Keywords: Systèmes de transport d'azote, interactions écologiques, Quercus petraea, Molinia caerulea Nitrogen transport systems, ecological interactions, Quercus petraea, Molinia caerulea

Une des difficultés rencontrées lors de la régénération du chêne (Quercus petraea) est l'interaction avec Molinia caerulea, une graminée forestière commune. Au-delà d'une compétition forte pour les ressources azotées, des interactions allélopathiques ont été documentées. Ces dernières ne sont, à ce jour, pas encore bien étudiées. C'est pourquoi cette étude se concentre sur les flux azotés résultant des interactions. Une approche de modélisation a permis de simuler le résultat des interactions en termes de biomasses et d'identifier les principaux manques de connaissances dans le système : la quantification de la rhizodéposition, des pertes par volatilisation et dénitrification, et le rôle des molécules allélochimiques. Un arrosage de jeunes chênes en pot avec un macérât de racines de molinie a démontré un effet retardataire sur le débourrement des chênes et un effet inhibiteur sur leur croissance relative en hauteur. Une étude d'absorption de nitrate, ammonium et glycine marqués en isotope 15 N a été effectué sur racines excisées utilisant la technique des « tea bags ». Elle a permis d'identifier les systèmes de transports d'azote comme cibles potentielles de l'allélopathie. Les taux d'influx et les capacités maximales d'influx en azote divergent et suggèrent une réponse plus complexe que présumée qui pourrait dépendre de la phénologie et de l'affinité des systèmes de transport.

I am extremely grateful to Philippe MALAGOLI and Phillipe BALANDIER. Without you the present pages would not exist! Thank you for your guidance, your support, patience, all of your explications and comments, the time, thoughts, energy and strength put into my project.

Deepest thanks to the PIAF laboratory and Marc SAUDRAU with his MEA team for accepting me as their intern. I would like to pay special regards to Antoine VERNAY.

Without your data my model would not exist. Special regards also to Marine FERNANDEZ.

Thank you for letting me use your data too, but also for all the help concerning the labeling.

What a pleasure to have oak tea with you! I would also like to thank Brigitte SAINT-JOANIS for showing me the lab, helping me gather all materials I needed and for warning me of the big PCHIT. I must also thank Patrice CHALEIL for taking care of my little oaks and Molinia. I am grateful to Aline FAURE who helped potting my plants. Especially, I would to thank Jean-Stéphane VENISSE for his help taking oaks out of their pots and preparing samples for RNAseq.

A very big thank you to Dominique TIZIANI. You helped me so much feeling welcome at Crouël and you sent my samples to Nancy just in time. I must also thank Marylou MANTOVA for sharing the lab on a "bridge day" and helping me out with some bottles. I should also appreciate Sandrine MEYNIEL and Valérie LEGUE for her administrative help.

Thank you a lot Norbert FRIZOT for providing IT support in times where it is needed. I would also like to acknowledge the help of LAS team for soil analysis and Christian HOSSANN and his team for performing IRMS. I am grateful to all my teachers of UCA for preparing me for my career and all my classmates for distracting me from all that work. Finally, I would like to thank my partner Eric who supported me morally when pressure tried to catch up with me.

Presentation of the host structure

The mixed research group « Physique et Physiologie intégratives de l'Arbre en environnement Fluctuant (PIAF) » is a result of the merger of two institutions: University of Clermont Auvergne (UCA) and INRAE (National Research Institute for Agriculture, Food and Environment).

UCA is a French public university comporting 22 teaching and research components.

The university obtained the label of excellence "label I-site". The trainee is enrolled at UCA in the second year of a Master of Science degreee "Plant Integrative Biology and Breeding". Attached to the INRAE departments AgroEcoEnv and Ecodiv, research of the mixed research group PIAF strives for a better comprehension of the functioning of trees exposed to biotic and abiotic constraints while taking into account the functional and architectural aspects of the whole annual cycle of the studied species (walnut, apple tree, poplar, rubber tree, oak).

All scales are studied from the molecular one to the vegetation cover over cells and organs.

The working group is composed of four teams: MEA (MicroEnvironment and Trees), SUREAU (Hydraulic system and resistance of trees facing drought), MECA (Mechanic Constraints and Activity of the growing zones) and FolEau (functional ecogenomic of water transport in leaves in fluctuating hydric plans).

I joined the MEA team that focuses on ecophysiology of trees while characterising the interactions between the vegetation cover and its structure as well as the tree's behaviour and microclimatic environment, in particular in the case of vulnerability of plants to bio aggressors, freezing, winter-spring phenology and multiple and frequent constraints as for example risks linked to global change. Table 1 VenSim equation codes for key variables Table 2 Calculated maximal influx capacities for Michaelis-Menten regressions

Abreviations

List of figures and tables

Introduction

France is the most important oak timber producer in Europe and second largest in the world with about one million cubic meters per year [START_REF] Drénou | Les racines: face cachée des arbres[END_REF][START_REF] Stassi | L'usine Nouvelle. Bisbilles autour des exportations de chêne français[END_REF]). However, it is confronted by a major issue in forestry: sustainability i.e. the regeneration of trees [START_REF] Zhu | Interactions between Kalmia and black spruce: Isolation and identification of allelopathic compounds[END_REF]. Natural oak regeneration has become difficult since the last three centuries [START_REF] Thomas | Abiotic and biotic factors and their interactions as causes of oak decline in Central Europe[END_REF], while regeneration difficulty increased with time.

Reasons for tree regeneration failure have been studied for more than several decades: [START_REF] Watt | On the Causes of Failure of Natural Regeneration in British Oakwoods[END_REF] showed that animals and seedbed properties are determining factors. [START_REF] Loftis | Regenerating northern red oak on high-quality sites in the southern Appalachians[END_REF] identified light scarcity as a problem. According to [START_REF] Mallik | Conifer regeneration problems in boreal and temperate forests with ericaceous understory: Role of disturbance, seedbed limitation, and keytsone species change[END_REF], disturbance, chemical and physical properties of seedbeds and plant-plant interactions play important roles. Whereas disturbance is relatively well studied, regeneration failure through negative plant-plant interactions is less. However, several authors showed that plant-plant interactions play an important role in tree seedling establishment (e.g. A large number of works was dedicated to inhibiting action of understory plant species on trees (e.g. Mallik 2003, Warren and[START_REF] Warren | Uptake of nitrate, ammonium and glycine by plants of Tasmanian wet eucalypt forests[END_REF] as reported for Q. rubra [START_REF] Timbal | Étude préliminaire sur l'effet dépressif de la molinie (Molinia caerulea) sur la croissance et l'état mycorhizien de semis de chêne rouge (Quercus rubra)[END_REF]). Currently, Q. petraea oak species seems particularly interesting because of its ecophysiological ability to face climate change [START_REF] Vernay | Régénération du chêne en compétition avec la molinie : un délicat dosage des ressources en eau et en lumière[END_REF]: Q. petraea is more drought-resistant than other members of the genus.

West European oaks are grown inter alia on temporarily flooded acid soils where Molinia caerulea is frequently observed [START_REF] Timbal | Étude préliminaire sur l'effet dépressif de la molinie (Molinia caerulea) sur la croissance et l'état mycorhizien de semis de chêne rouge (Quercus rubra)[END_REF]. M. caerulea, also called purple moor-grass, is a widely distributed Eurosiberian Boreotemperate (Fig. 2) Poaceae [START_REF] Preston | The geographical relationships of British and Irish vascular plants[END_REF]. It grows in tufts and easily dominates the vegetation due to its ability to quickly monopolize resources [START_REF] Vernay | Photosynthesis capacity of Quercus petraea (Matt.) saplings is affected by Molinia caerulea (L.) under high irradiance[END_REF]. It is known to interact with oak seedlings in an inhibiting manner [START_REF] Weise | Allelopatische Beeinflussung und Ökotypenbildung bei Molinia caerulea Moench[END_REF]). These interactions, disadvantageous for oak seedlings, might represent a main cause for oak regeneration failure. Q. rubra seedlings lost more than 73% biomass when grown with M. caerulea in non-fertilized systems [START_REF] Timbal | Étude préliminaire sur l'effet dépressif de la molinie (Molinia caerulea) sur la croissance et l'état mycorhizien de semis de chêne rouge (Quercus rubra)[END_REF]).

The following chapter will briefly recapitulate the present knowledge about interactions between tree seedlings and grass species and will focus on root nitrogen uptake, often closely related to interactions and in turn influencing resource cycles. Further chapters will concentrate on poorly studied processes: allelopathy and nitrogen flux dynamics between oak and moor grass.

1

Bibliographical summary 2.1 Ecological interactions within multi-species plant communities

As plants are sessile organisms, the only way for survival, growth and reproduction is to perceive and react to the environment. This is why all plants in natural environments are concerned by interactions with their neighbors. Among others, changes in soil nutrient availability or proximity to neighbors' roots releasing chemical compounds can act as information systems between plants. Plant performance therefore depends on the accuracy and timing of plastic responses to cues from their neighbors. Diverging definitions are found for the interactions between plants. The ones used for this project are detailed in the glossary (supplemental data).

Competition

What is resource competition?

Competition is a negative interaction leading to decrease in survival, growth and/or reproduction. It can be classified in two distinct manners. Firstly, plants compete for resources available in a limited amount in the same ecological niche at the same time (Fig. 3). Secondly, the interaction can be based on a secondary metabolite formed from one species and released into the common environment, inhibiting e.g. growth or physiological processes of neighboring species. In this chapter, I want to focus on resource-based competition because it can determine dominance establishment. According to [START_REF] Casper | Plant competition underground[END_REF], resource mediated competition consists in a "negative effect on the availability […] of resource to which [when available] another plant needs to show a positive response in growth, survival, or reproduction". Resource competition is characterized quite well [START_REF] Callaway | Positive interactions among plants[END_REF]Walker 1997, Goldberg and[START_REF] Goldberg | Patterns and Consequences of Interspecific Competition in Natural Communities: A Review of Field Experiments with Plants[END_REF], what is valid also between tree saplings and grasses [START_REF] Picon-Cochard | Competition for water between walnut seedlings (Juglans regia) and rye grass (Lolium perenne) assessed by carbon isotope discrimination and δ18O enrichment[END_REF], Coll et al. 2004and Balandier et al. 2006).

