Elise De

La Rochebrochard

François Thépot
email: francois.thepot@sante.gouv.fr

La Rochebrochard Elise (de

Introduction

En reproduction naturelle et médicalement assistée, les effets délétères de l'âge maternel sont bien connus. À l'opposé, les effets de l'âge paternel ont été peu explorés. Cette étude a pour but de mesurer l'impact de l'âge de l'homme sur les résultats des différentes techniques de PMA à savoir FIV et ICSI.

Matériels et méthodes

Cette analyse porte sur les tentatives de FIV classiques et d'ICSI enregistrées dans FIVNAT sur la période 1995-1999. Près de 10% des tentatives ont été exclues de l'analyse car l'information sur l'année de naissance de l'homme était manquante. La distribution des âges maternel et paternel de ces tentatives est présentée sur la Figure 1. Pour analyser l'âge paternel, il faut prendre en compte l'âge maternel qui a un effet important et qui est fortement corrélé à l'âge paternel. Aussi dans ce travail, nous avons comparés les différentes classes d'âge paternel (<30 ans, 30-34 ans, 35-39 ans, 40-44 ans, >44 ans) parmi des hommes ayant tous une partenaire âgée de 30-34 ans (Tableau 1 & Tableau 2).

Résultats

FIGURE 1 .

 1 FIGURE 1. Distribution des âges dans FIVNAT 1995-1999 (n=131 557)

Taux de succès en fonction de l'âge paternel Age paternel Taux de fécondation Taux d'embryons transférés

  Parmi les couples dont la femme est âgée de 30-34 ans, les techniques de FIV varient avec l'âge paternel. La part des FIV classiques avec spermatozoïdes de conjoint diminue chez les hommes plus âgés tandis que la part des ICSI et des fécondations avec spermatozoïdes de donneurs croit de manière régulière.Source :FIVNAT 1995FIVNAT -1999, hommes dont la partenaire est âgéede 30-34 ans (n=49 661)

		TABLEAU 2. Taux de	Taux de	Taux « au moins 1
				grossesses /	fausse	bébé à la maison »
				transfert	couche
		FIV classiques avec spermatozoïdes de conjoint
	(n=28 013)	(n=23 449)	(n=23 420)	(n=2 539)
	< 30	52,46 %	61,85 %	28,45 %	15,31 %		19,01 %
	30-34	50,85 %	62,86 %	30,22 %	14,29 %		20,39 %
	35-39	49,99 %	64,05 %	28,32 %	15,50 %		18,47 %
	40-44	50,61 %	63,65 %	27,32 %	40-44 ans 18,13 %	> 44 ans 17,97 %
	> 44	48,44 %	65,48 %	27,88 %	(n=4 222) 21,25 %	(n=2 140) 15,44 %
	FIV classique	64,85 %	58,63 %	56,34 %	53,79 %	51,12 %
	p	0,0019	0,0040	0,0119	0,3490
	ICSI	33,33 %	37,91 %	39,12 %	41,00 %	45,28 %
	Sperme Donneur	1,81 % ICSI avec spermatozoïdes de donneur 3,46 % 4,55 %	5,21 %	3,60 %
	100 % (n=18 749)	100 % (n=17 614)	100 % (n=17 587)	100 % (n=2 084)	100 %
	Source : FIVNAT 1995-1999, hommes dont la partenaire est âgée de 30-34 ans (n=49 661) < 30 57,07 % 67,34 % 28,49 % 13,04 % 22.12 %
	30-34	57,32 %	67,36 %	29,44 %	14,92 %		22.62 %
	35-39	56,68 %	68,40 %	28,24 %	14,74 %		21.85 %
	40-44	57,32 %	69,02 %	27,98 %	13,33 %		21.66 %
	> 44	56,80 %	70,08 %	30,44 %	17,65 %		22.24 %
	p	0,6797	0,0185	0,3901	0,8318

