Joël Bockaert
email: joel.bockaert@ccipe.cnrs.fr

S Claeysen

Valerie Compan

Aline Dumuis

HT4 RECEPTORS

Keywords: 5-HT4 receptors, splice variants, G proteins, neurotransmitter release, cognition, pain, anxiety, feeding, CNS drug targets

I. Historical overview

There are several distinct periods in the history of 5-HT4 receptors (5-HT4Rs): A short "Naughty but Nice" period (1988)(1989) (see [1]) characterized by a clear scepticism among many serotoninergic specialists about the existence of the receptor. Its birth certificate was difficult to obtain [2]. 5-HT4R was first described in colliculi and hippocampal neurons as a cAMP stimulatory 5-HT receptor, insensitive to classical 5-HT1, 5-HT2 and 5-HT3 receptor antagonists [3]. The only exception was tropisetron, a potent 5-HT3R antagonist, which is also a weak 5-HT4R antagonist (pA2 = 6.5). Benzamides, such as metoclopramide, renzapride, cisapride and zacopride were rapidly recognized as being potent agonists [4]. This formed a link between these 5-HTRs and an unclassified prokinetic 5-HT receptor in guinea-pig ileum.

The latter was insensitive to classical 5-HT1, 5-HT2 and 5-HT3 receptor antagonists, stimulated by benzamides and blocked by M concentrations of tropisetron (for a review see [5]).

Then came a "Flourishing Pharmacological period" (1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997). This was characterized by the description of the distribution of 5-HT4 receptors in brain and peripheral organs, the analysis of some of their cellular and physiological functions as well as by the synthesis of very specific agonists and antagonists (for reviews see [START_REF] Bockaert | Handbook of experimental pharmacology: Serotoninergic neurons and 5-HT receptors in the CNS[END_REF][START_REF] Eglen | [END_REF]).

An "Intense Molecular biology period" (1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002) was defined by the cloning of the rodent [8][9][10] and human [11][12][13][14] 5-HT4R gene. These studies carried out a structural analysis of ligand binding sites [15] and recognized the existence of multiple allosteric conformations which were stabilized by agonists, antagonists and inverse agonists [10,16]. The 5-HT4R gene is localized on chromosome 5, bands q31-q33 with both dopamine D1 and 2-adrenergic receptor genes [17] (Fig. 1). There are 38 exons in the 5-HT4R gene and nine splice variants have been cloned. They represent an important if not unique discovery amongst genes encoding 5-HT receptors [10,18,19] (Fig. 1). A common splicing site produces eight splice variants with an identical DNA sequence up to the codon encoding Leu 358 . On the contrary, the DNA sequence encoding the C-terminus is specific to each splice variant. One of the important issues will be to analyze the functional importance of these splice variants and their potential use as therapeutic targets.

The as yet "Unwritten period" needs to be characterized by an extensive analysis of the cellular and physiological functions of 5-HT4Rs so that their potential for the treatment of memory deficit, depression, addiction, epilepsy or eating disorders can be accurately assessed. Some 5-HT4R-directed drugs used to be (cisapride), or are on the market (metoclopramide, tegaserod, which is on the US market under the name of Zelnorm TM ). Tegaserod is used to treat functional gastro-intestinal disorders (FGIDs) including Irritable Bowel Syndrome (IBS).

The introduction of 5-HT4R drugs for psychiatric and/or neurological diseases seems to be a reasonable possibility.

II. Cloning and localization

II-1. Cloning

The cloning of the rat 5-HT4R gene was performed in 1995 by Gerald et al [8]. They isolated two cDNAs from rats that they called 5-HT4S (387 residues) and 5-HT4L (406 residues) receptors. According to the present NC-IUPHAR recommendations, they are now called 5-HT4a and 5-HT4b. Moreover, Van den Wyngaert et al. were the first to correct a sequencing error in the 5-HT4b (388 residues) receptor which is, in fact, only one residue longer than 5-HT4a whatever the species considered, including human [13]. From then on, several laboratories isolated 5-HT4R cDNA from rat, mouse and human tissues. Alignment of the putative C-termini amino-acid sequences predicted from all their cDNA (except one, see hereafter), revealed that the divergence in their sequence starts after position L 358 , their last common amino acid. Four C-terminal splice variants have been cloned in mouse, (a, b, e, f) [9,10], three in rat (a, b, e) [8,10] and eight C-terminal splice variants in human (a, b, c, d, e, f, g, n) [11,12,14,[20][21][22][23] (see Fig. 1A). The 5-HT4R isoforms are indeed splice variants generated from the same gene, as revealed by the human genome sequencing. The human 5-HT4R gene is one of the longest the G protein-coupled receptor genes (700kb) and consists of at least 38 exons (Fig. 1B). Its 5' non-translated region is exceptionally long (>500 kb) and complex compared to other 5-HTR genes [19]. The human 5-HT1R family has intronless genes [24,25], the human 5-HT2A gene (>20 kb) consists of three exons [26] and the human 5-HT2C gene (>230 kb) consists of six exons [27]. It must be noted that the gene of the ß2adrenergic receptor, a prototypal GPCR, is located in the longest intron 20 (Fig. 1B and [19]).

The 5-HT4R promoter contains potential binding sites for transcription factors (Sp-1, AP-2, AP-4 and GATA) but lacks TATA-and CAAT-boxes.

Variants e, f, and g overlap whereas variants e and f are generated as shorter versions of variant g due to internal 3'-acceptor sites in exon 35 (see Table 1 and insert in Fig. 1B). Note that Bender et al. published the correct sequence of 5-HT4c [18]. These authors also revealed the existence of a splice variant within the hepta-helical structure of the receptor, the 5-HT4h receptor [18]. This variant is a result of the insertion of 14 amino acids (exon 30) into the second extracellular loop of the receptor (Fig. 1). This variant is only found in the 5-HT4b isoform and therefore is called the 5-HT4hb variant.

The recent description of a 5-HT4n isoform containing 359 amino-acids (Fig. 1A) can be explained by two different 5'-donor sites at the end of exon 31 (Table 1) [22]. Thus, exon 31' can be generated and contains an in frame stop codon leading to the shorter C-terminal variant (see insert in Fig. 1B).

II-2. Localization

The distribution of 5-HT4R in the brain has been extensively studied using the labeled antagonists [ 3 H]-GR 113808 and [ 125 I]-SB 207710 in rat, mouse, guinea-pig, pig, calf, monkey and human (for a review see [START_REF] Bockaert | In 5-HT4 Receptor in the Brain and Periphery[END_REF]). 5-HT4Rs are expressed in limbic brain structures (hypothalamus, nucleus accumbens, amygdala), islands of Calleja, olfactory tubercle, fundus striati, ventral pallidum, septum, hippocampus, basal ganglia (striatum, globus pallidus) and substantia nigra.

In mice and rats, the [ 3 H]-GR 113808 binding site density is higher in the nucleus accumbens shell than in the core [START_REF] Compan | [END_REF]. The olfactory tubercles and fundus striati, like the striatum tail in the next posterior level, also exhibit strong labeling in mice. There are a few differences in the rat striatum where the density is identical in the rostral and caudal part, but higher in its lateral than medial part [START_REF] Compan | [END_REF]. In the rat cerebral cortex, there is an average concentration of binding sites with a predominant labeling of the cingulate (prefrontal cortex) as compared to the frontoparietal regions. A laminar pattern was observed in the hippocampal formation. The various hypothalamic and thalamic nuclei show moderate density of receptors. The density is weak in the dorsal and medial raphe nuclei in rodents [START_REF] Bockaert | In 5-HT4 Receptor in the Brain and Periphery[END_REF]30].

We know the cellular and subcellular localizations of 5-HT4Rs thanks to a diversity of methodological approaches: comparison between 5-HT4R mRNA (localized in cell bodies) and 5-HT4R binding site distribution, lesion and electrophysiological studies, as well as single cell PCR studies. The general observation is that 5-HT4Rs have a neuronal rather than a glial localization. In the striato-nigral pathways, 5-HT4Rs are mainly expressed in somato-dentritic compartments of intrinsic striatal neurons, mainly GABAergic, but their presence on cholinergic neurons is also likely. Some 5-HT4Rs are also present on terminals of striatal GABAergic neurons which project to globus pallidus and substantia nigra [START_REF] Compan | [END_REF]31]. In postmortem putamen of patients suffering from Huntington's disease [32] there is a 50% loss of 5-HT4Rs.

In the hippocampus, electrophysiological data indicate an expression in CA1 neurons [33][34][35] but also in granule cells and other neurons in the dentate gyrus [36]. In the prefrontal cortex, 60% of glutamatergic pyramidal neurons express 5-HT4Rs as determined by electrophysiological responses [37] and single cell PCR [38]. Much data indicates an effect of 5-HT4Rs activation on acetylcholine release in cortex [39], and also in hippocampus [35].

This suggests a localization on cholinergic neurons, although indirect effects cannot be excluded.

To better understand the putative differential functions of the different 5-HT4R splice variants, it will be important to know their differential regional and cellular expression in the brain.

Using specific oligonucleotides, but not quantitative PCR, three studies report expression of specific splice variant isoforms. In mouse brain, Claeysen et al. found an expression of 5-HT4a, b, e, f isoforms. The 5-HT4e, f isoforms were not detected in the periphery [10]. Bender et al. found a complex pattern of expression of human 5-HT4R isoforms, which was dependent not only on the brain region studied, but also on each individual brain. This raises the possibility that there is an individual polymorphism in the 5-HT4R variant pattern of expression in man [18]. Using non-quantitative PCR Vilaro et al. described a high expression of the 5-HT4n isoform in human brain [22]. A quantitative analysis of mRNA levels has been performed by Medhurst et al. using human brain [40]. Expression levels observed for the 5-HT4b splice variant were virtually identical to those obtained with primers that amplified all 5-HT4 splice variants. The results indicate that 5-HT4b was the dominant variant, followed by the 5-HT4a, c, g variants. Interestingly the pattern of expression of the different variants was brain region specific [40].