Which plant is the fittest? Two theories for predicting the outcome of competing species

Two theories to predict outcome of interacting species have marked research:

The first one was established by [START_REF] Grime | Primary strategies in plants[END_REF]: it categorizes plants in three groups depending on their success in survival under different environmental conditions (Fig. 4). On one hand, there are species that present efficient resource acquisition but perform poorly in environments with high stress conditions or disturbance (competitors). On the other hand, stress-tolerators show high levels of nutrient retention e.g. in storage organs but they are not well adapted to high levels of competition or disturbance. Eventually, ruderals acquire resources rapidly and invest them in high reproduction rates. Being well adapted to The second theory was proposed by [START_REF] Tilman | Resources: A Graphical-Mechanistic Approach to Competition and Predation[END_REF]: it aims to predict the outcome of a competitive relationship among multiple species. The most successful species in the competition for a common limiting resource would be the one that can survive at the lowest equilibrium resource level, i.e. the minimum concentration that is necessary for maintenance.

For instance, if species A needs a concentration of 15 mg/L and species B 25mg/L, species A will be more successful than species B in the case of non-substitutable resources. If species are limited by different resources they may coexist (Fig. 5). The two contrasting theories are coexisting and difficult to reconcile. Neither of the theories is sufficient to explain resource competition, but their different presumptions could complement one another [START_REF] Craine | Reconciling plant strategy theories of Grime and Tilman[END_REF].

How to be successful? Above-versus below-ground competition

Resource competition can be classified in above-and belowground competition corresponding to the location of the resources. Aboveground competition mainly concerns light that often is scarce in forest ecosystems. Accordingly, competition for light has been studied more intensively whereas below-ground competition is less documented.

Belowground interactions are more complex due to the various resources involved: water and a wide range of nutrients [START_REF] Casper | Plant competition underground[END_REF]. Additionally, [START_REF] Casper | Plant competition underground[END_REF]Jackson (1997), Coll et al. (2004) and [START_REF] Hangs | Interspecific competition for nitrogen between early successional species and planted white spruce and jack pine seedlings[END_REF] indicated that competition in forests, especially from grasses, was mainly based on belowground resources.

Monopolistic perennial grasses are known to be successful competitors for water and nitrogen (N) [START_REF] Provendier | Compared effects of competition by grasses (Graminoids) and broom (Cytisus scoparius) on growth and functional traits of beech saplings (Fagus sylvatica)[END_REF]Balandier 2008, Coll et al. 2004) (Callaway 1995, Hauggaard-Nielsen and[START_REF] Hauggaard-Nielsen | Facilitative root interactions in intercrops[END_REF].

Stress-Gradient-Hypothesis

Facilitation can occur in stressful as well as in competitive environments [START_REF] Bråthen | A portfolio effect of shrub canopy height on species richness in both stressful and competitive environments[END_REF]. However, it acts in the opposite direction of competition and therefore decreases competition in a common ecological niche [START_REF] Wit Ct De | Competition between herbage plants[END_REF]. Also, an initially competitive interaction can gradually become facilitative with increasing environmental severity [START_REF] Michalet | Facilitation in communities: Underlying mechanisms, community and ecosystem implications[END_REF]. A theory called Stress Gradient Hypothesis.

Nitrogen transfer between plants: an example of belowground facilitation

One of the most popular examples for facilitation is below-ground N transfer. It has been monitored primarily from legumes to non-legumes, subsequently to symbiotic N 2 -fixation. An example for tree to grass N transfer was found by [START_REF] Sierra | Transfer of N fixed by a legume tree to the associated grass in a tropical silvopastoral system[END_REF] between

Gliricidia sepium and Dichanthium aristatum. [START_REF] Eissenstat | A comparison of phosphorus and nitrogen transfer between plants of different phosphorus status[END_REF] was the first to hypothesize that N transfer could also be possible between two non-fixing species. [START_REF] Teste | Complementary plant nutrientacquisition strategies promote growth of neighbour species[END_REF] confirmed this hypothesis with four Australian species. Transferred amounts vary in the literature from 4 to 80% of total N [START_REF] Teste | Is nitrogen transfer among plants enhanced by contrasting nutrient-acquisition strategies? Plant[END_REF][START_REF] Thilakarathna | Belowground nitrogen transfer from legumes to non-legumes under managed herbaceous cropping systems. A review[END_REF]. This might be due to measuring techniques, multiplicity of species combinations and scanty knowledge about underlying mechanisms. Great variability is probably the reason why the phenomenon is not fully understood yet. It is not known yet which role microorganisms of the soil could play in this type of interaction.

Allelopathy is involved in plant-plant interference Definition and History

Allelopathy can take different directions, even though older reports on allelopathy seem to concentrate rather on negative impacts than stimulatory [START_REF] Zhang | Effect of allelopathy on plant performance: a meta-analysis[END_REF]. Co-occurrence with resource based interactions is possible.

Allelopathy has gained seriously in interest since the 1970s. Despite many open questions, a slowdown of research on the subject has been documented this year (Zhang et al.2021). Many examples of allelopathy are known [START_REF] Rice | Allelopathy--an update[END_REF]. Table 1 gives a nonexhaustive list of examples that show the broad range of species and ecosystems concerned.

What is known about allelochemicals?

Many species are known for their allelopathic properties without documentation of molecules conferring this ability [START_REF] Zhang | Effect of allelopathy on plant performance: a meta-analysis[END_REF]. This is also true for Poaceae [START_REF] Favaretto | Allelopathy in Poaceae species present in Brazil. A review[END_REF]. When allelochemicals are identified, their natural concentration in most cases is undocumented. Even though, effect intensity and direction depend mainly on concentration [START_REF] Khailov | The biochemical trophodynamics in coastal sea ecosystems[END_REF]. Allelochemicals might interact with other soil chemicals. They act simultaneously with other soil elements such as nutrients and mycorrhizae [START_REF] Inderjit | Can Kalmia angustifolia interference to black spruce (Picea mariana) be explained by allelopathy?[END_REF]. Nevertheless, the interdependence of multiple plant-plant interactions has not been described clearly and therefore overall effects cannot be predicted. [START_REF] Yan | Antagonistic and synergistic effects of main phenolic compounds present in continuously cropped sick cotton soil on its own seeds germination, seedling growth and antioxidant enzyme activities[END_REF] suggested that different molecules have antagonistic or synergistic effects. Huang et al. (2020) proposed that those were additive, while [START_REF] Su | Nonadditive allelopathic effects of decomposing mixed litters of Eucalyptus urophylla and Acacia mangium on radish, lettuce and Paspalum notatum[END_REF] reported non-additive effects.

Many studies described short-term observations and long-term experiences remain rare.

Transfer and targets of allelochemicals

Transfer of allelopathic compounds from one plant to another remains hardly studied. Figure 6 gives a schematic overview of documented transfer pathways: direct transfer by kolines (plant to plant signals) or indirect through microorganisms (phytoncides).

Soil microbes are not only able to transmit the signal of allelochemicals but play a crucial role in the connection between soil and plant e.g. mycorrhiza in nutrient uptake [START_REF] Voight | Mycorrhizae: proceeding of the first North American conference on mycorrhizae[END_REF]. Anyway, the impact of and on soil microbes in allelopathic interactions is debated [START_REF] Zhang | Effect of allelopathy on plant performance: a meta-analysis[END_REF]. Another unanswered question is the one about a link between allelopathy and plant nutrition. For example it seems clear that allelochemicals can, in some species combinations, affect uptake of nutrients such as N [START_REF] Jiao | Allelopathy of uncomposted and composted invasive aster (Ageratina adenophora) on ryegrass[END_REF]) but the molecular mechanisms remain unsolved.

Nutrient uptake: key physiological process targeted by plant interactions?

Plants need to take up 20 essential minerals from their substrate. While all of them need to be available in species specific extents for optimal growth, the commonly most limiting ones are N, phosphorous (P) and potassium (K). N also has an important role as "key structural component of macromolecules" [START_REF] Vidal | Nitrogen control of developmental phase transitions in Arabidopsis thaliana[END_REF] like in e.g. Ribulose-1,5bisphosphat-carboxylase/-oxygenase (RuBisCO), amino acids, chlorophyll, nucleic acids and phyto-hormones. Besides its necessity to growth, N compounds can also act as a signal in and in between plants [START_REF] Vidal | A systems view of nitrogen nutrient and metabolite responses in Arabidopsis[END_REF][START_REF] Alvarez | Integration of local and systemic signaling pathways for plant N responses[END_REF][START_REF] Gutiérrez | Systems biology for enhanced plant nitrogen nutrition[END_REF]. [START_REF] Lajtha | Nutrient uptake in eastern deciduous tree seedlings[END_REF] held that the highest efficiency of mineral uptake would be reached in most limiting conditions. [START_REF] Casper | Plant competition underground[END_REF] identified also plasticity of the root system as an important factor for N uptake. They suggested a trade-off between exploitation and exploration i.e. between resource use and extension of roots.

Nutrient absorption and release do not use the same transport systems. The following part will discuss root N acquisition, the one after that N return to the environment.

Different forms of nitrogen can be taken up

Soil N is available in mineral and organic forms. In low-anthropized systems, organic forms play a particular role i.e. the amount of leaf-litter is higher than in other ecosystems and organic forms enhance plant nutrition directly (e.g. [START_REF] Warren | Uptake of nitrate, ammonium and glycine by plants of Tasmanian wet eucalypt forests[END_REF]Adams 2007, Wang et al. 2012). Even if organic N uptake is rarely considered, [START_REF] Warren | Uptake of nitrate, ammonium and glycine by plants of Tasmanian wet eucalypt forests[END_REF] reported that organic N sources are directly absorbed from plants. For instance, they illustrated the direct uptake of urea and glycine (4.4µmol gDM -1 h -1 ) in Eucalyptus trees. They concluded that the most frequent forms in the natural habitat of a plant determine preference for N forms.

Persson and Näsholm ( 2001) demonstrated that amino acid absorption is a current trait in boreal forests. Nevertheless, the most commonly known forms of N remain nitrate (NO 3 -) and ammonium (NH 4 + ) [START_REF] Killpack | Nitrogen in the environment : nitrogen's most common forms[END_REF]. Both are relatively mobile in the soil [START_REF] Lajtha | Nutrient uptake in eastern deciduous tree seedlings[END_REF]).