En FIV classiques, nous observons une baisse significative du taux de fécondation. Le taux d'embryons transférés (qui est le nombre d'embryons transférés sur le nombre d'embryons obtenus lors de la fécondation) augmente significativement, indiquant que le " choix " d'embryons est moins grand chez les hommes âgés. Ce moindre choix est sans doute un élément important pour comprendre la baisse du taux de grossesses par transfert observée avec l'âge paternel. Le risque de fausse couche au premier trimestre ne varie pas de manière significative avec l'âge paternel, malgré une tendance à la hausse.Finalement, le taux de tentatives se soldant par au moins un enfant rentrant à la maison passe de 20,39% lorsque l'homme est âgé de 30-34 ans à 15,44% lorsque l'homme est >44ans. En ICSI, nous n'observons pas de variation significative des taux de succès avec l'âge paternel. Seul le taux d'embryons transférés varie avec l'âge paternel.

Discussion et conclusions

En FIV, l'augmentation de l'âge paternel se traduit par une augmentation de la part des ICSI et par une diminution des taux de succès en FIV classiques. Par contre, le taux de succès en ICSI semble peu sensible aux effets de l'âge paternel.

Pour conclure, l'effet de l'âge paternel apparaît modéré, en particulier en comparaison de l'effet de l'âge maternel. Cependant, il faut s'interroger sur son impact en terme de santé publique quand on considère qu'un homme sur quatre est 40 ans.


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Summary of the presentation


Stephen J Barnes

Marina A Yudovskaya

Giada Iacono-Marziano

Margaux Le Vaillant

Louise E Schoneveld

Alexander R Cruden

Role of volatiles in intrusion emplacement and sulfide deposition in the supergiant Norilsk-Talnakh Ni-Cu-PGE ore deposits

The Norilsk-Talnakh orebodies in Siberia are some of the largest examples on Earth of magmatic Ni-Cu-platinum group element (PGE) deposits, formed by segregation of immiscible sulfide melts from silicate magmas. They show distinctive features attributable to degassing of a magmatic vapor phase during ore formation, including: vesiculation of the host intrusions, widespread intrusion breccias, and extensive hydrofracturing, skarns, and metasomatic replacement in the country rocks. Much of the magmatic sulfide was generated by assimilation of anhydrite and carbonaceous material, leading to injection of a suspension of fine sulfide droplets attached to gas bubbles into propagating tube-like host sills ("chonoliths"). Catastrophic vapor phase exsolution associated with a drop in magma overpressure at the transition from vertical to horizontal magma flow enabled explosive propagation of chonoliths, rapid "harvesting" and gravity deposition of the characteristic coarse sulfide globules that form much of the ore, and extensive magmatic fluid interaction with country rocks.

