positive response to pleasure, governed by action and indolence. Whatever these latter be, an immediate consequence is that pleasure and happiness are noncomonotonous. This shows that though Hume's conception of happiness is indeed based on pleasure, he has not a strictly hedonistic conception of happiness like, for instance, some of his utilitarian followers.

In the discussion which comes after the above quoted passage, Hume analyses the consequences of a lack of proportion between indolence and action. If indolence predominates, it prompts "a languor and lethargy, that destroys all enjoyment" (Ibid., p. 270).

By contrast, if action dominates, the "quick march of the spirits, which takes a man from himself, and chiefly gives satisfaction, does in the end exhaust the mind" (Ibid.). This is a way to argue that the happiness-response to pleasure is at a maximum, for any given level of pleasure, for a specific proportion between indolence and action.

But again, the meaning of action and indolence, in their interaction with pleasure, are to be searched elsewhere. This leads us to one of the essays which Hume devoted to happiness, "The Sceptic" 1 .

To be happy, the passion must neither be too violent nor too remiss. In the first case, the mind is in a perpetual hurry and tumult; in the second, it sinks into a disagreeable indolence and lethargy. (Hume 1777, The Sceptic [1742], p. 167) This time, happiness is confronted to an emotional state, a passion. Indolence and action are not viewed as its ingredients, but as behavioural characteristics related to two mental states, "lethargy" and "tumult", accompanying two states of the passions, the one inactive ("remiss") and the other violent. The highest happiness-response to pleasure is obtained when the 1 Published from 1742, this essay is one among four texts ("The Epicurean", "The Stoic", "The Platonist", "The Sceptic") devoted to happiness. The question of knowing whether this essay corresponds to Hume's position is still discussed. John Immerwahr's interpretation, who argues that, while none of the four essays coincides exactly with the theses advanced in the Treatise, "The Sceptic" comes closest to them (see [START_REF] Immerwahr | Hume's Essays on Happiness[END_REF], is followed hereafter.

individual occupies this intermediary position between lethargy and tumult, between action and indolence, that is to say that his emotional state is that of a calm passion.

Stated in another way, this means that for a given impression of pleasure,

• happiness is first increasing with the degree of violence of the passion,

• then, it reaches a maximum when this degree of violence is that of a calm passion,

• and, at last, it decreases along with the increase of the degree of violence.

Moreover, the degree of violence of the passion also influences the impression of pleasure itself, in the same way as it influences happiness for a given impression of pleasure. That is to say, the degree of violence does not only determine the happiness-response to pleasure, but also the ability to pleasure, that is, the pleasure-response to the objects of choice. When Hume considers an individual who falls prey to a remiss or a violent passion, he depicts him or her as less happy than if he or she were under a calm passion, but also as less able to pleasure: under a remiss passion, for example, everything seems boring and does not lead to a significant pleasure. On the one hand, this means that for a same object,

• the impression of pleasure is first increasing with the degree of violence of the passion, • then, it reaches a maximum when this degree of violence is that of a calm passion,

• and, at last, it decreases along with the increase of the degree of violence.

And, on the other hand, it justifies the above noted non-comonotonicity of pleasure and happiness.

More formally, the previous considerations on the happiness-response, the pleasure-response, and the non-comonotonicity, lead to view happiness as a function H of the elements x of the set of choices X and of the degree of violence of the passion v, since it results, through a function denoted h, from a pleasure function p depending on x and v, and from v itself:

H (x, v) = h (p (x, v), v) [1]
It also results from the properties of the happiness-response and of the pleasure-response that for each x, H and p reach their respective maximum for a same degree of violence v which corresponds to the calm passion: [2] that H belongs to a class of functions depending on p, so that their respective maxima are obtained for the same values. This expresses the role that Hume grants to the calm passion. But both a stronger and a weaker statement might be conceived The stronger statement, which corresponds to the Moreover, if we consider that happiness is assessed over a context of choice S 1 , maximizing H and p would lead to a calm passion expressed by v and to an identical x (since otherwise, it would be possible to increase happiness by means of a decrease in pleasure, v remaining equal to v ):

v v max H(x, v) H(x, v) and max p(x, v) p(x, v) = = [2] 1 1 It comes from [1] and
x S,v x S,v ˆmax H(x, v) H(x, v) and ˆmax p(x, v) p(x, v) ∈ ∈ = = [3]
Now, the structure of the decisional valuation is similar. The operation of belief b also transforms the impression of pleasure according to the degree of violence and the object concerned into a decisional valuation U:

U (x, v) = b (p (x, v), x, v)
[4] The decision process leads to maximizing U on a context of choice S, v being given:

x S U(x *, v) max U(x, v) ∈ = [5]
For sake of convenience, the value of U depending on x* belonging to S and on v, will be denoted U*(S, v) U(x *, v) = .

In spite of this structural resemblance, maximizing U for any given degree v of violence leads to a choice x*, generally different from x which, in case the emotional state had been that of a calm passion, would have provided the greatest happiness.

According to Hume, the only exception is that of a calm passion. It has been noticed that under a calm passion, our decisions match our interest, that is, our greatest pleasure. This justifies what otherwise would have been a mere formal conjecture, that U and H are such that under a calm passion, our choices are those which give us the greater happiness:

( ) ( ) x S x S x x ârg max U(x, v) arg max H(x, v) v v ∈ ∈ = ⇔ = [6]
already mentioned strict hedonistic conception of happiness, further illustrated by Bentham, would lead to add explicitly a comonotonicity assumption:

