Mélissa De Wilde
email: melissa.de-wilde@outlook.com

Elise Buisson

Nicole Yavercovski

Loïc Willm

Livia Bieder

François Mesleard

Using Microwave Soil Heating to Inhibit Invasive Species Seed Germination

Keywords: Bohemian knotweed, Fallopia× bohemica (Chrtek and Chrtková) J. Bailey, giant goldenrod, Solidago gigantea Aiton, jimsonweed, Datura stramonium L Invasive plant species, microwave heating, seed bank, germination inhibition, soil moisture, seed depth, power, duration

Successful long-term invasive plant eradication is rare. The methods target only the adult stage, not taking into account plant development capacities from a large seed bank.

Heating by microwave has been considered because it offers a means to quickly reach the temperature required for the loss of seed viability and therefore inhibit germination. Previous results were not encouraging because homogenous and deep penetration of the waves was not achieved and the various parameters that can modify the effectiveness of treatment were rarely properly addressed as a whole. The aim of this study was to determine, under experimental conditions, the best microwave treatment to inhibit invasive species seed germination, in terms of power (2, 4, 6 kW) and duration (2, 4, 8 min) of treatments, and depending on the soil moisture (10, 13, 20, 30%) and seed depth in the soil (2, 12 cm). This was tested on 3 invasive species: Bohemian knotweed, giant goldenrod and jimsonweed. The most effective treatments required relatively high power and duration (2kW8min, 4kW4min, 6kW2min and 6kW4min; 4kW8min and 6kW8min were not tested for technical reasons), and their effectiveness diminished with increasing soil moisture: germination percentage between 0 and 2% for the lowest soil moisture and between 0 and 56% for the intermediate soil moisture compared with germination percentage between 27 and 68% in control treatments while for the highest soil moisture, only 2kW8min and 4kW4min lowered germination percentage between 2 and 19%.

In some cases, the germination of seeds located at 12 cm depth during treatment was more strongly affected. Seeds of giant goldenrod were the most sensitive, probably due to their small size. Results are sufficiently encouraging to justify further experiments to determine the most effective treatments that would be applied following development of a microwave device to treat large volumes of soil infested by invasive seed efficiently and with reasonable energy requirements . Other types of soil, in terms of texture and organic matter content, should also be tested in future experiments because they influence soil water content and consequently microwave heating.

Management Implications

Alien plant species often show a strong vegetative (e.g. rhizomes) and sexual (seeds) reproductive capacity, which together represent dispersal and resistance organs contributing to species invasiveness and affecting native community. However, seeds are the most highly resistant organs of plants, and preventing their germination from the seed bank impedes a species to recruit individuals and thus to persist in a community, but this is often underestimated. Inhibition of invasive seed bank germination relied on the use of a variety of methods and their combination which involve a range of constraints and are often not wholly effective. New and innovative methods for rapidly inhibiting invasive seed bank germination need to be explored to treat contaminated soil in situ in different ecosystem types (croplands, natural environments or construction sites). Heating by microwave has been considered because it offers a means to quickly reach the temperature required for the loss of seed viability and therefore inhibit germination. In order to determine the technical characteristics of a mobile continuous conveying tunnel with microwave equipment allowing the treatment of infested soil in situ, we carried out two experiments under laboratory controlled conditions. Our results showed that treatments 2kW8min and 4kW4min, requiring about 3.05kWh.m -2 (1097J.cm -2 ), allowed the relatively efficient inhibition of seed germination under different soil moisture levels (10 to 31.4%) and down to a depth of 12 cm, making this equipment potentially suitable for treating larger soil volumes compared to other equipment described in the various existing works. The use of microwave systems to inhibit rapidly and fully the invasive seed bank

Introduction

Invasive plant control and eradication measures [START_REF] Hulme | Beyond control: wider implications for the management of biological invasions[END_REF]) have relied on the use of a variety of methods and their combination (manual and mechanical removal, chemical control with herbicide use or biological controls; e.g. [START_REF] Beerling | The use of non-persistent herbicides, glyphosate, and 2, 4-D amine, to control riparian stands of Japanese knotweed (Reynoutria japonica Houtt.)[END_REF][START_REF] Boss | Improvement and application of the biocontrol fungus Stagonospora convolvuli LA39 formulation for efficient control of Calystegia sepium and Convolvulus arvensis[END_REF][START_REF] Atkins | Comparison of four techniques to control elephant ear[END_REF][START_REF] Derr | Common reed (Phragmites australis) response to mowing and herbicide application[END_REF]. These operations are time-consuming and expensive and usually have i) time-limited effect on target invasive plant species, and ii) a potential impact on nontarget native species and other ecosystem components [START_REF] Kettenring | Lessons learned from invasive plant control experiments: a systematic review and meta-analysis[END_REF].