Absorption through different nitrogen influx transport systems

The different forms of N are absorbed through multiple membrane bound transport systems (Fig. 7), specific to their substrate [START_REF] Wang | Uptake, allocation and signaling of nitrate[END_REF]. Absorption of nitrate and ammonium by roots varies according to the soil solution concentration in a biphasic manner [START_REF] Crawford | Molecular and physiological aspects of nitrate uptake in plants[END_REF]. Two transport systems have been characterized in roots handling low and high nitrate concentrations in an optimized way: when nitrate is available at low concentrations (0.5-1 mM), High Affinity Transport Systems (HATS) are active. They exhibit a high affinity for nitrate but they saturate at higher concentrations. Is the soil concentration beyond 1mM, Low Affinity Transport Systems (LATS) start their activity, in addition to the HATS (Fig. 8) [START_REF] Glass | Nitrogen absorption in higher plants[END_REF]. LATS have low affinity for nitrate but exhibit large uptake capacities. Nitrate influx by HATS is thermodynamically uphill (i.e. the process needs energy to take place) [START_REF] Mata | Influx, efflux and net uptake of nitrate in Quercus suber seedlings[END_REF]. Considering LATS, few studies demonstrated energy-independent activity as for instance no sensitivity to low temperatures was observed [START_REF] Malagoli | Modeling Nitrogen Uptake in Oilseed Rape cv Capitol during a Growth Cycle Using Influx Kinetics of Root Nitrate Transport Systems and Field Experimental Data[END_REF]. For urea, a high affinity transporter has been identified [START_REF] Nacry | Nitrogen acquisition by roots: Physiological and developmental mechanisms ensuring plant adaptation to a fluctuating resource[END_REF]. [START_REF] Nacry | Nitrogen acquisition by roots: Physiological and developmental mechanisms ensuring plant adaptation to a fluctuating resource[END_REF] reported also a possible passive transport via aquaporins. Amino acids can also be absorbed through different transporters.

How are the multiple transport systems regulated?

Transporters are known to be either constitutively expressed or induced, directly or indirectly, by environmental factors [START_REF] Nacry | Nitrogen acquisition by roots: Physiological and developmental mechanisms ensuring plant adaptation to a fluctuating resource[END_REF]. Their expression and activity can be regulated by local substrate concentration in the soil, while some seem to function as transceptors i.e. transporters having a substrate sensoring function at the same time (see [START_REF] Gojon | Nitrate transceptor (s) in plants[END_REF].

Another way of activity regulation is negative systemic feedback. E.g. glutamine or other N metabolites in the plant are used as indicators for its N content. Epigenetic regulation, regulation by phytohormones, and affinity switches according to N availability are also commonly observed [START_REF] Nacry | Nitrogen acquisition by roots: Physiological and developmental mechanisms ensuring plant adaptation to a fluctuating resource[END_REF]. For example the urea influx transporter is regulated by a promotor that responds to urea in absence of other N forms.

2.2.4

Nitrogen can be returned from plant to soil by multiple ways At plant scale, the nutrient cycle includes N release into the soil (Fig. 9): in natural ecosystems after uptake by plant roots, nutrients are allocated to construction and maintenance of biomass. Then one part is reabsorbed to perennial tissues, if any, during senescence. Another part is returned to the soil in form of litter, processed in the soil before restarting a new absorption [START_REF] Rahman | The Role of Quantitative Traits of Leaf Litter on Decomposition and Nutrient Cycling of the Forest Ecosystems[END_REF]).

At root level, a way to release nutrients is rhizodeposition. This comprises decay of senescing roots forming below-ground litter and exudation of organic compounds from intact roots. Through return into the soil, N can be transferred to neighboring plants.

Several compounds are exuded by the roots. They often are discriminated between low-and high molecular weight molecules. N forms are found in both categories: low-weight molecules include e.g. amino acids, organic acids and secondary metabolites [START_REF] Jones | Plant and mycorrhizal regulation of rhizodeposition[END_REF][START_REF] Haichar F El | Root exudates mediated interactions belowground[END_REF]) while high-weight compounds are foremost proteins. Exudation can vary greatly depending on biotic and abiotic factors such as phenology and soil microbes (e.g. [START_REF] Phillips | New approach for capturing soluble root exudates in forest soils[END_REF][START_REF] Qiao | Understory species regulate litter decomposition and accumulation of C and N in forest soils: A long-term dual-isotope experiment[END_REF][START_REF] Wang | Differences in root exudate inputs and rhizosphere effects on soil N transformation between deciduous and evergreen trees[END_REF]. Amino acids can be exuded through energy dependent carriers [START_REF] Nacry | Nitrogen acquisition by roots: Physiological and developmental mechanisms ensuring plant adaptation to a fluctuating resource[END_REF]) but also leaked out [START_REF] Jones | Plant and mycorrhizal regulation of rhizodeposition[END_REF]).

8

An original interaction model mixing competition and antagonistic facilitation between oak and Molinia

Quercus petraea regeneration failure results from a variety of origins. One of them is the disadvantageous interaction with neighboring Molinia caerulea (Fig. 10). [START_REF] Timbal | Étude préliminaire sur l'effet dépressif de la molinie (Molinia caerulea) sur la croissance et l'état mycorhizien de semis de chêne rouge (Quercus rubra)[END_REF] showed that red oak is in direct competition with Molinia caerulea. According to them, it reduces growth of oak, increases its root biomass to the detriment of shoots, affects root architecture and causes qualitatively disadvantageous mycorrhization state. When light is scarce, Molinia competes aboveground with Q. petraea.

In addition, M. caerulea has been identified as an efficient below-ground resource competitor [START_REF] Taylor | BIOLOGICAL F LORA OF THE BRITISH ISLES * Molinia caerulea ( L .) Moench[END_REF]. But rather than competition for light or water, one of the most problematic conditions for oak growth seems to be the severe competition from Molinia for N [START_REF] Collet | Effect of two forest grasses differing in their growth dynamics on the water relations and the growth of Quercus petraea seedlings[END_REF]. [START_REF] Fernandez | Below-ground nitrogen transfer from oak seedlings facilitates Molinia growth: 15N pulse-chase labelling[END_REF] showed that Q. petraea seedlings transferred part of their N to M. caerulea even though oaks are non-fixing species. However, this hypothesis could be coherent as [START_REF] Michalet | Facilitation in communities: Underlying mechanisms, community and ecosystem implications[END_REF] suggested that "facilitated species may have negative effects on their benefactors", a phenomenon called antagonistic facilitation [START_REF] Bronstein | The evolution of facilitation and mutualism[END_REF][START_REF] Schöb | The context dependence of beneficiary feedback effects on benefactors in plant facilitation[END_REF].

Molinia caerulea is a Poaceae, family well known for its allelopathic action [START_REF] Favaretto | Allelopathy in Poaceae species present in Brazil. A review[END_REF]. Its inhibitory action on Quercus species was described first in 1960 by

Weise and later by Becker and Lévy (1983). [START_REF] Timbal | Étude préliminaire sur l'effet dépressif de la molinie (Molinia caerulea) sur la croissance et l'état mycorhizien de semis de chêne rouge (Quercus rubra)[END_REF] observed direct effects on red oak but also on the mycorrhizal community that in turn affected oak. Neither the harmful molecules nor their concentrations under natural conditions have been identified yet.

However, the responsible molecules seem to originate in the roots [START_REF] Fernandez | Below-ground nitrogen transfer from oak seedlings facilitates Molinia growth: 15N pulse-chase labelling[END_REF].

Mineralization and nitrification seem to be affected by allelopathy in many ecosystems and N uptake has shown to be susceptible to allelopathy too [START_REF] Nilsson | Separation of allelopathy and resource competition by the boreal dwarf shrub Empetrum hermaphroditum Hagerup[END_REF]). Vernay et al. might be amino acids due to the transfer pace in her experience.

Even if altered rhizodeposition was observed, oak mineral absorption has not been characterized thoroughly in presence of Molinia. Often only nitrate or ammonium is examined, and no data on absorption and rhizodeposition of amino acids is available. The question on the origin of the N transfer between neighboring oak and Molinia is not completely settled, and N fluxes are not quantified yet. Nor are the transfer pathways identified. But there are reasons to belief that N transporters are targeted by the allelochemicals.

Modeling living systems

Modeling has become an essential part in science [START_REF] Hacking | Representing and Intervening[END_REF]) and still gains in interest (Frigg and Hartmann 2006). Models are simplified representations of the reality that permit understanding of complex phenomena. All models are wrong [START_REF] Box | Science, and statistics[END_REF] i.e. they cannot represent the reality in a fully correct way. Still, some are useful when exploring different hypothesis that cannot be actually fully investigated experimentally. They often employ mathematical language, informatics and geometry for representation [START_REF] Pavé | Modélisation des systèmes vivants: de la cellule à l'écosystème. Ed Lavoisier Persson J, Näsholm T[END_REF] model. This depends of course on the complexity of the model but computerization of a model allows relatively fast and automated outputs.

Hypothesis and aim of this study

The first part of this study aims to lay the cornerstone for a growth model predicting dominance outcomes of interacting Quercus petraea and Molinia caerulea.

Materials and Methods

The presented work consisted in two parts: the first is the conception of an N-related growth simulation model for mixed grown oak and Molinia. The second is an experiment conducted in pots under semi-natural conditions where oaks were watered with an aqueous macerate from Molinia roots, supposed to mimic release of allelochemicals in natural conditions. N absorption by oak roots was characterized by labeling with stable nitrogen isotope ( 15 N). This part aimed to test if allelochemicals in the macerate target the N absorption from oak.

