Magdalena Kristiawan

Mazen Vaclav Sobolik

Al Haddad

Karim Allaf

M Al Haddad

DIC process for treatment of organic materials

Keywords: Ylang-ylang, extraction, essential oil, steam distillation, Instantaneous Controlled Pressure Drop


Angham Boubou

Philippe Auger

Alain Migeon

Ruth Hufbauer

Maria Navajas Navarro

Traits leading to invasion: how did the tomato spider mite Tetranychus evansi colonize Europe?

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Posters Session 40

P40/03 Titre : Traits leading to invasion: how did the tomato spider mite Tetranychus evansi colonize Europe?

Angham Boubou -Philippe Auger -Alain Migeon -Ruth Hufbauer -Maria Navajas

What allows a species or population to invade once a propagule arrives to a new geographical area, remains poorly understood. There is much research focused on differences in the traits possessed by invasive species relative to non-invasive introduced species. However, the different evolutionary histories of the species, and often differences in the environments they invade, make difficult to know which traits play a large role in invasion. We are studying the invasion history and biology of the tomato spider mite, Tetranychus evansi, a mite that originates from South America and has recently emerged as a new threat to solanaceous crops in Africa and in the Mediterranean basin. Our research has revealed that two main lineages are present in Europe. Differences in their geographical distribution and population dynamics suggest that they differ dramatically in invasive potential. This provides an excellent opportunity to evaluate what biological traits differ between more invasive and less invasive lineage. We investigate two biological traits that appear likely to be key for the success of the invasion of T. evansi in newly colonized temperate climates: cold tolerance and host range. The species is not able to diapause, thus its invasion of a temperate environment is likely to rely upon its ability to tolerate cold. Additionally, though considered to be a specialist, as with many herbivorous insects, and its ability to exploit different species of plants is not equal, and the range of plants in the new environment likely differs from the native area. We experimentally compare life-history parameters of mites from the more and less invasive lineages and submitted them to different temperatures and host plants. We find that the more invasive lineages is more cold tolerant and has a broader host range. This supports the idea that 'general purpose genotypes' are particularly suited to invasion.

Angham Boubou -INRA, Centre de Biologie et Gestion des Populations -Montpellier -boubou@supagro.inra.fr

P40/04 Titre : Dispersion d'un insecte invasif dans un paysage socio-écologique tropical

Veronica Crespo-Perez -François Rebaudo -Jean-François Silvain -Olivier Dangles De nombreux insectes ravageurs sont des espèces invasives dont le succès est lié à la diminution d'ennemis naturels et à la disponibilité de nourriture dans les champs cultivés. Cependant, les capacités intrinsèques de dispersion des insectes sont rarement suffisantes pour en faire une espèce invasive. L'expansion des insectes invasifs est dite stratifiée puisqu'elle se produit selon un modèle associant diffusion simple (locale) et évènements de dispersion à longue distance souvent facilitée par les activités humaines. La modélisation des dynamiques de propagation des ravageurs invasifs dans des paysages agricoles ayant une forte hétérogénéité tels que les Andes tropicales représente un défit majeur et urgent car elle pourrait fournir aux pays en voies de développement des outils pour faire face aux risques liés à ces organismes. Le principal objectif de cette étude est de développer un modèle de type automate cellulaire pour simuler les dynamiques spatiales de l'invasion de la teigne de la pomme de terre Tecia solanivora dans une vallée agricole des Andes centrales d'Equateur où l'infestation a commencé en 2006. Ce modèle permet l'intégration de variables environnementales et sociales réelles du paysage et de comparer l'influence de l'hétérogénéité environnementale versus sociale sur la dispersion de ces insectes. Nous nous sommes intéressés plus particulièrement à la dispersion passive des insectes à longues distances. Pour cela nous avons intégré dans l'automate un modèle dit « de gravité » qui simule la dispersion à longues distances entre points discrets d'un paysage hétérogène. Nos simulations nous ont montré que les sauts à longues distances ont permis aux insectes d'envahir le territoire plus de deux fois plus rapidement que leur permettraient leurs seules capacités de dispersion. Grâce à l'inclusion de la dispersion à longues distances dans le modèle de gravité nous avons simulé avec succès la présence des insectes dans des points inatteignables par diffusion locale. Notre étude souligne l'importance d'intégrer l'hétérogénéité spatiale liée aux activités humaines (paysage social) pour une modélisation juste des dynamiques d'invasion de ravageurs dans les systèmes agricoles tropicaux.

Veronica Crespo-Perez -CEFE/CNRS -Equipe BIOFLUX -Montpellier -maria-veronica.crespo-perez@cefe.cnrs.fr


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text:
Keywords:

• brown rot caused by Monilinia species, can provoke as much as 30 to 40% of crop losses

• no other alternative than chemical treatment is available : fungicide applications are generalized and occur till pre-harvest • all cultivated peaches are more or less sensitive to brown rot • mechanisms of resistance may be complex and largely linked to fruit characteristics including fruit craking

Genotype

Cracking and practices

Comment citer ce document :

Adapted from Bertin et al, 2010 Fruit mass (g)

Criteria to optimize

Comment citer ce document :

Criteria and parameters

Complex interactions Direct influence of Lx

  photosynthesis stem carbon balance stone and flesh dry growth

Days after bloom Photosynthesis and vegetative growth Fruit dry matter growth and fruit photosynthesis Sugar accumulation Cuticular conductance Water fluxes Stone-pulp partition Sensibility analysis

		55 parameters	6 genotypic parameters involved in different processes
	fruit mass PARAMETERS DEFINITION	PROCESSES REFERENCE	MINI	MAXI
	coeff.transfo1	sweetness crack density Part of the leaves in the structural part of the leafy shoots	Vegetative structure	0.766	0.672 0.842*
	MuF	Initial relative fruit growth rate	Fruit demand	0.0035	0.001	0.01**
	ca1	Proportion of carbon as sucrose in phloemic sap	Sugar metabolism	0.347	0.23	0.54***
	FSsat	Parameter of the relationship between stone dry mass and total fruit dry mass	Stone-pulp partition	6.78	6.10	7.46**
		Parameters of the equation of
	cut.be	the relative elongation rate of	Transpiration	1.26	1.134 1.386*
		the cuticle
	Lx	Conductivity of the composite membrane for water transport	Water fluxes	0.23328	0.0769 0.667**
		Comment citer ce document :	parameters

* ± 10 % variations ** Observed variability within BC2 population (Quilot et al 2005) *** Extreme

values from litterature Genetic parameters

	CRITERIA	OPTIMISATION	MINI	MAXI
	Fruit mass (g)	maximiser	50	300
	Sweetness (%)	maximiser	4	20
	Crack density (%)	minimiser	0	20

loops

-are their genotypes good in different scenarii ?

• try to develop methods from Operations Research and compare results with those from Artificial Intelligence methods (NSGA)

Comment citer ce document :

Thank you for your attention


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text:
Prerak Bhatnagar

M C Jain

Jitendra Singh

Patrick Borel

Fabien Szabo De Edelenyi

Stéphanie Vincent-Baudry

C Malezet-Desmoulin

Alain Margotat

Bernard Lyan

Jean-Marie Gorrand

Nathalie Meunier

Sophie Drouault-Holowacz

Severine Bieuvelet

Anti-Glycation Activity

Marina Figueiredo Ferreira De Souza

Mariana Darro Canela

Alejandro Gugliucci

Deborah Helena Markowicz

Bastos Brazil

Deborah Markowicz Bastos

John Schulze

Alejandro Gugliucci Brazil

Eric Reynaud

Gamze Aydin

Ralph Rühl

Olivier Dangles

Catherine Caris-Veyrat

Kelly Décordé

Pierre-Louis Teissèdre

Thibault Sutra

Emilie Ventura

Jean-Paul Cristol

Jean-Max Rouanet

Dominique Lacan

Jeanne Ramos

Jean-Paul Cristol1

Daniel L Graham

Michel Carail

Gordon M Lowe

S H Mexico

Claire Dufour

Michèle Loonis

Marie-Noëlle Corre

Jean-Luc Poëssel

Pascale Talamond

J Amengual

Erwan Gouranton

Y Van Helden

S Hessel

J Ribot

E Kramer

B Kiec-Wilk

U Razny

G Lietz

A Wyss

A Dembinska-Kiec

A Palou

J Keijer

Jean-François F Landrier

Louise Hansen

Lars O Dragsted

Thaer Barri

Mette Kristensen

Anja Olsen

Jane Christensen

Kim Overvad

Balling Søren

Rasmus Engelsen

Anne Bro

Tjønneland Denmark

Micronutrients Céline Riollet

Christiane Malezet

Marie-Josèphe Amiot

Nuria Vázquez

Javier García-Alonso

Sergio Bravo

María Jesús

Periago Spain

Graça Miguel

Susana Anahi Dandlen

Florinda Gama

Maribela Pestana

Amílcar Duarte

Alcinda Neves

Dulce Antunes Portugal

Pascale Goupy

Kati Froehlich

Volker Boehm

France P1

Skaltsounis A L Greece

P1-1 Socioeconomic Status of Emerging Mandarin Belt in Jhalawar district


Alexis Michaud

Jacqueline Vaissière

Reflections about the phonemic analysis of Yongning Na (Tibeto-Burman): perceptual transcription and acoustic data

Keywords: phonemics, acoustics, allophony, perception, Na/Naxi/Mosuo phonèmes, acoustique, allophonie, perception, na/naxi/mosuo

A preliminary phonemic inventory of the dialect of the Na language spoken in Yongning, China (a.k.a. Eastern Naxi 纳 西语东部方言/ Mosuo 摩梭话) is presented, on the basis of first-hand fieldwork data. Some reflections are offered on three interrelated issues commonly encountered in fieldwork, namely (i) To what extent does perceived allophonic variation correspond to articulatory/acoustic reality, to what extent does it merely reflect the investigator's perceptual expectations? (ii) How can acoustic data help select International Phonetic Alphabet symbols for the phonemic units brought out by distributional analysis? (iii) How can acoustic data help characterise the vowels and consonants encountered in fieldwork, both in a structural (language-internal) perspective, and in a cross-language perspective?

Introduction 1.Usefulness of acoustic description. The project of an acoustic description of Yongning Na.

The selection of International Phonetic Alphabet symbols for the phonemes of a given language is essentially based on structural arguments and expert listening, rather than on acoustic analysis and modelling. This is true both for the most documented languages, because their description is usually still based on a tradition that predates modern acoustic phonetics, and for newly described languages, because acoustic analysis is seldom a priority in fieldwork.

IPA notations are oriented towards the transcription of the language's phonemic oppositions. They offer some indications on the articulatory characteristics of the sounds at issue, but cannot be expected to provide a full specification of the pronunciation of the sounds under study: they do not encapsulate enough information to reproduce the sound at issue.