This can be partly explained by the fact that the methods target only the adult stage and do not take into account the plant development capacities from a large propagule bank [START_REF] Regan | Optimal eradication: when to stop looking for an invasive plant[END_REF][START_REF] Richardson | Seed banks of invasive Australian Acacia species in South Africa: role in invasiveness and options for management[END_REF].

Alien plant species often show a strong vegetative (e.g. rhizomes) and sexual (seeds) reproductive capacity, which together represent dispersal and resistance organs contributing to species invasiveness and affecting native community invasibility and viability [START_REF] Gioria | Soil seed banks in plant invasions: promoting species invasiveness and long-term impact on plant community dynamics[END_REF]. However, seeds are the most highly resistant organs of plants, and preventing their germination from the seed bank impedes a species to recruit individuals and thus to persist in a community [START_REF] Regan | Optimal eradication: when to stop looking for an invasive plant[END_REF][START_REF] Richardson | Seed banks of invasive Australian Acacia species in South Africa: role in invasiveness and options for management[END_REF], but this is often underestimated.

A possible method to inhibit invasive plant seed germination is the extraction of contaminated soils, which is not without risk due to possible contamination during transport, followed by soil solarization which involves a range of constraints, such as suitable weather conditions, setting land aside, duration of treatment and is often not wholly effective [START_REF] Cohen | Soil Solarization and Weed Management[END_REF]). An alternative option for depleting the invasive seed bank is to limit seed production by implementing a control method (e.g. herbicides, fire; Richardson and Kluge 2008) immediately after seedling emergence, either by promoting seed bank emergence (e.g. by soil tillage and/or irrigation; [START_REF] Benvenuti | Seedbank reduction after different stale seedbed techniques in organic agricultural systems[END_REF] or by exploiting the difference in germination phenology, if it exists, between native and alien species [START_REF] Marushia | Phenology as a basis for management of exotic annual plants in desert invasions[END_REF][START_REF] Wolkovich | The phenology of plant invasions: a community ecology perspective[END_REF]. However, both methods represent a control method which is not applicable in the natural environment where the remaining seed bank is sensitive to natural disturbances and where long-term eradication requires the repetition of the operations over several years [START_REF] Benvenuti | Seedbank reduction after different stale seedbed techniques in organic agricultural systems[END_REF][START_REF] Richardson | Seed banks of invasive Australian Acacia species in South Africa: role in invasiveness and options for management[END_REF][START_REF] Marushia | Phenology as a basis for management of exotic annual plants in desert invasions[END_REF].

Consequently, new and innovative methods for rapidly inhibiting invasive soil seed bank germination need to be explored to treat contaminated soil in situ in different ecosystem types (croplands, natural environments or construction sites).

Some studies have considered the potential of the microwave to control invasive and pest species for commercial, agricultural or ecological purposes, in particular in the interests of developing non-chemical techniques [START_REF] Barker | Inhibition of weed seed germination by microwaves[END_REF][START_REF] Fleming | Efficacy of commercial microwave equipment for eradication of pine wood nematodes and cerambycid larvae infesting red pine[END_REF][START_REF] Sahin | A research about microwave effects on the weed plants[END_REF][START_REF] Ambrose | Effect of microwave heat treatment on inhibition of corn seed germination[END_REF]. Microwave radiation causes dielectric heating of moist materials and offers the means to rapidly reach the temperature needed for loss of seed viability and inhibition of germination (in a 60-90°C range, depending on the authors; [START_REF] Barker | Inhibition of weed seed germination by microwaves[END_REF][START_REF] Mavrogianopoulos | Energy efficient soil desinfestation by microwaves[END_REF][START_REF] Bebawi | Effect of microwave radiation on seed mortality of rubber vine (Cryptostegia grandiflora R.Br.), parthenium (Parthenium hysterophorous L.) and bellyache bush (Jatropha gossypiifolia L.)[END_REF]Brodie et al. 2007a;[START_REF] Sahin | Effects of microwaves on the germination of weed seeds[END_REF], and can be considered as a thermal weed control method that has no direct environmental drawbacks, especially as there is no residue to contaminate the surroundings, unlike herbicides . The results have generally not been encouraging for the development of these microwave treatments, either in terms of lack of effectiveness, or because of the excessive costs that this method generates. However, the cited studies used microwave equipment which did not enable the homogenous and deep penetration of the waves (e.g. frequency of 2450 MHz, only one generator, static batch, horn antenna). The commonly used pyramidal horn antenna led to nonhomogeneous vertical and horizontal temperature distribution in the soil, with a peak temperature (around 90°C) occurring between 2 and 5 cm below the soil surface along the center line of the horn antenna, making this equipment effective in inhibiting seeds germination only at low depths along the center line of the horn antenna [START_REF] Bebawi | Effect of microwave radiation on seed mortality of rubber vine (Cryptostegia grandiflora R.Br.), parthenium (Parthenium hysterophorous L.) and bellyache bush (Jatropha gossypiifolia L.)[END_REF]). Furthermore, the different parameters that can limit or enhance the treatment's effectiveness (soil moisture, power, duration) were rarely addressed satisfactorily as a whole [START_REF] Barker | Inhibition of weed seed germination by microwaves[END_REF][START_REF] Bebawi | Effect of microwave radiation on seed mortality of rubber vine (Cryptostegia grandiflora R.Br.), parthenium (Parthenium hysterophorous L.) and bellyache bush (Jatropha gossypiifolia L.)[END_REF]. Previous studies showed that seed mortality was greater in moist soil rather than dry soil [START_REF] Bebawi | Effect of microwave radiation on seed mortality of rubber vine (Cryptostegia grandiflora R.Br.), parthenium (Parthenium hysterophorous L.) and bellyache bush (Jatropha gossypiifolia L.)[END_REF]Brodie et al. 2007a). However, they used sand that has the lowest dielectric constant and does not allow testing of the effect of high soil moisture on microwave treatment efficiency. Although moisture is needed to cause and transfer heat, higher moisture content may require higher treatment power and/or duration to inhibit seed germination [START_REF] Mavrogianopoulos | Energy efficient soil desinfestation by microwaves[END_REF], Brodie et al. 2007b).