1 2 1 2 1 1 2 2 1 1 2 2 x , x , v , v H(x , v ) H(x , v ) p(x , v ) p(x , v ) : ∀ ≥ ⇔ ≥ [2]'
This would imply that a greater pleasure always comes along with a greater happiness. Symmetrically, weaker conditions, according to which neither [2] nor [2]' holds, would not change drastically the analysis. For instance, one might argue that, in spite of the fact that happiness depends on pleasure, both maxima do not match up and, because of the violence of the passion, what pleases us the more might be different from what makes us the happier. This would evidently lead us to give up the eminent role that Hume associated to the calm passion and to weaken the importance of pleasure in the determination of the greatest happiness. 1 According to an alternative terminology, S can conveniently been called a "budget". More formally, S is an element of the "domain of choice" F, which is itself a subset of the set of the non-empty parts of X, the "set of reference of choice". This makes obvious the difficulties linked to Humean (emotion-driven) individuals, in the general case where the degree of violence of their passion is different from the one of a calm passion:

i. Since they have no direct control of their emotions, they cannot obtain more happiness than through the choice of x* in the context S, which maximizes U for a given degree of violence. That is, their level of happiness cannot exceed H(x*, v)

≤ x S ˆˆmax H(x, v) H(x, v) ∈ =
, the greatest possible happiness over S, under a calm passion.

ii. Could a benevolent, quasi-omniscient, and omnipotent legislator make better?

• He or she might know the value x which would maximize happiness on S when associated to v , and we can imagine that, at least in principle, he or she can restrict the context of choice S so that the individual chooses x . But since he or she has no possibility to govern directly the emotional state of the individuals, which would amount to implementing also v , such a policy would not lead to a first best solution H( x , v ), and even not to a second best solution,

x S max H(x, v)

∈ , since H( x , v) ≤ x S max H(x, v) ∈ . • Only this latter (the solution x to x S max H(x, v) ∈
) might be viewed as the best available policy for a benevolent legislator. This is clearly better than what the individual alone can achieve, but it is generally not the greatest happiness which can be reached under a calm passion.

• In order to reach this greatest happiness, the legislator should be not only benevolent and omniscient, but also omnipotent, which is much beyond the power of any legislator. So that when Hume explicitly discusses such an issue, he has to assume that the Almighty is playing the part of the legislator:

Suppose the same number of men, that are at present in GREAT BRITAIN, with the same soil and climate; I ask, is it not possible for them to be happier, by the most perfect way of life that can be imagined, and by the greatest reformation that Omnipotence itself could work in their temper and disposition? To assert, that they cannot, appears evidently ridiculous (Hume 1777, Of Refinement in the Arts [1752], p. 279).

To sum up, both the individual and the public authority might pretend to some kind of control over the consequential part of happiness (depending on x). But none of them has control over its emotional part (depending on v). All this looks like a dead end. If reason, as Hume argues, is only subordinate to our emotions, how can we even imagine a hold over these latter?

HUME'S SOLUTION

Again in the Sceptic, the character who is speaking to Hume's readers first seems to follow this path. He depicts an individual, prisoner of his or her affections, and grants only to the philosopher the appropriate temper which would lead him or her to the happiness conveyed by a calm passion and the related choices. However, this character is not Hume himself. In a footnote, he warns his reader: "The Sceptic, perhaps, carries the matter too far" (Hume 1777, The Sceptic [1742], p. 177 n.). And a little further, again in a footnote, he discloses his own opinion through an imaginary dialogue:

Propose not a happiness too complicated. But does that depend on me? Yes: The first choice does. Life is like a game: One may choose the game: And passion, by degrees, seizes the proper object. (Hume 1777, The Sceptic [1742], p. 178 n.) At first sight, this is most disconcerting. In contrast to the character of the Sceptic, Hume seems to argue that we do have some kind of authority upon our own choices. Not during our whole life, since "passion, by degrees, seizes the proper object", but at the moment of the first choice, when we have the opportunity to "choose the game". Some commentators like John [START_REF] Immerwahr | Hume's Essays on Happiness[END_REF] have concluded that Hume accepted the idea of a control over our emotions that would enable us to decide to bring ourselves closer to happiness 1 . Such is not the interpretation which I will favour. But this requires a clarification of what Hume precisely meant when he says that "life is like a game".

Obviously, the reference to a "game" should be taken metaphorically: the quest for some kind of strategic interaction is presumably not the most convenient way to grasp what Hume meant. If "life is like a game", it is because between the moment of an initial choice and the one of an arbitrary remote final choice, that will make an individual finally more or less happy, he or she has to make way for the passion. This latter establishes a connection between the initial choice and the conditions (the context of choice and the degree of violence) of the last choice. The underlying mechanism is that of the "double relation", of ideas and impressions, which Hume constructed in the Treatise in order to explain how the passions and their objects are transformed 2 . From the point of view of the degree of violence of the passions, this amounts to saying that, through the working of the double relation, an original emotional state associated with an initial choice will be progressively transformed ("passion, by degrees, seizes the proper object") together with the context of choice. Hume gave many instances of modification of the degree of violence, whose effects on standard intertemporal consistency are not that simple 3 : the repetition of an event (Hume 1739-40, II, pp. 418-9), the proximity or remoteness of an object (Ibid. p. 419), the asymmetry between past and future 1 On the contrary, see for instance Robert Fogelin (1985, pp. 117ff.).

2 "The present theory of the passions", Hume says, "depends entirely on the double relations of sentiments and ideas, and the mutual assistance, which these relations lend to each other" (Hume 1757, p. 158). The principle of the "double relation" is introduced in Book II of the Treatise (Hume 1739-40, II, pp. 282-4), where it is mentioned repeatedly (for example, Ibid. pp. 438-9) before being reminded again in Book III (Ibid., III, p. 574). On the place of the double relation in the decision process, see Diaye and Lapidus 2005, pp. 100-2. 3 See, for instance, Lapidus (2000, pp. 45-9) and [START_REF] Palacios-Huerta | Time-Inconsistent Preferences in Adam Smith and David Hume[END_REF]. objects (Ibid. p. 431). Now, the mere existence of such a connection changes the way individuals view their last choice opportunities 1 .