The acoustic theory of speech production [START_REF] Fant | Acoustic theory of speech production, with calculations based on X-ray studies of Russian articulations[END_REF] allows for a representation of acoustico-perceptual characteristics of speech sounds by reference to the resonantial properties of the vocal tract: the F-pattern. Unlike IPA notation, a characterisation in terms of F-pattern is sufficiently detailed to serve as input for speech synthesis, via articulatory modelling [START_REF] Maeda | Phonemes as concatenable units: VCV synthesis using a vocal-tract synthesizer[END_REF]. (To be quite precise, the F-pattern needs to be supplemented by information on nasality, if any, and on phonation type.) In the belief that speech sounds can be characterised very accurately in terms of a target F-pattern and of the articulatory configuration used to attain this pattern, the second author of this article is currently developing a notation [START_REF] Vaissière | Area functions and articulatory modeling as a tool for investigating the articulatory, acoustic and perceptual properties of the contrast between the sounds in a language[END_REF] to describe a given phoneme by reference to certain fixed acoustical properties. The aim of this research is to some extent comparable with that of Daniel Jones in defining the cardinal vowels: to provide a stable reference point for linguistic description. However, to our knowledge, the cardinal vowels have not been explicitly related to formant characteristics: they are defined in articulatory terms, and the audio renderings proposed to illustrate them fluctuate somewhat, e.g. some of the cardinal vowels recorded by Peter Ladefoged are somewhat different from those of Daniel Jones (see [START_REF] Vaissière | Area functions and articulatory modeling as a tool for investigating the articulatory, acoustic and perceptual properties of the contrast between the sounds in a language[END_REF] for more details). It appears worth investigating in which ways an acoustic definition of the sounds of a given language can supplement the IPA notations for this language and facilitate cross-language comparisons.

The present article presents preliminary observations on how acoustic observations and reflections can help overcome some difficulties encountered in fieldwork. The object of study is the Na language (Tibeto-Burman family) as it is spoken in Yongning, China (Chinese coordinates: 云南省丽江市宁蒗彝 族自治县永宁乡平静村). This language is also known as Mosuo (摩梭话) or Eastern Naxi (纳西语东部方言). Subsection 1.2 of the Introduction offers explanations on the provisional notation of tones used in this article. Section 2 provides a (likewise provisional) phonemic inventory, with specific explanations about the palatalisation of velars (2.1), the three-way contrast between /k/, /kʰ/ and /kʶ/ (2.2), consonantal nuclei (2.3) and rhotic rhymes (2.4). Acoustic analyses proper are set out in section 3. In conclusion, language-specific remarks (subsection 4.1) and remarks on acoustic analysis in fieldwork (4.2) open into the broader project of a monographic study of the acoustics of dialects of the Na language (4.3).

Preliminary remarks on the prosodic system of Yongning Na

Like all the Na dialects documented to date -such as Lijiang Na, a.k.a. 'Western dialect of Naxi', and Namuyi [START_REF] 黄布凡 | [END_REF]-, Yongning Na makes use of three tonal levels: High, Mid and Low, here transcribed as ˥, ˧, ˩. However, unlike Lijiang Na, which essentially has a syllable-tone system (one tone per syllable), with only a few processes of tonal change [START_REF] Michaud | Reassociated tones and coalescent syllables in Naxi (Tibeto-Burman)[END_REF][START_REF] Michaud | Tonal reassociation and rising tonal contours in Naxi[END_REF], Yongning Na appears to have word-tones: the lexical tonal schemes are partly neutralised in citation form. For instance, [gi˧zɯ˧] 'little brother' and [gu˧mi˧] 'little sister' have the same tonal pattern in citation form, yet they do not belong in the same tonal class, as demonstrated by their behaviour when followed by the copula [ŋi], e.g. in the carrier sentence [ʈʂʰɯ. __ .ŋi], "This is…" ([ʈʂʰɯ] is a deictic): [ʈʂʰɯ˥gi˧zɯ˧ ŋi˥] "this is little brother" (tonal scheme: HMMH) vs. [ʈʂʰɯ˥gu˧mi˧ ŋi˩] "this is little sister" (tonal scheme: HMML).

The tonal system of Yongning Na is currently under analysis. It is reminiscent of the 'tonal accent'/'pitch accent' of Japanese and of the 'tonal schemes' of Subsaharan languages such as Bambara [START_REF] Rialland | Réanalyse des tons du bambara: des tons du nom à l'organisation générale du système[END_REF], and has some analogues in other Tibeto-Burman languages (see [START_REF] 齐卡佳 ( | 在重音与声调的连 续体上看史兴语[END_REF] and references therein). The notation of tones in this article is provisional.

The tonal classes are exemplified in table 1. The carrier sentence used for nouns is "This is…", [ʈʂʰɯ. __ .ŋi], as has just been exemplified for the words 'little brother' and 'little sister'. Monosyllabic nouns and disyllabic nouns are provisionally placed in different categories-four for monosyllables, seven for disyllables-; progress in the analysis of the tone system should allow for a unified account of the tonal classes of these two sets. Tonal classes for predicative words (verbs and adjectives) are established on the basis of their behaviour when followed by the particle /ze˩/, which conveys accomplished aspect, in the carrier phrase /le. __ .ze/, e.g. [le˧dzɯ˥ze˩] "has eaten". A first overview suggests that there are no disyllabic predicative words apart from reduplicated forms, and that their tonal scheme can be derived straightforwardly from that of the corresponding monosyllables, so they are not included in table 1.

Phonemic inventory of Yongning Na

The present phonemic inventory of Yongning Na is based on fieldwork conducted in 2006 and 2007. As the word list comprises only some 2,000 entries, it is possible that more phonemic oppositions will be discovered in future.

The inventory presented here differs somewhat from that proposed by [START_REF] Lidz | A synopsis of Yongning Na (Mosuo)[END_REF], due in part to dialectal differences ( [START_REF] Lidz | A synopsis of Yongning Na (Mosuo)[END_REF] is based on fieldwork in the village of Luòshuǐ 洛水, whereas the present data come from 平静村, in the Yongning plain), in part to differences in phonemic analysis. A detailed comparison of the two analyses falls outside the scope of this paper.

Syllabic structure in Yongning Na is simply (C)(G)V, where C is a consonant, G a glide -with a severely restricted distribution -and V a vocalic element; the brackets indicate that C and G are optional. It therefore appeared simplest to present the inventory in table 2 in terms of initials, corresponding to consonants, and rhymes, corresponding to (G)V. The following subsections provide some explanations about table 2.

The palatalisation of velars and its consequences

As compared to the Na dialects spoken in and around the city of Lijiang (a.k.a. Western dialects of Naxi [START_REF] Michailovsky | Syllabic inventory of a Western Naxi dialect, and correspondence with Joseph F. Rock's transcriptions[END_REF][START_REF] Michaud | Three extreme cases of neutralisation: nasality, retroflexion and lip-rounding in Naxi[END_REF]), Yongning Na has undergone a thorough palatalisation of velars before /i/ and /j/. The empty slots in the phonemic system created by this evolution have been filled by syllables whose vowel underwent fronting, as shown in table 3. Table 3. Some Yongning Na ("Eastern" Na) cognates of velar-initial syllables of Lijiang Na ("Western" Na).

"Eastern" Na (Yongning) "Western" Na (data from [START_REF] Vaissière | Area functions and articulatory modeling as a tool for investigating the articulatory, acoustic and perceptual properties of the contrast between the sounds in a language[END_REF][START_REF] 黄布凡 | [END_REF] The case of 'to have' is slightly more complex. In addition to the palatalisation of the initial, from /g/ to [ɟ] and further to [dʑ], the rhyme appears to have diphthongised to [ju]; the resulting syllable, in the present-day state of the language, can be analysed phonemically either as /dʑ/+/ju/ or as /dʑ/+/u/. The former analysis may carry an etymologising bias, reflecting diachronic hypotheses rather than synchronic, phonetic reality. We choose the analysis as /dʑ/+/u/, which reflects the intuition that the frontness of the earlier rhyme has been entirely transferred onto the initial.

Palatalisation is also having consequences on other phonemes of Yongning Na. The extreme fronting of the syllables /tɕʰi/, /tɕi/, /dʑi/ brings them in the phonetic vicinity of the syllables /tsʰɯ/, /tsɯ/, /dzɯ/. The rhymes of both sets of syllables can be described as the voiced continuation of the initial: for instance, /tsɯ/ is realised as [tsz̩ ], and /tɕi/ can be approximately transcribed in IPA as [tɕʑ̍ ], rather than [tɕi]. (The diacritic indicating syllabic status is placed over the [ʑ̍ ], not underneath it, for the sake of clarity.)

It can be imagined that the continuous evolution towards fronting combined with an extreme degree of syllable-level coarticulation may threaten the distinction between these two sets (/tɕʰi/, /tɕi/, /dʑi/ on the one hand, /tsʰɯ/, /tsɯ/, /dzɯ/ on the other). The high functional load of the difference between the two sets goes against their confusion, however. So does the ever growing influence of Mandarin Chinese, where both sets exist: alveolo-palatal as in 七 / 1 tɕʰi/ 'seven' and 鸡 / 1 tɕi/ 'chicken', with less palatalisation than in Yongning Na; dental as in 此 / 3 tsʰɯ/ DEICT. and 子 / 3 tsɯ/ 'child', less fronted than in Yongning Na. To venture a remark on possible future developments: If the growing proficiency of Na speakers in Mandarin led them to adopt a Mandarin-like pronunciation for their palato-alveolars (i.e. less fronted than they are now in Na), this would restore a greater phonetic distance between them and the dental affricates.

As for the alveolo-palatal fricative /ʑ/, it is exclusively found in combination with /i/. Examples include / m1 ʑi/ 'monkey', / m4 ʑi/ 'family', / 4 ʑi/ 'to sleep', and / 3 ʑi/ 'to flow (river, water)'. It appears to be an example of an empty slot in the phonemic system being filled in the course of language evolution: Yongning Na has a voicing distinction with a high functional load, so that the introduction of a voiced counterpart to /ɕ/ fits in well within the system. How this evolution actually took place is an issue for future investigations.

The affricated velar stop /kʶ/ as a phoneme

The affricated velar stop [kʶ] is attested before /ae/, /ɑ/, /wɑ/ and /v̩ /. Before the first three, it can be treated as an allophone of /kʰ/; indeed, it is often accompanied by some aspiration (hence the notation as [kʰʶ] in table 4 below). However, it contrasts with /kʰ/ (as well as with /k/) before /v̩ /. The combination /kʶv̩ / is found in the words for 'hole', 'six', 'to fold', 'throat'; /kʰv̩ / in 'dog', 'year', 'to cut (grass)', 'to steal'; / m4 kv̩ / means 'garlic'. This quasi-complementary distribution is shown in table 4. As a conclusion, phonemic status has to be granted to the affricated velar stop /kʶ/. (i) The voiced fricative /v/ can only appear as a rhyme, not as an initial. The diacritic / ̩ / is thus implied in what follows. After bilabial initials, it is slightly trilled (i.e. /bv/ is realised close to /ʙ̩ /, /pv/ close to /pʙ̩ ), though less markedly so than in Lijiang Na. On the whole, the friction for /v/ is much less salient than in Lijiang Na.

(ii) The vowel /ɯ/ has fricative allophones after dental and retroflex fricatives and affricates, like the vowel /i/ in Mandarin Chinese. For instance, / 1 tsʰɯ/ "hot" is realised

[ 1 tsʰz̩ ], / m4 ɖʐɯ/ "market, city" is realised [ m4 ɖʐ ̍].
(iii) A rhotic element is also present in some rhymes. From an acoustic point of view, studies of various languages have shown that typical rhotic vowels always have a lowering of the third formant (as mentioned e.g. by [13, page 313]). Unlike Lijiang Na, whose rhotic vowel /ə˞/ clearly presents this characteristic, Yongning Na does not have a canonical rhotic rhyme; lexical correspondences confirm that rhoticity in Yongning Na and Lijiang Na are distinct phenomena, since out of 34 words containing the rhyme /ə˞/ in Lijiang Na and which have likely cognates in Yongning Na, 16 have the vowel /ae/ in Yongning, 10 have /v/. The situation in Yongning Na therefore warrants further analyses. Section 2.4 is a first step in this direction.