III. Multiple structural conformations, pharmacological differences between splice variants, coupling to G proteins, and tool molecules

III-1. Multiple structural conformations

Transfections of the different splice variants in several cell lines revealed that 5-HT4Rs have a high constitutive activity even when expressed at low and physiological densities (<500 fmol/mg) [10]. At a similar density, they show a much higher constitutive activity than the native and mutated 2-adrenergic receptors. Therefore, 5-HT4Rs have a high capacity to isomerize from an inactive (R) to an active (R*) isoform, even in the absence of agonist. We found that 16% of the WT receptors are under the R* form. Interestingly, the short C-terminal isoforms (5-HT4e, f receptors) have a higher constitutive activity than the long C-terminal isoforms (5-HT4a, b receptors). Progressive truncation of the C-terminal further increases the constitutive activity [10]. Several cysteines (Cys 328 , Cys 329 , and Cys 386 ) of the C-terminal have been shown to be palmitoylated. Cysteine palmitoylation is stimulated by receptor activation [41]. The palmitoylated cysteine 386 is only present in the 5-HT4a receptors splice variant, whereas Cys 328 and Cys 329 are present in all splice variants. Mutations of Cys 328 , Cys 329 into Ser, significantly increases the capacity of receptors to convert from the R to the R* form [41,42]. When tested on constitutively active mutants some 5-HT4R antagonists have been found to be neutral antagonists (for example, RS 100235 and GR 113808), partial agonists (for example SB 204070) or inverse agonists (for example GR 125487, SB 207266 or RS 116-0086) [10,43]. Inverse agonists have been proposed to stabilize the R form of GPCRs and therefore to reduce their constitutive activity. We found that 5-HT4R inverse agonists stabilize a third "silent" form. A specific transmembrane (TM) network, implicated in the stabilization of this "silent" form but not the stabilization of the R* form, has been described. It includes, the Asp 100 (3.32) in TMIII, Phe 275 (6.51) in TMVI and Trp 272 (6.48) in TMVI [16]. D100 is highly conserved within the biogenic amine receptor family and is indeed necessary for the binding and activity of 5-HT, tryptamines and small indole carbazimidamides. However, D100 is not necessary for the binding of benzamides and other non-indole 5-HT4 agonists and antagonists. These ligands have affinities in the range of nanomolar concentrations for a mutated 5-HT4R D100A [44]. More interestingly, two antagonists of native 5-HT4Rs are agonists of this mutated Gs-coupled receptor [44]. The mutated 5-HT4R D100A can be added to a class of mutated GPCRs called RASSLs (Receptors Activated Solely by Synthetic Ligands). The idea is to engineer receptors (RASSLs) that would be insensitive to their endogenous ligands but can be fully activated by synthetic ligands [45]. Heterogeneously expressed in tissues, they can be used to control signal transduction and cellular physiology in a research or therapeutic perspective.

III-2. Pharmacology and coupling to G-proteins

Several reviews describe in detail the pharmacology of 5-HT4Rs [START_REF] Bockaert | Handbook of experimental pharmacology: Serotoninergic neurons and 5-HT receptors in the CNS[END_REF]46]. We will only discuss the possible difference in pharmacology of the splice variants and the "non G s", described signaling pathways (see Table 2).

All the 5-HT4R splice variants have the transmembrane domain core and therefore the same primary binding site for 5-HT as well as for most of the synthetic ligands. In binding assays, the pharmacology of the variants (including the 5-HT4hb) [18] are not significantly different.

However, when functional studies are considered, some differences have been noted in their signaling properties: 1) as already discussed, the constitutive activity of the variants depends on the sequence of their C-terminal [10]; 2) the classical 5-HT4R neutral antagonist, GR 113808, is a partial agonist on the 5-HT4hbvariant [18]; 3) renzapride is a full agonist on the 5-HT4b and 5-HT4d isoforms and a partial agonist on the 5-HT4a and 5-HT4e/g isoforms [20]; 4) 5methoxytryptamine and prucalopride are more potent on the 5-HT4b variant, whereas SDZ-HTF 919 and SB 204070 are more potent on the 5-HT4a variant [47]; 5) in CHO cells, a selective benzodioxanoxadiazolone (SL 65.0155) is an inverse agonist on 5-HT4aR but a partial agonist on 5-HT4b and 5-HT4e variants [48]; 6) a difference in desensitization of the splice variants is reported in CHO cells, the 5-HT4d variant is more rapidly uncoupled to adenylyl cyclase than the 5-HT4e variant [49]. In these cells, the desensitization is PKAdependent. Note that in colliculi neurons, the desensitization of 5-HT4Rs is homologous and thus results in an action of G-protein kinase (GRK), independent on PKA activity [50]; 7) an interesting set of data reports that in HEK 293 cells, 5-HT4b but not 5-HT4a variants are coupled to G i/G o [47] (Table 2); 8) the 5-HT4a variant is much more potent than 5-HT4b in increasing membrane bound Ca 2+ channel activity in HEK 293 cells [47] (Table 2); 8) in COS cells, 5-HT4b variant activates the ras and rap1 pathways, via PKA [51] (the other variants have not been tested). The activation of ras but not rap1 led to the downstream activation of ERK1/2 (Table 2); 9) finally, the 5-HT4a variant (the other variants have not been tested) has been shown to be coupled to G 13 in Sf9 cells, but also in mammalian cells, including the neuroblastoma x glioma NIE-115 and fibroblasts NIH 3T3 (Table 2). In NIE-115 cells, 5-HT4aRs provoke a RhoA-dependent neurite retraction and cell rounding [52].

Although interesting, all of the described experiments were performed in heterologous systems and often used overexpression. They indicate that differences in coupling and pharmacology are "possible" but need to be demonstrated in native cells and tissues before their true relevance can be judged.

In a recent series of experiments in brain, we were able to identify GPCR interacting proteins (GIPs) using the different C-termini of 5-HT4a, b, e splice variants as bait. The last C-terminus residues of 5-HT4aR (SCF) and 5-HT4eR (PVPV) correspond to one of the PDZ (type I and type II ligands, respectively [53]). On the contrary, the 5-HT4b C-terminus (SQS) is not typical of a PDZ ligand. Interestingly, proteins associated with the different C-termini of different variants suggest that some functional differences mediated via these GIPs may exist (L.

Joubert et al. in preparation).

IV. 5-HT4 receptor ligands

Structure-activity relationship studies (SAR) of 5-HT4 receptor ligands have been recently reported (for reviews, see [46,[START_REF] Clark | In 5-HT4 receptors in the brain and periphery[END_REF]). Here, we describe the significant progress made over the last decade in discovering potent and selective 5-HT4R agonists, antagonists and inverse agonists and point out those that are commercially available and those whose potential use in CNS disorders has yet to be determined (Table 3).

As previously noted, the 5-HT4R ligands are currently related, with some exceptions, to five main chemical classes: the indoles (including analogues of 5-HT, the indole carboxylates and the indole carboxamides), the benzamides, the benzoates, the aryl ketones and the benzimidazolones.

IV-1. Agonists

The first class of 5-HT4R agonists includes the substituted tryptamines or 5-HT analogues, as well as the substituted indole carbazimidamides. 5-Methoxytryptamine is an interesting tool because it lacks affinity for the 5-HT3R [55]. From a series of indole carbazimidamide derivatives, HTF 919 (tegaserod) was found to be a potent partial agonist with high affinity at 5-HT4R. It is 40-to 80-fold selective over the 5-HT1A receptor, 25-fold selective over the 5-HT2C and has no appreciable affinity for 5-HT3 or dopamine receptors [START_REF] Buchheit | Pfannfucke in Ref 57)[END_REF]57]. In vivo studies show that tegaserod enhances gastrointestinal motor activity and normalizes impaired motility throughout the gastrointestinal tract. Tegaserod maleate or Zelnorm TM is prescribed for IBS [58]. Further pharmacokinetic investigations in animals revealed a negligible penetration into the brain and so do not represent a useful tool for CNS research. The second class of 5-HT4R agonists includes the first generation benzamides bearing the 2-methoxy-4-amino-5-chloro substitution [4]. These benzamides are found to be non-selective and always have antagonistic activity at the 5-HT3 receptor (zacopride, renzapride and metoclopramide). Structural modification of the basic chain of the benzamides, cisapride SB 205149 and SC 53116 lead to the identification of more potent 5-HT4R agonists with lower affinity for 5-HT3 than the first generation benzamides [59][60][61]. Nevertheless, cisapride has appreciable affinity for 5-HT2A and a1-adrenergic receptors.

Interestingly, newer benzamides with large substitutions in their basic chain, such as prucalopride, mosapride and Y-34959, are highly selective but show varying degrees of intrinsic activity depending on the in vitro preparations of the 5-HT4R used [62][63][64].

When the amide linkage in benzamide was substituted by an ester, this led to benzoate derivatives with an increased affinity for 5-HT4R. The first of this series was ML 10302 with a high affinity for 5-HT4 receptors and a weak affinity for 5-HT3 receptors [65]. ML 10302 was also inactive at other 5-HT receptor subtypes. ML 10302 was characterized as being the first potent and selective 5-HT4R partial agonist but its susceptibility to hydrolysis limited its utility for in vivo investigation. Recently, Moser and coworkers synthesized SL65.0155, a novel compound with high affinity for 5-HT4R related to the benzodioxanes [48]. This compound acts as a partial agonist with a remarkable selectivity over other receptor subtypes, except for the s receptor and a1D-adrenoceptor.

In the fourth class, the benzimidazolones, BIMU 8 and BIMU 1 are potent and efficacious 5-HT4R agonists [66,67] that enter the CNS. However, their high affinity for the 5-HT3R and s2 recognition site limits their use for CNS applications [68,69].

The aryl ketones, related to the 5-HT4R ester ligands, were prepared in an attempt to overcome their metabolic lability: replacing the ester linkage of the antagonist RS 23597 produced RS 17017 which has a similar affinity for the 5-HT4R but has partial agonist activity [70].

Increasing the size of the alkyl group led to a progressive increase in agonist activity with maximal efficacy being achieved with RS 67333 and RS 67506 [71]. They were found to have good selectivity and bioavailability. The incorporation of an n-butyl group on the piperidine ring increases hydrophobicity and, consequently, brain penetration [72,73].

However, the compounds also bind to s1 and s2 receptors [71].

IV-2. Antagonists

In the indole class, GR 113808 was the first 5-HT4R antagonist with a high affinity for 5-HT4R and a low affinity for 5-HT3R [74]. This indole ester provided a pharmacophore model that assisted the search for other selective 5-HT4R antagonists. Furthermore, [ 3 H]GR 113808 was the first commercially available radioligand for 5-HT4R-binding studies [75]. The indole ester analogue, GR 125487 is more potent in the CNS and in the periphery, and also has higher bioavailability, presumably because the ester linkage is more stable [76]. SB 203186 is an indole ester with potent and selective 5-HT4R antagonist properties in various physiological assays but its short half-life limits its use in vivo [77]. In contrast, SB 207266 is a highly potent and selective antagonist with a long duration of action after oral administration [78]. SB 207266 is a very useful tool for research in the CNS [79,80].