INTRODUCTION

The Ni-Cu-platinum group element (PGE) deposits of the Norilsk-Talnakh camp in Arctic Siberia are among the most valuable economic metal accumulations of any kind on Earth [START_REF] Barnes | Introduction to a Special Issue on the Norilsk-Talnakh Ni-Cu-platinum group element deposits[END_REF]. They are part of the Siberian large igneous province, which was cataclysmically emplaced ca. 252 Ma, synchronous with the Permian-Triassic mass extinction [START_REF] Kamo | Rapid eruption of Siberian flood-volcanic rocks and evidence for coincidence with the Permian-Triassic boundary and mass extinction at 251 Ma[END_REF][START_REF] Burgess | High-precision geochronology confirms voluminous magmatism before, during, and after Earth's most severe extinction[END_REF]. The deposits have been extensively studied for more than a century, yet many aspects of their genesis remain poorly understood. The currently dominant paradigm for these and other magmatic sulfide deposits of this type is the "conduit model" [START_REF] Rad'ko | Model of dynamic differentiation of intrusive traps in the northwestern Siberian platform[END_REF][START_REF] Naldrett | Geology and geochemistry of intrusions and flood basalts of the Noril'sk region, USSR, with implications for the origin of the Ni-Cu ores[END_REF], whereby ore formation is inferred to take place in subvolcanic feeder conduits as a result of assimilation of crustal sulfur (S) by silicate magma, formation of entrained immiscible sulfide liquid, scavenging of Ni, Cu, and PGEs by that liquid, and final deposition in mechanical trap sites. Since the formulation of this model, numerous lines of evidence have emerged to challenge key aspects, particularly at Norilsk. Detailed local geologic data from Russian sources have become available (reviewed by [START_REF] Barnes | Introduction to a Special Issue on the Norilsk-Talnakh Ni-Cu-platinum group element deposits[END_REF] that are inconsistent with the interpretation of the Norilsk intrusions as feeder conduits to the overlying lavas. Important advances have been made in understanding the physics of sulfide liquid droplets [START_REF] Robertson | Dynamics of magmatic sulphide droplets during transport in silicate melts and implications for magmatic sulphide ore formation[END_REF][START_REF] Yao | A preliminary model for the migration of sulfide droplets in a magmatic conduit and the significance of volatiles[END_REF] and the role of magma degassing and vapor-related transport and deposition of sulfide liquids in ore formation [START_REF] Mungall | Transport of S, Cu and Au in magmas by flotation of sulphide melt on vapour bubbles[END_REF][START_REF] Iacono-Marziano | The critical role of magma degassing in sulphide melt mobility and metal enrichment[END_REF]. Analogue experiments have provided new insights into the mechanisms of dike and sill propagation [START_REF] Kavanagh | The mechanics of sill inception, propagation and growth: Experimental evidence for rapid reduction in magmatic overpressure[END_REF]. Here, we summarize these developments and synthesize them into a new model for the explosive emplacement of the host intrusions and sulfide ores, accounting for hitherto neglected magmatic-hydrothermal characteristics.

NORILSK-TALNAKH GEOLOGY

The Norilsk-Talnakh region (Fig. 1) contains a roughly 5-km-thick stack of tholeiitic basalts, forming part of the vast ca. 250 Ma Permian-Triassic Siberian large igneous province (SLIP). The ore deposits are found within a very specific intrusive component of the SLIP: a suite of shallow, strongly differentiated mafic-ultramafic intrusions that intrude the Carboniferous to Upper Permian platform sequence, which is more than 3 km thick, comprising clastic sediments, carbonates, evaporites (containing anhydrite and abundant bituminous material), and carbonaceous rocks (argillites and coal). The Talnakh and Kharaelakh intrusions that host the major deposits are emplaced at two distinct levels within the Devonian and Permian sediments, respectively (see the Supplemental Material1), <2 km below the Paleozoic land surface. These are unusually shallow depths for this class of ore deposit, compared with typical depth ranges of 3-25 km [START_REF] Naldrett | Magmatic Sulfide Deposits: Geology, Geochemistry and Exploration[END_REF]. The ore-bearing intrusions are roughly skishaped or wing-shaped elongate sills, representing a type of mafic-ultramafic intrusion called chonoliths (Fig. 1). They are dominantly gabbroic, with olivine-rich cumulates toward the base and highly contaminated inclusion-rich upper and lower margins. Mine-scale geology has shown that some of these bodies, particularly the Kharaelakh intrusion, are closed off at the propagating "frontal" end [START_REF] Krivolutskaya | Geology of the western flanks of the Oktyabr'skoe deposit, Noril'sk district, Russia: Evidence of a closed magmatic system[END_REF]. Host-rock lithology played a key role in localizing magma emplacement at particular horizons (e.g., [START_REF] Godlevsky | Traps and ore-bearing intrusions in the Noril'sk district: Moscow[END_REF][START_REF] Naldrett | Magmatic Sulfide Deposits: Geology, Geochemistry and Exploration[END_REF], involving both injection into and replacement of the host sediment.