Model conception and implementation

A growth simulation model was designed for oak seedling N economics in presence of respond to the aim of the present work but ideas of e.g. rhizodeposition models (Kuzyakov andDormanski 2002, Molina et al. 2001), extended BIOME-BGC [START_REF] Pietsch | Modeling effects of hydrological changes on the carbon and nitrogen balance of oak in floodplains[END_REF], an oak regeneration model [START_REF] Davis | Survival, growth, and photosynthesis of tree seedlings competing with herbaceous vegetation along a water-light-nitrogen gradient[END_REF]) and Azodyn-IC [START_REF] Malagoli | Modelling nitrogen and light sharing in pea-wheat intercrops to design decision rules for N fertilisation according to farmers' expectations[END_REF]

Plant Material

Molinia caerulea was collected on January 27, 2021 from the French National Forest of Vierzon (47°16'4"N 2°07'1"E). Plants were dug including the main part of the root system and then stored in plastic bags to maintain humidity during transport to the laboratory. 60 tufts were potted on January 28, 2021 in 10L plastic pots. Concomitantly, 113 two-year-old

Quercus petraea seedlings coming from a tree nursery were potted.

Experimental site and design

The whole experience (illustrated in Fig. 12) was carried out at INRAE Clermont-Ferrand, 45°77'3''N, 3°14'3''E (394m a.s.l.). All plants were maintained under semi-natural conditions:

The pots remained in outdoor conditions. They were weeded manually and received irrigation from the beginning of March to avoid any water limitation. The soil used for both species had a typical loam texture (sand 51%, silt 29% and clay 20%), with a pH water of 5.95. The C:N ratio (9.2) indicated an active decomposition. The total nitrogen content was 2.1 g kg - 1 indicating that N was not a limiting factor. Nitrogen in the form of ammonium was 32.1 mg kg -1 and in the form of nitrate 123 mg kg -1 . Phosphorus, potassium and the cation exchange capacity were not limiting. Plants were potted separately to avoid resource-based interactions.

From January 28, 2021 to April 07, 2021, plants acclimated to pot and environmental conditions before start of new growth. By April 07, 2021, Molinia growth was sufficient to use grown roots for macerate, whereas bud burst was reached in 30% of the oaks (Fig. 13).

From April 07, 2021 treatments began: Molinia roots were excavated and a root macerate was prepared. This macerate was used to water half of the oak seedlings. The macerate is (2020), who observed an effect of macerates few weeks after treatment begin.

Action of the allelochemicals on N transport systems has been tested by the following.

After 6 weeks of treatment (the week of May 17, 2021), oaks were excavated and divided in aerial parts and roots. Soils containing root systems were coarsely sifted with a sieve of 2 mm mesh diameter. Roots were sorted by diameter. Fine roots with a diameter below 1 mm were selected for influx analysis. All fine roots were maintained under fresh and humid atmosphere to ensure absorption capacity [START_REF] Lucash | Estimating nutrient uptake by mature tree roots under field conditions: Challenges and opportunities[END_REF]) before carrying out influx analyses a few hours after harvest on the same day.

Macerate of Molinia root exudates

To convey Molinia allelochemicals to oak roots a root macerate was used. Molinia roots keep the capacity to exudate secondary metabolites into their environment several days after removal of the aerial parts [START_REF] Lucash | Estimating nutrient uptake by mature tree roots under field conditions: Challenges and opportunities[END_REF]. Intact roots from freshly excavated plants have been squeezed and placed in clean hermetic lunch boxes of 1L containing distilled water in an amount so that the final concentration of the solution was 2% (DW/V). Boxes have been placed in the dark at temperatures between 20 to 25°C to mimic natural conditions during 48h, the mean duration before inactivity of the roots. The macerate was applied to treat half of the oak seedlings, while others received an equivalent volume of distilled water.

Measurements

Monitoring of oak growth and budburst

Growth of oak seedlings was monitored weekly by measuring collar diameter of the stem and maximal height of aerial parts during treatment. First appearance of a leave in at least one bud were noted as budburst. Dry weights were assessed at oak plantation and harvest. After oak excavation, roots and aerial parts were dried for two days at 60°C in paper bags to assess dry weight. A fresh sub-sampling of roots was performed to check presence of ectomycorrhiza with stereo microscopy by the end of the experience. chosen because it has been shown to be directly absorbed by trees [START_REF] Warren | Uptake of nitrate, ammonium and glycine by plants of Tasmanian wet eucalypt forests[END_REF].

For the influx analysis in vitro culture pots containing 500mL of solution were used in the laboratory under temperatures between 20 and 25°C. All solutions were air bubbled to ensure oxygenation and homogeneity of nutrient availability in the solutions. Solutions of different nitrogen concentrations were prepared: 50µM and 500µM to assess HATS activity and 1500µM for assessing LATS activity. For each combination of N form and concentration the analysis was repeated using 5 different oak seedlings. Four different phases of the influx measurement can be distinguished:

1. Acclimation: Oak roots already in tea-bags were washed with 0.5mM CaSO 4 solution for 30 min to free roots from soil leftovers while maintaining membrane integrity (e.g. [START_REF] Boss | Effects of Divalent Cations and Polyethylene Glycol on the Membrane Fluidity of Protoplast[END_REF]Mott 1980, Breton et al. 1977). Then roots were placed for 1h in unlabeled solutions containing the tested concentrations of N. Roots acclimated to the ionic environment that they met later during the labeling phase. Equilibrium between apoplast and N solution was established and stable state of N influx was reached where N influx remains unchanged when left in the same N concentration.

2. Labeling with 15 N: In the following, tea-bags containing roots were placed in a solution similar to the previous except that N forms were 15 N-labelled. Corresponding concentrations of 15 N forms (K 15 NO 3 , ( 15 NH 4 )SO 4 or 15 Glycine) were used. Roots bathed in those bubbling solutions for 10 min (Kronzucker et al. 1995a).

3. Rinses (Fig. 15): Two steps of washing were performed, both in N solutions equal to those used for acclimation. The first lasted 5 sec and aimed to free roots from labelled N adsorbed to root surfaces. The second one lasted 2 min aiming to remove apoplastic 15 N. Timing was adapted from efflux studies to exclusively measure influx activities (Kronzucker et al. 1995(a,b), [START_REF] Britto | Studies of nitrogen absorption and assimilation in plants by use of N-13[END_REF].

4. Grinding and analysis of the 15 N/ 14 N ratio (Fig. 15): Labelled samples have been cut manually into smaller pieces before transferring into 10 mL plastic tubes. Then, automated ball mill was used to obtain between 3 and 4 mg of root powder, which has been filled into pewter microcapsules. These samples have been sent to INRAE SILVATECH for Isotope-Ratio Mass Spectroscopy (IRMS) analysis of total N and 15 N contents.

Calculations of budburst rate and relative growth rates

Relative budburst rate for a given time t was computed at population scale as follows:

𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑏𝑢𝑑𝑏𝑢𝑟𝑠𝑡 𝑟𝑎𝑡𝑒 (𝑡) = %𝑏𝑢𝑟𝑠𝑡(𝑡)-%𝑏𝑢𝑟𝑠𝑡(𝑡-1) %𝑏𝑢𝑟𝑠𝑡(𝑡-1)

(1)

14 Similarly relative height and diameter increments (%) were calculated for each seedling: Isotopic abundance (IA) is the ratio of 15 N over total N present in the sample. This can be described as

𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 ℎ𝑒𝑖𝑔ℎ𝑡 𝑖𝑛𝑐𝑟𝑒𝑚𝑒𝑛𝑡 = ℎ𝑒𝑖𝑔ℎ𝑡(𝑡)-ℎ𝑒𝑖𝑔ℎ𝑡(𝑡-1) ℎ𝑒𝑖𝑔ℎ𝑡(𝑡-1) (2)
𝐼𝐴 = 15𝑁 𝑎𝑚𝑜𝑢𝑛𝑡 𝑁 𝑡𝑜𝑡 𝑥 100. (6)
Influx rates of nitrate, ammonium and glycine (I Nit , I Amm and I Gly respectively, [µmol h - 1 g(DW) -1 ]) were determined with the following equation: IA solution is the isotopic abundance of the nutritive solution enriched with 15 N (IA=99%), MM 15 N the molar mass of the labeling isotope (in this case 15 g/mol) and d the duration of the influx monitoring (10 min). The underlying hypothesis for ( 7) is that the different N isotopes are absorbed without distinction from the transport systems.

Statistical analyses

All tests were performed under R Studio software (version 1.2.5033, using R edition 3.6.3). This is true for processing of PIAF data as well as data obtained during the described experiment. For the experimental part one root tea-bag represents an experimental unit. The effect of the different factors (N concentration, N form, treatment with Molinia root macerates) and their interactions on the variable (absorption rate) has been tested on the entire dataset. Significance levels were set to α = 5%. Normality conditions were verified with Shapiro-Wilk test and QQ plots, homoscedasticity with Bartlett test. ANOVA was performed and statistical groups were established with Tuckey's honestly significant different test.

Variation degree was calculated for each factor combination. Michaelis-Menten (Fig. 16) package "drc" [START_REF] Ritz | Dose-Response Analysis Using R[END_REF]. Differences in oak height and diameter increments and relative budburst rates were analyzed with Wilcoxon's sum rank test. DW analysis was performed with multi factor ANOVA where statistical groups were formed using pairwise ttest using Bonferroni correction.

regression

Results

Growth simulation model

In this study a conceptual simulation model for oak and Molinia growth was established (Fig. 17) based on the interactions for nitrogen in order to predict interaction outcomes. The present model can be referred to as a supply demand model. It is divided into four compartments:

oak, Molinia, their interactions and a compartment including processes from surroundings influencing the total amount of N in the system. All compartments comprise different types of variables and links. Variables are N pools, dry weights or calculable interaction indices.

Links connect the variables and are either logical relations or represent N flows. Almost all relations described by the model were found in literature for nitrate, some also for ammonium and a few data was available for other N forms.

An in and output compartment is included because surrounding biotic and abiotic conditions can provoke N import and export from the system. For instance, high atmospheric N concentrations can lead to N deposition in the soil and animals can insert N into the system via their excrements [START_REF] Bassirirad | Nitrogen deposition potentially contributes to oak regeneration failure in the Midwestern temperate forests of the USA[END_REF][START_REF] Rumpel | The impact of grassland management on biogeochemical cycles involving carbon, nitrogen and phosphorus[END_REF]. N can also be lost from the system through leaching (Gundersen et al. 1998), microbial activity (Puertes 2020) and volatilization [START_REF] Porporato | Hydrologic Controls on Soil Carbon and nitrogen cycles[END_REF]. These losses depend on various factors: leaching, for instance, depends on carbon dynamics, soil type and climate (Gundersen et al. 1998).