Recently, the indazole carboxamide, LY 353433 was also found to be a potent and selective 5-HT4R antagonist with clinically suitable pharmacokinetics [81,82].

Surprisingly, there are no 5-HT4 receptor antagonists among the benzamides which only display agonistic activity [4]. However, it is interesting to note that when the amide is substituted by an ester, the compound becomes an antagonist. The first example was the 5-HT4R antagonist SDZ 205557 which is the ester analogue of metoclopramide [83]. Increasing the size of the substituent results in an increase in the affinity and selectivity of the drugs. RS 23597, ML 10375 and SB 204070 are good example [86]. The corresponding iodinated compound [ 125 I] SB 207710 is an excellent radioligand for binding studies with a remarkable selectivity (>5000-fold) over the other receptor subtypes [87]. The metabolic lability of the ester function leads, however, to limitations with respect to in vivo studies. Lack of selectivity of the benzimidazolone derivatives (DAU 6215, DAU 6285) compromised their utility for 5-HT4R antagonist studies [88,89]. New benzimidazole carboxamides and carboxylates have recently been synthesized by Lopez Rodrigez et al. [90,91]. Some of them exhibit high affinity (sub-nanomolar) for the 5-HT4 binding site and no significant affinity for the 5-HT3R.

The aryl ketone class contains molecules that present several advantages; first the replacement of the ester by a ketone provides excellent oral bioavailability. Secondly they enter the CNS following systemic administration. Over the last five years, Roche Bioscience has achieved higher affinity, selectivity and bioavailablility as shown by RS 39604 which has subnanomolar affinity and is now commercially available [92] together with RS 100235 and RS 100302 [START_REF] Clark | In 5-HT4 receptors in the brain and periphery[END_REF]93].

A new series of tricyclic benzonaphthyridine and azepinoquinoline derivatives has been synthesized (e.g. ATBI 221). They have a very high affinity for the 5-HT4R and a high selectivity over other 5-HTR subtypes and non-serotoninergic receptors. The connection of the acyl group with the piperidine ring through an iminoether linkage provides high bioavailability and brain penetration [94].

IV-3. Inverse agonists.

Three specific, high affinity 5-HT4R antagonists (GR 125487, SB 207266 and ML 10375) have been reported to exert inverse agonist activity [43,95]. Recently Roche Bioscience have synthesized three potent 5-HT4R inverse agonists, RO 116-2617, RO 116-0086 and RO 116-1148 [16]. RO 116-0086 is the des-amino, des-chloro derivative of the antagonist, SB 204070, and RO 116-1148 is the corresponding amide.

V. Control of neuronal ion and receptor channel activity and synaptic transmission

5-HT4Rs have been shown to regulate several ion currents and channels in native neurons

(Table 2). In colliculi neurons and in CA1 pyramidal neurons of hippocampus, 5-HT4Rs reduce the after-hyperpolarization (AHP) that follows action potentials [96][97][98]. In colliculi neurons, a concomitant broadening of action potentials and a reduction of spike accommodation were observed [98]. These activities are mediated by cAMP and PKA activation and contribute to increased neuronal excitability. They can be explained by inhibition of K + channels including Ca 2+ -activated K + channels [33,98]. In CA1 neurons, a decrease in the calcium-induced calcium release from intracellular stores contributes to the action of cAMP on AHP [33]. In colliculi neurons, a remarkable observation was that short term application of 5-HT4 receptor agonists or 8-Br-cAMP produces a long lasting inhibition of K + channels due to a long lasting blockade of phosphatases [98]. In addition to a reduction in AHP, 5-HT4Rs also increase depolarization in hippocampal CA1 neurons; one group has provided evidence for an activation of the hyperpolarization-activated current Ih by 5-HT4Rs as a mechanism of this depolarization (in mice) [34]. All these electrophysiological effects could influence neuronal excitability and facilitation of neurotransmitter release (see section VI).

Recently, two reports described the effects of 5-HT4Rs on GABAA receptor activity and GABAergic synaptic transmission. In prefrontal cortex pyramidal neurons, 5-HT4Rs have a bi-directional (activation and inhibition) regulation of GABAA receptor channels and GABAergic synaptic transmission (measured by the amplitude of the spontaneous GABAA receptor mediated inhibitory postsynaptic potentials (IPSPs)) [37]. The authors present evidence for a role of PKA as well as AKAP (A Kinase Anchoring Proteins) in both effects.

In guinea-pig dentate gyrus neurons, including granule cells, 5-HT4Rs have a different effect on GABAergic transmission. Their activation increases the frequency of GABAA-mediated IPSPs [36]. This is a pre-synaptic effect. The latter can be explained by the effects on K + channels described above and by data showing a stimulation of GABA release by 5-HT4R

agonists (see section VI).

A conditional regulation of dorsal raphe nucleus 5-HT neuronal activity has also been observed following intravenous injection of 5-HT4R ligands. When the basal firing rate of raphe neurons was high, 5-HT4R agonists and antagonists enhanced and reduced the firing rate, respectively [99]. In contrast, when the firing rate of the raphe neurons was low, the same drugs were inactive. These results indicate that 5-HT4Rs exert both a tonic and a phasic positive, frequency-related control of 5-HT neurons raising the possibility that 5-HT4R may constitute a possible therapeutic target to treat depression.

All these results favor an intriguing role for 5-HT4Rs in the fine tuning of neuronal activity.

They clearly indicate that their physiological effect may depend on the nature and activity of the neurons in which they are expressed, perhaps explaining why 5-HT4R ligands are active in very specific situations (morphine-treated animals, aged animals, scopolamine-induced cognitive deficits, for example).

The long-term potentiation (LTP) of the Schaffer collateral-CA1 synaptic transmission, as well as the population spike amplitude in the CA1 field evoked by Schaffer collateral stimulation is enhanced by the 5-HT4R agonist, SC 53116 [35]. The 5-HT4R augmented LTP effect was blocked both by a 5-HT4R antagonist as well as by the muscarinic antagonist, scopolamine. These findings suggest functional interactions between the serotonergic system mediated via 5-HT4Rs and cholinergic systems associated with cognitive processes.

A very interesting effect of 5-HT4Rs on a subpopulation of DRG (dorsal root ganglion) neurons has been described [101]. These DRG are sensitive to capsaicin and express tetrodotoxin (TTX)-insensitive Na + channels. They represent subclasses of Ad-and C-type afferent nociceptors. 5-HT via 5-HT4Rs and prostaglandins increases the activity of these particular Na + channels. The mechanisms by which 5-HT4Rs act are unclear. The 5-HT effect was delayed by 20-30s and was not mimicked by cAMP. This suggests that 5-HT4Rs may be involved in the generation of hyperesthesia.

VI. Control of neurotransmitter release

VI-1. Acetylcholine release

In line with the effects of 5-HT4Rs on K + channels and neuronal excitability, there are numerous reports demonstrating the ability of 5-HT4Rs to modulate the release of various neurotransmitters. Because of earlier suggestions that these receptors may be implicated in cognitive functions, and the fact that they facilitate ACh release in gastro-intestinal tract, central ACh release has been particularly studied. Consolo et al. were the first to report that i.c.v. injections of the 5-HT4R agonist / 5-HT3R antagonist, BIMU-1 caused ACh release in the frontal cortex [39]. Yamaguchi et al. raised extracellular 5-HT with the 5-HT re-uptake blockers (citalopram or indeloxazine) or a releaser (p-chloroamphetamine) and found that in the frontal cortex, the 5-HT4R antagonists, RS 23597 and GR 113808, blocked the associated release in ACh [104]. In the hippocampus, one report found no ACh release following i.c.v; injection of BIMU-1 [39], whereas another group found an increase in ACh release by a local application of the agonist, SC 53116 [35]. As already discussed, the same authors found that the SC 53116-induced enhancement of LTP was mediated by a cholinergic mechanism. In guinea pig brain slices, BIMU-8 increases the electrically-stimulated ACh outflow in cerebral cortex, hippocampus and nucleus basalis magnocellularis slices [105]. In the hippocampus, 5-HT4Rs-induce ACh release and stimulate and inhibit GABA release via muscarinic M1 and M4 receptors, respectively [106]. 5-HT4R antagonists did not decrease ACh release under basal conditions. This indicates that 5-HT4Rs do not exert a tonic effect on cholinergic neurons.

VI-2. Dopamine release

There are numerous studies that have reported an effect of 5-HT4R agonists on DA release. However, a simple picture of the results is difficult to make due to the various experimental conditions used in the studies and also some contradictory results. In general, in vitro and in vivo studies have reported that when 5-HT or 5-HT4R agonists are locally applied to the striatum or substantia nigra, a 5-HT4R-mediated increase in DA release is observed (see [25] [ 99,107]). Systemic administration of 5-HT4R agonists and antagonists is usually ineffective.

Striatal DA release induced by haloperidol or morphine but not that induced by cocaine or amphetamine, is reduced by intraperitoneal injection of 5-HT4R antagonists and increased by intraperitoneal injection of a 5-HT4R agonist [107,108]. Using identical protocols, mesoaccumbal dopaminergic function was not regulated by 5-HT4R ligands. To be able to specifically activate either the nigro-striatal or the mesoaccumbal pathways may be of great therapeutic interest. However, note that systemic injection or local perfusion of the 5-HT4R antagonist, SDZ 205557 into the nucleus accumbens shell inhibits cocaine-induced hyperactivity. This result could be explained by an effect of SDZ 205557 on 5-HT3Rs or by an unknown indirect effect [109].

The cellular mechanisms by which the state-dependent facilitatory control of the nigro-striatal pathway occurs are still unclear. The finding that 5-HT4Rs are able to influence DA release in striatal slice preparations indicates that they may control local circuitry within the striatum (cholinergic or GABAergic neurons) (see [25]). Indeed, 5-HT4Rs are present on cell bodies of striatal neurons. However, the finding that 5-HT4Rs modulate the firing rate of nigral DA neurons raises the possibility that striatal 5-HT4 receptors also affect DA release through an indirect control of DA neurons [107] via modulation of the activity of striatal efferent GABAergic neurons (striato-pallidal or striato-nigral).

VI-3. Serotonin release

The activation of 5-HT4Rs increases 5-HT release in the hippocampus while the 5-HT4R antagonists, GR 113808 and GR 125487, reduced basal 5-HT release. This indicates the presence of an endogenous tone on 5-HT4R in this preparation [110], perhaps consistent with the finding that 5-HT4 binding sites increase in number after the innervation by serotonin neurons has been abolished [START_REF] Compan | [END_REF].