The origin of such tube-shaped intrusions remains an unsolved problem. Several models have been proposed, mostly involving development of finger-like lobes at the propagating edges of sills and dikes [START_REF] Magee | Three-dimensional magma flow dynamics within subvolcanic sheet intrusions[END_REF][START_REF] Köpping | Magnetic fabrics reveal three-dimensional flow processes within elongate magma fingers at the margin of the Shonkin Sag laccolith[END_REF], but based on the evidence of extensive mine-scale drilling, the Norilsk-Talnakh bodies cannot be interpreted as the leading edges of extensive sheet-like intrusions.

CRITICAL OBSERVATIONS AND CONSTRAINTS ON GENETIC MODELS Interaction with Country Rocks

Based on isotopic evidence, the NorilskTalnakh orebodies are widely thought to have derived their S from assimilation by basaltic melt of the anhydrite-rich sedimentary sequence [START_REF] Gorbachev | The sulfur isotope ratios of the sulfides and sulfates of the Oktyabr'sk sulfide deposit, Noril'sk region, and the problem of their origin[END_REF][START_REF] Grinenko | Sources of sulfur of the nickeliferous and barren gabbro-dolerite intrusions of the northwest Siberian platform[END_REF]. [START_REF] Naldrett | Magmatic Sulfide Deposits: Geology, Geochemistry and Exploration[END_REF] suggested that coupled assimilation of coal or other carbonaceous material provided the reductant essential to produce immiscible sulfide melt from dissolved sulfate in the silicate magma.

Potential reductants are carbonaceous shales along with abundant bitumen and other hydrocarbons within the Devonian evaporites and carbonates [START_REF] Ryabov | The source of sulfur in sulfide deposits in the Siberian platform traps (from isotope data)[END_REF]. [START_REF] Iacono-Marziano | Assimilation of sulfate and carbonaceous rocks: Experimental study, thermodynamic modeling and application to the Noril'sk-Talnakh region (Russia)[END_REF] demonstrated this mechanism experimentally and showed that this process simultaneously generates C-H-S-bearing fluids in close physical association with fine sulfide liquid droplets. Semi-massive sulfide veins and disseminated ores developed within flanking and overlying sedimentary rocks, and also beneath the intrusions, above or below the underlying massive sulfide orebodies [START_REF] Lightfoot | Geological relationships between the intrusions, country rocks and Ni-Cu-PGE sulfides of the Kharaelakh intrusion, Noril'sk region: Implications for the role of sulfide differentiation and metasomatism in their genesis[END_REF]. These Cu-rich "exo-contact" assemblages are referred to as cuprous ores. Their wide variety of textures shows clear evidence of dynamic intrusion involving mechanical injection, impregnation, partial melting, and chemical dissolution of sedimentary host rocks.

The major deposits are flanked by a variety of distinctive skarns and hornfelses showing extensive brecciation, with later salt-anhydritecarbonate veining and selective replacement of fine-scale bedding by sulfide within marl and argillite (Fig. 2). These features developed within extensive hydrothermal alteration aureoles extending ∼200 m away from mineralized intrusions and only a few meters around barren ones [START_REF] Pokrovskii | Interaction conditions of Noril'sk trap intrusions with their host rocks: Isotopic (O, H, and C) evidence[END_REF]. Country rocks were evidently invaded extensively by overpressured magmatic fluids.