As long as they consider that the conditions of their last choices do not depend on their initial choice, they have no reason to take them into account in order to perform the initial choice. They behave according to the decisional value of this initial choice, that is, according to [5]. It does not imply that future goods are not desirable (they are more or less desirable according to the violence of the passion), but that a lack of belief in the determining role of our present choices on the conditions of our future choices prevents us from taking them into account in our initial choice and makes the future independent of present choices.

On the contrary, when individuals are convinced, as Hume argues, that there really is a connection between their initial choice and the conditions of their final choice, this independency no longer prevails. Their final happiness relies on their final choice, but insofar as their initial choice brings with it the conditions of this final choice. Denoting by the superscripts 0 and f the initial and final magnitudes, the relation between the initial possible choices x 0 on S 0 and the conditions (S f , v f ) for the final choice can be represented as follows by two applications α and β, from S 0 to the sets of possible final contexts of choices S f , and of the possible final degrees of violence of the passion v f :

( ) ( ) 0 0 f 0 0 0 f 0 α,β : x S S α x x S v β x ∈ = ∈ = [7] 2
The final choice x f * is a solution of the maximization of the decisional value on S f for v f as determined by [7]:

( ) ( ) ( ) f f f f f f f f x S f f f f 0 0 max U (x , v ) U (x *, v ) U *(S , v ) U * α x ,β x ∈ = = = [8]
1 In Lapidus 2010, pp. 24-7, emphasis was laid on the difficulty for the individual to get a complete information on the final context of choice, and therefore on the final choice. Other aspects of the problem are favoured hereafter. 2 A more general formulation might have taken as well into account (as Herrade Igersheim suggested it to me) the initial degree of violence of the passion, so that [7] could have been rewritten as:

( ) ( ) ( ) ( ) 0 0 0 f 0 0 0 0 0 f 0 0 α, β : x S , v S α x , v x S ,v v β x , v ∈ = ∈ = [7]'
However, all examples provided by Hume indicate that regarding the future situation of the individuals, their initial choices are decisive, and their emotional state seems to have only a minor influence. Moreover, from a technical point of view, the initial choice x 0 is a variable, determined by an optimization program, whereas v 0 appears as a given parameter. But in any case ([7] or [7]'), the following of the analysis remains essentially unchanged.

On the basis of [8], it will be convenient to express the final choice x f * as a function γ of x 0 :

( )

f 0 x * γ x = [9]
The maximization of the decisional value on S 0 therefore leads to an initial choice x 0 * which is also dependent on the belief in the final pleasure provided by x f *: Choosing x 0 * therefore amounts to choosing also S f and v f which will give rise to the final choice x f *. This helps to understand the kind of control that an individual might exert over his own emotions and his resulting choices: not a direct one, as [START_REF] Immerwahr | Hume's Essays on Happiness[END_REF] sometimes seems to argue, but an indirect control, through an initial choice which knowingly determines a future context of choice and an emotional state.

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0
The problem is that under a so general point of view, we cannot determine the precise consequences in terms of happiness. For instance, there is no objection to my imagining that in spite of a passionate present, alas not as happy as I would have liked it to be, my future life, such as determined by my present choice, might be the happiest I could ever dream, and (this should be emphasized) not necessarily because my passion will get calmer, but because my future context of choice would provide me with considerable opportunities of pleasure.

However, Hume goes further. He acknowledges not only the existence of a connection between the possible initial choices and the resulting conditions for the final choice, but he also emphasizes two relevant properties of this connection, from which normative conclusions might be drawn: a happiness-dominant property, and a stabilizing property.

The happiness-dominant property is a consequence of the confidence that Hume grants to the effects of a calm passion. This confidence is expressed in his plea for a style of life in which, as John Immerwahr (1992) explained in an investigation on both the academic philosophical works and the Essays, calm passions are favoured on the basis of their effects on so different matters as religion, morality, politics and, as a result, happiness. In the second Enquiry, for instance, Hume's discussion of the eligibility of our objects of choice (Hume 1751, p. 239) is a means to contrast the type of life which can be reached under a calm passion, and the one that is brought by violent passions, which, by favouring close pleasures, is the "source of all dissoluteness and disorder, repentance and misery" (ibid.). And in the Sceptic, again, he explains why a calm passion ensures the most pleasure: through the double relation, it leads to other calm passions, which will themselves bear more pleasures, and which are in a way more durable than that which could be realised by a more violent passion. He argues that violent passions relate to more ephemeral objects: "where the temper is the best disposed for any enjoyment, the object is often wanting" (Hume 1777, The Sceptic [1742], p. 167), the main reason for this difference in durability being that calm and violent passions are respectively directed to internal and external objects:

"[T]he passions, which pursue external objects, contribute not so much to happiness, as those which rest in ourselves; since we are neither so certain of attaining such objects, nor so secure in possessing them.

A passion for learning is preferable, with regard to happiness, to one for riches." (Hume 1777, The Sceptic [1742], pp. 167-8)

The consequence of the happiness-dominant property is that among all the pairs (S f , v f ) generated by all the possible x 0 , the one which will give rise to the highest final happiness is such that v f is equal to the degree of violence of the calm passion, v 1 :

( ) ( ) ( ) ( ) ( ) ( ) ( ) 0 0 0 0 0 0 0 0 0 f x S , ˆˆîf x S is such that H γ x ,β x H γ x ,β x , ˆthen β x v v ∀ ∈ ∈ ≥ = = [11]
The stabilizing property is at least implicit in Hume's already quoted advice, "[p]ropose not a happiness too complicated". It suggests that some initial choices, in the neighbourhood of the one which would have been achieved in case of a calm passion (but not necessarily this one, which would be "too complicated"), transform the conditions of the final choice so that they correspond to the calm passion and produce the highest happiness. This constitutes a tranquilizing set of choices C 0 within the initial context of choice, so that when the degree of violence of the initial passion is low enough, a type of virtuous evolution might take place. For instance, in the essay Of the Delicacy of Taste and Passion2 , Hume describes the way a calm passion, through a "cultivated taste for the polite arts", "improve[s] […] our sensibility for all the tender and agreeable passions" ( More formally, the stabilizing property assumes the existence of a tranquilizing set C 0 , within which an initial choice y 0 leads at f to the highest happiness, associated to a calm passion:

( ) ( ) { } 0 0 0 0 0 0 0 0 0 C y S : x S ,H γ(y ),β(y ) H γ(x ),β(x ) = ∈ ∀ ∈ ≥ [12]
in which it is obvious, from the happiness-dominant property [11], that β (y 0 ) = v .