VII. 5-HT4Rs: potential therapeutic CNS drugs targets

VII-1. Cognition

We proposed several years ago that 5-HT4Rs may have pro-cognitive properties [113,114].

More recent data support this possibility [35,100]. 5-HT4Rs are localized in numerous structures, such as hippocampus and cortex, that are considered important for mnemonic processes. In the hippocampus, localization and functional studies indicate that they play a modulatory role on LTP formation. The latter effect suggests the involvement of a cholinergic relay. 5-HT4Rs stimulate ACh release in frontal cortex and hippocampus. There is evidence for a loss of 5-HT4Rs in Alzheimer's disease in the cortex (-23%) and, particularly, in the hippocampus (-66%) [31]. Furthermore, in transfected CHO cells, 5-HT4Rs were found to stimulate the secretion of non-amyloidogenic soluble amyloid precursor protein (sAPP ), thought to have neuroprotective and memory enhancing effects [115]. Behavioral experiments have generally confirmed a pro-cognitive effect of 5-HT4R ligands with several aspects of memory performance being modulated.

Memory acquisition

• BIMU-1 (5-HT4 agonist / 5-HT3 antagonist) increased social olfactory memory in rats when administered before training. This effect was reversed by GR 125487, a specific 5-HT4R antagonist [116].

• BIMU-1 and BIMU-8 enhanced acquisition of an auto-shaping task when injected before training. This effect was blocked by GR 125487 [117].

• BIMU-1 and BIMU-8 as well as the specific 5-HT4R partial agonist, RS 67333, induce a substantial improvement of acquisition of an olfactory associative memory when injected before training [118,119] (Fig. 2).

• RS 67333 improved the acquisition of place and object recognition memory in young and old rats. This effect was blocked by GR 125487 [120].

• RS 67333 accelerated learning acquisition in the Morris water maze task when the inter-trial intervals were high (2 h), but not low (30sec). This indicates that 5-HT4R agonists can improve memory processes in a high demand memory task [121].

• RS 17017 (a relatively hydrophilic 5-HT4R agonist) administered orally and chronically enhanced delayed matching performance in young as well as in old macaques [122].

Memory deficit

• RS 67333 reversed the performance deficit induced by atropine in the Morris water maze test, an effect eliminated by the 5-HT4R antagonist, RS 67532 [73].

• RS 67333 and, to a lesser extent, RS 17017, reversed the deficit in the acquisition of olfactory associative memory induced by the 5-HT4 antagonist, RS 67532 [119] (Fig. 2).

• The 5-HT4R agonist, SC 53116 improved the scopolamine-induced deficit in the passive avoidance test [35].

• BIMU1 and RS 67333 reversed scopolamine-induced impairments in spontaneous working memory, confirming a role for 5-HT4R in cholinergically-mediated memory processes.

Taken together, the results suggest that there could be a potential therapeutic role for 5-HT4 agonists in restoring memory deficits related to short-term working memory disorders [123].

Memory consolidation

The effect of 5-HT4R ligands on memory consolidation is less clear. Meneses and Hong [117] reported that BIMU-1 and -8 have a negative effect on an auto-shaping learning task when injected during the consolidation phase. In contrast, Lamirault and Simon [120] found an increased consolidation of object recognition in old rats with RS 67333. Sanofi-Synthelabo is currently testing SL 65.0155 (Phase II) in an attempt to treat dementia of the Alzheimer type. The compound does not induce any change in either rat gastrointestinal peristalsis or in rat and dog cardiac rhythm [48]. In particular, SL 65.0155 has been found to alleviate cognitive deficits in aged rats using a linear maze test, as well as scopolamineinduced deficits in Morris water maze performance [48]. Moreover, SL 65.0155 and the cholinesterase inhibitor rivastigmine have a synergic effect in the object recognition test (Fig. 2) and in linear maze performances in aged rats [48]. Similarly, combined treatment with galanthaminium, a new cholinesterase inhibitor and RS 67333, enhanced place and object recognition in young and aged rats [124]. These synergisms are particularly interesting as they suggest a possible co-treatment in Alzheimer's disease and offer the possibility of reducing the therapeutic dose of cholinesterase inhibitors and, consequently, their side effects.

VII-2. Pain

A centrally-mediated antinociceptive effect of both the 5-HT4R agonists and the 5-HT3R antagonists BIMU-1 and -8 has been reported following noxious thermal (hot-plate test), chemical, (abdominal constriction test) and mechanical (paw pressure test) stimuli [125].

However, the effects of BIMU-1 and -8 may be related to their inactivation of 5-HT3 receptors; although the 5-HT3R / 5-HT4R antagonist, SDZ 205557, and a new selective 5-HT4R antagonist, ATBI 221, have been found to reduce visceral pain [94,126]. An increase in 5-HT4R mRNA has been found in dorsal root ganglia following hind paw inflammation.

The partial 5-HT4R agonist, tegaserod (Zelnorm TM ), which could be acting as an antagonist, is reported to reduce the symptoms of abdominal pain, bloating and constipation [58,127].

Tegaserod may produce abdominal analgesia via a reduction in the activity of extrinsic spinal afferents to the colon. Overall, the results suggest that an inactivation of 5-HT4Rs may decrease some types of clinical pain.

VII-3. Anxiety and Stress

The selective 5-HT4R antagonists SB 204070, SB 207266 and GR 113808 display anxiolyticlike effects in the elevated plus-maze test, albeit at high doses [128,129]. In contrast, both SDZ 205-557 and SB 204070 have been reported to attenuate the effects of diazepam and did not modify behavior when administered alone [130]. Similarly, stress-induced anxiety-like behavior, was enhanced in the 5-HT4R knockout male mice, again using the elevated plusmaze test ( [131] and in preparation). Complex and bi-directional modulation of GABAergic systems by 5-HT4 receptors, as described by Cai et al., may account for such discrepancies [37].

VIII-4. Reward and motor behavior

The high density of 5-HT4Rs in the striatum and nucleus accumbens suggests an involvement in the control of reward and motor behavior. However, the supporting data is not clear and is often contradictory. Under basal conditions, no effect on locomotion has been detected following the administration of the partial 5-HT4 receptor agonists, RS 67333 or RS 67506 [73,109]. Similarly, the 5-HT4R antagonist, SB 204070 did not alter amphetamine-induced changes in rat locomotor activity or rotational behavior induced by the unilateral lesion of the nigrostriatal dopaminergic projection [132]. Conversely, it has been shown that hyperlocomotion following 5-MeOT administration was abolished or attenuated by local injection into the hippocampus of the 5-HT4R antagonists GR 125487, SB 204070 or RS 23597 [133]. We have further found that 5-HT4R knockout mice do not exhibit a change in locomotion in their home cage but show a marked hyposensitivity to novelty-induced locomotion in the open-field, elevated plus-maze and alley tests. Given the high levels of 5-HT4 receptors in the shell of the nucleus accumbens [START_REF] Compan | [END_REF] and taking into account that 5-HT4R null mice have been found to be less sensitive to stress-induced anorexia [131], it is hypothesized that 5-HT4R null mice will be less sensitive to the motor, rewarding and/or addictive properties of cocaine.

Conclusion

Although 5-HT4Rs are the targets for earlier (metoclopramide, cisapride) or recent (tegaserod) therapeutic drugs to treat gastrointestinal diseases, as yet no 5-HT4R ligands are used to treat CNS disorders. This is probably due to the lack of availability of specific and stable drugs able to cross the blood brain barrier (Table 3). To our knowledge, SL 65.0155, which is being tested for dementia of the Alzheimer types [48], is the only 5-HT4 receptor ligand in development (phase II) for a CNS disorder. However, in the light of the emerging profile of the behavioral pharmacology of 5-HT4 receptor ligands, the possibility that they may also be of therapeutic value in pain, especially of intestinal origin, anxiety and other stress-related disorders cannot be dismissed. TABLE 1 Exon-intron boundaries of the human 5-HT4 receptor gene.

Legends to Tables

From [18,19]. Completed using NCBI Human Genome Resources:

(http://www.ncbi.nlm.nih.gov/genome/guide/human/) and Model Maker for HTR4.

This table presents all the identified splicing sites and the corresponding exons in the human

5-HT4Rs ligands that could be of interest in CNS research

A range of affinities taken from the literature (pKi and pEC50) is indicated for several ligands. the odor and water ports to interrupt the light beam only when S+ is delivered. Response to odor designated as negative resulted in presentation of non-aversive light, and water was not delivered. Individual trials were presented in a quasi-random fashion. A daily session was made up of 60 trials and five sessions were made with one session per day. The latency to give a response was analyzed and given as mean latencies in seconds for the positive and negative odors. In controls a significant latency difference between S+ and S-was only observed from session 4. After injection of the partial agonist RS 67333 the difference was observed after session 3. After injection of the antagonist RS 67532 the difference was only observed after session 5 whereas a situation similar to the control was observed when both the partial agonist and the antagonist were co-injected (modified from [119]).

Synergy between subliminal doses of a 5-HT4 partial agonist (SL 65.0155) and an inhibitor of cholinesterase (rivastigmine) in the object recognition test: Each experiment consisted of 3 sessions. During the first session the animals were allowed to become familiar with the box. Twenty-four hours later, the animals were again placed in the enclosure in the presence of two identical objects for the amount of time necessary to spend 20s exploring these objects. After another interval of 24 hours, the rats were again placed in the box with a previously presented object and a novel object. Time spent exploring the familiar object and the novel object was measured. Drugs (SL 65.0155: 0.1 g/kg po and rivastigmine: 0.03mg/kg ip) were administered separately or together before each session (modified from [48].

5 -

 5 HT4R gene. Exons 1 to 25 correspond to the 5'-untranslated region (5'UTR) and promoter region of the gene. Exons 26, 27, 28, 29, and 31 are present in all the splice variants cloned and constitute the common part of the receptor. Exon 30 and exons 31' to 38 are alternatively spliced to produce the 8 human splice variants cloned to date. Splice donor and acceptor sequences between exons (uppercase) and introns (lowercase) are given in bold. The size of exons and introns are indicated. ND: not determined.

  (F): full agonist; (P): partial agonist; (S): specific; (HS): highly specific; (1): commercially available; CNS: useful in CNS research.