Evidence for Vapor-Phase Saturation within the Intrusions

Several lines of evidence indicate that the magmas were volatile-saturated at the time of ore deposition. Infilled vesicles are commonly attached to sulfide globules in the distinctive globular ores that account for much of the sulfide budget in the intrusions. The vesicles take the form of subspherical gaps within the cumulus framework of these olivine orthocumulate rocks (Figs. 3A-3C); they are filled with the crystallization products of strongly differentiated trapped intercumulus silicate liquid, and variable components of hydrothermal minerals, forming "segregation vesicles" and amygdules [START_REF] Barnes | Droplets and bubbles: Solidification of sulphide-rich vapour-saturated orthocumulates in the Noril'sk-Talnakh Ni-Cu-PGE ore-bearing intrusions[END_REF]. These features are interpreted as sulfide liquid droplets that were physically attached to gas bubbles, a phenomenon recognized in high-temperature experiments and attributed to the mutual surface affinity of the two phases [START_REF] Mungall | Transport of S, Cu and Au in magmas by flotation of sulphide melt on vapour bubbles[END_REF]. Crystallization under supercooled conditions [START_REF] Donaldson | An experimental investigation of olivine morphology[END_REF]) is indicated by the minor but widespread presence of skeletal olivine grains in picrodolerite (Fig. 3D). A similar but more complex association occurs in the low-S PGE ores toward the upper margins of the intrusions [START_REF] Sluzhenikin | Low-sulfide PGE ores of the Norilsk-Talnakh ore cluster[END_REF]. These ores contain Pt and Pd in concentrations of a few parts per million, similar to the globular ores below, but with much less sulfide. They are characterized by abundant vesicles, typically with a higher proportion of lower-temperature amygdule filling to segregated silicate melt, coating of bubbles by oxide films, and the presence of irregular mats or schlieren of Tichromite and Cr-magnetite (Fig. 3C; [START_REF] Chayka | Hybrid nature of the platinum group element chromite-rich rocks of the Norilsk 1 intrusion: Genetic constraints from Cr spinel and spinelhosted multiphase inclusions[END_REF][START_REF] Schoneveld | Oxidesulfide-magma-bubble interactions in spinelrich taxites from the Norilsk-Talnakh intrusions[END_REF][START_REF] Sluzhenikin | Low-sulfide PGE ores of the Norilsk-Talnakh ore cluster[END_REF][START_REF] Chayka | Origin of chromitites in the Norilsk-1 intrusion (Siberian LIP) triggered by assimilation of argillaceous rocks by Cr-rich basic magma[END_REF]. The proportion of bubbles to sulfide, and the proportion of platinum group minerals (PGMs) to sulfides, is much greater than that in the globular ores. In contrast to the globular ores, where the PGMs are spatially attached to sulfides, PGMs in the low-S ores are mainly isolated, separated at a scale of millimeters from the sulfide droplets, which show evidence of having lost S to an escaping volatile phase [START_REF] Barnes | Spatial association between platinum minerals and magmatic sulfides imaged with the Maia Mapper and implications for the origin of the chromite-sulfide-PGE association[END_REF][START_REF] Gritsenko | Quantitative assessment of the relative roles of sulfide liquid collection, magmatic degassing and fluidmediated concentration of PGE in low-sulfide ores of the Norilsk intrusions[END_REF], a process that stabilizes PGMs and also raises the effective PGE concentration of the remaining sulfide [START_REF] Peregoedova | The formation of Pt-Ir alloys and Cu-Pd-rich sulfide melts by partial desulfurization of Fe-Ni-Cu sulfides: Results of experiments and implications for natural systems[END_REF][START_REF] Iacono-Marziano | The critical role of magma degassing in sulphide melt mobility and metal enrichment[END_REF].

Mass Balance and Timing of Sulfide Liquid Formation

The orebodies present a mass balance problem: The aggregate mass of chalcophile elements, particularly Pt and Pd, is much greater than could have been derived from a volume of magma comparable to that of the host intrusions. [START_REF] Naldrett | Geology and geochemistry of intrusions and flood basalts of the Noril'sk region, USSR, with implications for the origin of the Ni-Cu ores[END_REF] estimated that a volume of magma 15-200 times the volume of the intrusions would have been required to supply the PGE. A more conservative estimate based on known deposit dimensions, an estimate of 2.5 wt% sulfide in the Kharaelakh intrusion [START_REF] Zen'ko | Spatial and petrologic aspects of the intrusions of the Noril'sk and Talnakh ore junctions[END_REF], and an estimate of 20 ppb Pt + Pd in the parent silicate magma (maximum contents measured in lavas of the Noril'sk region; [START_REF] Naldrett | Magmatic Sulfide Deposits: Geology, Geochemistry and Exploration[END_REF] gives a lower estimate of around 10 times the volume of the intrusion, still requiring a large excess. These constraints rule out models that involve in situ sulfide liquid generation entirely within the intrusions themselves. Hence, most of the generation of and metal scavenging by the sulfide liquid must have taken place prior to transport of sulfide droplets into the sills. This requires that assimilation of the anhydrite and the C-rich reductant must have happened either in some deepseated subchamber, as modeled by [START_REF] Yao | Linking the Siberian flood basalts and giant Ni-Cu-PGE sulfide deposits at Norilsk[END_REF], or within a feeder sill-dike complex, involving a total volume of magma of at least 100 km3 based on the PGE mass balance argument. Magma flow in this system may have been as much lateral as vertical, based on evidence for lateral injection of large dikes in large igneous provinces [START_REF] Ernst | Giant radiating dyke swarms on the Earth and Venus[END_REF], such that an unseen "deep chamber" may not have been necessary.