Let us now suppose, to illustrate the consequences of this construction, an individual who is, at an initial stage, under a (not too) violent passion.

• If he or she is not aware of the connection between his or her initial choice and the conditions of his or her final choice represented by α (x 0 ) and β (x 0 ) ([7]), only his or her initial situation (that is, his or her initial emotional state v 0 and context of choice S 0 ) would be relevant, and x f * would not have been taken into consideration in [10]1 . And it is only if the initial degree of violence of his or her passion leads him or her towards a choice in the tranquilizing set C 0 that he or she will reach the highest final happiness. • If he or she is aware of this connection, the future pleasures in the final situation now play a role in the initial decision. The causal relation between the initial choice and the future impression of pleasure is clearly established, and allows a belief, at the initial stage, in the idea of this final pleasure. The intensity of this belief, conveyed by the relation of contiguity, depends on the initial degree of violence. But anyway, the consequence is that allocations within the tranquilizing set become more attractive, so that they can be chosen even in an emotional state which would have been too violent to lead to them, at least for an individual unaware of the causal relation between his or her initial choice and his or her pleasures at the final stage. This is the scope of Hume's message in the life game he mentions so briefly. He just says: "Don't imagine that your initial choice has no incidence on your future happiness! It does have. And taking only that into account can lead you to initial choices which otherwise you would have believed out of range. They are not. And they can make you happy". This is a way to circumvent the difficulty raised by the irreducible existence of an emotional part of happiness. A control on x 0 is not only a limited control over the consequential part of initial happiness leading, at most, to a second-best solution relatively to this initial situation: it is also, through α and β, a control over the consequential part and the emotional part of final happiness which could give rise, at least in principle, to a first-best solution relatively to the final situation. In its more general form, a welfare policy would therefore rest on an 1 The possible ignorance of the links α and β between a choice in S 0 and the final context of choice and emotional state should be considered cautiously: it does not mean that, if I am unaware of α and β, I am so myopic that I am also unaware of future goods. Of course, such is not the case and I already take future goods into account in S 0 . My ignorance of α and β only means that I am unaware of the technology through which "passion, by degrees, seizes the proper object", and that I am consequently unable to consider the new context of choice S f and emotional state v f which result from my choice in S 9 . intermediate objective: see to it that the initial choice falls into the tranquilizing set. The policy conclusions are straightforward.

They first concern the awareness by the individuals themselves of such a tranquilizing set and, therefore, of the link which might unite the initial choice with final happiness. In other words, it deals with education. This is clearly an issue, for example, of the already quoted essay on the Delicacy of Taste, when Hume explains that it is not in the "good or ill accidents of life", but in ourselves, in the "books we shall read", the "diversions we shall partake of", and the "company we shall keep" (Hume 1777, Of the Delicacy of Taste and Passion [1741], p. 5) that we can find the main resources for this initial choice. The other part of a Humean welfare policy is best suggested in the Refinement in the Arts, through what Hume calls "industry, knowledge, and humanity" (Hume 1777, Of the Refinement in the Arts [1752], p. 271). These are the three components of what should be viewed as a cultural policy 1 , whose aim is to influence the individual contexts of choice in order to enlarge the tranquilizing set, and that he describes as producing increasing returns in terms of happiness:

Another advantage of industry and of refinements in the mechanical arts, is, that they commonly produce some refinements in the liberal; nor can one be carried to perfection, without being accompanied, in some degree, with the other. [...] The spirit of the age affects all the arts; and the minds of men, being once roused from their lethargy, and put into a fermentation, turn themselves on all sides, and carry improvements into every art and science. Profound ignorance is totally banished, and men enjoy the privilege of rational creatures, to think as well as to act, to cultivate the pleasures of the mind as well as those of the body. [...]The more these refined arts advance, the more sociable men become: nor is it possible, that, when enriched with science, and possessed of a fund of conversation, they should be contented to remain in solitude (Hume 1777, Of the Refinement in the Arts [1752], pp. 270-271).

It might be convenient to the reader to interpret this plea for a cultural policy, rooted in industry, science and art, and sociability, as a special instance of the attempt to transform "passion" into "interest" that Albert [START_REF] Hirschman | The Passions and the Interests -Political Arguments for Capitalism before its Triumph[END_REF] identified at the origin of capitalism. Behind differences in the vocabulary, a similar idea did seem to emerge: our happiness evidently depends on the goods that we enjoy, but still more on our emotional state, and we have to find a way to influence it. Hume's solution (tranquilizing the passions by way of a large cultural policy) is not necessarily the most convincing to every contemporary reader. But the terms in which he raised the problem are hardly avoidable.

  p. 419). As a result, if I am under a calm passion, the relation of contiguity has no influence: I do not overweight a present pleasure when compared with a future pleasure, and I desire the most what pleases me the most. On the contrary, if I am under a violent passion, the relation of contiguity has a great influence: I overweight a present pleasure when compared with a future pleasure, what I desire the most reflects this overweighting and might take me away from what pleases me the most. Hume explicitly imagines such kinds of comparisons in the above quoted passages from book II of the Treatise and from the second Enquiry (Hume 1751, p. 239) when he argued, in the Treatise for example, that "[m]en often act knowingly against their interest" (Hume 1739-40, II, p. 418; 1757, p. 162; and for a formal discussion, see Lapidus 2010, pp. 12-5).