TABLE 2 5-HT4Rs signaling in excitable cells and cell lines. For details see the text

 2

TABLE 3

 3

Table 1

 1

	Exon	Positions	Exon size			Intron size
	number	in cDNA	(bp)	3'-Acceptor site	5'-Donnor site	(kpb)
	1	1-193	193		GGGCCCAGgtgagttt	10
	2	194-292	99	ttctccagGTAAAGAA	TAATCCAGgtatccaa	4.3
	3	293-420	128	tctttaagACCTGACA	TGTTTAAGgtgagcat	3.4
	4	421-526	106	ttacgtagGACCTCTC	TAATTTAGgtatggta	1.7
	5	527-670	144	cttcttagGCTACGTA	ACAGGAAGgtgagtgt	1.1
	6	671-872	202	atccacagGCCACTTC	TTCCATCAgtgagtag	0.8
	7	873-946	74	attggcagGTGGTTCC	TCAGATTGgtatggct	2.1
	8	947-1142	196	ttccacagGCAGAGGA	TCCCCAATgtgagtat	6.6
	9	1143-1276	134	cgatgcagGAGCACGA	CCGGCTCAgtgagtgt	2.9
	10	1277-1318	42	ctacttagGTGGGTTT	TCTGAGTGgtgagtag	0.1
	11	1319-3013	1695	ccttacagCATCCCAG	TCTAAAGAgtaagtat	1.8
	12	3014-3194	181	gtgttcagGTCAGCTT	ACCGCCAGgtgagtca	15
	13	3195-3344	150	gtccccagGTCCCTCA	GCCTGCAGgtaggcct	2.2
	14	3345-3467	123	ccacctagGCAGCCAT	ACTACCGAgtaagtcc	1.3
	15	3468-3618	151	gttcctagGCTGGAGC	AGTCACAGgtcacagg	1.8
	16	3619-3819	201	attcttagGAGATCAG	AGCTGAAGgtaagagc	3.0
	17	3820-3938	119	tgagacagTTTCTCCT	AACTACAGgcaggtgc	>50
	18	3939-4151	213	atttgtagGGCAGTTG	AAGGCAAGgtaagtaa	30.5
	19	4152-4351	200	tctgatagATGGCTTC	GGTAAAGGgtgaatat	0.5
	20	4352-4418	67	tcacacagCAAAAGAC	CCAGAACTgtaagaaa	>240
	21	4419-4672	254	tatttcagTTCCCATG	TAAGTGAGgtgatgag	2.5
	22	4673-4716	44	tctcatagGTCCATAG	CATTCAAGgtaacata	7.5
	23	4717-4758	42	aactacagAGGGAGAG	GATTGAAGgtaagttt	1.8
	24	4759-5006	248	tcttcaagGTACTTTA	GCCTGGAGgtgagttg	2.9
	25	5007-5088	82	tcctctagAGACCTCT	TCCAAAAGgtagatct	25
	26	5089-5161	73	cattttagGACCCTGT	AATGTGAGgtatgtta	86
	27	5162-5287	126	tctttcagTTCTGAGG	CAGCTCAGgtgagcag	1.3
	28	5288-5488	201	actcacagGAAAATAA	CTGGATAGgtaaggac	25
	29	5489-5642	154	ctctccagGTATTACG	TTGATTTGgtgagtat	2.2
	30	5643-h	42	ttttcaagGAAAGGAG	TTCATGCGgtatgtca	11
	31	5643-6211	569	actctcagATAGAAAA	GTACTAAGgtgagtat	26
	31'	5643-n	708	actctcagATAGAAAA	TACTATCTggtcatgg	-
	32	6212-b	234	ctctctagGGATGCAG	TCGCTGGGcttttcct	1.4
	33	6212-c	≥160	tactttagTTCTGGAA	ND	≤4.7
	34	6212-d	110	cctaccagATTTTGAG	TGGATGTAtttgtttg	11
	35	6212-g	76	actaaaagTGGCTGTT	AGTGCTCTgtaagtct	-
	36	6212-e	55	GTCTCCAGCTTCCTCC	AGTGCTCTgtaagtct	-
	37	6212-f	31	TGCAATAGACCAGTTC	AGTGCTCTgtaagtct	14
	38	6212-a	157	ctttctagGTACACCG	CCTGGCATcacttctg

Table 2 Figure 2

 22

Legend to figures

B. Organization of the human 5-HT4R gene. From [18] and [19]. Completed using NCBI Human Genome Resources: (http://www.ncbi.nlm.nih.gov/genome/guide/human/) and Model Maker for HTR4.

Olfactory associative task:

In this task, rats, deprived of water for 48 hours, were trained to make two odor-reward associations. Each odor had to be associated with a specific reward, one arbitrary designed as positive (S+) and the other as negative (S-). Rats had to approach Table 3 Figure 1


Marco Andrello
email: marco.andrello@ird.fr.

Pierre De Villemereuil
email: pierre.devillemereuil@ephe.psl.eu

Marta Carboni
email: marta.carboni@gmx.net

Delphine Busson
email: delphine_busson@yahoo.fr

Marie-Josée Fortin
email: mariejosee.fortin@utoronto.ca

Oscar E Gaggiotti

Irène Till-Bottraud

Marco Andrello¹

Pierre De Villemereuil²

Accounting for stochasticity in demographic compensation along the elevational range of an alpine plant

Keywords: Arabis alpina, Brassicaceae, elasticity, elevation, population dynamics, stochasticity

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

INTRODUCTION

One of the processes shaping population performance across species ranges is demographic compensation between different vital rates, such as recruitment, survival, growth and reproduction [START_REF] Doak | Demographic compensation and tipping points in climate-induced range shifts[END_REF][START_REF] Villellas | Demographic compensation among populations: what is it, how does it arise and what are its implications[END_REF]. Demographic compensation arises when different vital rates change in opposite directions across populations in response to environmental gradients, and has been proposed as a mechanism increasing the range of environments over which a species can occur and to explain the apparent stability of species range margins despite strong temporal environmental changes [START_REF] Doak | Demographic compensation and tipping points in climate-induced range shifts[END_REF][START_REF] Sheth | Demographic compensation does not rescue populations at a trailing range edge[END_REF]. So far, the paradigm of demographic compensation has considered spatial differences in vital rates averaged over years, while disregarding the role of spatial differences in temporal variation of vital rates [START_REF] Villellas | Demographic compensation among populations: what is it, how does it arise and what are its implications[END_REF]. However, because temporal variation in vital rates can be higher in some parts of a species geographical range (for example, at range margins; [START_REF] Angert | The niche, limits to species' distributions, and spatiotemporal variation in demography across the elevation ranges of two monkeyflowers[END_REF][START_REF] Pironon | Geographic variation in genetic and demographic performance: new insights from an old biogeographical paradigm[END_REF]), population growth rates might vary across species ranges not only because of spatial variation in mean vital rates, but also in their temporal variability.

Population dynamics in temporally varying environments have received much attention in ecology and conservation [START_REF] Tuljapurkar | Population Dynamics in Variable Environments[END_REF][START_REF] Lande | Stochastic Population Dynamics in Ecology and Conservation[END_REF]. Theory predicts that temporal variability should decrease population growth rates in both structured and unstructured populations [START_REF] Lewontin | On Population Growth in a Randomly Varying Environment[END_REF][START_REF] Tuljapurkar | Population Dynamics in Variable Environments[END_REF]) and empirical studies support these predictions [START_REF] Morris | Longevity Can Buffer Plant and Animal Populations Against Changing Climatic Variability[END_REF]. In addition, positive temporal covariations between vital rates can potentially amplify the effects of environmental stochasticity on population dynamics, while negative temporal covariation can buffer it [START_REF] Doak | Correctly Estimating How Environmental Stochasticity Influences Fitness and Population Growth[END_REF][START_REF] Jongejans | Plant populations track rather than buffer climate fluctuations[END_REF][START_REF] Compagnoni | The effect of demographic correlations on the stochastic population dynamics of perennial plants[END_REF]. For example, positive covariances between reproduction and survival rates tend to magnify the effect of variability and lead to lower population growth rates than in the case of zero or negative covariances [START_REF] Jongejans | Plant populations track rather than buffer climate fluctuations[END_REF]. Finally, the elasticities of population growth rates, which measure the change in population growth rate caused by a change in demographic parameters, determine the ultimate effects of temporal variation and vital rate correlations on the population growth rate [START_REF] Caswell | Matrix population models. Construction, analysis and interpretation[END_REF][START_REF] Tuljapurkar | The many growth rates and elasticities of populations in random environments[END_REF]. The interplay of these factors is perhaps best summarized by writing the stochastic population growth rate logλs using the small-noise approximation, as a function of the intrinsic growth rate logλd (calculated using the temporal means of vital rates) minus a product containing temporal coefficients of variation of vital rates (CVk and CVl), correlations between vital rates (ρkl) and vital rate elasticities (ek and el) [START_REF] Tuljapurkar | Population Dynamics in Variable Environments[END_REF]:

𝑙𝑜𝑔𝜆 𝑠 ≈ 𝑙𝑜𝑔𝜆 𝑑 - 1 2
∑ 𝐶𝑉 𝑘 𝐶𝑉 𝑙 𝜌 𝑘,𝑙 𝑒 𝑘 𝑒 𝑙 𝑘,𝑙 (eq. 1)

Thus, a full picture of how population dynamics change across populations requires quantifying the differences in how mean vital rates, their temporal variation, their correlations and the elasticities change between populations. Such differences between populations can ultimately determine processes of demographic compensation and can thus inform on the stability and dynamics of species ranges [START_REF] Doak | Demographic compensation and tipping points in climate-induced range shifts[END_REF][START_REF] Villellas | Variation in stochastic demography between and within central and peripheral regions in a widespread short-lived herb[END_REF].

Elevational ranges offer a unique opportunity to study range-wide variation in vital rates and population dynamics at a tractable spatial scale. For plants, elevational ranges have been associated with large differences in life-histories [START_REF] Laiolo | Life-History Responses to the Altitudinal Gradient[END_REF]. Species living at lower elevations have often larger sizes, higher mortality rates, shorter lifespans and higher fecundities, while species living at higher elevations have smaller sizes, lower mortality rates, longer life spans and reduced flowering rates [START_REF] Nobis | Adult age of vascular plant species along an elevational landuse and climate gradient[END_REF][START_REF] Laiolo | Life-History Responses to the Altitudinal Gradient[END_REF]. These life-history patterns have been related to predictions from the r-K selection theory [START_REF] Pianka | On r-and K-Selection[END_REF], the metabolic theory of ecology [START_REF] Brown | Toward a metabolic theory of ecology[END_REF]) and the acquisitive and stress-tolerant strategies of functional ecology [START_REF] Read | Convergent effects of elevation on functional leaf traits within and among species[END_REF]. While many studies have uncovered elevational patterns in plant life-histories across species, studies on population dynamics are less common, and patterns of variation in plant population growth rates along elevational gradients are less clear. Indeed, the few studies focusing on dynamics of herbaceous plant populations on elevational gradients report increasing [START_REF] Miller | Impacts of insect herbivory on cactus population dynamics: experimental demography across an environmental gradient[END_REF][START_REF] Giménez-Benavides | Demographic processes of upward range contraction in a long-lived Mediterranean high mountain plant[END_REF], decreasing [START_REF] Kim | Demographic, developmental and life-history variation across altitude in Erysimum capitatum[END_REF][START_REF] Pena-Gomez | Life history variation and demography of the invasive plant Eschscholzia californica Cham. (Papaveraceae), in two altitudinal extremes, Central Chile[END_REF] and stable [START_REF] García-Camacho | Small-scale demographic compensation in a highmountain endemic: the low edge stands still[END_REF] patterns of population growth rates with elevation.