Rhotic rhymes

2.4.1.

The phoneme /ɻ/ Yongning Na has several rhotic-like sounds. One of these is the retroflex approximant, /ɻ/, which can serve as an initial, as a rhyme, or constitute a syllable in itself.

It appears as an initial in the words / m1 ɻae/ 'seed' and /1 ɻwae/ 'to cry, to shout [of animals or people]'; also in the second syllable of / d1 sɯ.ɻae/ 'table', / d4 ʈʰae.ɻae/ 'book, scripture', / d2 kʰwae.ɻae/ 'mat'. The phoneme /ɻ/ is not phonologically specified for voicing -indeed, there does not exist an IPA symbol for an unvoiced counterpart to /ɻ/, which means that such a contrast has not been reported to date in any language. In initial position, the /ɻ/ of Yongning Na appears to be partly devoiced.

The phoneme /ɻ/ is observed as a rhyme in three contexts: after /ʈ/; after /ʈʂʰ/; and on its own, the morpheme /ɻ/ being a verbal suffix, e.g. / 1 hu/ 'wait', [ɖɯ˧hu˧ɻ˥] 'Wait!' (/ɖɯ/ is the numeral 'one').

The syllable /ʈɻ/ contrasts with several syllables that are articulatorily close to it, having either back vowels or consonantal rhymes: /ʈv/, /ʈɯ/ (e.g. in / d7 kʶwae.ʈɯ/ 'turban'), /ʈɤ/ (e.g. / 1 ʈɤ/ 'to pull'), and /ʈwɤ/ (e.g. / 1 ʈwɤ/ 'to call out [of cock], to cock-a-doodle-doo'; tone not verified).

In the process of comparing spectrograms of these various phoneme combinations, we realised that an understanding of their acoustics required a comparison of all five members of the /ʈ/-initial set with one another, with /t/-initial syllables, and with affricated-initial syllables. After obtaining these data, we still required additional information on the vowels, since their realisation after /ʈ/ can hardly be studied without a knowledge of their intrinsic acoustic characteristics, which in turn requires observations on these vowels in a variety of consonantal contexts. The conclusion, which will be taken up in section 4.3 below, is that such analyses require a systematic approach -a monograph on the acoustics of the language.

2.4.2.

The phoneme /ɻ ̃/

The phoneme /ɻ ̃/ is the nasal counterpart of the phoneme /ɻ/ studied in the previous section. This phoneme, /ɻ ̃/, is used to transcribe a syllable that occurs only once in the vocabulary list: /ɻ ̃/ 'bone' (also found in many compounds, such as /sɯ.ɻ ̃.mi/ 'vertebral spine' and /ɻ ̃.ku/ 'knee'). It is a nasal, retroflex, approximant sound. Other notations would be possible, for instance as a nasal rhotic vowel: /ə˞ /. The symbol /ɻ ̃/ was chosen because the units transcribed as /ɻ/ and /ɻ ̃/ have similarities, and it appears plausible that they actually stand in a relation of structural opposition, the one nasal, the other oral.

The other nasal rhymes of Yongning Na are found only after /h/, where they contrast with oral rhymes, e.g /hae/ 'wind' vs. /hae/ 'lime', /hɑ/ 'evening' vs. /hɑ/ 'food', /hĩ/ 'human being; relativizing particle' vs. /hi/ 'rain'. Before oral rhymes, /h/ is realised with a friction source at a point in the vocal tract determined by the following vowel, e.g. palatal before /i/, velar before /ɑ/ and /ae/, and labiodental before /v̩ / (hence [çi], [xɑ], [xae], and [fv̩ ]), whereas the friction is very weak, due to an already lowered velum, in [hĩ], [hɑ], [hae],

[hv̩ ]. The analyses proposed in [START_REF] Michaud | Reassociated tones and coalescent syllables in Naxi (Tibeto-Burman)[END_REF] concerning the diachronic origin of nasal/oral vowel oppositions in the Na dialect of Fèng Kē apply to the Yongning Na nasal vowels.

Acoustic analysis of the close, front vowel of

Yongning Na ("/i/") The standard way of reporting on such fieldwork observations is to describe the phoneme at issue as having two allophones, and to make a reasoned choice of one of these allophones to represent the phoneme: for instance, one could choose to transcribe /i/ for [i, e], and /u/ for [u, o]. This amounts to saying that the difference between the phonetic realisation of these phonemes in the two sets of consonantal contexts listed in table 5 goes beyond what can be predicted from coarticulatory properties of the preceding consonant: that the two contextual variants are phonetically different sounds.

This raises an important issue: does our classification of the realisations of one phoneme into two phonetic categories (e.g. transcribing [i] in [ m1 i] 'spot, pimple' vs. [e] in [ m4 ʈʂe] 'earth') actually reflect an acoustic difference between these two realisations in Yongning Na, or does it merely reflect our perception as non-native speakers? Our perceptual expectations may not be adequate for the language under description, detracting from the precision and usefulness of the descriptions we produce.

Acoustic analysis can arguably provide decisive evidence on this issue, supplementing auditory impressions. Untrained listeners go by the categories of their native languages (for experimental evidence of an effect of linguistic experience on the perception of front vowels, see, e.g., [START_REF] Willerman | Cross-language speech perception: Swedish, English, and Spanish speakers' perception of front rounded vowels[END_REF]). It is not very likely that trained phoneticians can fully cast off this bias. Phonetic transcriptions done in the field are commonly considered to reflect a (narrow) phonetic level, on top of which phonemic/phonological analyses can be built; however, a different perspective can in fact be adopted: field notations can be considered as perceptual materials for linguistic analysis and reflection. An important step consists in reflecting on the reasons why the investigators, given their linguistic and scholarly background, chose one notation rather than another.

In the case of the present investigation, conducted by native speakers of French, the issue can be phrased as: What are the acoustic properties that led to the perception of the sounds [i] and [e]? To preview the result, it will appear

• that the phoneme at issue differs acoustically both from French /i/ and from French /e/; • that our perception of [i] in some contexts and [e] in others can be explained by the coarticulatory effects of the preceding consonant.

Acoustic observations on a female speaker

The native language of the authors, 'Standard' ('Parisian') French, has phonemic /i/ and /e/, as part of a vocalic system which -in its more conservative varieties -has the full set of cardinal vowels, /i e ɛ a, u o ɔ ɑ/. In the notation currently being developed by the second author of this article, prototypical French /i/ corresponds to the acoustic configuration {palatal (⇑F3F4) 3200Hz }, i.e. F3 is maximal, it corresponds to a resonance of the front cavity, and since F3 comes in the vicinity of F4, the amplitude of one of the two formants, or of both, is reinforced. For a male voice this spectral prominence is located at about 3,200 Hz; however, the exact value in itself is less important than the concentration of energy -a phenomenon which the notion of F'2 (read "F2-prime") captures well [START_REF] Carlson | Some studies concerning perception of isolated vowels[END_REF][START_REF] Bladon | A two-formant model and the cardinal vowels[END_REF]. This vowel (French /i/) is "the most acute voiced, noise-free sound that a vocal tract can generate" [START_REF] Vaissière | Area functions and articulatory modeling as a tool for investigating the articulatory, acoustic and perceptual properties of the contrast between the sounds in a language[END_REF]. This characterisation has recently been verified by the statistical examination of formant values extracted from large databases of broadcast speech in eight languages: the average distance between F3 and F4 for /i/ is much smaller in French than in the seven other languages investigated, namely German, English, Arabic, Spanish, Italian, Mandarin Chinese and Portuguese [START_REF] Gendrot | Les voyelles /i/ et /y/ du français : aspects quantiques et variations formantiques[END_REF]. On the other hand, the acoustic configuration for French /e/ is one in which F1 is higher than the F1 of /i/, and where, for an adult male speaker, F2, F3 and F4 are roughly equidistant, i.e. not clustering together, unlike in /i/ (clustering of F3 and F4: ⇑F3F4) or /y/ (clustering of F2 and F3: ↓F2F3).

An examination of spectrograms will offer some insights into the Yongning Na sound which had at first been transcribed as /i/. Spectrograms 1a, 2a and 3a (placed at the end of the article) show data from a female speaker aged about 55 at the time of the recordings, 1b, 2b and 3b from a male speaker aged about 35. The items are pronounced in isolation. Spectrogram 1 shows a realisation of Yongning Na / m1 i/ 'spot, pimple'.

The syllable begins with a semi-consonant: in Yongning Na (as in Lijiang Na), syllabic vowels are phonetically preceded by a semi-consonant acting as empty-onset filler. In Lijiang Na, the notation that has been proposed by [START_REF] Michailovsky | Syllabic inventory of a Western Naxi dialect, and correspondence with Joseph F. Rock's transcriptions[END_REF] for syllabic /i/ is [ji]. Given the amount of friction noise observed on spectrograms 1a-b, transcription of the onset as the fricative [ʝ] appears more adequate for Yongning Na.

The vocalic part of the syllable in spectrogram 1a is clearly diphthongised. The measurements in table 6 are taken at 1/4 th of the vowel, a time point chosen after [18, p. 94], and at 5/6 ths of the vowel, where F1 is at its highest. Formant frequencies were estimated by using the PRAAT software package (www.praat.org). The first formant rises in the course of the vowel, while the distance between F2 and F3 increases. During the first half of the vowel, much intensity is concentrated around 3000 Hz; this cluster appears to be made up of F2 and F3. A superficial examination would conclude that these characteristics are very much unlike those of French [i]: to a French ear, the perception of [i] requires, in terms of a male voice, an F3 frequency that is closer to that of F4 than to that of F2, or, said differently, a strong difference between F3 and F2 frequencies: F3-F2≈1000 Hz. On the other hand, from a perceptual point of view, it appears to be the frequency of the resulting spectral prominence that plays a key role in perception, whether such an acoustic prominence results from the clustering of F3 and F4 in a male voice or of F2 and F3 in a female voice. "It appears that in female and children's voices the relative role of individual formants may differ while an overall pattern aspect, yet to be defined, could be similar" [18, p. 98]; see also the discussion of speaker normalisation in speech perception, and of the notion of 'auditory Gestalt recognition', by [START_REF] Johnson | Speaker normalization in speech perception[END_REF]. This is in keeping with our auditory impressions. When listening to the first half and the second half of the vowel separately, our perceptual impression is [i] for the first half, [e] for the second half. It is known that a higher F1 can lead French subjects to perceive /e/ as opposed to /i/.

Spectrogram 2a shows a realisation of Yongning Na [ m2 tɕi] 'cloud' said in isolation by the same female speaker. Again, F1 rises (from 220 Hz to about 625 Hz) in the course of the rhyme, and F2 decreases (from 2420 to about 2170). F2 values are slightly lower than on spectrogram 1a; the amplitude of F2 movement is similar.

Spectrogram 3a shows the word for 'earth', initially transcribed as [ m4 ʈʂe]. Interestingly, its vowel actually resembles those represented on spectrograms 1a and 2a. F2 is even higher than on spectrogram 2a. These facts are taken up in the following section.