Microbial activity is influenced e.g. by water availability [START_REF] Porporato | Water Resources Research[END_REF] and presence of earthworms [START_REF] Binet | Significance of earthworms in stimulating soil microbial activity[END_REF]. Volatilization depends on N forms and their availabilities in the soil, soil pH, wind and availability of other nutrients such as phosphorous [START_REF] Porporato | Hydrologic Controls on Soil Carbon and nitrogen cycles[END_REF]. According to Silla and Escuerdo (2003) herbivory and browsing on the plants might be negligible as N outputs.

Interactions determine resource sharing

Three types of interactions have been observed between oak and Molinia [START_REF] Timbal | Étude préliminaire sur l'effet dépressif de la molinie (Molinia caerulea) sur la croissance et l'état mycorhizien de semis de chêne rouge (Quercus rubra)[END_REF][START_REF] Taylor | BIOLOGICAL F LORA OF THE BRITISH ISLES * Molinia caerulea ( L .) Moench[END_REF][START_REF] Fernandez | Below-ground nitrogen transfer from oak seedlings facilitates Molinia growth: 15N pulse-chase labelling[END_REF]) and all might be linked to N dynamics among oak, soil and Molinia: Competition strength decides on sharing of the soil N thus determining N absorption from both species. Even though the strength of N competition has been shown to depend on multiple factors such as available soil N, specific root length and root-shoot ratio of the species (e.g. Coll et al. 2004[START_REF] Lajtha | Nutrient uptake in eastern deciduous tree seedlings[END_REF][START_REF] Vernay | Photosynthesis capacity of Quercus petraea (Matt.) saplings is affected by Molinia caerulea (L.) under high irradiance[END_REF],2018), a simplification is desirable to prevent complexification of the model. An integrative competition index based on dry weight information has been chosen [START_REF] Markham | Measuring plant neighbour effects[END_REF]. The index related DW of the two species, describing strength and direction of competition (Tab. 1).

Resource sharing is revised in favor of Molinia by antagonistic facilitation:

supplementary exudation of N forms by oak in presence of Molinia creates an N transfer towards the competitor [START_REF] Fernandez | Investigating the role of root exudates in the interaction between oak seedlings and purple moor grass in temperate forest[END_REF]). However, this transfer might be (at least predominantly) independent from soil and is thought to take place at least partly through

Mycorrhizae network [START_REF] Fernandez | Mécanismes écophysiologiques impliqués dans les interactions antagonistes entre le jeune chêne sessile (quercus petraea (Matt.) Liebl.) et la molinie bleue[END_REF].

Allelopathy is the third type of interaction that has been observed at least partly between these two species. The presence of allelochemicals released from Molinia reduces indirectly the dry weight of oak [START_REF] Timbal | Étude préliminaire sur l'effet dépressif de la molinie (Molinia caerulea) sur la croissance et l'état mycorhizien de semis de chêne rouge (Quercus rubra)[END_REF]. Released chemicals might inhibit N transport systems in oak roots and thus reduce N absorption from oak [START_REF] Fernandez | Investigating the role of root exudates in the interaction between oak seedlings and purple moor grass in temperate forest[END_REF].

Belowground N flows

The N flows in oak and Molinia are described by two separate plant compartments. Directly connected to soil N is the N uptake from oak and Molinia. Information from literature is not sufficient for a distinction of the different N forms in particular for the oak compartment although it would be important at this level. In both species, uptake is modeled as difference between absorption and rhizodeposition of the plant [START_REF] Mata | Influx, efflux and net uptake of nitrate in Quercus suber seedlings[END_REF]. Absorption has been shown to depend on N demand and sharing of available soil N between species (Tab. 1).

Rhizodeposition in trees is dependent on the soil type, net primary production and nitrogen use efficiency [START_REF] Scandellari | Assessing nitrogen fluxes from roots to soil associated to rhizodeposition by apple (Malus domestica) trees[END_REF](Scandellari et al. , 2008)), variables that would lead to high complexification of the model. It was implemented based on measured data from Vernay 2017.

One important factor determining N uptake is plants demand. In grass species, it is typically represented as N nutrition index (NNI) [START_REF] Lemaire | N Uptake and Distribution in Plant Canopies BT -Diagnosis of the Nitrogen Status in Crops[END_REF]. NNI is the ratio between current N content in the plant and N content deduced from a critical N dilution curve.

Whereas actual content is predictable, critical dilutions for neither of the species are published. Perennial rye grass dilution curve [START_REF] Gislum | Validity of accessible critical nitrogen dilution curves in perennial ryegrass for seed production[END_REF] (Fig. 18) was used for Molinia.

After uptake, internal N dynamics of the two species differ.

Molinia and oak have different internal N dynamics

While N uptake in oak contributes directly to the plants N content, that itself constitutes the source for concomitant storage and growth [START_REF] Glatzel | Mineral nutrition and water relations of hemiparasitic mistletoes: a question of partitioning. Experiments with Loranthus europaeus on Quercus petraea and Quercus robur[END_REF], Molinia N uptake is completely used for growth [START_REF] Tomassen | Stimulated growth of Betula pubescens and Molinia caerulea on ombrotrophic bogs: Role of high levels of atmospheric nitrogen deposition[END_REF]. Whereas, in the oak compartment uptake and content are directly related, in Molinia they are not. Uptake in the model still influences the simulation of N content indirectly through growth simulation and resulting dry weight.

N storage in Molinia takes place exclusively by resorption from senescing tissues in autumn and is remobilized for early growth in spring [START_REF] Tomassen | Stimulated growth of Betula pubescens and Molinia caerulea on ombrotrophic bogs: Role of high levels of atmospheric nitrogen deposition[END_REF]. Stored N amount is negatively correlated with soil N availability [START_REF] Van Heerwaarden | Internal nitrogen dynamics in the graminoid Molinia caerulea under higher N supply and elevated CO2 concentrations[END_REF]. Oak N storage is built up from an N pool regrouping uptake and resorbed N during senescence.

In both species, growth (mass increment) can therefore be promoted from storage N or uptake. Timing depends on phenology and species. Growth ultimately determines dry weight, which reflects the outcome of the present interaction model. compartments and influences resource sharing. This compartment is greatly lacking knowledge except for competition that is well established when occurring alone. Although, it is difficult to determine when co-occurring with facilitation and allelopathy because there is only few information about the way and extent in which these model compartments could interact [START_REF] Fernandez | Investigating the role of root exudates in the interaction between oak seedlings and purple moor grass in temperate forest[END_REF]. Facilitation is another variable only based on relative values on a relatively coarse time-scale. It is not clear on which factors facilitation strength depends.

Also, there is no information if allelopathy from Molinia could target the N dynamics of oak and if so in which extent. Data on the role of allelochemicals and their concentration are only exploitable for growth simulation if strong hypotheses are made. Observation of DW decline through allelochemicals has been made for Q. rubra [START_REF] Timbal | Étude préliminaire sur l'effet dépressif de la molinie (Molinia caerulea) sur la croissance et l'état mycorhizien de semis de chêne rouge (Quercus rubra)[END_REF]) as well as for Q. petraea [START_REF] Fernandez | Investigating the role of root exudates in the interaction between oak seedlings and purple moor grass in temperate forest[END_REF]). However, either kinetics of this reduction is established nor the putative dependency on the concentration of chemicals [START_REF] Zhang | Effect of allelopathy on plant performance: a meta-analysis[END_REF].

The models in and output compartment substantially lacks knowledge. Input is relatively well studied but losses from the system such as leaching and volatilization lack quantification (Gundersen 1998). Losses therefore cannot be simulated accurately.

The whole model was implemented making hypotheses about lacking knowledge (software available on request) and gave realistic results (Fig. 19) with oak saplings that gain in DW during spring and summer and loose a great part of that gained DW due to leaf senescence. In Many model entities were considered as not sufficiently studied. The experiment carried out in this work aimed to contribute to a better understanding of the simulated system.

More precisely it was investigating if N transport systems in oak roots were actually targets of moor grass originated allelochemicals.

Molinia root extracts influence phenology and height growth of oak saplings

During treatment oak shoot height, collar diameter and budburst rates were assessed weekly. Interestingly, there was a significant effect of treatment on the budburst rate (p = 0.049). While control plants presented budburst rates of 0.31 on average during the experiment, treated oaks' average is only about half of this value (Fig. 20a). By the end of the experiment 85% of control oaks and only 62% of treated ones had leaves.

Relative height increment (RHI) (Fig. 20b) shows a significant negative response to treatment (p = 0.0207).While control plants had RHI of 1.58% ± 0.19 (SD), treated showed values of 1.00% ± 0.17 (SD). Inspecting absolute height values in function of time (Fig. 21), a significant treatment effect can be observed beginning in week 4 (p = 0.004), when control plants measure 86.32cm ± 1.72 (SE) and treated 81.50cm ± 2.33 (SE). Relative diameter increment did not vary significantly according to treatment (data not shown). Dry Weight (DW) of oak plants was assessed after sampling for influx analyses. Multifactor ANOVA was performed on DW data from leaves, stems and roots using harvest date, treatment and plant compartment as parameters. No significant differences were observed for harvest date or for treatment, whereas there was a substantial difference (p = 2 x 10 -16 ) for compartments. No significant effect of treatment on root-shoot ratio can be reported (data not shown).

N absorption kinetics respond to treatment with Molinia macerates

Nitrogen influx capacities of oak roots were assessed through establishment of kinetics of 15 N-nitrate, 15 N-ammonium and 15 N-glycine influx. All roots successfully absorbed supplied nitrogen independently of treatment.

A positive response was also observed depending on substrate concentrations (p = 4.55 x 10 -10 ). Influx rates under low concentrations were low and rose quickly with rising concentration. Further concentration increase led to slowdown of this increment ending in a plateau when concentrations reached 1500µM. Therefore dynamics were presumed to follow Michalis-Menten function.

Further, Michaelis-Menten regression was performed to obtain values for maximal influx capacities (V max ) and Michaelis-Menten Constants (K m ) describing the affinity of the transport systems for their substrate. Regressions fitted the data relatively well since residual standard error (RSE) values were small compared with calculated influx rates except for nitrate, where RSE were highest compared to influx rates but remained acceptable. P-values for V max computation were all smaller than 0.025.