Here, we aimed at testing whether spatial patterns in temporal variation, temporal correlations and elasticities could be involved in demographic compensation beyond the spatial variation of average vital rates, thereby contributing to the stabilization of species elevational ranges. To this end, we carried out a population dynamics study on Arabis alpina (Brassicaceae), a broadly distributed arctic-alpine perennial herb, across most of its elevational range in the European Alps. Specifically, our goals were twofold. First, we aimed at quantifying the spatial variation of four different descriptors of stochastic population dynamics (means, coefficients of variation, correlations and elasticities of plant vital rates) across an elevational gradient. Second, we aimed at quantifying the contributions of each of the four descriptors to the stochastic population growth rate and test for demographic compensation between different descriptors.

MATERIALS AND METHODS

Model species

Arabis alpina (L., Brassicaceae) is emerging as a new model organism in plant ecology and evolutionary biology (e.g. [START_REF] Wang | PEP1 regulates perennial flowering in Arabis alpina[END_REF][START_REF] De Villemereuil | Patterns of phenotypic plasticity and local adaptation in the wide elevation range of the alpine plant Arabis alpina[END_REF] due to its perennial life-cycle and wide elevational distribution. It occurs primarily in the subalpine and alpine belts, predominantly in open, unstable, moist sites with low vegetation cover such as glacier forelands, scree slopes, rock ledges, footpaths and small streams, often in association with calcareous soil [START_REF] Lauber | Flora Helvetica -Flore illustrée de Suisse[END_REF]. Seedlings germinate and establish throughout the growing season, plants flower for a few weeks and produce fruits (siliques), and flowering stems eventually wilt and die [START_REF] Wang | PEP1 regulates perennial flowering in Arabis alpina[END_REF]. Seeds can persist in the soil and form a permanent seed bank [START_REF] Diemer | Estimates of Alpine Seed Bank Size in Two Central European and One Scandinavian Subarctic Plant Communities[END_REF][START_REF] Philipp | Hidden biodiversity in the Arctic -a study of soil seed banks at Disko Island, Qeqertarsuaq, West Greenland[END_REF].

Data collection

This study was conducted in six sites spanning most of the elevational range of A. alpina in the European Alps using permanent plots (Table 1, Figure S1), which were visited once a year after flowering between 2008 and 2014 to record the number of stems and siliques of each individual (See Appendix S1.1 in Supporting Information). In-situ germination tests were not successful, so germination rates could not be estimated locally and seed bank dynamics was disregarded in the matrix population model, but we conducted a sensitivity analysis to assess the effects of uncertainty in seed germination on the results [START_REF] Nguyen | Consequences of neglecting cryptic life stages from demographic models[END_REF]; Appendix S1.5, S2.2).

Microclimatic conditions, soil chemistry and species composition of the vegetation were measured in each plot to model plant vital rates in function of environmental conditions. Temperature data loggers (iButton® Hygrochron, Maxim Integrated™) provided estimates of summer daily mean temperature (Tmean) and daily temperature range (Trange; Table 1). Missing records (due to malfunctioning of the dataloggers) were imputed using data from nearby weather stations, resulting in ten resampled datasets (Appendix S1.2). Soil acidity (pH), total soil carbon and nitrogen content were determined following standard methods (Schinner et al. 1996). Abundance-dominance (Braun-Blanquet) lists of plant species were used to calculate abundance weighted means for vegetative height and specific leaf area (SLA), using values from the ANDROSACE [START_REF] Thuiller | Are different facets of plant diversity well protected against climate and land cover changes? A test study in the French Alps[END_REF]) and the TRY [START_REF] Kattge | TRY -a global database of plant traits[END_REF] databases. After performing a principal component analysis on the three soil variables and the two vegetation variables (Appendix 2.1, Figure S3, S4), we retained the first two axes to predict plant vital rates: SoilVeg1 (explaining 52% of the variance), positively related to acidic soils with high C and N content, and SoilVeg2 (explaining 29% of the variance), summarizing variation from slow-growing short vegetation to fastgrowing tall vegetation.

Analysis

We used a five-step approach to test how four descriptors (µ: means; CV: coefficients of variation; e: elasticities; ρ: temporal correlations) of seven life-cycle components (S: survival; G -: retrogressive growth; G = : stasis; G + : progressive growth; F0: reproduction; F1: fecundity; F2: recruit size) contribute to demographic compensation across the elevational range of A. alpina. First, we constructed matrix population models for each site and year using statistical models predicting plant vital rates from environmental variables (Step 1). Second, we used the matrix models to calculate the seven life-cycle components, stochastic population growth rate logλs and elasticities of logλs (Step 2). Third, we tested for significant relationships between elevation and population dynamics variables (Step 3). Fourth, we performed a stochastic life-table response experiment (SLTRE) in order to decompose the differences in logλs between sites into contributions 𝐶 𝑙 𝑘 of each life-cycle component l and each descriptor k (Step 4).

Finally, we assessed demographic compensation by testing for negative and positive correlations between the SLTRE contributions 𝐶 𝑙 𝑘 (Step 5).

Step

Prediction of plant vital rates

The plant vital rates used to construct the matrix population models were survival (whether the plant survives to t + 1 or not), size (the size of the plant at time t + 1, conditional on survival), reproduction (whether the plant bears siliques or not at time t), reproductive output (the number of siliques of the plant at time t, conditional on reproduction) and recruit size. Plant vital rates were predicted using generalized linear mixed models (GLMMs; [START_REF] Zuur | Mixed Effects Models and Extensions in Ecology with R[END_REF]) as a function of plant size at time t (except for recruit size that, by definition, did not exist at time t), Tmean, Trange, SoilVeg1 and SoilVeg2 treated as fixed effects; plant size at time t and Tmean were also included as quadratic terms. Site, year nested within site and plot nested within site were included as random effects on the intercept and the slopes when significant. The error structure of the models was Gaussian (for log10-transformed reproductive output),

Bernoulli (for survival and reproduction), or negative binomial (for growth and recruit size). We accounted for uncertainty in the data using a total 2000 bootstrap samples over the ten imputed climatic datasets. For each bootstrap sample, we fitted the 2 7 =128 models corresponding to the combinations of the predictors, sampled one of them according to its Akaike weight [START_REF] Burnham | Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach[END_REF], obtained site-and year-specific predictions of vital rates (by setting predictors to their mean values over the plots of each site and year) and constructed matrix models to perform all the subsequent population dynamics analyses. Means and 95% confidence intervals for the reported results were calculated from the 2000 predicted values using the percentile method. All analyses were run in R 3.6.0 with packages lme4 1.1-21 and MuMIn 1.43.6 [START_REF] Bartoń | MuMIn: multi-model inference[END_REF][START_REF] Bates | Fitting Linear Mixed-Effects Models Using lme4[END_REF]; Appendix S1.3).

Step

Population dynamics analyses

We defined a matrix population model [START_REF] Caswell | Matrix population models. Construction, analysis and interpretation[END_REF] with 50 size classes of one-stem each, which covered the range of variation in plant sizes observed in the field. The projection matrix A was the sum of the transition matrix P = [pij] and the fecundity matrix F = [fij], which were constructed using the predicted vital rates obtained in Step 1:

𝑝 𝑖𝑗 = 𝑠 𝑗 𝑔 𝑖𝑗 𝑓 𝑖𝑗 = 𝜀𝐹 0,𝑗 𝐹 1,𝑗 𝐹 2,𝑖 (eq. 2)
where j is plant size in year t; i is plant size in year t+1; sj (survival) gij (growth), F0,j (reproduction), F1,j (reproductive output) and F2,i (recruit size) are the predicted vital rates. ε = 0.02 is a seedling establishment coefficient converting the number of fruits in one year to the number of seedling in the following year, and was set equal to the median value of the ratio of the observed number of seedlings to the number of fruits in the previous year over all plots and sites.

Life-cycle components for each site and year were calculated as averages of the predicted vital rates over size classes weighted by the stable stage distribution vector [START_REF] Salguero-Gómez | Fast-slow continuum and reproductive strategies structure plant life-history variation worldwide[END_REF]. Specifically, S, F0 and F1 were calculated as weighted averages of the sj's, F0,j's and F1,j's (eq. 2), respectively. G - represents transitions from larger to smaller size classes and was calculated as the weighted average of all the gij's for which i < j. Similarly, G = (representing individuals not changing in size) and G + (representing transitions to larger size classes) were calculated as weighted averages of all the gij's for which i = j and i > j, respectively. F2 was calculated as the mean recruit size distribution F2,i.

For each site, we calculated the temporal means and coefficients of variation of each life-cycle component and temporal correlations between pairs of life-cycle components (Pearson's correlation) over years. The stochastic population growth rate logλs was calculated via the simulation method by randomly sampling one of the year-specific matrix at each iteration (Caswell 2001, p. 396). We then calculated the elasticities of logλs to changes in the mean and standard deviation of the stage-specific vital rates [START_REF] Tuljapurkar | The many growth rates and elasticities of populations in random environments[END_REF]. We obtained the elasticities to the mean and standard deviation of life-cycle components by summing the elasticities of the respective vital rates [START_REF] Franco | A comparative demography of plants based upon elasticities of vital rates[END_REF]; Appendix S1.4).

Step 3. Elevational patterns

We used linear regressions to test for significant relationships between elevation and population dynamics variables: mean life-cycle components, coefficients of variation of life-cycle components, temporal correlations between life-cycle components, logλs and elasticities.

Step 4. Stochastic life-table response experiment (SLTRE)

We calculated the differences in logλs (∆ log λ s (m) ) between each site m and a common reference site defined by the means of vital rates over sites. The ∆ log λ s (m) were decomposed into the contributions Finally, we used linear regressions to test for significant relationships between elevation and the net contributions 𝐶 𝑙 𝑘 .