Comments and perceptual hypotheses

The allophonic variation between [i] and [e] transcribed on the basis of auditory impressions does not match with the observations made on the female voice: the vowel itself is realised by a fairly constant formant pattern. It may be described as an opening diphthong, somewhat like [i] at its beginning and like [e] at its end. The next step in analysis consists in finding out the reason for our original perception of two distinct allophones.

Our perception of [e] in the word for 'earth', as in the other words with initial retroflex fricatives and affricates, may in fact be due to characteristics of the consonant /ʈʂ/, rather than of the vowel itself. The friction in /ʈʂ/ has an overall low frequency, with a peak at about 4,100 Hz as against 6,700 for the friction in /tɕ/ (spectrogram 2a). It is plausible that the perception of the initial portion of the vowel is influenced by the spectral characteristics of the initial consonant (for a review of evidence for perceptual context dependence in various languages, see [20, p. 61]). In spectrograms 2a and 3a, the fricative noise continues until after voicing begins, i.e. into the beginning of the vowel; by itself, this is suggestive of a close vowel -corresponding to a configuration where the area of greatest constriction has a small area, hence the production of turbulence noise by egressive airflow. However, since the retroflex fricative (spectrogram 3a) has an overall lower spectrum than other fricatives -alveolo-palatal, as in spectrogram 2a, or dental -, the superposition of its friction noise onto the beginning of the following vowel may lower slightly the perceived main spectral prominence of the following vowel. Since the vowel at issue is acoustically inbetween our reference points for [i] and [e] in the first place, this small perceptual influence from the preceding consonant could account for the perception of [e] rather than [i]. This hypothesis is tested by means of a (sketchy) experiment reported in the next section.

A pilot cross-splicing test

Cross-splicing, made easy by digital sound processing, can shed light on issues such as the one set out in the preceding section. The initial /tɕ/ of spectrogram 2a was placed before the vowel in spectrogram 3a. Our perceptual categorisation of the resulting stimulus confirms the expectations: after /tɕ/, we perceive this vowel as [i]. (This stimulus is available, together with the original sounds, at the internet address indicated in section 6.) Conversely, when the initial /ʈʂ/ of spectrogram 3a is placed before the vowel in spectrogram 2a, this vowel is not perceived as [i] anymore, but as a more open front vowel, [e] or [ɛ].

This result can be extended to the [u]-vs.-[o] allophonic pairs of the first fieldwork notations.

Observations on a male speaker

The data from the male speaker are shown on spectrograms 1b, 2b and 3b. The vowels in spectrograms 1b and 2b have a similar F-pattern, whereas 3b shows a rising F2. These data suggest that in the case of the male speaker, who is one generation younger than the female speaker, there is actually a certain amount of allophonic variation of the close front vowel phoneme under investigation: the acoustic realisation of this phoneme after a retroflex initial differs from its realisation in isolation and after a palato-alveolar fricative. Needless to say, this observation will need to be confirmed by the examination of more data, and of more speakers of the same age group.

Conclusions and perspectives

On the hypothesised allophonic variation of close vowels

The acoustic observations on the sounds initially transcribed as distinct allophones, [e] and [i], differ for the female speaker and for the male speaker.

In the data from the female speaker, a member of the older generation who speaks Yongning Na on a day-to-day basis, the contextual variants of the phoneme at issue are much closer than the first fieldwork notations suggested. This phoneme is an opening diphthong; to a foreign ear expecting a stable vowel quality, it can be perceived as [i] due to the high frequency of the spectral prominence found at vowel onset, or as [e] when the spectral properties of the preceding consonant have the effect of lowering the perceived spectral prominence.

On the other hand, in the data from the male speaker, who is one generation younger and has much greater proficiency in Chinese (local dialect, 西南官话, and Standard Mandarin, 普 通话), preliminary observations actually suggest the presence of some allophonic variation of this vowel.

Implications for fieldwork: usefulness of acoustic observations

It is well known that field workers need to be careful to describe the phonetic categories of the language they investigate in their own right, rather than basing their judgments on analogies with sounds found in other languages that they know, such as their mother tongue or other varieties of the language under analysis. In the case of Yongning Na, the first author's earlier experience of fieldwork in 2002 and 2004 on a closely related language variety, Lijiang Na, certainly exercised an unwanted influence on phonetic notations: in Lijiang Na, there is a contrast between /i/ and /e/ (the latter actually closer to [ɛ]), e.g. /mbe˧/ 'village', /mbi˧/ 'urine') and between /o/ and /u/ (e.g. /kʰo˧/ 'noise, sound', /kʰu˧/ 'door'), which may have unwittingly led to an expectation that Yongning Na, too, had close vowels and midclose vowels.

The results in section 3 illustrate the fact that a simple acoustic analysis can offer some evidence to overcome the uncertainties of auditory impressions. On the other hand, these results also suggest that the acoustic study needs to be conducted in a systematic way, collecting data from several speakers and building a corpus containing each phoneme in a variety of contexts, in order to obtain reliable results. This conclusion opens into a project which is outlined in the next section.

Issues of transcription: necessity of a systematic acoustic overview. Project of monograph on the acoustics of Yongning Na.

Concerning the notation of the high front diphthong studied in section 3, a decision can hardly be made in isolation, without considering the broader picture of the acoustic characteristics of the phonemes of Yongning Na. The choice between a notation as /ɪ/, /i/, or again a notation that would represent both the beginning and endpoint of the diphthong (such as /ɪ e / or /i e /) will depend in part on how this sound compares with other vowel units in the language, and in part on how the formant structure observed in Yongning Na compares with the reference values available for an increasing number of languages: American English [START_REF] Peterson | Control methods used in a study of the vowels[END_REF], Swedish [18, p. 94], French, German [START_REF] Gendrot | Impact of duration on F1/F2 formant values of oral vowels: an automatic analysis of large broadcast news corpora in French and German[END_REF]… A consequence of the structural/functional notion of phonemic system is that the full picture of the language's contrasts should be taken into account before an adequate acoustic characterisation of individual sounds can be proposed. We therefore plan to produce a monograph on the acoustics of Yongning Na, on the basis of recordings by two women and two men.

The ultimate aim would be to propose a characterisation of each vocalic and consonantal phoneme by means of the fine-grained acoustic notation put forward by [START_REF] Vaissière | Area functions and articulatory modeling as a tool for investigating the articulatory, acoustic and perceptual properties of the contrast between the sounds in a language[END_REF]. To this end, the more phonetic instruments can be taken into the field, the better: acoustic modelling requires acoustic-articulatory modelling, and the articulatory component requires more information than spectrograms can offer. Comparable acoustic results can be obtained by different articulatory configurations, so that spectrographic analysis often leads to hypotheses that can only be verified by means of physiological data. We therefore plan to supplement audio data by recording multisensor data, such as oral and nasal airflow for the study of nasality, and electroglottography for the study of the voice source.

Table 1 .

 1 Provisional classification of Yongning Na lexical items into tonal classes, on the basis of their behaviour in carrier sentences (see main text).

		Categories m1 to m4: monosyllabic nouns; d1 to d7:
		disyllabic nouns. For predicates: four categories.
	number	tones in	examples
	assigned	frame	tones in citation+in frame	meaning
	m1		˩ ˥	ɖae˩˥ → ɖae˩ ŋi˥	dust
	m2		˥ ˩	ʁwɤ˥ → ʁwɤ˥ ŋi˩	mountain
	m3		˩ ˩˥	ŋv̩ ˥ → ŋv̩ ˩ ŋi˩˥	silver
	m4		˧ ˥	ɻ ̃ ˥ → ɻ ̃˧ ŋi˥	bone
	d1		˧ ˧ ˩	gu˧mi˧ → gu˧mi˧ ŋi˩	little sister
	d2		˧ ˧ ˥	gi˧zɯ˧ → gi˧zɯ˧ ŋi˥	little brother
	d3		˩ ˩ ˥	nv̩ ˩mi˩˥ → nv̩ ˩mi˩ ŋi˥	heart
	d4		˥ ˩ ˩	ʁu˥dzɯ˩ → ʁu˥dzɯ˩ ŋi˩ Tibetan
	d5		˩ ˧ ˥	zi˩baeᅴ → zi˩bae˧ ŋi˥	lightning
	d6		˩ ˥ ˩	ɑ˩ʁu˥ → ɑ˩ʁu˥ ŋi˩	home
	d7		˧ ˥ ˩	zu˧mv̩ ˥ → zu˧mv̩ ˥ ŋi˩ child
	predicates	1 2 3 4	˧ ˧ ˧ ˧ ˥ ˩ ˥ ˩ ˩ ˧ ˧ ˥	li˧ → le˧ li˧ ze˧ se˥ → le˧ se˥ ze˩ ʈʰɯ˩˥ → le˥ ʈʰɯ˩ ze˩ lɑ˩˥ → le˧ lɑ˧ ze˥	to watch to walk to drink to strike
		In what follows, the tonal category is indicated in
	superscript characters at the beginning of the syllable, e.g.
	/ m2 dʑi/ 'water' belongs in tonal category m2.

Table 2 .

 2 A preliminary inventory of the phonemes of Yongning Na. Initials (left) and rhymes (right).

		bilabial	coronal	retroflex	velar	uvular glottal	i	ɯ	u, ju
	plosive	pʰ p b	tʰ t d	ʈʰ ʈ ɖ	kʰ k g			v ̩
					kʶ
	affricate		tsʰ ts dz	ʈʂʰ ʈʂ ɖʐ					ɤ, wɤ, jɤ
			tɕʰ tɕ dʑ
	nasal	m	n		ŋ			ɻ
	fricative		s z	ʂ ʐ		ʁ	h
			ɕ ʑ					ae, wae, jae
	lateral approximant		l						ɑ, wɑ, jɑ
	lateral fricative		ɬ					+/ĩ/, /v̩ /, /ũ/, /w̃ɤ/, /ae/, /ɑ/ after /h/,
	approximant			ɻ				and /ɻ ̃/ on its own as a syllable

Table 4 .

 4 Distribution of [kʰ], [kʶ]/[kʰʶ], and [k] inYongning Na; "-" indicates unattested combinations.

		ae	ɑ	wɑ	i	o	u	v̩
	k	kae	kɑ	kwɑ	ki	ko	ku	kv̩
	kʰ kʶ	kʰʶae kʰʶɑ kʰʶwɑ	k ʰi -	kʰo -	kʰu -	kʰv̩ kʶv̩
	2.3

. General remarks on consonantal nuclei In

Yongning Na, some consonantal sounds function as syllable nuclei -which amount to rhymes, in the absence of any final consonants. The IPA term for this is to call them 'syllabic', because they function as syllable nucleus (though they do not constitute a syllable by themselves). Fricative syllabics are an areal characteristic: in particular, they are also common in neighbouring Yi languages, belonging to the Nasoid subgroup of Loloish (a.k.a. Ngwi; see

[12, page 70]

). The local dialect of Mandarin also has a fricative allophone of /u/ in words such as 'lake', 湖, pronounced [fv] (Standard Mandarin: /hu/).

There are three sets of consonantal rhymes in Yongning Na:

Table 5 .

 5 Distribution of close and mid-close vowels in the first field notations of Yongning Na vocabulary.

	3.1. The issue: coarticulation, or categorical allophony?
	One of the issues encountered in fieldwork was the notation
	of high vowels. The first, tentative notations of Yongning Na
	included [e] as well as [i], [o] as well as [u]. Looking back at
	these transcriptions, it appears that close vowels [i], [u] are in
	complementary distribution with close-mid vowels [e] and
	[o]. Table 5 shows their distribution 1 .
	rhyme	[e], [o]	[i], [u]
	initial	retroflex (fricatives,	zero initial; labials;
	consonant	affricates and stops);	dental stops; laterals;
		dental fricatives and	alveolo-palatals;
		affricates	velars; glottal; nasals

Table 6 .