Influx rates clearly responded to different chemical forms (p = 2 x 10 -16 ). One could state that ammonium had the highest influx capacities, with V max of 80.69 µmol/h/g(DW)

for control plants ( Measured nitrate absorption rates of treated roots were unquestionably higher than in roots of control plants at the supplied concentrations, whereas influx for both was very small (Fig. 22A). This was true for the three tested concentrations. Glycine influx instead showed no significant response to treatment with macerate (Fig. 22B). Ammonium influx rates did not respond to treatment with Molinia macerate, except for 500µM solution, where the difference between treated and control was statistically convincing (Fig. 22C).

Discussion

Molinia macerate treatment efficiency

Overall treatment effect on relative budburst rates can be observed and relative height increment responded significantly after 4 weeks to treatment with Molinia extracts. To my knowledge this is the first study to report budburst lag in oak due to allelopathic chemicals from Molinia. Collar diameter did not depend on treatment. Diameter assessment is limited by measurements carried out only in north-south direction. Supplementary assessments in eastwest direction could raise precision.

The fact that no response of DW to treatment was found is consistent with the absence of response in diameter as in spring primary growth is predominant compared to secondary growth which takes place later in the year. Results for DW and root-shoot ratio also are in line with literature [START_REF] Fernandez | Investigating the role of root exudates in the interaction between oak seedlings and purple moor grass in temperate forest[END_REF]. Another variable influencing the outcome of treated plants might be the relatively short time span of the experience.

One can conclude that treatment was effective early on height increment and budburst but perhaps time scale was too small to reveal DW and diameter response.

15 N influx rates respond to N source, concentration and allelopathic treatment

Oak roots presented different absorption rates according to supplied nitrogen sources. This result is in line with the literature. According to [START_REF] Warren | Uptake of nitrate, ammonium and glycine by plants of Tasmanian wet eucalypt forests[END_REF], plants prefer N forms that they meet most in their natural habitats. Oaks interacting with moor grass are mainly found on acidic soils which supply nitrogen predominantly in form of ammonium (Singh et al. 2003). Recording highest absorption capacities for ammonium is therefore not surprising.

A completely new observation is that the glycine absorption capacity in oak is higher than its capacity to absorb nitrate. These results are in line with the observations by [START_REF] Warren | Uptake of nitrate, ammonium and glycine by plants of Tasmanian wet eucalypt forests[END_REF] who suggested organic N forms to be key nutrients for late successional species. Oak absorbed even higher amounts of glycine compared to values reported by them for Eucalyptus (mean 4.4 ± 2.6 µmol/h/g(DW) at substrate concentration of 100µM) despite little development of plants used for 15 N-influx assessment in my study. This justifies that the study of organic N forms should not be enhanced in order to elucidate the processes in N nutrition. Nitrate influx rates were inferior to others and in line with results documented for Q. suber [START_REF] Mata | Influx, efflux and net uptake of nitrate in Quercus suber seedlings[END_REF].

As expected, absorption rates responded to supplied concentrations in all N forms, and dynamics followed Michaelis-Menten kinetics. Being aware of the depressive effects of Molinia macerate on oak morphological and phenological features, the findings on nitrogen absorption rates are surprising: Treatment had stimulatory effect on mineral absorption. This could be explained by different factors:

Possibly, N transport systems are induced in order to compensate for a lack of soil N or water uptake, irrigation was stopped 10 days before harvest. As N and water cycles are closely related, roots would increase their N influx to ensure N absorption when water uptake is possible. Potentially, Molinia root macerate was altered in the present study as a result of the relatively early execution of the experiment in the year (from early budburst) and/or the particularly cold temperatures this year (extreme frost event in April). Experiments from other authors were conducted mainly in summer [START_REF] Fernandez | Investigating the role of root exudates in the interaction between oak seedlings and purple moor grass in temperate forest[END_REF], when both species are actively growing. Season and temperatures could affect composition and/or reduce allelochemical concentration of the macerate because root systems of Molinia were not well established but still in their first growth period. The macerate might contain more turnover residues than exudates coming from active roots. [START_REF] Zhang | Effect of allelopathy on plant performance: a meta-analysis[END_REF] stated that allelopathic effects were strongly concentration dependent: molecules that provoke inhibitory effects on their target plants often have at least partly stimulatory effects when present in low concentrations. This possibility would reinforce the hypothesis of mineral N transport systems as direct targets of the allelochemicals produced by Molinia but instead of the supposed inhibitory effect a season dependent effect could be conceivable. Another hypothesis could be that responses differ on phenological stage. This means that budburst of oaks might be inhibited as a "side effect" of the chemicals and that if there are already leaves, stimulation of N influx or affinity of N transport systems can take place.

In contrast to mineral N forms, organic N absorption did not respond significantly to the treatment. Comparison between treated and control should be cautious, because plants used to asses organic N absorption were not homogenous in terms of budburst. Control plants presented leaves whereas treated did not.

Decreased 15 N-ammonium and 15 N-glycine maximum influx capacities

In contrast to average 15 N influx rates at supplied concentrations, maximal absorption capacities are decreased by treatment concerning glycine (33%) and ammonium (51%).

However, V max of nitrate is increased by treatment (52%). This means that at high N availability less glycine and ammonium and more nitrate could be absorbed when treated.

Maximal absorption capacities were thus lowered by treatment for the quantitatively most important N sources. This argues in favor for the hypothesis that moor grass root extracts inhibit N transport systems in oak. It also explains the repressive effect on relative height increment.

Ambivalence between results for absorption rates and maximal influx capacities makes it difficult to explain effects on oak height and budburst. Discordance could originate from a depressive effect on K m (values not significant). It would be interesting to have more data points by testing more different concentrations in order to obtain significant values of Michaelis-Menten constant. This would give information about the affinities of the different transport systems.

Surely reduced are N absorbing ectomycorrhizae (Fig. 23) in this experiment.

According to [START_REF] Fernandez | Mécanismes écophysiologiques impliqués dans les interactions antagonistes entre le jeune chêne sessile (quercus petraea (Matt.) Liebl.) et la molinie bleue[END_REF], mycorrhization of oaks receiving Molinia exudates is reduced, and species composition of symbiotic fungi is altered in a disadvantageous fashion for oaks N uptake. If solely mycorrhizal N transport systems were targeted, lack and modification of mycorrhizal communities would be a possible consequence which in term could explain the lower influx capacities of treated roots and an enhancement of high affinity transport systems.

Modeling interaction between oak and moor grass needs more information

The model established in the beginning of this study fulfills its aim to lay the cornerstone for a more holistic model. Though, interactions between the two species are more complex than assumed for model creation. As we have seen in the experimental part of the present work, allelopathic action is not sufficiently elucidated for getting ideal simulations. The model needs now to be upgraded by the information gained in the experiment and other experiments should be carried out to improve the model further. Concretely, allelopathic links between oak and moor grass need to be revised in order to allow stimulatory action on nitrogen uptake capacities. Operation mode of allelochemicals needs to be identified and the role of mycorrhizal hyphae should be detailed.

Besides, more information is needed to distinguish different N forms in the model.

Another important component would be the inclusion of water dynamics in the system because water and nitrogen status are closely related. After integration of these compounds one could think about an implementation of interactions considering light for example.

Additionally, it would be worthwhile to develop a variable, which assigns a phenological state to each time step.

Experimental data revealing discordances with the model, underline perfectly the complexity of the system and the poor knowledge about interference mechanisms on one hand side and the need to devote further investigations on the subject on the other.

Nevertheless, the constructed model allows becoming aware of the functioning of N dynamics between oak and Molinia. One can clearly see that the two species have different N dynamics inside the plant. While oak allocates a great part of N taken up to storage in autumn [START_REF] Bazot | Distribution of non-structural nitrogen and carbohydrate compounds in mature oak trees in a temperate forest at four key phenological stages[END_REF], Molinia adjusts its storage capacity depending on available soil N [START_REF] Van Heerwaarden | Internal nitrogen dynamics in the graminoid Molinia caerulea under higher N supply and elevated CO2 concentrations[END_REF]. Also, moor grass has no direct conversion of N taken up to storage N (Heerwaarden et al. 2005). The synthesis of storage forms and subsequent remobilization cost more energy than direct use of absorbed resources. This might be a disadvantage to oak interacting with Molinia.

Conclusion and Outlook

The aim of this study was dual: Firstly, nitrogen transport systems for nitrate, ammonium and glycine in Quercus roots were tested as possible targets of allelochemicals contained in root extracts from Molinia caerulea. An inhibitory effect of those molecules was presumed. Indeed, results reinforce the assumption of allelochemicals targeting N absorption. Although, mode of action might be more complex than supposed Increase in nitrate and ammonium influx rates was observed. As well, altered influx capacities (elevated for glycine and ammonium, reduced for nitrate) have been documented. N transport systems are undoubtedly responding to treatment with Molinia macerate but a clearer identification would be needed for understanding: Other mechanisms could be targeted too, like regulation of growth regulators and nutrient storage. Are targeted transport systems originating from the plant itself or from symbiotic mycorrhiza? Are targets eventually only low affinity transport systems or are high affinity transport systems as well altered? Does the effect on N fluxes depend on season or temperature? In order to elucidate those and related problems several actions can be suggested:  The model should be adjusted to the observations following experimental work of this study. This would help to test for possible seasonal effects and contribute to a more useful prediction of interaction outcomes between the two species.

 The direction of the treatment effect on N dynamics is not completely clear in this study.

Repeating the same experiment with more biological replicates and more different labeling concentrations would lead to trustworthy Michaelis-Menten constants, indicating affinity of the targeted transport systems. This could show which type of transport systems is affected and in which way or if HATS and LATS are affected at the same time.

 N transport responds to treatment with macerate in the present study. This result could be validated by a different approach such as RNAseq or an experiment using mutants for the concerned transport systems. RNAseq would have the advantage to give a more global impression of the plants response to macerate irrigation because other putative targets such as aquaporins could be tested at the same time. Additionally, RNAseq could be followed by geneontology which would permit a integrative comprehension of oaks response to Molinia macerates not only on a genetic basis but also involving linked biological mechanisms.