  Refinement in the Arts [1752], pp. 269-70)

  Hume 1777, Of the Delicacy of Taste and Passion [1741], p. 6), avoids the emotions and objects induced by a violent passion, and confirms and increases the initial calm disposition: "[N]othing is so improving to the temper as the study of the beauties, either of poetry, eloquence, music, or painting. […] The emotions which they excite are soft and tender. They draw off the mind from the hurry of business and interest; cherish reflection; dispose to tranquillity." (Hume 1777, Of the Delicacy of Taste and Passion [1741], pp. 6-7)

This is evidently not a trivial assumption. One might argue, for instance, that some x 0 generate v f different from v but also S f on which x f would provide the greatest happiness, although the emotional state is not the one of a calm passion.

This text introduced the first edition of the Essays in 1741. After the poor initial success of the Treatise this essay presented a terminological renewal, after which "taste" and "passion" replaced "calm passion" and "violent passion" respectively, "delicacy" indicating which of them prevailed.

17.03.2011 -17:40

The part played by the material element represented by "industry" should not be underestimated, from a both historical and analytical viewpoint (see Margaret Schabas

2008).


Guillermo Bueno

Isabel C Barrio

Ricardo García-González

Concepción L Alados

Daniel Gómez-García

C G Bueno
email: cgbuenog@gmail.com

Does wild boar rooting affect livestock grazing areas in alpine grasslands?

Keywords: Digging, Disturbance, Cattle, Sheep, Stocking rate, Sus scrofa

Interactions between traditional livestock management practices and wildlife activities are important in the conservation of many mountain ecosystems including the summer rangelands in the Spanish Central Pyrenees, where rooting by wild boar (Sus scrofa) is a large disturbance that can reduce the amount of area available to grazing livestock. This study explored the likely impact of wild boar rooting on Pyrenean grasslands. It quantified the extent of wild boar rooting in livestock grazing areas and determined whether wild boars selected or avoided areas depending on the type of livestock and stocking rates. Wild boar rooting affected 16% of livestock grazing area and occurred in sites that were grazed by cattle, rather than by sheep. In addition, a preference for areas that had intermediate stocking rates was found. The relationship between the increase in the number of wild boars and trends in livestock management suggests that the extent of wild boar rooting will increase especially in cattle grazing areas, and therefore, the area available for cattle grazing in Pyrenean mountain rangelands would decrease significantly.

Introduction

Mountain grasslands are mostly protected habitats and a major conservation priority in Europe (Council of the European Communities 1992). Those habitats have high socio-economic value because of the traditional livestock management practices, which sustain local economies, preserve cultural values and produce high quality food [START_REF] Luick | Ecological and socio-economic implications of livestock-keeping systems on extensive grasslands in southwestern Germany[END_REF][START_REF] Aldezabal | El sistema de pastoreo del Parque Nacional de Ordesa y Monte Perdido (Pirineo Central, Aragón). Publicaciones del Consejo de Protección de la Naturaleza de Aragón[END_REF][START_REF] Fillat | Experimental investigations of colonisation by north temperate dung beetles of different types of domestic herbivore dung[END_REF]. Traditional European livestock management practices provide a balance between grassland production and conservation [START_REF] Luick | Ecological and socio-economic implications of livestock-keeping systems on extensive grasslands in southwestern Germany[END_REF][START_REF] Olff | Effects of herbivores on grasslands plant diversity[END_REF], maintain and enhance the structure and diversity of mountain grasslands [START_REF] Dullinger | A resampling approach for evaluating effects of pasture abandonment on subalpine plant species diversity[END_REF][START_REF] Dennis | The effects of livestock grazing on foliar arthropods associated with bird diet in upland grasslands of Scotland[END_REF][START_REF] Sebastià | Grazing as a factor structuring grasslands in the Pyrenees[END_REF]) and prevent shrub encroachment [START_REF] Pasche | Are meadows with high ecological and patrimonial value endangered by heathland invasion in the French central Pyrenees?[END_REF]).