 6 Formant frequency measurements on spectrogram 1a, showing evidence of vowel diphthongisation. The time point is indicated as a function of the total length of the vowel.

	time point	F1	F2	F3
	1/4 th	420	2740	3190
	5/6 ths	500	2510	3310

Note that[START_REF] Lidz | A synopsis of Yongning Na (Mosuo)[END_REF] analyses the 'fricative vowels' mentioned in section

2.3 above as allophones of /i/ (i.e. the way things stand in Mandarin Chinese): [dz̍ ], e.g. in the verb 'to eat', is analysed as /dzi/, whereas we analyse it as /dzɯ/. Thus,[START_REF] Lidz | A synopsis of Yongning Na (Mosuo)[END_REF] does have a contrast between /i/ and /e/, because she transcribes with an /e/ the syllable which we transcribe as /dzi/, e.g. / d1 dzi.lɯ/ 'wheat'.

th Phonetics Conference of China, Beijing, April 19-21, 2008. (No page numbers: Proceedings released as a CD-ROM.)

Acknowledgments

The first author expresses his heartfelt thanks to Latami Dashi (拉他咪•达石) for his help and advice during fieldwork in Yongning, and to the language consultants in Yongning for their hospitality and their patience. Our thanks to Liberty Lidz for kindly providing additional explanations about the phenomena that she observed in Luòshuǐ and elsewhere.


domain: sdv shs

text:
Biodiversity and animal feed -future challenges for grassland production

• The grassland landscape as a base for animal production -present, past and future • Biodiversity and productivity in grasslands -strategies and limitations • Forage as part of the food chain • Efficient resource utilisation for sustainable conventional and organic grassland production • Grassland-based production in Europe -pathways for future success The programme will offer plenary, parallel and poster sessions. Master-classes will be organised for young scientists. A major multidisciplinary Swedish research programme 'Management of Seminatural Grasslands -Economy and Biodiversity (HagmarksMistra)' will present final reports during the meeting.

All scientific sessions and the poster exhibition will take place at Ultuna Campus, Swedish University of Agricultural Sciences, 5 km south of Uppsala centre.

Sightseeing in Uppsala -Cathedral, Garden of Anatomical Theatre, Old Uppsala. Visit to Stockholm, the Venice of the North -Old Town, Stockholm Castle and the Vasa museum, with the only intact 17 th Century ship in the world -or shopping.

Welcome reception, BBQ and conference dinner.

Pre-conference tour to western Sweden: Farm land rich in biodiversity and beautiful scenery, castles and cultural sites, SLU -Skara campus, research farms, private farms with beef, dairy, sheep and horse breeding, agricultural industries. Mid-conference tours around Uppsala: University farm, private dairy and beef farms, equestrian centre, field research, biodiversity research on seminatural pastures. Post-conference tour to northern Sweden, Land of the Midnight Sun: Lapland -reindeer and culture, SLU -Umeå campus, forage research, forage-based milk and meat production. Hotels are in Uppsala city but some are close to the Campus. Bus transfer will be available between city hotels and the conference venue.

The fee 4 000 SEK (approx €400) includes scientific programme, proceedings, lunches and coffee, welcome reception, BBQ evening and Mid-conference tour

European Grassland Federation

 Uppsala, Sweden 9-12 June 2008

Sweden is a small nation in a big country -fewer than nine million inhabitants in an area larger than California and nearly as large as France or Spain.

Forages, which cover one third of the arable land in Sweden, are important for maintaining a biodiverse landscape and as for cattle, sheep and horses. The long, moderately hot days summer result in forage with a high nutritional value for livestock. Sweden has large areas (approx 500,000 ha) of seminatural grasslands that are among its most species-rich habitats, harbour many rare species and have significant historical and cultural values.

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Sweden's oldest botanical garden, the Garden of Linnaeus, is situated in Uppsala. Carl Linnaeus' professorial residence is situated within the garden, while just outside the city is his summer residence, Linnaeus' Hammarby.

Uppsala boasts the largest cathedral in Scandinavia, one of Sweden's most famous locations of prehistoric artefacts (Old Uppsala), the unique anatomical theatre built in the 1600s by Olof Rudbeck the Elder, the great university library (Carolina Rediviva) with the Silver Bible, Uppsala Castle dating back from the mid-1500s, and many more marvellous sites and attractions.

Uppsala is located only 30 minutes from Stockholm-Arlanda international airport and 40 minutes from Stockholm, the Swedish capital, which makes it an attractive venue for meetings.


domain: math info

text:
Antoine Perasso

Béatrice Laroche

Suzanne Touzeau

Identiability analysis of an epidemiological PDE model

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

I. INTRODUCTION

Epidemiological models are useful tools to describe the spread of a disease in a population, to predict its evolution and control its outbreak. They usually derive from the classical SIR model, a compartmental model in which the population is structured in susceptible, infected and recovered individuals.

The model we investigate in this paper is a SIR-like model, a simplified version of a model developed to study the spread of scrapie in a sheep flock [START_REF] Stringer | A mathematical model of the dynamics of scrapie in a sheep flock[END_REF]. It is characterised by a long and variable incubation period, during which individuals are infectious but cannot be detected. At the end of this period, detectable clinical signs appear. Then, either infected individuals recover and become immune or they die from the disease. Vertical (in utero) transmission is neglected. The population is assumed to be a well-mixed population confined on a limited territory, so the space dimension can be omitted. It is however structured in age (a ∈ [0, A]) and infection load (θ ∈ [0, 1]). Newly infected individuals are distributed along θ according to a probability density function Θ (support [0, 1]). The infection load θ then grows exponentially with time during the incubation period, which ends when θ reaches 1. An alternative option would have been to structure the infected population according to an age of infection instead, leading to a model similar to [START_REF] Arino | A model with 'growth retardation' for the kinetic heterogeneity of tumour cell populations[END_REF]. Whatever the modelling, it yields a distributed delay structure. At the end of the incubation period, a fraction α ∈]0, 1[ of infected individuals die. The other individuals recover and become immune. The resulting susceptible (S), infected (I) and recovered (R) population densities evolve with time (t ∈ [0, +∞[) according to the following nonlinear integropartial differential dynamical system of transport reaction Antoine Perasso is with UMR5251 Institut Mathématiques de Bordeaux; Université Bordeaux 2, CNRS; F-33076 Bordeaux, France antoine.perasso@u-bordeaux2.fr

∂ ∂t + ∂ ∂a + cθ ∂ ∂θ I(t, a, θ) = -(µ + c) I(t, a, θ) + Θ(θ)β S(t, a) I(t), (2) ∂ ∂t + ∂ ∂a R(t, a) = -µR(t, a) + (1 -α) c I(t, a, 1), (1)
where

I(t) = A 0 1 0 I(t,
S(t, 0) = B(t), I(t, 0, θ) = I(t, a, 0) = 0, R(t, 0) = 0 (
m(t, a) = µ N (t, a), (7)
the case incidence outflow

i(t, a) = αc I(t, a, 1), (8)
the recovered inflow

r(t, a) = (1 -α) c I(t, a, 1). ( 9
)
Function B is known. The uniqueness of mortality rate µ is a direct consequence of (6) and (7) and can be estimated [START_REF] Laroche | Parameter identification for a PDE model representing scrapie transmission in a sheep flock[END_REF]. Similarly, disease-induced mortality proportion α can be deduced from (8) and (9 Unlike the other parameters, epidemiological parameters c, β and function Θ need to be identified from output observations. An important issue is therefore to check whether these epidemiological parameters are identifiable, i.e. whether they can be uniquely determined from the input, initial conditions and observed outputs. It is an inverse problem that consists in establishing that the map from parameters to outputs is into, the input and initial conditions being known. This property is a prerequisite to the model identification, in which parameters are estimated from observed data.

The paper is organised as follows: identifiability results are stated in Section II; Section III establishes an input-output (IO) relation for the model; the proofs, based on algebrodifferential elimination are given in Section IV. Finally, results are illustrated by simulations in Section V.

II. IDENTIFIABILITY RESULTS

The parameters of interest are gathered into a vector p = (c, β, Θ) T belonging to P = (R + * ) 2 × A 0 , where A 0 is the set of real-analytic functions on ]0, 1[, continuous on [0, 1], with zero values at 0 and 1.

Let us denote

H + 1 = L 2 ([0, A], R + ), H + 2 = L 2 ([0, A] × [0, 1], R + ) and let C p (J 1 , J 2 ) be the set of piecewise contin- uous functions from J 1 to J 2 . It has been shown in [3] that for T > 0, (S 0 , I 0 ) ∈ H + 1 × H + 2 , B ∈ C p ([0, T ], R + ), and p ∈ P system (1-5) has a unique mild solution (S, R, I) in C([0, T ], (H + 1 ) 2 × H + 2 ), with outputs (N, j) in C([0, T ], (H + 1 )
2 ). Moreover, with stronger regularity assumptions on the initial conditions, namely

(S 0 , I 0 ) ∈ C p ([0, A], R + ) × C p ([0, A] × [0, 1], R + ), the solutions are such that (S(t), I(t)) ∈ C p ([0, A], R + ) × C p ([0, A] × [0, 1], R + ).
Consequently, the outputs N (t, •) and j(t, •) are both in

C p ([0, A], R + ).
We assume in the sequel that all these assumptions are verified. Hence the parameter to output map O is defined from P to the set

O ={(N, j) ∈ C([0, T ], (H + 1 ) 2 ) / ∀ t ∈ [0, T ], (N (t), j(t)) ∈ C p ([0, A], R + ) 2 }. A subset Q of P is said to be identifiable if the restriction O| Q is into.
We are now in a position to state our first identifiability result.

To this end, we define the following notations

• for B ∈ C p ([0, T ], R +
), B and B, are defined as

B = {t ∈ [0, T ], B(t) = 0}, B = inf B, (11)
• for Θ ∈ A 0 and c ∈ R + * , Ψ(c, Θ) ∈ A 0 is defined as ∀θ ∈ [0, 1], Ψ(c, Θ)(θ) = cθ c Θ(θ c ) (12)
and F(c, Θ) is defined as

∀θ ∈ [0, 1], F(c, Θ)(θ) = θ c 0 Θ(ξ)dξ. ( 13
)
We assume that the initial conditions (S 0 , I 0 ) are fixed, but they are not known. Then we have Theorem 1:

Let G ⊂ A 0 be such that for all (Θ, Θ) ∈ G 2 , ∀(c, c) ∈ (R + * ) 2 , ∀(α, ᾱ) ∈ (R + * ) 2 , (Ψ(c, Θ) = Ψ(c, Θ)) ⇒ (c = c, Θ = Θ) (14)
and

Ψ(c, Θ) α - Ψ(c, Θ) ᾱ = F(c, Θ) -F(c, Θ) ⇓ (15) (α = ᾱ, c = c and Θ = Θ). Then Q ⋆ G = (R + * ) 2 × G is identifiable. Theorem 1 ensures
that, given a suitable parametric family for the first infection load distribution, Q ⋆ G is identifiable under the realistic hypothesis that the birth function is piecewise continuous, and the initial conditions are piecewise continuous, fixed and unknown.This theorem has a very strong practical interest, because when dealing with parameter identification on experimental data, Θ is indeed restricted to a parametric family of p.d.f., such as for instance the two-parameter family of Beta p.d.f. with support in [0, 1]. For this family, it is easily checked that conditions ( 14) and (15) hold.