 An experiment could be conducted similar to the one presented, where treatment periods vary in function of the season. This would show if direction of effects depends on season and if yes in which way. Also, it could show eventually effects on leaf fall and dormancy.

 In situ hybridization would allow the localization of altered transport systems and distinction of mycorrhizal and plant proper N transport systems and so if both are affected by Molinia extracts or only one of them.

 Identification of allelochemicals contained in the root extracts would help identifying their targets. It would be conceivable that soil N availability for oaks is targeted or that mechanisms downstream the absorption are affected such as integration of N in more complex molecules.

Further, this study encourages all other experiments that might be conducted to become aware of the role of mycorrhiza between the two studied species, the distinction and quantification of the different N forms in the N cycle, and especially the role of organic N sources in forest ecosystems. Those are too numerous to develop here but all contributing to a more integrative understanding of N fluxes and sharing between species and possibly helpful to improve (Fig. 24) the model established for a better understanding of oak regeneration problems.

Skills developed during the internship at PIAF laboratories

During my internship I had various tasks (field work, culture monitoring, laboratory analysis and PC work). I perfected my organizational skills and managed to combine these very different tasks in an efficient time table. I conceptualized and carried out an experience following a long term schedule, which I adapted to external disturbances. Occasionally, I dealt with hard time pressure while keeping rational and precise in my work.

I improved my scientific approach. That means: I am able to formulate a scientific problem, to understand and obtain a synthetic view of bibliography from a specialized field. I can formulate a well-founded hypothesis, evolve and carry out a strategy to test this hypothesis, analyze result data and present and interpret results.

Likewise I applied my knowledge from university lectures. This concerns particularly the course units about ligneous, herbaceous and modeling. Furthermore I extended those competences by conceptualizing and implementing my own model using the interface VenSim. Additionally I perfected my competences acquired in the first year of my master's degree such as statistical analysis with R software.

A supplementary laboratory technique I acquired, is the handling of stable isotopes (storage, use and disposal). In terms of plant cultivation, I learned to monitor growth and phenological state and to evaluate hydrological state and abiotic influences such as freezing of trees and grass cultures.

I learned to integrate a workplace in face-to-face conditions in a country that is foreign to me. Especially in the beginning of my internship I improved my abilities to manage all contacts with the professional world being in home office. In the last weeks I also interconnected with experts off my specialty working on an interdisciplinary project. I learned to determine grass species "off-season" without any green tissues.

The internship clearly reinforced my wish to continue my education with a PhD.

  INRAE is a French public Research Institute placed under the double guardianship of the Ministry of Food, Agriculture and Fishing and the Ministry of Higher Education and Research. It is the world's first research organism focussing on agriculture, food and environment. By its size (>10,000 employees) it is the most important agronomic research organism in Europe. The aim of INRAE is to use research to guide the emergence of sustainable agricultural and food production systems. INRAE also wants to dedicate their science to life, humans and the planet. This includes finding solutions to the most pressing concerns like inter alia climate change, loss of biodiversity or depletion of fossil fuels.

FigureFigureFigureFigure

  FigureSurvival of tree seedlings depending on grass biomass

Figure 1 :

 1 Figure1: Seedling survival of Brazilian tree species correlates negatively with grass biomass[START_REF] Hoffmann | The invasive grass, Melinis minutiflora, inhibits tree regeneration in a Neotropical savanna[END_REF]

Figure 2 :

 2 Figure 2: Distribution of Molinia caerulea over northern hemisphere[START_REF] Hultén | Atlas of North European vascular plants north of the Tropic of Cancer[END_REF]

Figure 3 :

 3 Figure 3: Plant competition as characterized by Goldberg (1990), corresponding to the definition of below-ground resource competition in the present work (Figure from Casper and Jackson 1997)

Figure 4 :

 4 Figure 4: Resource use strategies and their presence in different environments according toGrimes theory[START_REF] Clokie | Rethinking Phage Ecology by Rooting it Within an Established Plant Framework[END_REF]

Figure 5 :

 5 Figure 5: Schematic illustration of the prediction of competitive outcomes between two species limited by two essential resources( R1, R2) according to Tilmans theory: A and B are the consumption curves of species A and B for the two resources. Six different situations are possible: 1. Resources are too scarce, neither A nor be can exist, 2: Only species B can exist, 3: species B outcompetes A, 4: coexistence, 5 species A outcompetes B, 6: only species A can exist (McGinley 2011)

5 5

 5 Most studies on facilitation have been carried out relatively recently. A common example is N transfer between plants. But as it has many variables and implications, itreclaims further research. The past chapters focused on resource driven interactions, the following will concentrate on interactions based on secondary metabolites.

Figure 6 :

 6 Figure 6: Schematic illustration of possible transfer pathways for allelochemicals to their target[START_REF] Zhang | Effect of allelopathy on plant performance: a meta-analysis[END_REF]

Figure 7 :

 7 Figure 7: Schematic representation of membrane bound nitrogen transport systems responsible for absorption in Arabidopsis thaliana roots[START_REF] Nacry | Nitrogen acquisition by roots: Physiological and developmental mechanisms ensuring plant adaptation to a fluctuating resource[END_REF]. Ammonium is taken up by the ammonia transporter (AMT) family comprising High-affinity transport systems (HATS). Nitrate absorption is ensured by two groups of nitrate transport systems (NRT) where NRT1 are low-affinity transport systems (LATS) and NRT2 HATS. NRT1.1 is also a LATS when not phosphorylized. The function of NAR2.1 has not been elucidated but the protein is necessary for the activity of NRT2. For the uptake of amino acids proteins from the AAP family, LHT1 and ProT2 have been identified. DUR3 is an urea HATS but also involved in internal urea transport. TIPS are involved in urea storage rather than uptake. NIPS seem to be the most important passive transport systems for urea. Big letters indicate major roles in uptake. Question marks stand for results that have not been confirmed..

Figure 8 :

 8 Figure 8: Nitrate influx rates into roots of white spruce as a function of soil nitrate concentration(2.5-1000µM). The curve is biphasic representing the functioning of HATS and LATS separated with dotted line.(Kronzucker et al. 1995)

Figure 9 :

 9 Figure 9: Model of nutrient cycling in forest ecosystems[START_REF] Rahman | The Role of Quantitative Traits of Leaf Litter on Decomposition and Nutrient Cycling of the Forest Ecosystems[END_REF]

  Organic and mineral forms of N can be absorbed through different transport systems discriminating concentration of available soil N. Regulation of the transport can be systemic or local. N absorption is an important step in the N cycle but N is also returned from plants into the soil. Organic and mineral forms of N can be absorbed through different transport systems, discriminating the outer concentration of available N. The regulation of the transporters can be systemic or local. N absorption is an important step in the N cycle but several N losses from the plant can also occur.N can be released by the plant. It gets back into the environment through dead matter decay and exudation. While absorption is mainly an active process, exudation can take place also passively and molecules can be more complex. The next chapters will focus on interactions between M.caerulea affecting N uptake of Q. petraea.

Figure 10 :

 10 Figure 10: Seedling of sessile oak in a Molinia infested patch (Vernay et al. 2019)

(Figure 11 :

 11 Figure 11: Different steps in mathematical model conception of biologic systems. Results are in rectangular boxes, procedures (dynamic processes) in rounded rectangles. Not each modeling project needs the whole pathway described in this scheme.Figure according to Pavé (2012).

  so model makers need interdisciplinary skills. Models aim to facilitate understanding, define, quantify, visualize, simulate and predict. For instance models are useful when schematizing flower morphology, predicting climate change or understanding social networks. Modeling contains various tasks (e.g. Fig.11) identification of the factors and processes involved in the studied phenomenon, dissociation from those that are not relevant, reduction so that only important details remain (depending the research question addressed) and decomposition of the studied process into individual segments. The model maker needs to aggregate these segments to a "big picture" representing the full system he analyzes before abstraction of the reality. For modeling living systems, the first step is to analyze the biological situation and to develop a synthetic view over the studied processes. This allows in the following to choose the most relevant formalizations and to ensure minimal digression from the biological reality. When parameters and variables are identified, the processes are formalized through physical, chemical and biological laws. This leads to a functional diagram that might be translated into a mathematical language. Implementation can be important for use and interpretation of the 10 8 Q. petraea and M. caerulea are plant species that closely interact. Besides competition for nitrogen and facilitation of Molinia through N transfer from oak, allelopathy has been observed between the two species. Inhibitory effects in oak are caused by allelochemicals from Molinia. Their target might be the N transport systems in oak roots.

  The purpose was to conceptualize a growth simulation model taking into account the different interactions between those species peculiarly linked to nitrogen resources. Integration was attempted into a visual representation of the complex mechanisms observed from data and literature. The ambition was to identify possible lacks of knowledge and to explore their relative effects.Subsequent to the observations concerning inhibitory allelopathic action from M. caerulea on Q. rubra[START_REF] Timbal | Étude préliminaire sur l'effet dépressif de la molinie (Molinia caerulea) sur la croissance et l'état mycorhizien de semis de chêne rouge (Quercus rubra)[END_REF]) and Q. petraea(Fernandez el al. 2021), the experimental part of this study aims to elucidate a putative target of the allelopathic compounds. A great indication was the altered N nutrition of oak monitored by[START_REF] Vernay | Photosynthesis capacity of Quercus petraea (Matt.) saplings is affected by Molinia caerulea (L.) under high irradiance[END_REF] and[START_REF] Fernandez | Below-ground nitrogen transfer from oak seedlings facilitates Molinia growth: 15N pulse-chase labelling[END_REF]. I hypothesized that allelochemical compounds of Molinia roots target (inter alia) nitrogen transport systems in sessile oak. More precisely, I wanted to investigate (i) whether transport system activities for N absorption are decreased and (ii) which influx among inorganic and organic nitrogen in oak roots or associated Mycorrhiza might be inhibited by allelochemicals.

Molinia.Figure 12 :

 12 Figure 12: Timeline of the experimental part of the study, excavation of Molinia, root maceration and watering with macerate was repeated six times.