In the last century, changes in land use have had a significant impact on the structure and use of mountain ecosystems in Spain. Changes in grazing practices, i.e. a decrease in extensive livestock practices and a trend towards an increase in the number of cattle and a decrease in the number of sheep in extant herds because of the crisis in transhumance systems [START_REF] Luick | Ecological and socio-economic implications of livestock-keeping systems on extensive grasslands in southwestern Germany[END_REF][START_REF] Lasanta-Martínez | Mountain Mediterranean landscape evolution caused by the abandonment of traditional primary activities: a study of the Spanish Central Pyrenees[END_REF], have led to the abandonment of grazing activities in some areas mostly used for sheep herding [START_REF] Sm | Analysis of spatial and temporal evolution of vegetation cover in the Spanish Central Pyrenees: role of human management[END_REF]. On the other hand, rural abandonment and an increase in forested areas [START_REF] Lasanta-Martínez | Mountain Mediterranean landscape evolution caused by the abandonment of traditional primary activities: a study of the Spanish Central Pyrenees[END_REF] have indirectly increased wild boar populations because boars find more abundant and persistent shelters from hunting [START_REF] Herrero | Reproductive and demographic parameters in two Iberian wild boar Sus scrofa populations[END_REF]). Wild boar disturbances, i.e. rooting, have severely altered the structure and composition of grasslands in mountain ecosystems [START_REF] Gallo Orsi | Where and when: the ecological parameters affecting wild boars choice while rooting in grassland in an alpine valley[END_REF]Welander 2000b;[START_REF] Bueno | Understanding the main factors in the extent and distribution of wild boar rooting on alpine grasslands[END_REF]. In digging for food, wild boars turn over the soil, which can impact from a few square centimetres to hundreds of hectares [START_REF] Gallo Orsi | Where and when: the ecological parameters affecting wild boars choice while rooting in grassland in an alpine valley[END_REF][START_REF] Massei | The environmental impact of wild boar[END_REF]. Thus, they can disturb large areas, which can reduce the amount of area available to livestock [START_REF] Tisdell | Wild pigs: environmental pest or economical resource?[END_REF]. Such a reduction can have an impact on traditional livestock management and local economies [START_REF] Gortázar | Historical examination of the status of large mammals in Aragon, Spain[END_REF]. The need to quantify the extent of wild boar rooting in areas used by livestock is especially important in protected areas where livestock grazing is coupled with wildlife management and conservation (Council of the European Communities 1992). Several studies have contributed to the understanding of the main factors involved in the extent and distribution of wild boar rooting in mountain grasslands [START_REF] Gallo Orsi | Where and when: the ecological parameters affecting wild boars choice while rooting in grassland in an alpine valley[END_REF][START_REF] Welander | Spatial and temporal dynamics of a disturbance regime: wild boar (Sus scrofa) rooting and its effects on plant species diversity[END_REF][START_REF] Bueno | Understanding the main factors in the extent and distribution of wild boar rooting on alpine grasslands[END_REF], but there is little information about the interactions between wild boar rooting and traditional livestock management practices, especially in mountain environments. Livestock grazing appears to influence the occurrence of wild boar rooting in some areas [START_REF] Bueno | Understanding the main factors in the extent and distribution of wild boar rooting on alpine grasslands[END_REF]), but most studies have focused on the impact of wild boar disturbances on crops, rather than livestock [START_REF] Meriggi | Factors affecting damage by wild boars to cereal fields in Northern Italy[END_REF][START_REF] Calenge | Efficiency of spreading maize in the garrigues to reduce wild boar (Sus scrofa) damage to Mediterranean vineyard[END_REF][START_REF] Wilson | Rooting damage to farmland in Dorset, southern England, caused by feral wild boar Sus scrofa[END_REF][START_REF] Herrero | Diet of wild boar Sus scrofa L. and crop damage in an intensive agroecosystem[END_REF]) and, to a lesser extent, on competition between wild boar and livestock for grazing areas [START_REF] Kuiters | Facilitate and competitive interactions between sympatric cattle, and wild boar in Dutch woodland pastures[END_REF]. The aim of this study is to explore the occurrence of wild boar rooting within livestock grazing areas in alpine grasslands, to determine its likely impact on livestock grazing activities. To address this objective, we quantify the extent of wild boar rooting in livestock grazing areas and evaluate the selection of wild boar rooting for areas used by cattle and/or sheep. We also evaluate if wild boar rooting occurs preferably at certain stocking rates, to infer to which extent grazing activities might be affected by wild boar rooting in the near future considering the current trends in livestock management.

Methods

Study area

The study was conducted in Ordesa and Monte Perdido National Park (OMPNP) (42°36′N, 0°00′) in the Spanish Central Pyrenees. The study area comprised 3,863 ha of natural grasslands between 1,500 and 2,800 m a.s.l, where the average annual temperature is 5°C and average annual precipitation is about 1,720 mm, which is concentrated in spring and autumn [START_REF] García-González | Valoración ecológica y productiva de los pastos supraforestales en el Parque Nacional de Ordesa y Monte Perdido[END_REF]). The topography, lithography, and vegetation of the study area were broadly representative of the Spanish Central Pyrenees. Within the area, livestock management involves large herds of cattle and sheep, which use about 35% of the area during the grazing season (from July to October). In 2004, the numbers of cattle and sheep in the area were 1,350 and 9,580, respectively (data provided by the OMPNP). In the region, wild boars are abundant (∼3.3 boars/km 2 ) despite being heavily hunted [START_REF] Herrero | Fruits and roots: wild boar foods during the cold season in the southwestern Pyrenees[END_REF]. They inhabit nearby forests and frequently visit mountain grasslands to search for food, especially when food is scarce in the forests and grassland soils are friable [START_REF] Welander | Spatial and temporal dynamics of a disturbance regime: wild boar (Sus scrofa) rooting and its effects on plant species diversity[END_REF][START_REF] Herrero | Fruits and roots: wild boar foods during the cold season in the southwestern Pyrenees[END_REF]. Hunting and providing supplementary feeding is not allowed within the National Park.

Wild boar rooting and stocking rate maps

To determine the extent and distribution of wild boar disturbances, the study area was mapped during summer 2005 (June-August). Disturbance patches were drawn on an aerial photograph (scale 1:3,500), georeferenced by more than 1,600 GPS points and incorporated into a GIS, generating a digital disturbance map (scale 1:5,000). The minimum mapping unit was 5 m 2 , and disturbances separated less than 1 m were mapped jointly within the same disturbed patch. The accuracy of the map was 90.6%, obtained by performing a confusion matrix [START_REF] Congalton | Assessing the accuracy of remotely sensed data: Principles and practices. Lewis Publisher, Boca Raton Council of the European Communities[END_REF]. Two hundred forty points were randomly located in the digital disturbance map, stratified between disturbed and undisturbed areas (120 points each) and checked in the field (for more details in this methodology, see [START_REF] Bueno | Understanding the main factors in the extent and distribution of wild boar rooting on alpine grasslands[END_REF]). The map of the stocking rates was generated using a previous map for OMPNP based on an intensive monitoring of livestock movement during a whole grazing season in 1991 [START_REF] Aldezabal | El sistema de pastoreo del Parque Nacional de Ordesa y Monte Perdido (Pirineo Central, Aragón). Publicaciones del Consejo de Protección de la Naturaleza de Aragón[END_REF]) and updating the numbers of cattle and sheep for 2004 (García- [START_REF] García-González | Valoración ecológica y productiva de los pastos supraforestales en el Parque Nacional de Ordesa y Monte Perdido[END_REF]), which were expressed in standard livestock units (a 500-kg cow or six sheep) per hectare (SLU/ha; for more details see García- [START_REF] García-González | Valoración ecológica y productiva de los pastos supraforestales en el Parque Nacional de Ordesa y Monte Perdido[END_REF]). Shepherds and cowboys did not change from 1991 to 2004 (R. García-González, personal communication), so the same overall grazing areas used by livestock during the grazing season can be safely assumed (García [START_REF] González | Pattern of livestock use in time and space in the summer ranges of the western Pyrenees: a case of study in the Aragon valley[END_REF][START_REF] García-González | Valoración ecológica y productiva de los pastos supraforestales en el Parque Nacional de Ordesa y Monte Perdido[END_REF][START_REF] Fillat | Experimental investigations of colonisation by north temperate dung beetles of different types of domestic herbivore dung[END_REF].