The aim of this study was thus to assess, under experimental conditions, the most effective combination of power and duration to inhibit the seed germination of invasive plant species when treating soil with microwave, taking into account soil moisture and the depth of seeds in the soil. We tested the effect of microwave treatments on the germination capacity of seeds of three invasive species widespread in Europe (Datura stramonium L., Fallopia× bohemica (Chrtek and Chrtková) J. Bailey and Solidago gigantea Aiton; [START_REF] Pyšek | Alien vascular plants of Europe[END_REF]. Effective treatments correspond to treatments inhibiting all seed germination, thus preventing any germination that could lead to a new invasion. The results of this work, carried out under laboratory controlled conditions, will subsequently determine the technical characteristics of a continuous conveying tunnel with microwave equipment allowing the treatment of infested soil collected in situ. The present work is included in the project P.A.R.I.S ("Process Accéléré de Réduction des espèces InvasiveS") attempting to develop a process prototype to locally eradicate invasive plant species using microwave radiations. The process consists of heating large quantities of soil infested with invasive plant species (vegetative parts and seeds) in situ, with a mobile microwave oven. The project is led by a consortium of companies specialized in renaturation, civil engineering, microwaves, energy supply and research laboratories.

Material and Methods

Biological Material. The experiments were performed on seeds from three invasive plant species that have the specific feature of producing a large number of seeds and are widely available in Europe.

Datura stramonium (Solanaceae) is an annual herb that persists in cropping systems and disturbed areas (Weaver and Warwick 1984;[START_REF] Kleyer | The LEDA Traitbase: a database of life-history traits of the Northwest European flora[END_REF]. Its region of origin is America and Mexico is an major center of diversity of the genus [START_REF] Symon | Datura (Solanaceae) is a new world genus[END_REF]. The fruits are thorny capsules up to 4 cm in length and may contain up to 650 kidney-shaped seeds [START_REF] Van Kleunen | Reproductive assurance through selffertilization does not vary with population size in the alien invasive plant Datura stramonium[END_REF]) of 3-4 mm long, 2-3 mm wide and 8.7-10.7 mg [START_REF] Kleyer | The LEDA Traitbase: a database of life-history traits of the Northwest European flora[END_REF].

Fallopia× bohemica (Polygonaceae) is a perennial herb resulting from the hybridization between Fallopia japonica (Houtt.) Rons Decr and Fallopia sachalinensis (F. Schmidt) Rons Decr and the resulting backcrosses with the parent species, both native to Asia. These plants thrive in alluvial areas and the banks of rivers where moisture and nutrient rich substrates enable it to achieve optimal growth, leading to single-species stands, but it is also found in ruderal environments such as road sides and abandoned land [START_REF] Beerling | Fallopia japonica (Houtt.) Ronse Decraene[END_REF]. The seeds are carried by achenes 2-4 mm long and 2 mm wide [START_REF] Beerling | Fallopia japonica (Houtt.) Ronse Decraene[END_REF].