Note that in Theorem 1, the initial conditions are assumed to be fixed but unknown. Assuming now that they are not fixed, they have to be included in the unknown parameter vector. Hence the "extended parameter" to output map is now defined on

P E = P × C p ([0, A], R + ) × C p ([0, A] × [0, 1], R + ).
Theorem 2: Let G ⊂ A 0 be as in Theorem 1, and assume that B = 0. Then for all p = (c, β, Θ, S 0 , I 0 ) T ∈ P E , p = (c, β, Θ, S0 , Ī0 ) T ∈ P E such that I(0) = Ī(0),

O(p) = O(p) ⇒ (c = c, β = β, Θ = Θ).

III. INPUT-OUTPUT RELATIONSHIPS

A standard strategy to investigate identifiability problems is to seek differential IO relationships of the model. To this end, we use an alternative expression of the incidence (10). It can be deduced from the mild solution of (1-5) given in [START_REF] Perasso | Well-posedness of an epidemiological problem described by an evolution PDE[END_REF] by

S(t, a) = S 0 (a -t)e -(µt+β t 0 I(s) ds) for a t, B(t -a)e -(µa+β t t-a I(s) ds) for a t, (16)
I(t, a, θ) = (17)         
S 0 (a -t)e -µt t 0 e c(s-t) Θ θe c(s-t) βI(s)e -β s 0 I(u)du ds +I 0 (a -t, θe -ct )e -(µ+c)t for a t, B(t-a)e -µa t t-a e c(s-t) Θ θe c(s-t) βI(s)e -β s t-a I(u)du ds for a t.

Let us define the non-negative real-analytic function on R + * , continuous on R + X(τ ) = Ψ(c, Θ)(e -τ ).

(

) 18
Note that X is the p.d.f. corresponding to the incubation period (τ = -1 c ln θ). Then, for (t, a) ∈ [0, T ] × [0, A] and t a, one has j(t, a) =S 0 (a -t)e -µt t 0 X(t -s)βI(s)e -β s 0 I(u)du ds

+ cI 0 (a -t, e -ct )e -(µ+c)t , (19) and
In the sequel we shall also denote

D B = {(t, a) ∈ D, t -a ∈ B}, D = ∂ a + ∂ t .
Therefore, y is known on D B since y(t, a) = j(t,a)

B(t-a)e -µa on D B . Moreover, the following key result holds.

Proposition 1: On D, y and Dy are C 1 , ∂ a y is differentiable and

D∂ a y(X(a) -y) = ∂ a y(X ′ (a) -Dy). (22)
On D B , Eq. ( 22) defines an IO relation for the system. Proof 1: Consider ỹ defined on D by ỹ(t, a) = c t t-a e 2c(s-t) Θ ′ (e c(s-t) ) β I(s) e -β s t-a I(u)du ds.

From Eq. (17) the function t → I(t) is differentiable on [0, T ] and has a piecewise continuous derivative. Consequently, t → e -β t 0 I(u)du ∈ C 1 ([0, T ]) and y(t, a) has partial derivatives in a and t on D, expressed as

∂ a y = X(a)βI(t -a) -βI(t -a) t t-a X(t -s)βI(s)e -β s t-a I(u)du ds = X(a)βI(t -a) -βI(t -a)y(t, a) = βI(t -a) (X(a) -y) , (23)
and

∂ t y = -X(a)βI(t-a)-c t t-
D∂ a y = β I(t -a) (X ′ (a) -Dy). (25)
Eq. ( 22) is obtained by combination on D of Eq. ( 23) and (25).

IV. PROOF OF THEOREMS 1 AND 2

Let (S 0 , I 0 ) and B be given and consider (p, p)

∈ P 2 such that O(p) = O(p). ( 26
)
In the sequel, the population densities, the p.d.f. of first infection load and incubation period, the output vector associated to p shall be denoted as S, Ī, Θ, X, j and N ; more generally, all the quantities wearing a bar will be related to p. The same quantities without bar will be related to p. Note that (26) implies ȳ = y on D B .

As mentioned in the introduction, we start with an algebrodifferential elimination step where ȳ = y is combined with Eq. ( 22) in order to obtain some relationships between p and p.

We obtained the following fundamental result.

Proposition 2: If (26) holds, then either X = X, or ∃ (α, ᾱ) ∈ (R + * ) 2 / α = ᾱ and 1 α X′ - 1 ᾱ X ′ = X -X.
In this last case, t → βI(t) and t → β Ī(t) are non zero constant functions on B, whose values are α and ᾱ respectively. Let us define M y (t, a) = (Dy, y)

T , and also M ∂ay , Y (a) = (X ′ (a), X(a))

T and Ȳ (a) = X′ (a), X(a) T and finally

for x > 0, R(x) = X ′ (x) X′ (x) ∆(x) X (2) (x) X(2) (x) ∆ ′ (x) X (3) (x) X(3) (x) ∆ (2) (x) , ( 27
)
where we set ∆ = X -X on R + . Note that from (26), M y (t, a) = M ȳ (t, a) and M ∂ay = M ∂a ȳ on D B . We sketch the proof of Proposition 2, the detailed proofs can be founded in [START_REF] Perasso | Identifiability analysis of an epidemiological model in a structured population[END_REF]. Proposition 2 follows from three technical lemmas that make an extensive use of the following remark.

Remark 1: Since Θ and Θ are analytic on ]0, 1[, X, X, ∆ and all their derivatives are real-analytic functions on R + * . Consequently, either they have isolated zeros in R + * or they are identically equal to zero. The first lemma is Lemma 1: If (26) holds one gets for all (t, a)

∈ D B D∂ a y(X(a) -X(a)) -∂ a y(X ′ (a) -X′ (a)) = 0 (28) [X ′ X -X X′ ] -y [X ′ -X′ ] + Dy [X -X] = 0. ( 29
)
Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems -MTNS 2010 • 5-9 July, 2010 • Budapest, Hungary Substituting X = X in Eq. ( 23), one has for all (ξ, a) ∈ B × [0, A] ∂ a y(ξ + a, a) = βI(ξ) X(a) -y(ξ + a, a) , ∂ a y(ξ + a, a) = βĪ (ξ) X(a) -y(ξ + a, a) .

Term to term subtraction yields

βI(ξ) -βĪ (ξ) X(a) -y(ξ + a, a) = 0. (41)
By contradiction, assume that there exists ξ 0 ∈ B such that βI(ξ 0 ) = βĪ (ξ 0 ). Since B is piecewise continuous and ξ → (βI -βĪ )(ξ) is continuous, there exists an interval V(ξ 0 ) included in B, containing ξ 0 , not reduced to a singleton set, such that (βI -βĪ )(ξ) = 0 for all ξ ∈ V(ξ 0 ). Therefore, (41) reduces to

X(a) = y(ξ + a, a), ∀(ξ, a) ∈ V(ξ 0 ) × [0, A]. (42)
This implies that

∂ t y(ξ+a, a) = 0 for (ξ, a) ∈ V(ξ 0 )×[0, A].
Consequently, Eq.( 23) becomes ∂ a y(ξ + a, a) = 0 on V(ξ 0 ) and differentiating (42) w.r.t a yields

X ′ (a) = ∂ t y(ξ + a, a) + ∂ a y(ξ + a, a) = 0, for all a ∈ [0, A]. It follows that X ≡ 0 on [0, A].
Then Remark 1 implies that X is null on R + , which contradicts its definition as a p.d.f., and consequently yields

β I(t) = β Ī(t), ∀t ∈ B. (43)
If B = 0, (43) immediately yields β = β and Theorem 1 is proved. Otherwise if B > 0, we deduce from (26) and (6) that on [0, B]

(I -Ī)(t) = A 0 S(t, a)da - A 0 S(t, a)da, ∀t ∈ [0, T ]. (44)
Therefore, since for a ∈ [0, t], B(t -a) = 0, multiplying Eq. ( 44) by β and using Eq. ( 16), one gets x-y

β(I -Ī)(t) = βe -µt A-min(t,A) 0 S 0 (a)da × e -β t 0 Ī(ξ)dξ -e -β t 0 I(ξ)dξ . (45)
if x = y, e -x if x = y. (46)
Eq. ( 45) can be rewritten as

β I -Ī (t) = g ′ (t) g(t) t 0 βĪ -βI (ξ)dξ. ( 47
)
By contradiction, let us assume that β > β. Then we have

β I -Ī (t) (βI -βĪ )(t),
and, consequently to (47), we get

- g ′ (t) g(t) t 0 βI -βĪ (ξ)dξ (βI -βĪ )(t), (48)
which implies that t → g(t)

t 0 βI -βĪ (ξ)dξ is increasing on [0, B]. At t = 0, one has (βI -βĪ )(0) = (β -β)I(0) > 0 and, by a continuity argument, there exists 0 < ε 0 < B such that βI -βĪ is positive on [0,

ε 0 ]. Since 0 < g < 1, for all t ∈ [ε 0 , B] t 0 βI -βĪ (ξ)dξ g(t) t 0 βI -βĪ (ξ)dξ Λ 0 ,
where Λ 0 = g(ε 0 ) ε0 0 βI(ξ) -βĪ (ξ) dξ > 0. Using this inequality and the expression of -g ′ (t) g(t) in (48), we deduce that for all t ∈ [ε 0 , B] βe -µt

A-min(t,A) 0 S 0 (a)da × f β t 0 Ī(ξ)dξ, β t 0 I(ξ)dξ Λ 0 (βI -βĪ )(t).
Evaluating the above expression at t = B yields a contradiction with Eq. ( 43), and then β = β, which ends proof of Theorem 1.

When the initial conditions are not fixed, using (43) and B = 0, we get βI(0) = βĪ (0). If I(0) = Ī(0), it follows that β = β, which proves Theorem 2.

V. NUMERICAL SIMULATIONS

In this section, we illustrate our identifiability results through a simulation scenario that represents Theorem 1 for the Beta distribution family.

For this scenario, system (1, 2, 3, 4, 5) is integrated with parameter values given in Table I. The birth function B is constant. The initial susceptible population density follows an exponential distribution S 0 (a) ∝ e -µa . The initial infected population density I 0 (a, θ) is uniformly distributed over [a min , a max ] × [θ min , θ max ]. The initial recovered population density is 0. Scaling coefficients are adjusted to obtain the initial population sizes given in Table I. Parameter values are chosen to mimic realistic epidemiological situations.

The differences between the parameter vectors p and p are the infection load growth rates c and c, and the first infection load distributions Θ and Θ. They are both Beta distributions with the same standard deviations σ Θ = σ Θ, but different means m Θ = m Θ. Parameters c and c are adjusted to obtain the same mean incubation period of 3 years for the distribution given in (18). First infection load and incubation period distributions are represented in Fig. 1.