Resource selection analysis

To determine whether wild boar rooting was related to grazing areas, we performed a resource selection analysis comparing the rooted (hectare) to the available (hectare) surface, in which statistical inferences were based on the Chi-squared test. The null hypothesis was that wild boars randomly selected areas used or not by livestock in proportion to availability [START_REF] Manly | Resource selection by animals: statistical design and analysis for field studies, 2nd edn[END_REF]). When the observed and expected use of areas differed significantly from that based on availability, we used Bonferroni's confidence intervals to detect significant selection or avoidance of areas by wild boar [START_REF] Manly | Resource selection by animals: statistical design and analysis for field studies, 2nd edn[END_REF][START_REF] Alldredge | Design and analysis of resource selection studies for categorical resource variables[END_REF]. In addition, within livestock grazing areas, we distinguished between the areas used by cattle and those used by sheep. Areas used mutually (<18% of the area grazed) were categorised as cattle grazing or sheep grazing areas depending on their relative contributions (>50%) to the overall stocking rate. To extract data from the GIS maps, we used ArcGis 9.2.

Generalised additive models

To describe the relationships between the presence/absence of wild boar rooting and the stocking rates of cattle and sheep, we used univariate binomial Generalized Additive Models (GAM) with a logit link [START_REF] Hastie | Generalized additive models[END_REF][START_REF] Nogués-Bravo | Assessing the effect of environmental and anthropogenic factors on land-cover diversity in a Mediterranean mountain environment[END_REF]. To generate the response variable, i.e. occurrence of wild boar rooting, a sample of 1,000 points was stratified into two classes based on the presence or absence of wild boar rooting (500 points inside and 500 points outside disturbed areas). To avoid spatial autocorrelation, points were chosen randomly but were ≥50 m apart [START_REF] Bueno | Understanding the main factors in the extent and distribution of wild boar rooting on alpine grasslands[END_REF]. Predictor variables for each model, i.e. sheep and cattle stocking rates, respectively, were modelled using cubic regression splines, and the optimal amount of smoothing was estimated via cross-validation [START_REF] Zuur | Mixed effects models and extensions in ecology with R[END_REF]). To improve the fit of the model, stocking rates were log-transformed, which was appropriate because, within the study area, a few areas were used very intensively by livestock and most areas were used rarely or not at all [START_REF] Aldezabal | El sistema de pastoreo del Parque Nacional de Ordesa y Monte Perdido (Pirineo Central, Aragón). Publicaciones del Consejo de Protección de la Naturaleza de Aragón[END_REF]. All statistical analyses were performed using R 2.7.2 (R Development Core Team 2008) and the mcgv package [START_REF] Hector | Plant diversity and productivity experiments in European grasslands[END_REF].

Results

In OMPNP, rooting by wild boars was evident in 16.2% of the area used by livestock (206.6 ha out of 1268.2 ha); 20.8% of the areas used by cattle (103.01 ha out of 495.25 ha) and 13.4% of those used by sheep (103.58 ha out of 772.96 ha) were rooted. According to their availability within the total area studied in OMPNP, areas previously grazed by livestock were selected by wild boar for rooting, and non-grazed areas were avoided (Fig. 1a; Chi-squared = 146.85, p<0.001). Within grazed areas, those holding cattle were significantly selected whereas those used by sheep were avoided by foraging wild boars (Fig. 1b; Chi-squared = 10.29, p<0.05).

Both sheep and cattle stocking densities showed a non-linear pattern on the response. After cross-validation, the effective degrees of freedom were set to 3.272 and 2.198 for sheep and cattle, respectively. Effective degrees of freedom reflect the ruggedness of the smoothing parameter, being values close to one straight line and higher values indicating non-linearities. In both models, the smoothing term was highly significant (sheep Chi-squared=69.85, p=0.000; cattle Chi-squared = 201.9, p=0.000). Areas grazed by cattle had a higher occurrence of wild boar rooting among a wider range of stocking rates compared to the areas grazed by sheep (Fig. 2). The presence of wild boar rooting reached its maximum where the sheep stocking rate was 0.03 SLU/ha (Fig. 2a). At higher stocking rates (up to 0.36 SLU/ha), this presence was reduced, and no response was shown further on. Wild boar rooting was largest at cattle stocking rates between 0.04 and 0.26 SLU/ha, and at higher rates, rooting affected a smaller extent (Fig. 2b).