Droplet Physics, Bubble Formation, and Sulfide Harvesting

The large size of the sulfide droplets in the globular ores (Fig. 3) presents a problem. If droplets were indeed transported over kilometer-scale vertical distances [START_REF] Yao | Linking the Siberian flood basalts and giant Ni-Cu-PGE sulfide deposits at Norilsk[END_REF], they must have been of the order of hundreds of microns or at most a few millimeters in size; larger droplets would either have settled out or broken up due to shear stress in the emulsion [START_REF] Robertson | Dynamics of magmatic sulphide droplets during transport in silicate melts and implications for magmatic sulphide ore formation[END_REF]. The >2 cm droplets observed in the disseminated ores (Fig. 3A) can only have been generated very close to the site of deposition. Analogue experiments [START_REF] De Bremond D'ars | Analog experimental insights into the formation of magmatic sulfide deposits[END_REF] and theory [START_REF] Robertson | Dynamics of magmatic sulphide droplets during transport in silicate melts and implications for magmatic sulphide ore formation[END_REF] predict that coalescence of fine sulfide droplets is unlikely during transport in dilute emulsions. Experiments by [START_REF] Iacono-Marziano | The critical role of magma degassing in sulphide melt mobility and metal enrichment[END_REF] showed that generation of vapor bubbles during or after generation of sulfide liquid droplets causes multiple small droplets to become collected on the surfaces of the bubbles, thus providing a means by which fine droplets will rapidly coalesce into large ones. This requires that a burst of bubble nucleation and droplet "harvesting" took place synchronous with deposition. Two distinct episodes of vapor bubble generation may have occurred: the first associated with assimilation and generation of a population of small transportable droplets, and the second coincident with intrusion emplacement.

Sill Inception and Overpressure Release

Laboratory experiments by [START_REF] Kavanagh | The mechanics of sill inception, propagation and growth: Experimental evidence for rapid reduction in magmatic overpressure[END_REF] using gelatine and water as analogues for upper-crustal rocks and mafic magma, respectively, found that a large transient release of overpressure occurs when a vertically ascending dike transitions to a horizontally propagating and vertically inflating sill. The associated stress drop scales to equivalent values in nature from ∼250 to 100 MPa at depths between 1 and 10 km. In cases where the magma is already at volatile saturation, this pressure drop would be accompanied by a sudden catastrophic degassing event, causing rupturing of country rocks and rapid injection of magma into the sill. [START_REF] Kavanagh | The mechanics of sill inception, propagation and growth: Experimental evidence for rapid reduction in magmatic overpressure[END_REF] proposed this pressure drop as a potential trigger for volcanic eruptions, but it may also explain the sudden pressure drop associated with the initial emplacement of the host chonoliths, with important consequences, including:

1. Conversion of transported fine droplet "mist" into a "rain" of large globules due to harvesting by a new generation of vapor bubbles; 2. Wall-rock fragmentation, creating fracture networks for magma injection, accompanied by intrusion breccias and highly contaminated marginal zones; 3. Extensive volatile influx on scales of 10-100 m into the reactive country rocks, giving rise to hydrofracturing, breccias, and skarns; and 4. Generation of "damage zone" footwall fracture arrays, facilitating invasion by sulfide liquid to form exo-contact massive ores, localized degassing at the leading edge of the sill, causing pore-fluid overpressure, and channeling of silicate magma into resulting fractures to form the chonoliths.