With such similar incubation period distributions, one could fear the model not to be identifiable. However, Theorem 1 guarantees that the model is identifiable. This is illustrated in Fig. 2 that for both parameter sets represents output j, given by (10), integrated over age. These outputs

1 0I

 1 [START_REF] Perasso | Identifiability analysis of an epidemiological model in a structured population[END_REF] where B is the birth function, and initial conditions by S(0, a) = S 0 (a), I(0, a, θ) = I 0 (a, θ) R(0, a) = 0. (5)The system input is the birth function B. Infected individuals cannot be distinguished from susceptible individuals during their infectious incubation period. The system outputs are observed on a given finite time horizon T > 0 and consist of the age density of the total population N (t, a) = S(t, a) + R(t, a) + (t, a, θ) dθ, (6) the total basic mortality outflow

  , for (t, a) ∈ [0, T ] × [0, A] and t a, j(t, a) = B(t -a)e -µa t t-a X(t -s)βI(s)e -β s t-a I(u)du ds. (20) We now define D = {(t, a) ∈ [0, T ] × [0, A], a t} and introduce the function y defined on D by y(t, a) = t t-a X(t -s)βI(s)e -β s t-a I(u)du ds.

  Consider the continuous functions g : [0, T ] →]0, 1] defined byg(t) = expdξ ds ,where the continuous function f : R 2 →]0, 1] is defined by f : (x, y) → -e -x -e -y

Fig. 1 .

 1 Fig. 1. Distributions represented for the two parameter sets given in Table I: (c, Θ) plain line & (c, Θ) dashed line.

  ) Yearly incidence difference (indiv.) (b) Difference between the yearly cumulated outputs j.

Fig. 2 .

 2 Fig. 2. Outputs j corresponding to the two parameter sets given in Table I: (c, Θ) plain line & (c, Θ) dashed line. The model is identifiable.

  a, θ) dθ da denotes the force of infection defined as the total number of infected individuals. All parameters are positive: basic mortality rate µ, unitary horizontal transmission rate β, infection load growth rate c ( dθ

dt = cθ), and disease-induced mortality proportion α ∈ [0, 1]. Boundary conditions are given by

TABLE I PARAMETER

 I VALUES USED FOR THE SIMULATIONS. It is even more obvious on the yearly cumulated outputs in Fig.2.

	Parameter definition	symbol	value
	initial population size	-	600 indiv.
	initial infected population size	-	30 indiv.
	-age range	[a min , a max ] [0.625, 1, 04] years
	basic mortality rate	µ	0.15 year -1
	horizontal transmission rate	β	3 10 -3 (indiv. year) -1
	disease-induced mortality proportion	α	0.5
	birth rate	B	70 indiv./year
	maximum lifespan	A	13 years
	observation period	T	4 years
	initial infection load range	[θ min , θ max ]	[0.68, 0.73]
	infection load growth rates	(c, c)	(0.35, 0.12) year -1
	first infection load distribution Θ: mean	m Θ	0.35
	-: standard deviation first infection load distribution Θ: mean	σ Θ m Θ	0.05 0.7
	-: standard deviation	σ Θ	0.05
	exhibit notable differences.

Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems -MTNS 2010 • 5-9 July, 2010 • Budapest, Hungary

Then the second lemma is Lemma 2: If (26) holds one gets for all (t, a)

-y [X ′ -X′ ] 2 -[X (2) -X( 2) ] [X -X] = 0.

(30) And finally, Lemma 3: If (26) holds then R(x) = 0 for all x ∈ R + * . We now proceed with the proof of Proposition 2. Lemma 3 and (26) imply that, for all x > 0, there exists λ(x), µ(x), ν(x) ∈ R such that

where λ, µ, ν are minors of determinant (27). We can choose ν associated to ∆ (2) , given by ν = X ′ X(2) -X′ X (2) . Then two cases may arise.

Case 1. Assume that ν(x) = 0 for all x > 0. The function X′ is a non zero function on R + * , otherwise, by continuity, X would be constant and equal to zero on R + . Therefore, we can find x 1 > 0 such that X′ (x 1 ) = 0. By continuity, this is still true in a neighbourhood V(x 1 ) of x 1 . Then, for all x ∈ V(x 1 ),

which implies that there exists a constant c 0 such that X ′ = c 0 X′ on V(x 1 ). From Remark 1, we get

Case 2. Assume that there exists x 2 > 0 and a neighbourhood V(x 2 ) ⊂ R + * such that ν(x) = 0 for all x ∈ V(x 2 ). Then, from system (31), we deduce that the following equations are satisfied on V(x 2 ),

where λ = -λ ν , μ = -µ ν . Differentiating (32) and subtracting (33) yields, for x ∈ V(x 2 ), λ′ X ′ + μ′ X′ = 0.

(35)

In the same way, differentiating (32) twice and subtracting (34) yields

Finally, differentiating (35) and combining it (36), we get

From ( 35) and (37), we have W = 0 on V(x 2 ) where

Otherwise, there would exist an open subset V ⊂ V(x 2 ) such that W (x) = 0 for x ∈ V. The unique solution of system (35,37) would be X ′ , X′ = (0, 0) on V. This would imply ν(x) = 0 on V, which is impossible. We now distinguish the two following subcases.

Case 2.1. If there exists an open subset V ⊂ V(x 2 ) on which λ′ (x) = 0, then W = 0 on V(x 2 ) implies that d dx (μ ′ / λ′ ) = 0 in V. Consequently, there exists a constant c 0 such that X ′ = c 0 X′ on V and we can conclude as in Case 1 that X = X on R + . Case 2.2. If λ′ = 0 on V(x 2 ), then λ is a constant function on V(x 2 ) whose value is denoted λ0 . Since X′ has isolated zeros, Remark 1 and (35) imply that μ is also a constant function on V(x 2 ) whose value is denoted μ0 . Consequently, on V(x 2 ), equalities (32) and (33) become respectively

By Remark 1, these equalities can be extended to R + * and can be used to simplify (30). On D B one therefore has

and

By Remark 1, since ν = 0, we conclude that

Then, either λ0 + μ0 = 0, and integrating (38) yields ∆ = X -X = 0. Or λ0 + μ0 = 0 and consequently for all


Cesaer Marie-Luce Ghib
email: marie-luce.ghib@enesad.inra.fr

Keywords: life annuity program, land policy, retirement, farm succession, Romania

This paper is based on preliminary research in the context of a Ph.D. prepared at the CESAER, in Dijon. The Ph.D. is

The so called "transition" period in Romania has not yet ended, almost 20 years after the revolution, particularly in the agricultural sector. A major retrocession of land property was implemented after the revolution and is still visible in terms of plot size division. The retrocession process has been blamed for causing a delay in the land market phenomenon. The law which established the right to sell land dates only from 1999. Today, the land is split into a multitude of small parcels and a large number of Romanians still work in agriculture: 36% of the active population as opposed to an average of 15% in the other new European Union member states. This patchwork of small farms is perceived as a factor slowing down improvement in Romanian agriculture and preventing the country from fully benefiting from its widely recognized agro-climatic potential [START_REF] Cotea | Sa ridicam agricultura la potentialul ei natural[END_REF]. The optimal size of agricultural holdings is a source of debate, notably in terms of the possibility of return to scale in agriculture [START_REF] Boussard | Economie de l'agriculture[END_REF]. In addition, this retrocession participates in the economic absorption of the social consequences of the post-communist transition [START_REF] Pouliquen | L'agriculture néo-paysanne roumaine : le tampon social contre la relance globale[END_REF]. At the same time, what Alain Pouliquen qualifies as "neo-peasant microfarms" are part of the Obstacles to a global economic revival [START_REF] Alexandri | Study on possible measures to enhance consolidation of farms in the context of accession to the European Union : the Romanian case[END_REF]. He linked during this period, over-employment in agriculture and hidden unemployment [START_REF] Pouliquen | L'agriculture néo-paysanne roumaine : le tampon social contre la relance globale[END_REF]; we will focus here on the relationship between over-employment and retirement in the agricultural sector. In the eyes of many observers, peasant agriculture is a primitive production system; for others itis a modern tool with agro-environmental and socio-economic characteristics which enable it to respond to the social and environmental challenges posed by the new EU [START_REF] Darrot | La paysannerie polonaise peut-elle être durable et moderne ?[END_REF][START_REF] Solliec | 40 ans de politiques agricoles : bilan et enjeux[END_REF]. In this paper, we will evaluate farm structure using the new data from the 2002 census (INS, 2003) and the 2005 Farm Structure Survey (INS, 2006(a)). We will particularly look at holding size in terms of agricultural land. We will also examine production destination and farm manager age. We will then compare the expected results of the life annuity program and the first administrative data concerning the program. The apparent failures point to certain difficulties in the implementation of the program. After a short field survey, we will discuss in some detail one hypothesis for the program's relevancy in light of "delayed entries" in agricultural activity. By means of national data comparisons on farm managers and urban-rural migration, we will demonstrate that Romania exhibits a specific transmission modality.

Farm structure in terms of plot size and farm manager composition

Thanks to the 2002 General Agricultural Census and the 2005 Farm Structure Survey, we can use recent data to learn more about the structure of farms in Romania. According to the Farm Structure Survey of 2005, Romanian farm structure appears to be dual (Table 1) with a large number of farms on very small plots (an average of 2.15 ha) and a few farms ranging widely in terms of land area (an average of 263 ha). More than 4 million individual holders currently cultivate 65.5% of the total agricultural surface and only 18,000 of legal status occupy the other 34.5%. The land retrocession process is primarily responsible for this structure. But the farm structure was maintained in response to the significant recession in the industrial sector after the revolution and maintained after the economic crisis in 1997. People lost their jobs and found it difficult to obtain new employment. Many of these people were oriented to a pre-retirement program and went back to the rural areas in order to cultivate plots for subsistence purposes. The duality of the Romanian agricultural system is clearly visible in the destination of the production. For more than 80% of individually held farms, over 50% of the production is destined for self-consumption, compared to 21% of the production on farms with a legal status. And inversely, only 16% of individual farms sell more than 50% of their production, compared to 52.1% on farms with a legal status. The proportion of subsistence farming is preponderant and linked to the on-going difficulties in the economic context. The life annuity program and Romanian choices The life annuity program was created in this context. The first objective of the government was to decrease the active population in agriculture to the level of 15% of the total population as in other European Union new member countries. This meant a reduction of 2 million people in agriculture, and a wide reorganization of rural communities as well, as job opportunities were mainly concentrated in the urban areas. To reach this objective, the government, pushed by the Commission and the World Bank, implemented the first policies for land reform and the acceleration of farm transmission. The life annuity program was one of the most important measures taken. The conditions of eligibility for the indemnity were defined thus: being over 62 years old, owning land surface totaling not more than 10 ha, and reducing the farming activity to 0.5 ha for self-subsistence purposes by renting or selling land. The amount of the indemnity1 was fixed at 100 euros per year in the case of a sale and 50 euros per year in the case of leasing until the death of the landowner. The life annuity program is a structural policy tool according to definition formulated by Allaire and Daucé (1995): i.e. it acts on the dynamics of the structure? and results from the fact of obstacles to land mobility and to the professional mobility of farmers. A structural policy aims to promote new models, perceived as more profitable ones, for farming companies. Policies based on income compensation for farmers in financial difficulty? are social policies generally designed to encourage farmers to stop agricultural activity. Tools similar to the life annuity program have been implemented in other EU countries. In Romania, implementation took place in a context of specific conditions, objectives and processes which are not necessarily comparable to those in other EU member states.

Established in 2005along with another program of the ministry of agriculture "Fermierul", the life annuity program aimed to stimulate the land market and to facilitate the reorganization of the very compartmentalized land by releasing elderly owners' lands [START_REF] Dumitru | Dezvoltare rurala si reforma agriculturii Romanesti[END_REF].