Discussion

In the protected Pyrenean alpine grasslands of the OMPNP, Spain, wild boar rooting affected up to 16% of the area available to grazing livestock, which might represent a serious threat to the already declining livestock grazing activities. In addition, several factors suggest that the trend is worrisome. In recent decades, populations of wild boar have increased in Europe [START_REF] Geisser | Efficacy of hunting, feeding and fencing to reduce crop damage by wild boars[END_REF][START_REF] Acevedo | Factors affecting wild boar abundance across an environmental gradient in Spain[END_REF][START_REF] Schley | Patterns of crop damage by wild boar (Sus scrofa) in Luxemburg over a 10-year period[END_REF]. Larger populations might lead to an increase in wild boar disturbances, which has been observed in feral pig populations in other protected mountainous areas [START_REF] Hone | Feral pigs in Namadgi National Park, Australia: dynamics, impacts, and management[END_REF]. Furthermore, in the OMPNP, disturbances were not randomly distributed among livestock types and stocking rates. For foraging, wild boars appeared to prefer areas that had intermediate stocking rates and those grazed by cattle, and some of the areas grazed by sheep appeared to be avoided. Although the number of livestock in the area has decreased, sheep have been replaced by cattle because the latter are more profitable and less demanding; consequently, the relative number of cattle has increased in mountain ecosystems [START_REF] Luick | Ecological and socio-economic implications of livestock-keeping systems on extensive grasslands in southwestern Germany[END_REF][START_REF] Lasanta-Martínez | Mountain Mediterranean landscape evolution caused by the abandonment of traditional primary activities: a study of the Spanish Central Pyrenees[END_REF]. Given the relationships between wild boar rooting and the type of livestock and stocking rates, if current livestock management practices continue, wild boar rooting might expand in the near future.

Livestock activities influence the physical properties of soil and nutrient cycles [START_REF] Bezkorowajnyj | The effect of cattle foot traffic on soil compaction in a silvo-pastoral system[END_REF][START_REF] Mikola | Defoliation and patchy nutrient return drive grazing effects on plant and soil properties in a dairy cow pasture[END_REF], which might directly or indirectly influence the foraging behaviour of wild boars. The diet of wild boars in mountain ecosystems is not well studied, but the evidence suggests a clear relationship between rooting activity and the foraging for nutrient-rich foods such as animal proteins and plant storage structures [START_REF] Baubet | Les lombriciens dans le régime alimentaire du sanglier (Sus scrofa L.) en montagne[END_REF][START_REF] Schley | Diet of wild boar Sus scrofa in Western Europe, with particular reference to consumption of agricultural crops[END_REF]. Two of the local effects of grazing can explain the differences in wild boar rooting activities among stocking types and rates: faecal droppings differ between sheep and cattle because cattle produce larger scats and sheep disperse smaller pellets widely and in smaller quantities [START_REF] Aldezabal | El sistema de pastoreo del Parque Nacional de Ordesa y Monte Perdido (Pirineo Central, Aragón). Publicaciones del Consejo de Protección de la Naturaleza de Aragón[END_REF]. Furthermore, cattle dung attracts more insects (Finn and Giller 2002), earthworms [START_REF] Baubet | Les lombriciens dans le régime alimentaire du sanglier (Sus scrofa L.) en montagne[END_REF][START_REF] Baubet | Seasonal and annual variations in earthworm consumption by wild boar (Sus scrofa scrofa L.)[END_REF] and voles [START_REF] Evans | To graze or not to graze? Sheep, voles, forestry and nature conservation in the British uplands[END_REF]) than does sheep dung, and wild boars actively seek these types of foods. In addition, trampling is more homogeneous and extensive in sheep grazing areas than in cattle grazing areas because sheep have a greater tendency to cluster [START_REF] Albon | Quantifying the grazing impacts associated with different herbivores on rangelands[END_REF]). Cattle trampling is heterogeneous and mostly limited to specific pathways, which leaves some patches untouched [START_REF] Bezkorowajnyj | The effect of cattle foot traffic on soil compaction in a silvo-pastoral system[END_REF][START_REF] Albon | Quantifying the grazing impacts associated with different herbivores on rangelands[END_REF]). Areas that have high stocking rates might be less preferred by wild boar because of the soil compression caused by trampling [START_REF] Kuiters | Facilitate and competitive interactions between sympatric cattle, and wild boar in Dutch woodland pastures[END_REF][START_REF] Albon | Quantifying the grazing impacts associated with different herbivores on rangelands[END_REF], which makes the soil more difficult to dig [START_REF] Bowman | Feral pig (Sus scrofa) rooting in a monsoon forest-wetland transition, northern Australia[END_REF][START_REF] Gallo Orsi | Where and when: the ecological parameters affecting wild boars choice while rooting in grassland in an alpine valley[END_REF][START_REF] Bueno | Understanding the main factors in the extent and distribution of wild boar rooting on alpine grasslands[END_REF]. Therefore, differences in the use of space by cattle and sheep might explain why cattle grazing areas were more strongly affected by rooting than were the areas grazed by sheep.

Given the current trends in livestock management in Spanish Pyrenees, i.e. an overall decline in the number of livestock and a trend towards cattle, rather than sheep, herding and the increase in wild boar populations, the heterogeneous impact of wild boar rooting might increase in the near future. One result might be a significant reduction in the amount of area suitable for grazing cattle, which might have an adverse effect on the economy in the already depressed extensive livestock management systems in mountain summer rangelands in Spain.

Fig. 1

 1 Fig. 1 Wild boar rooting a in Ordesa and Monte Perdido National Park and b within livestock-grazed areas. Whiskers in the percentages of available surface (light grey bars) represent Bonferroni confidence intervals: non-random selection by wild boar occurred if these intervals are exceeded by the proportion of disturbed area (dark grey bars) while significant avoidance occurs when these intervals are not reached. Asterisks indicate significant cases (p<0.05)

Fig. 2

 2 Fig.2Estimated smoothing curves (cubic regression splines) and point-wise 95% confidence intervals for the Generalized Additive Models containing, respectively, the stocking rates of sheep (a) and cattle (b) as predictor variables, and the presence/absence of wild boar rooting as the response variable, in Ordesa and Monte Perdido

Eur J Wildl Res (2010) 56:765-770

Acknowledgements We thank the staff of OMPNP for the support and data provided. This research was funded by the Spanish Ministry of Science and Innovation and the Spanish Ministry of Environment (MAM 2484/2002-059/2002 and PN-MEC CGL2005-01131/BOS respectively), including a pre-doctoral fellowship to CGB. Earlier versions of the manuscript were considerably improved by S. Palacio, and B. MacWhirter improved the English version.