𝐶 𝑥 𝑖 ,𝑥 𝑗 𝑘,(
Step

Demographic compensation

To test for demographic compensation and its effectiveness in reducing the spatial variation in population growth rates, we extended the approach of [START_REF] Villellas | Demographic compensation among populations: what is it, how does it arise and what are its implications[END_REF] to all descriptors of life-cycle components. We tested for demographic compensation by testing for negative and positive Spearman correlations between the net contributions 𝐶 𝑙 𝑘 . The occurrence of a significantly higher number of significant negative correlations (or a significantly lower number of significant positive correlations) than expected by chance is indicative of demographic compensation and was tested by permuting 1000 times the 𝐶 𝑙 𝑘 over sites. This permutation test assesses only the occurrence of demographic compensation but not its effectiveness in reducing the variance in logλs among sites, 𝜎 log λ s 2

. We then performed additional : this randomization procedure eliminates as much as possible the negative correlations while preserving the important positive correlations and indicates the overall effectiveness of demographic compensation [START_REF] Villellas | Demographic compensation among populations: what is it, how does it arise and what are its implications[END_REF].

RESULTS

Step 1. Prediction of plant vital rates

Plant size had significant effects on all vital rates (Table 2). Size and reproductive output were positively affected by SoilVeg2, which was itself positively related to vegetative height and SLA of the surrounding vegetation (Appendix S2.1). Survival was positively affected by mean temperature squared (𝑇 𝑚𝑒𝑎𝑛 2

), while recruit size was negatively affected by temperature range (Trange). However, the models for survival and recruit size had remarkably low explanatory power (marginal R 2 = 0.07 and 0.04, respectively). All vital rates showed considerable spatial and temporal variation that was unexplained by our environmental variables (conditional R 2 larger than marginal R 2 ).

Step

Population dynamics analyses

On average, survival probability was S = 0.5 (except in GAL where S = 0.75), progressive growth (G + ) was larger than retrogressive growth (G -) and stasis (G = ), reproduction was F0 = 0.5, reproductive output was F1 = 12 siliques and recruit size was F2 = 1.5 stems (Figure 1 andS5). Coefficients of variations (CV) were mostly comprised between 0.1 and 0.6 across all life-cycle components. Over all sites and pairs of lifecycle components, we observed 21 (17%) significant negative temporal correlations and 21 (17%) significant positive temporal correlations (Figure S6).

The stochastic population growth rate logλs was negative in all sites (Table 1). One site (GAL) had higher logλs than the other sites. The largest elasticities of logλs to the temporal means of life-cycle components were associated with S, while the elasticities to G + were the second-largest (Figure 1). The elasticities of logλs to the standard deviation of life-cycle components were largest and negative for S, intermediate for G + and F1, and smallest for G -, G = , F0 and F2.

Step

Elevational patterns

Mean survival (S), retrogressive growth (G -) and stasis (G = ) increased significantly with elevation (Figure 1), while mean progressive growth (G + ), reproductive output (F1) and recruit size (F2) decreased significantly with elevation. The CV of S, G -and G = decreased significantly with elevation.

While the elasticities to mean S did not change with elevation, the elasticities to mean G + significantly decreased with elevation. The elasticities to the means of the other life-cycle components were much smaller and showed significant positive (G -and G = ) or negative (F0, F1 and F2) relationships with elevation.

The elasticities to the standard deviation of life-cycle components did not change significantly with elevation, nor did the temporal correlations between life-cycle components.

The stochastic growth rate logλs did not change significantly with elevation (Figure S7).

Step

Stochastic life-table response experiment (SLTRE)

The SLTRE showed that all four descriptors of life-cycle components (means, coefficients of variation, temporal correlations and elasticities) contributed to differences in logλs between sites (Figure 2). Means had the largest total effects in all sites, but the other descriptors were not negligible and could account for up to 50% of the difference in the stochastic growth rate (Figure 2a): the largest effects were due to coefficients of variation, while elasticities and correlations had smaller effects. When looking at the total effects of each life-cycle component (Figure 2b), the largest ones were due to survival (S) and progressive growth (G + ), while the other life-cycle components had smaller effects.

The net contributions of means and coefficients of variation of S (𝐶 𝑆 𝜇 and 𝐶 𝑆 𝐶𝑉 ) increased (became more positive) with elevation, while the net contributions of mean G + (𝐶 𝐺 + 𝜇 ) decreased (became more negative) with elevation (Figure S8).

Step 5. Demographic compensation

There were 18 significant positive correlations and 22 significant negative correlations between the net contributions of life-cycle components across sites. This constitutes substantial evidence for the existence of demographic compensation according to the criterion proposed by [START_REF] Villellas | Demographic compensation among populations: what is it, how does it arise and what are its implications[END_REF], since the number of negative correlations was much higher than expected by chance (permutation test,

Figure 3).

The negative correlations involved all four descriptors of population dynamics. While the correlations linking G -, G = and G + together are trivial as they emerge from the same vital process (growth), the other correlations are ecologically meaningful (Figure S9). Among these, there were significant negative correlations involving mean life-cycle components (S, G + , F1 and F2), their coefficients of variation (S), temporal correlations (S, G -and G = ) and elasticities (G -and G + ). Significant negative correlations linked together the same descriptor of different life-cycle component (e.g. mean S and mean F1), different descriptors of the same life-cycle component (e.g. mean G + and its elasticity) and different descriptors of different life-cycle components (the CV of S and the mean of G + , F1 and F2).

The parameters contributing the most to demographic compensation were mean S, mean G + and mean F1, as their permutation generally increased the variance of logλs between sites, 𝜎 log λ s 2 (Figure 4a-d).

Conversely, the permutation of the CV of S led to smaller 𝜎 log λ s 2 , indicating that this parameter increases the variance in logλs relative to what would be expected by chance; this was the result of the numerous positive correlations involving the CV of S (Figure 3). The other parameters did not change 𝜎 log λ s 2 considerably. Randomizing only the parameters that reduced the variance in logλs between sites indicated that the observed 𝜎 log λ s 2 was 59% of the median 𝜎 log λ s 2 expected under the hypothesis of minimal negative correlations, but not significantly smaller (p = 0.17; Figure 4e).

DISCUSSION

In this work, we studied variation in population dynamics of A. alpina across most of its elevational range in the European Alps (2000m). Contrary to the expectation that peripheral populations have lower demographic performance than central populations [START_REF] Pironon | Geographic variation in genetic and demographic performance: new insights from an old biogeographical paradigm[END_REF], A. alpina showed surprisingly little variation in population growth rates logλs across its full elevational range. Conversely, most lifecycle components significantly varied with elevation. We showed that this pattern could be partly explained by demographic compensation, i.e. negative correlations between the contributions of different life-cycle components to spatial differences in logλs. In particular, compensatory effects across the elevational range did not arise only through opposite spatial patterns in mean vital rates, but also in their temporal variation, elasticities and temporal correlations. This highlights a previously overlooked, but potentially important, role of stochastic processes in offsetting mean changes in vital rates and stabilizing population dynamics at range margins. We now discuss the origin, significance and generalities of the patterns of demographic compensation observed in this study.

The origin of negative correlations between the different descriptors of life-cycle components should be searched in their patterns of variation along the elevational gradient (Figure 1). First, mean vital rates changed in opposite directions: survival (S) increased along the elevational gradient while reproductive output (F1) decreased, resulting in a negative correlation between 𝐶 𝑆 𝜇 and 𝐶 𝐹 1 𝑒 (Figure S9). However, stochastic descriptors also contributed to demographic compensation along elevation. For example, the decrease in mean progressive growth (G + ), by itself, should have resulted in lower population growth rates logλs at higher elevations. However, the elasticity to mean G + also decreased with elevation and counterbalanced the negative effects of lower G + , because smaller elasticities dampen the effects of changes in life-cycle components on logλs. The CV of survival also decreased with elevation, further offsetting the negative effects of lower G + , since smaller CV have positive effects on logλs. The resulting negative correlations between the net contributions of these parameters to logλs (namely, between 𝐶 𝐺 + 𝜇 and 𝐶 𝐺 + 𝑒 and between 𝐶 𝐺 + 𝜇 and 𝐶 𝑆 𝐶𝑉 ) partly explain why population growth rates did not change with elevation despite marked elevational gradients in life-cycle components. Overall, the observed patterns are in agreement with the known higher occurrences of smaller and longer lived species and individuals at higher elevations (Nobis & Schweingruber 2013; Laiolo & Obeso 2017) and higher variability of survival at lower elevations [START_REF] Angert | The niche, limits to species' distributions, and spatiotemporal variation in demography across the elevation ranges of two monkeyflowers[END_REF].

Such elevational patterns could be due to opposite responses of vital rates to common environmental drivers [START_REF] Knops | Negative correlation does not imply a tradeoff between growth and reproduction in California oaks[END_REF]). The main environmental driver of variation in growth and reproductive output was SoilVeg2, which summarizes variation in specific leaf area (SLA) and vegetative height (Appendix S2.1), meaning that A. alpina tends to grow larger and produce more fruits when the surrounding vegetation is composed of tall plants with large SLA. This relationship could indicate a response to high competitive pressure or a common effect of temperature, because SLA and vegetative height in plants tend to increase with temperature and decrease with elevation [START_REF] Moles | Which is a better predictor of plant traits: temperature or precipitation[END_REF][START_REF] Read | Convergent effects of elevation on functional leaf traits within and among species[END_REF][START_REF] Rosbakh | Specific leaf area correlates with temperature: new evidence of trait variation at the population, species and community levels[END_REF]. In contrast, the environmental drivers of survival are not easy to identify, because the statistical model linking plant survival probability to environmental variables had very low explanatory power. These results seem corroborated by a common garden experiment using the same six populations as this study, which found that temperature was significantly associated with total fruit length (a measure of reproductive output) but not with survival [START_REF] De Villemereuil | Patterns of phenotypic plasticity and local adaptation in the wide elevation range of the alpine plant Arabis alpina[END_REF].

Elevational patterns in survival, growth and reproductive output could also be driven by other environmental factors not considered in our analysis, such as soil phosphorus content, diversity of root microbiota or herbivore damage, all of which affect various traits of A. alpina across its range [START_REF] Almario | Root-associated fungal microbiota of nonmycorrhizal Arabis alpina and its contribution to plant phosphorus nutrition[END_REF][START_REF] Buckley | Variation in growth and defence traits among plant populations at different elevations: Implications for adaptation to climate change[END_REF]. Negative correlations between life-cycle components could also be due to energetic trade-offs and structural constraints [START_REF] Williams | Life history evolution under climate change and its influence on the population dynamics of a long-lived plant[END_REF]. In A. alpina, higher rates of flowering are associated with reduction of plant survival, because all stems wilt and die after setting seeds, to the point that mutants for perpetual flowering show an annual life-cycle [START_REF] Wang | PEP1 regulates perennial flowering in Arabis alpina[END_REF].