Figure 13 :

 13 Figure 13: Some of the oaks at treatment beginning (early April 2021) Tubes serve irrigation to field capacity. 30% of oaks passed bud break at treatment start (right).

  were used to conceptualize the presented model. This method was complemented by considerations of the author and data assessed during the PhD theses of Marine Fernandez and Antoine Vernay (data available from PIAF laboratory). The result is a model interlacing different N fluxes and theoretical interaction indices with a morphological trait, dry weight of both species. Each established link was then separately reviewed in order to get a mathematical description when possible. A ranking was established according to the state of the art on the concerning model entity. The whole model was implemented with VenSim simulation software (Ventana Systems, Inc.) Strong hypotheses had to be made in order to implement the relations lacking information.

Figure 14 :

 14 Figure 14: Experimental setup for 15 N absorption potential measurements with different 15 N sources (nitrate, ammonium and glycine) among different concentrations (left) and subsequent steps (top).

3. 5 . 2 Figure 15 :

 5215 Figure 15: Succession of steps and experimental setup established after labeling. Method was used on excised oak roots.

Figure 16 :

 16 Figure 16: Graphical (left) and mathematical (right) description of Michaelis-Menten reaction kinetics with reaction rate (v) maximal reaction rate (V max ), Michaelis-Menten constant (K m ) and substrate concentration ([S]).

  DW roots respectively representing nitrogen content (%DW) and DW [mg] of the roots. The amount of 15 N in the sample ( 15 N amount , [µg]) was completed using the equation 15 of the labelled samples (IA sample ) and natural ones (IA reference ).

𝐼 = 15

 15

  Figure 117: Diagram of a model simulating growth of oak and Molinia interacting during early phase of oak regeneration. Grey boxes represent

Figure 18 :

 18 Figure 18: Critical nitrogen dilution curve for perennial ryegrass described by Gislum and Boelt 2009) following the equation 6.36*(dry weight / 10) -0.71 .

4. 5 A

 5 model that shows the substantial lack of knowledge about N fluxes A ranking was established according to the state of the art of each model entity and relation estimating current understanding. According to D'Odorico et al. (2003) a daily time step would be ideal for this type of model. This was taken into account for the ranking, which allowed distinction of three classes: well established, already possible to implement and without sufficient information. Only few elements of the model are well established such as oak dry weight evolution, N uptake in both species and N demand of Molinia. A great majority of entities and links are relatively easy to implement or need little parametrization. This is particularly true for the plant compartments. Still, there are some entities that lack sufficient information. No information was found about the storage capacities in Molinia and very few on the amounts resorbed from foliage. Resorption has no sufficient temporal resolution for meaningful implementation (seasonal time steps). Only relative values on long-term are reported for rhizodeposition of both species, not sufficient for an implementation of the dynamics. Another crucial lack concerns the absorption of N from oak. This process is documented based on relative values on a seasonal time-scale. For an implementation a finer scale would be required and the determining factors should be identified. The interaction compartment is the most theoretical one in this model. It contains variables that reflect the three different types of interactions and the common resource pool of the soil. It takes into account a great number of variables from the plant

Figure 19 :Figure 20 :

 1920 Figure 19: Simulated dry weights for oak (top) and Molinia (bottom) for one year for initial dry weights of oak 12 g and Molinia 15 g and an initial soil N of 180 mg/kg. Note the different scales on the y-axes. X-axis is scaled in weeks

contrast,

  Molinia gains in DW beginning in week 10 (earlier than oak). It grows very fast until week 15, and then growth slows down and stops after week 45. It gains in DW during autumn although it loses its leaves, observation coherent with (Heerwaarden et al. 2005).

Figure 21 :

 21 Figure 21: Treatment effect on oak stem height during treatment phase of the experience. Asterisks indicate significant differences between control and treated plants at one time point.

Figure 22 :

 22 Figure 22: Kinetics of influx rates of 15 N-nitrate (A), 15 N-glycine (B) and 15 N-ammonium (C) in roots of oak. Red dots stand for values obtained from control plants, blue ones from treated with Molinia root extract. Lines represent Michaelis-Menten regression of control plants (red) and plants treated (blue). Regression lines are accompanied by residual standard errors (RSE). P-values indicate differences between treatments at same concentrations of 15 N. Lower case letters show significance levels between concentrations for the same treatment modality. Note that y-axis scales are very different between the tree 15 N sources.

Figure 23 :

 23 Figure 23: Comparison between fine roots (pictures take in 12x) of control plants (top) and treated plants (bottom) by stereomicroscopy. Control plants presented mycelium mantle covering fine roots while treated plants did not.

Figure 24 :

 24 Figure 24: Complementarity of models and experiments. Black boxes represent steps undertaken (at least partly) in this study. Orange boxes show steps that remain to be performed for model fulfilling its aim entirely. Scheme adapted from Colbach (2006).

Resource competition has been studied for long. However, resources are manifold and theories are not always validated. In particular belowground competition needs more attention because of many unanswered questions. This chapter focused on negative plant-plant interactions, although stimulatory interactions exist. Resource competition has been studied for long. However, resources are manifold and theories are not validated even though they might complete each other. In particular below- ground competition needs more attention because of its importance in dominance establishment and great number of unanswered questions. This chapter focused on negative plant-plant interactions, although stimulatory interactions exist.

	proliferation, fine root demography, lifespan, branching pattern) and symbiosis with soil
	microorganisms like mycorrhiza that are crucial.
	. Their success is based on
	favorable root morphology (Picon-Cochard et al. 2006). Competition for water can result in
	reduced growth. N competition is decisive in N depleted environments: e.g. N capture
	efficiency may determine species dominance (Vernay et al. 2016).
	In general, outcome of resource-based relationships depends on several mechanisms
	(Casper and Jackson 1997). The different processed determining nutrient availability are:
	mass flow and diffusion, chemical form, production rate of absorbable chemical forms as well
	as retention by clay-humic complex, root interception i.e. number and density of uptake
	transporters, affinities for nutrients, the minimal usable concentration (i.e. nutrient
	concentration under which nutrients cannot be taken up), plasticity of the roots (i.e.

What we do not understand (yet)

	Despite advanced knowledge on competition for resources, a great number of questions are
	still unanswered: for example, there are still difficulties in defining if an individual is included
	into the neighborhood of a plant or not. Neighboring does not mean physically near but
	closely interconnected by e.g. root intermingling or soil microbes. Neither is it possible to
	predict how soil microbes alter competition between plants. Fundamental questions are still
	open because of the dependency on numerous factors such as species, climate and resources
	(Jensen et al. 2011) and therefore needs further research.
	2.1.2 Facilitation
	Definition
	Facilitation describes positive interactions of one species enhancing growth or survival of
	another. In general, they can be classified into direct and indirect. Direct facilitation describes
	a direct positive impact on availability of limiting resources, elimination of potential
	competitors, introduction of beneficial organisms or protection from herbivores. All other
	facilitative interactions are called indirect e.g. plant A exudes an amino acid that can be
	mineralized by microorganisms in the soil and through what the mineral N availability for
	species B is enhanced

Table 1 :

 1 VenSim equation codes for the models "key" entities with the references that influenced the choice of equation.

	Model entity	Equation code for oak	Equation code for molinia	Bibliographical
				inspiration
	N Status	N content oak	N content molinia	Gislum and Boelt
		+ N storage oak	/ critical dilution	2009, Glatzel
		-senescence		1983, Lemaire and
				Gastal 1997
	N Absorption	IF THEN ELSE(Time < 45	IF THEN ELSE(Time < 47	Fernandez et al.
		:AND: Time > 13, IF	:AND: Time > 9, IF THEN	2020, Malagoli et
		THEN ELSE(Soil N -	ELSE(Soil N > 55, (27.5 +	al. 2020, Zhang et
		absorption molinia >	(13.75 * Competition Index))	al. 2021
		33,16.5 + (11* -	* IF THEN ELSE(NNI < 1,
		Competition Index), 0), 0)	ABS(NNI -1) +1, 0.2), 0), 0)
	N	IF THEN ELSE(actual N	rhizodeposition table	Fernandez 2019,
	Rhizodeposition	pool oak * rhizodeposition	molinia(Time) / 100 * N	Scandellari et al.
		table oak(Time) >0,	content molinia	2007, 2010,
		rhizodeposition table		Sawatsky and
		oak(Time) * actual N pool		Soper 1991,
		oak, 0)

Table 2 :

 2 Maximal influx capacities (V max ) in µmol/h/g(DW) and their associated p-values computed with Michaelis-Menten regressions for treatment-source combinations.

Table 2

 2

	). Absorption of glycine was smaller by factor 10 and nitrate
	absorption was smallest with values ranging from close to zero in 50µM solution to about
	1µmol/h/g(DW) at 1.5mM solution (Fig 22).
	Calculated V max differed greatly between N sources and slightly between treatments
	within the same N form. V max values range from 0.56µmol/h/g(DW) for nitrate absorption to
	80.69µmol/h/g(DW) for ammonium influx, both in control oaks. Treated oaks presented V max
	values smaller than control for glycine and ammonium labeling and higher for nitrate labeled
	20

Allelopathy has already been observed since the antiquity but has gained interest in research relatively recently. Even though a great number of species are identified and the consequences on receiver species are well characterized, a great gap in knowledge on molecules and their transfer and molecular and physiological targets persist. It is suspected to have an important role in nutrient cycling, which will be detailed in the following.

N concentration (µM)[START_REF]3 Decreased 15 N-ammonium and 15 N-glycine maximum influx capacities[END_REF] N concentration (µM)

Acknowledgments

Supplemental Data

Glossary

Allelopathy:

Biochemical interactions between all types of plants, detrimental and beneficial reciprocal biochemical interactions (Molisch 1937).

Competition:

"the process in which two individual plants […] interact such that at least one exerts a negative effect on the other" (Vandermeer 1989).

Facilitation:

"occurs when one species enhances the growth or survival of another" [START_REF] Callaway | Positive interactions among plants[END_REF]

Kolines

Regeneration (natural):

In the context of forestry, natural regeneration is the operation insuring the renewal of the forest by seedlings coming from the trees in place.

Storage:

Resource that builds up in the plant and can be mobilized in the future to support biosynthesis (Chopin et al. 1990).

Transceptor:

Transport system that possesses a sensoring function [START_REF] Gojon | Nitrate transceptor (s) in plants[END_REF] Uptake:

Uptake of minerals at the plant level is the difference of mineral absorption and loss of minerals of any form (adapted from Mata