NEW EMPLACEMENT MODEL

A vertically propagating narrow dike (Fig. 4A) channels a volatile-saturated, overpressured magma containing a fine mist of sulfide droplets rafted on vapor bubbles previously generated during assimilation within the magma column. On reaching a horizon of weakness or competency contrast (e.g., the argillite-bearing Razvedochninsky formation for the Kharaelakh intrusion and the coal-bearing Tunguska group for the Talnakh and Norilsk 1 intrusions; see the Supplemental Material), a new sill begins to propagate as a chonolith, resulting in a sudden drop in overpressure and collapse of the dike (Fig. 4C). The droplet-harvesting process generates a wide range of bubble to droplet ratios (Fig. 4B), from bubbles with very little sulfide to virtually bubble-free sulfide that detaches from the vapor phase under its own weight [START_REF] Yao | A preliminary model for the migration of sulfide droplets in a magmatic conduit and the significance of volatiles[END_REF]. Dense sulfide-rich droplet-bubble pairs sink rapidly; the earliest sinking globules reach the floor and coalesce to form the basal massive ores, whereas later ones accumulate into the accreting bed of olivine cumulates. Bubbles with little or no attached sulfide float to the roof, becoming coated with spinel grains and accumulating in the upper taxite breccias. Ongoing degassing here drives destruction of sulfide, growth of PGMs, and the formation of the low-S PGE zone. A continuing influx of magma splits the two ore zones (S rich and S poor) and eventually crystallizes to form the relatively uncontaminated olivine-poor central gabbro-dolerites (Fig. 4D). This model is by no means the first to incorporate volatiles (e.g., [START_REF] Marakushev | Petrological model for the formation of Noril'sk nickel-copper deposits[END_REF], but it is the first to link explosive intrusion emplacement with a mechanism for collecting a large volume of previously generated dispersed sulfide droplets. While it leaves some complex problems unaddressed, such as the mismatch between the Pt/Pd ratios of the orebodies and the likely parent basaltic magmas, extensive differentiation of the sulfide liquid, and the nature or even existence of staging magma chambers, it provides a testable working hypothesis.

Figure captions Figure 1 .

 captions1 Figure captions Figure 1. (A) Location map. (B-C) Long section through Kharaelakh (K) and Talnakh (T) intrusions. (D) Schematic three-dimensional view of a "composite" Norilsk-Talnakh chonolith complex, showing internal differentiation, disposition of ore types, and flanking sills and breccias.

Figure 2 .

 2 Figure 2. Skarn and breccia ores in Talnakh intrusion footwall. (A) Footwall below massive sulfide in Talnakh intrusion: Sandstone blocks (darker) are boudinaged among microfolded mudstone (lighter); Skalisty Mine. (B) Sulfide-rich bands in banded forsterite-monticellite skarn after marl; serp-serpentinite; f-grained-fine-grained. (C) Massive sulfides and veinlets rimmed by serpentinized forsterite skarn (FS) in brecciated marble. (D) Banded massive sulfides along relict bedding in meta-argillite hornfels.

Figure 3 .

 3 Figure 3. Globular ores. (A) Large sulfide globules in taxitic picrodolerite (PGD). (B) Phase map of PGD (from synchrotron X-ray fluorescence microscopy [XFM] image) showing sulfides (sulf) and silicate cap within void in olivine framework. (C) Upper taxite, segregation vesicles, and sulfides within Crspinel mat (Cr-Fe-Ti XFM map). (D) Picrodolerite with skeletal olivine (green) and segregation vesicles (Cr-Fe-Ca XFM map). Minerals: amyg-amygdule, apapatite; Ccp -chalcopyrite; cpx-clinopyroxene; hb/h'blende-hornblende; Ol/olv-olivine; plag/plg -plagioclase; Pn-pentlandite; Po-pyrrhotite.