In view of these objectives, the conditions stipulated the age of the holder (minimum 62 years old), the maximum size of the owned land before the request (maximum 10 ha), the date or means of acquisition of the land (law 18/1991, 1/2000 or previous), the amount of land retained after the request (maximum 0.5 ha for self-subsistence purposes only).

The ministry wanted to encourage new farming models and tried to stimulate the land market [START_REF] Aliantei | Programul Aliantei PNL-PD pentru Dezvoltare Rurala, Agricultura, Silvcultura si Piscicultura, MARD[END_REF]. With this measure, the ministry expected to obtain several objectives:

increased production by the sale of arable lands abandoned by elderly urban landowners, -structural change encouraged by stimulation of the land market through the release of farm land belonging to elderly farmers demographic renewal, assuming that new landowners would be younger, whether from the same family or not. Transmission of the farm in this context is assumed to be? a transmission of land property, or transmission of land management by official renting. Young people are known to invest more in their professional activity than older people [START_REF] Butault | La disparition des exploitations s'accélère sans concentration excessive[END_REF]. This is why they were encouraged to become the official managers of their farms.

Expected efficiency of the measure:

At the beginning, the ministry wanted to specifically target the population of agricultural pensioners who were still landowners or/and workers. In this context, the goal was centered on the welfare of this category of the population, given the inadequacy of retirement pensions. The expected amount for the indemnity was also greater. It later appeared another categories of pensioners, who benefited from retrocession and who could no longer work on their land: those living in urban areas, those of advanced age, those with health problems... The consequences of the measure were neglect of the land and increase in wild land. The ministry choose to enlarge the target population in order to resolve the different issues and, at the same time, changed the nature of the objective from structural change/welfare to structural change/production.

Finally, the population targeted by the life annuity program is composed of landowners who are still working on their land: more than 1.5 million people, according to the General Agricultural Census as well as land-owners who no longer more work their land, and may be living in urban areas, possibly leasing their land. Consequently, only complex investigations of cadastral data would provide us with the exact number of targeted individuals for the second category of landowners. As precise monitorisation is not possible, the ministry decided to decrease the previous amount of the subsidy. We base our analysis on only those people working their land and we assume that in the next five years, 1.9 million people could apply for the program. Using the mean of 2 ha per holding, it seems that potentially 3.8 million ha could be released of the total 13 million ha of Romanian UAA. Potentially, one third of the UAA could thus begin a restructuring process.

In fact, the first results show a disappointing number of applications: 35,000 cumulated applications as of 3 rd July 2007. In 2005, there were a very few number of applications, due to the delayed implementation on the part of the administrative agencies. In 2006, 25,304 applications were registered among the various locations. The internal objective-line for 2007 is to reach 70,000 applications at the end of December.

Another important result of this first investigation is the large proportion of landowners who chose to lease their land: an average of 85% of the land is ceased under a renting contract, whereas only 15% of landowners decided that selling their land was the more interesting option. In trying to understand these results, we have pinpointed the following obstacles:

inadequate information: the measure was promoted by the media, but the agents responsible for its implementation did not have the possibility to organize the meetings needed to assure the success of the program.

property rights are still not clarified in several cases, and people cannot prove their ownership of the land transaction costs for the selling contract option have been identified as the main obstacle fot the developing of land market, combined with the low land prices they discourage potential buyers in the context of modest retirement pensions and the small average size of farms (2.15ha), the amount of the indemnity seems to be too low to be an incentive, self-consumption being a very important part of the income for rural population [START_REF] Duma | Roumanie : une agriculture de survie, après l'industrialisation forcée[END_REF] the last hypothesis is linked to transmission modalities: we wanted to understand what the rules for effective and official transmissions are. Many rural families are practice cohabitation of generations: elderly people live with one or more of their children and sometimes with their grandchildren. The cost of living independently is too high for young people [START_REF] Duma | Roumanie : une agriculture de survie, après l'industrialisation forcée[END_REF]. This cohabitation is the basis of a hidden pre-transmission of Romanians farms. The elderly are still the land-owner but their children are already working on the land. In this context, we assume that the decisions are not totally in the hands of young generation until the real transmission occurs. Yet we do not know when and how the real transmission occurs in the sense defined above.

In order to clarify these institutional rules, we carried out a field survey of 35 elderly landowners. We then verified our hypothesis by using national data.

Outcomes from the field survey:

The subjects were chosen according to their eligibility for the life annuity program [START_REF] Ghib | Restructuration foncière et sortie de l'agriculture en Roumanie:analyse de la mesure de rente viagère[END_REF]. We chose 50 people from the registry of agriculture at the local level. We finally met 35 people, as 5 people had died, 3 people refused to participate in the survey and others were absent. Our subjects were all over 62 years old and owned at least 0,5 ha of arable land.

None of them were engaged in the life annuity program although 2 heard about it, but were not very well informed of the modalities. Moreover, 17 people had partially anticipated the transmission of their land, in 11 cases by giving the management to a family member and in 6 cases, by an official renting act with an exterior party.

Figure 2: Family situation under farm management status

Without surprise, anticipated transmissions seem to depend on the age and gender of the land owner. Older people and women seem more likely to cede the management of their land, but such arrangements still remain informal.

Generally, the transmission is not planned to occur before the death of the owner. Only two people began the transmission process while still living, but this was under a care-contract and motivated by serious health issues.

In addition, the plans for transmission concerned the subjects' children. We met only two people who gave their land to their grand' children or planned to do so. Cohabitation is the rule for a large majority of our sample and only 4 people did not have their children in the nearby village or town.

Children are almost all involved in an activity other than agriculture and if they are only farmers, they often own their own tractor. To conclude, for a majority of our sample, agricultural activity is engaged in only for personal consumption.

Our sample is to small to lend itself to any statistically relevant analysis and our previous observations are valuable in terms of simple description. But we can try to elaborate some hypotheses to be tested: -people officially obtain the status of farm manager late in life transmission occurs with the parents death or as a result of serious health issues.

In the following section, we report further investigations based on national data: including the Agricultural General Census, and the Farm Structure Survey. We began with the 2002 farm manager population. We know the age distribution of this population in 2002. We projected this distribution in 2005, and corrected it by an estimation of people deceased during the three year lapse. (INS, 2006(d)). Finally, we compared this distribution to those establish in 2005 by the Farm Structure Survey. This comparison shows early exits of farm managers between the ages of 28 and 37, as net entries took place in general starting from the age of 58. The Romanian dynamic reveals a different phenomenon than the one expected: delayed entries. Agricultural activity did not attract young people, at least they were not immediately managers of the exploitation. In addition, data shows that new manager are generally over the age of 40.

Subsistence activity in agriculture and its link with retirement

This comparison was made using data from the farm structure survey concerning only 8% of farms. The results were later extrapolated. The goal of the Farm Structure Survey was to provide representative information on orientations in productions and on the economic dimension of farming. Farm manager age was not taken in account to build the survey. Consequently, these results can only be considered as indications of the current process requiring confirmation by further investigations. For this reasons, we studied analyses of internal migration between urban and rural areas 2 between 1996 et 2006.

2 For more about rural and urban area definiton in Romania see Emsellem, 2002 Chart 3 displays rural-urban, urban-rural migration ratios by age. The use of a ratio remove the number effect of migrants. Actually, we know that younger people are more likely to migrate than their elders. Thus, during these10 years, 77,000 people in the 20-39 age group moved per year, compared to 30,000 for the 40-59 group and 8,500 the over 60 age group. In addition, the closer the age group is to the value 1, the more equal the migrations between rural and urban areas are. The higher this ratio is, the stronger the group's preference to migrate towards an urban area. Inversely, when the ratio is close to 0, the majority of people involved migrate towards rural areas.

As a result, people between the ages of 20-39 migrate mainly towards urban areas. Older people migrate mainly towards rural areas. We can suppose a life cycle determinded by employment and residency. The development of cities and their expansion into rural areas may explain part of the migrations, with residential purpose. However, in the Romanian context a large number of rural inhabitants engage in agricultural activity, (85% of rural area inhabitants are involved in agriculture, at least as a second activity [START_REF] României | Ministerul Agriculturii, Padurilor si Dezvoltarii Rurale, Planul National Strategic pentru Dezvoltare Rurala 2007-2013[END_REF]). Correspondence between migrations and entries in agricultural activity, even of small plots, is strongly plausible. It concurs that entry into agriculture is linked to retirement or to the freeing up of the family house or land after the death of parents or when a parent faces serious health problems.

Conclusion

As we have seen, we need to distinguish the different modalities of transmission. Informal transmission does not allow young people to invest in the farm as they are not the owners of the land and cannot make major decisions on their own. Although anticipated transmissions appear to be frequent, they generally concern people over 40 years old, as young people seem unlikely to attain and retain the status of farm manager. The dynamics we have outlined seem to be a reproduction of farm structure by a reproduction of living conditions (inadequate retirement pensions) and production systems. We can suppose that these practices participate in the general structural immobility, which hampers modernization of the agricultural sector, notably because older people are marked by a lower propensity to invest.

  In 2002 and 2005, elderly farm owners were identified as the largest category of subsistence farmers. According to Eurostat 2005, no less than 45% of Romanian farmers are over 65 years old.

Figure

  Figure 1: Farm Managers by age in 2002

  In order to verify these empiric observations, we constructed a comparison by age for farm managers between 2002 and 2005. Data are from the 2002 Agricultural General Census and the 2005 Farm Structure Survey. The result is the map of entries into and exits from agricultural activity by age.

Figure 3 :

 3 Figure 3: Differences in distribution of farm manager age ASA 2005 and RGA projectedcorrected

Figure 4 :

 4 Figure 4: rural-urban/ urban-rural migration ratios by age

Table 1 : Farms structure in terms of UAA class

 1

		Number of				UAA
		holdings	0-5 ha	5-10 ha		10-50 ha	50-100 ha	> 100 ha
	Individual	4,103 ,404 99.6 % 3,730,501 90.9 % 286,987 7.0 % 79,782 1.9 % 3,919 0.1 % 2,215 0,1 %
	holdings*
	Farms with	17,843 0.4 %	5,317 29.8 % 2,588	14.5	2,242 12.6	1,020 5.7 % 6,676 37,4 %
	legal status*				%	%
	total*	4,

121, 247 100 % 3,735, 818 90.6 % 289,575 7.0 % 82,024 2.0 % 4,939 0.1 % 8,891 0.2 % total UAA 13,906, 701 100 % 5,102,111 36.7 % 1,926,391 13.9 % 1,319, 957 9.5 %336, 183 2.4 % 5,222,058 37.6 %

	* farms using agricultural area
	UAA: Utilised Agricultural Area
	Source: ASA 2005 (INS, 2006(a))

Table 2 : Description of Romanian farm structure in terms of status and destination of production Number of farms Average area used Agricultural area used Selfconsumption > 50% of the total production Direct sales > 50% of the total production Individual farms

 2

		4,23,889 99.6% 2.15 ha	9,102,018 65,5	3,444,757	81.3% 693,917	16.4%
					%
	Farms with a	18,263	0.4 % 263.08 ha 4,804,683 34,5	3,833	21.0% 9,525	52.1%
	legal status				%
	total	4,256,152	3.27 ha	13,906,701 3,448,590	81.0% 703,442	16.5%
	Sources: ASA 2005 (INS, 2006 (a), (b))

For further discussion concerning the amount of the life annuity see Alexandri,