Slower rates of stem production and/or lower rates of flowering could thus increase the longevity of the entire plant, resulting in negative correlations between growth, reproduction and survival.

Spatial patterns in elasticity are not very documented, but increasing elasticities to survival with elevation could result from their positive correlation with longevity [START_REF] Silvertown | Comparative Plant Demography -Relative Importance of Life-Cycle Components to the Finite Rate of Increase in Woody and Herbaceous Perennials[END_REF][START_REF] Franco | A comparative demography of plants based upon elasticities of vital rates[END_REF]) and from the positive correlation between longevity and elevation [START_REF] Nobis | Adult age of vascular plant species along an elevational landuse and climate gradient[END_REF]. In contrast, decreasing elasticities to fecundity and growth with elevation, as found in our study, could be expected given that these elasticities correlate with SLA [START_REF] Adler | Functional traits explain variation in plant life history strategies[END_REF] and SLA is known to decrease with elevation [START_REF] Read | Convergent effects of elevation on functional leaf traits within and among species[END_REF]. However, within-species patterns of elasticities are also influenced by the level of environmental disturbance [START_REF] Oostermeijer | Temporal and Spatial Variation in the Demography of Gentiana Pneumonanthe, a Rare Perennial Herb[END_REF][START_REF] Silvertown | Interpretation of Elasticity Matrices as an Aid to the Management of Plant Populations for Conservation[END_REF], which may not show consistent variation with elevation.

The correlations between life-cycle components involved all descriptors of population dynamics but their effectiveness for reducing the variance in logλs (𝜎 log λ s

2

) was higher in the case of mean life-cycle components. The effectiveness of a single descriptor for reducing 𝜎 log λ s 2 through demographic compensation depends on the strength and number of its negative correlations relative to its positive correlations (Figure 3) and its contribution to the differences in logλs between sites, Δlogλs (Figure 2).

Only parameters making large contributions change 𝜎 log λ s 2 through their correlations, decreasing it when most of their correlations are strong and negative. Mean progressive growth was the most important parameter for demographic compensation by offsetting variation in survival. Mean survival and mean reproductive output were the second most important parameters, thanks to their large contributions to Δlogλs and the negative correlation between them. Conversely, temporal correlations and elasticities showed many significant negative correlations but they were not as important for demographic compensation because the net contributions to Δlogλs were small, in line with what is observed in other plant species [START_REF] Jongejans | Plant populations track rather than buffer climate fluctuations[END_REF][START_REF] Compagnoni | The effect of demographic correlations on the stochastic population dynamics of perennial plants[END_REF][START_REF] Davison | Stochastic effects contribute to population fitness differences[END_REF]. Finally, the CV of survival made relatively large contributions to Δlogλs, but showed too many positive correlations that led to an increase of 𝜎 log λ s 2 rather than a reduction.

Although our results are comparable to findings over multiple species in the deterministic case [START_REF] Villellas | Demographic compensation among populations: what is it, how does it arise and what are its implications[END_REF], our study is the first assessing demographic compensation in a stochastic framework.

Assessing whether the results obtained here are representative of other species will require additional studies quantifying both the contributions of all descriptors of population dynamics to Δlogλs and their pairwise correlations. The first exercise has been done by [START_REF] Davison | Stochastic effects contribute to population fitness differences[END_REF] on a set of 62 species,

showing that more than one quarter of contributions to Δlogλs can be attributed to the effect of coefficients of variations, elasticities and temporal correlations. However, the importance of these descriptors of population dynamics for demographic compensation remains unknown, as it depends critically on the relative number and strength of negative vs. positive correlations in which they are involved.

Even with demographic compensation, the stochastic population growth rate was negative in all sites, indicating that populations are projected to decline in size and eventually go extinct locally. However, A.

alpina could persist thanks to germination from its persistent seed bank and immigration from other sites [START_REF] Hastings | Persistence of spatial populations depends on returning home[END_REF]. Its frequent occurrence in unstable sites suggests that populations could show an extinction-recolonization dynamics typical of metapopulations [START_REF] Ouborg | Toward a Metapopulation Concept for Plants[END_REF].

The inclusion of a seed bank led to higher, sometimes positive population growth rates and confirmed the existence of demographic compensation (Appendix S2.2). The effects of immigration are more difficult to study in absence of estimates of seed dispersal rates, but the strong spatial genetic structure of the populations (FST = 0.6, de Villemereuil et al. 2018) suggests that dispersal rates might be low. The patterns of demographic compensation revealed here could thus be different in models integrating empirical estimates of seed dormancy and germination rates and extinction-recolonization dynamics, potentially unmasking greater importance for coefficients of variation, elasticities and temporal correlations.

So far, demographic compensation has been discussed mainly in terms of spatial variation in mean vital rates [START_REF] Doak | Demographic compensation and tipping points in climate-induced range shifts[END_REF][START_REF] Villellas | Demographic compensation among populations: what is it, how does it arise and what are its implications[END_REF][START_REF] Sheth | Demographic compensation does not rescue populations at a trailing range edge[END_REF]). Our study is the first to highlight that temporal variation, elasticities and temporal correlations can be involved in demographic compensation, even if their effect was smaller than that of means. Nonetheless, temporal variation in vital rates could become more important under future expected increasing frequencies of extreme climatic events [START_REF] Meehl | More Intense, More Frequent, and Longer Lasting Heat Waves in the 21st Century[END_REF][START_REF] Schär | The role of increasing temperature variability in European summer heatwaves[END_REF], such as summer heatwaves and drought, that can cause large temporal variation in vital rates [START_REF] Smith | The ecological role of climate extremes: current understanding and future prospects: Ecological role of climate extremes[END_REF][START_REF] Andrello | Effects of management regimes and extreme climatic events on plant population viability in Eryngium alpinum[END_REF]. Assessing the importance of all descriptors of population dynamics for demographic compensation could thus provide a more complete understanding of the dynamics of elevational as well as geographical species ranges in a context of global change. Trange 11 (6.0, 18.6) 16.9 (11.5, 21.9) 15.9 (9.7, 36.1) 6.3 (3.1, 9.6) 8. 1 (5.8, 13.3) 16.3 (11.8, 23.2) logλs -0.4 (-0.5, -0.2) -0.3 (-0.5, -0.2) -0.5 (-0.6, -0.4) -0.5 (-0.8, -0.

  (eq. 3) From this decomposition, we derived the net contributions 𝐶 𝑙 𝑘 of each life-cycle component l and each descriptor k by summing the 𝐶 𝑥 𝑖 ,𝑥 𝑗 𝑘,(m) according to the definition of life-cycle components given above. The total effect 𝐶 𝑙 of each life-cycle component was calculated by summing the absolute values of its contributions over the four descriptors, 𝐶 𝑙 = ∑ |𝐶 𝑙 𝑘 | 𝑘 . Similarly, the total effect 𝐶 𝑘 of each descriptor was calculated by summing the absolute values of its contributions over life-cycle components, 𝐶 𝑘 = ∑ |𝐶 𝑙 𝑘 | 𝑙 .

Figure 1 .Figure 2 .

 12 Figure 1. Elevational patterns in life-cycle components and elasticities. Elevational patterns in mean

Figure 3 .

 3 Figure 3. Demographic compensation. Correlogram of Spearman's correlation coefficients between the

Figure 4 .

 4 Figure 4. Effectiveness of demographic compensation. (a), variance of population growth rate logλs

FIGURE

  FIGURE 1 602

  Figure S2.

1 602 FIGURE 2 604 FIGURE 3 606 FIGURE 4 608Table 1 . Characteristics of the study sites.

 1

	Site	BRU	CHA	VIL	LAU	GAL	PIC
	Longitude	5.61112	5.59267	5.57083	6.39034	6.40375	6.38426
	Latitude	45.15065	45.07117	45.01809	45.02846	45.06049	45.06385
	Elevation (m)	930	1480	1980	2090	2590	2930
	Aspect	South	North	South	North	North	South
			Calcareous
	Habitat	Calcareous scree	grassland, scree	Calcareous scree	Schists, torrent	Calcareous scree	Schistose scree
	Initial N	46	145	104	90	110	50
	Number of plots	2	3	3	3	3	4
	Tmean	14.7 (12.8, 17.5)	15.7 (12.9, 18.2)	12.9 (9.3, 17.5)	10.4 (8.0, 12.1)	7.7 (5.3, 10.3)	9.1 (5.9, 12.1)

ACKNOWLEDGEMENTS

We thank Serge Aubert, Rolland Douzet and Bénédicte Poncet for helping us find the populations, Hannah Secher Frommel and Cindy Arnoldi for soil analyses, Anne Delestrade for providing the weather station data, three anonymous reviewers whose comments helped us improve the manuscript and all the people who helped us in the field (in particular Florian Alberto, Perrine Augrit, Anne-Lise Bartalucci, Justine Bisson, Jérémy Camazzola, Loïc Chalmandrier, Julie Chauvin, Lucas Hemery, Elsa Jullien, Aymeric Pilleux, Blaise Tymen and Stefan Willhoit). MA and PDV were funded by a PhD scholarship by the French Ministry of Research. This research was partially conducted at the Jardin Alpin du Lautaret, a member of the AnaEE network (Infrastructure for Analysis and Experimentation on Ecosystems), and has used plant trait values from the TRY initiative and data base (http:// www.try-db.org), which is hosted, developed and maintained by J. Kattge and G. Bonisch (Max Planck Institute for Biogeochemistry, Jena, Germany), and currently supported by DIVERSITAS/Future Earth and the German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig.

The data and R code used in this study are openly available in GitHub at https://github.com/MarcoAndrello/Stoch_Demogr_Comp_Arabis

SUPPORTING INFORMATION

Additional Supporting Information may be downloaded via the online version of this article at Wiley Online Library (www.ecologyletters.com). For each of the five vital rates, the table reports the standardized coefficients of fixed effect, the standard deviation of random effects (intercepts and slopes), the correlations between random intercept and slopes and marginal and conditional R 2 [START_REF] Nakagawa | The coefficient of determination R2 and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded[END_REF]. Only the random effects that were retained after model selection on the random structure are shown. Means and 95% confidence intervals were calculated by randomly sampling statistical models over 200 bootstrapped demographic datasets and 10 resampled imputed datasets. The predictors whose confidence intervals do not overlap with zero are in bold.