Figure 4 .

 4 Figure 4. Schematic illustration (not to scale) of model for explosive emplacement and sulfide droplet deposition in propagating chonolith. (A, B) Time T1: Inception of chonolith and explosive injection of volatile-saturated magma containing transported fine sulfide droplets. (C, D) Time T2: Ongoing magma injection and inflation of chonolith. (E) Microcomputed tomography (micro-CT) image of experimental run showing multiple sulfide droplets (yellow) "harvested" by a gas bubble (blue), ∼1 mm across. PGE-platinum group element.

Figure 1 Figure 2 Figure 3

 123 Figure 1

Figure 4

 4 Figure 4

ACKNOWLEDGMENTS

Micro-X-ray fluorescence spectrometry (micro-XRF) images were collected on the X-ray fluorescence microscopy (XFM) beamline of the Australian Synchrotron, part of the Australian Nuclear Science and Technology Organisation (ANSTO). We thank Craig Magee, Ivan Chayka, and an anonymous referee for helpful reviews. M.A. Yudovskaya was supported by Russian Science Foundation grant 21-17-00119. G. Iacono-Marziano received funding from the program TelluS of the Institut National des Sciences de l'Univers, Centre National de la Recherche Scientifique (CNRS).


Marion Naveau

Guillaume Kon

Kam King

Renaud Rincent

Laure Sansonnet

Maud Delattre

High-dimensional variable selection in non-linear mixed-effects models using a stochastic EM spike-and-slab

High-dimensional variable selection in nonlinear mixed effects models using a stochastic EM spike-and-slab Marion Naveau 1 , Guillaume Kon Kam King 1 , Renaud Rincent 1 , Laure Sansonnet 1 , Maud Delattre High-dimensional variable selection is widely documented in standard regression models, but there are still few tools to address it in nonlinear mixed-effects models, where data is collected repeatedly on several individuals. For all 1 ≤ i ≤ n and 1 ≤ j ≤ n i , y ij the response of individual i at time t ij is modelled as follows:

y ij = g(φ i , t ij ) + ε ij , ε ij i.i.d. ∼ N (0, σ 2 ), φ i = µ + β ⊤ V i + ξ i , ξ i i.i.d. ∼ N q (0, Γ),
where g is non-linear with respect to an individual parameter φ i which is q-dimensional. Identifying the relevant covariates for all individual parameters amounts to selecting the support of β ∈ M p×q , defined by S * = (ℓ, m) ∈ {1, . . . , p} × {1, . . . , q} β * ℓm ̸ = 0 , where β * is the true fixed effects matrix, and p is the number of covariates. To solve this problem in a high-dimensional context, that is when p >> n, the assumption of sparsity is made, that is each row of β * is sparse. The main difficulty here is that variable selection concerns latent variables of the model.

In this work, variable selection is approached from a Bayesian perspective and a selection procedure is proposed, combining the use of a spike-and-slab prior [START_REF] George | Approaches for Bayesian variable selection[END_REF] and the SAEM algorithm [START_REF] Delyon | Convergence of a stochastic approximation version of the EM algorithm[END_REF]. The first step of this procedure is to reduce the number of candidate models: similarly to Lasso regression, a grid of values for the spike parameter is explored to obtain a collection of promising sub-models ( S ν 0 ) ν 0 ∈∆ . Then, an information criterion can be used to choose the final model: a pragmatic and effective choice is to use the eBIC (extended Bayesian Information Criterion, [START_REF] Chen | Extended Bayesian information criteria for model selection with large model spaces[END_REF]) which is tailored to the high-dimensional setting.

This approach is much faster than a classical MCMC algorithm and shows very good selection performances on simulated data. The efficiency of the proposed method is illustrated on a problem of genetic markers identification, relevant for genomic assisted selection in plant breeding. The current aim is to achieve consistency in model selection for this problem, which is a work in progress.