Solidago gigantea (Asteraceae), native to North America, is a perennial herb and a major invader, often forming dense monospecific stands. Although S. gigantea prefers rich and rather moist soils, it occurs over a wide range of soil fertility and texture conditions. It is most vigorous in ruderal and riverside habitats, but also grows at drier sites, such as road sites and embankments [START_REF] Weber | Biological flora of central Europe: Solidago gigantea Aiton[END_REF]. The branches contain numerous flower heads (1200( ± 190, Schmid et al. 1988) producing abundant pubescent achenes 1-1.8 mm in length and 0.06-0.074 mg in weight, with long hairs so that they are readily dispersed in the wind [START_REF] Weber | Biological flora of central Europe: Solidago gigantea Aiton[END_REF][START_REF] Kleyer | The LEDA Traitbase: a database of life-history traits of the Northwest European flora[END_REF].

Achenes of Fallopia× bohemica and Solidago gigantea were collected in March 2015 along the Isère River in Savoie (France). Seeds of Datura stramonium were collected in October 2014 from D. stramonium stands growing along Rhône River in the Drôme (France). The achenes and seeds were collected randomly from 10 individuals of the same population and then pooled. The achenes and seeds were stored under dry conditions at room temperature until they were used for experiments. Previous works showed that these storage conditions for short amount of time (as in this experiment) do not affect achene and seed viability and the germination capacity of species used [START_REF] Benvenuti | Light environment, phytochrome and germination of Datura stramonium L. seeds[END_REF][START_REF] Engler | Seed characteristics and germination limitations in the highly invasive Fallopia japonica s.l. (Polygonaceae)[END_REF][START_REF] Bochenek | Do the seeds of Solidago gigantea Aiton have physiological determinants of invasiveness?[END_REF]). In the rest of the manuscript, only the term 'seed' will be used.

Microwave System. The AMW200 batch microwave system (SAIREM SAS, Neyron, France, http://www.sairem.com) used in this study is designed for testing purposes, not for industrial use. The results obtained with this equipment will subsequently determine the technical characteristics of a continuous conveying tunnel with microwave equipment, designed for the treatment of infested soil collected in situ.

The 304 L microwave oven is a stainless steel chamber which can contain a 600 x 400 x 250 mm block maximum size and 30 kg maximum weight. The microwave system is equipped with a polyethylene sliding table with a 840 x 620 mm usable surface and a pneumaticallydriven sliding door, making easier block loading/unloading. The microwave system operates at 915 MHz which is more penetrating and allows the treatment of thicker products (up to 25 cm) compared to the frequently used 2450 MHz microwave frequency (approximately 3 times higher). Heating homogeneity is achieved by the use of microwave coupling from the top and bottom of the product as well as the rotation of a turntable. The output power of 10kW maximum is produced by 2 x 5kW generators (magnetron) and is adjustable from 1kW to 10kW. The system is water-cooled.

Experimental Design. Microwave Treatments. The study was subdivided into two experiments.

Experiment 1. The aim of this experiment, conducted on April 13, 2015, was to assess the most effective combination of power × duration to inhibit the germination of the three target species seeds, buried at two depths, when treating soil by microwave.

The experiment was carried out on samples of 8 kg of soil each contained in a cardboard box (35× 25 ×15 cm) covered on the bottom and sides with plastic bubble wrap to prevent water vapor emanating from the soil from softening the cardboard and significantly complicating handling. The topsoil used was collected on a wooded slope (Gard, France), and consisted of a sandy loam soil (55.5% sand, 31% silt and 13.5% clay; according to USDA soil classification).

The seven treatments (power × duration combinations) used for this experiment (Table S1) were determined through tests and soil temperature measurements at the periphery and in the middle of the soil with mercury thermometers immediately after microwave tests in a replicate for each test. The pre-treatment soil temperature was 14.7°C and soil moisture (defined as mass water content and expressed as a percentage = ([wet soil massdry soil mass]/dry soil mass)*100) was 13.5%±4.4 (Hexp1). Homogeneous temperatures equal to or higher than 90°C,considered as a temperature needed for the loss of seed viability and thus inhibition of seed germination [START_REF] Barker | Inhibition of weed seed germination by microwaves[END_REF], were achieved by four power × duration combinations (Table S1), for which we assume no post-treatment germination will be observed.

To define the lower limits of effectiveness, three other combinations of these powers and durations were performed (Table S1). For safety reasons (formation of electric arcs within the cavity with a high risk of magnetron damage), higher treatments could not be performed (4kW8min and 6kW8min).

For each species, two bags containing 20 seeds were placed in each cardboard box containing soil. Baking paper bags were used to keep the seeds in place during the experiment and to easily extract the seeds from the soil after treatment. In order to assess the effect of seed burial in the soil, one seed bag was placed at 2 cm depth (top) and the others at 12 cm depth (bottom). There were five replicate boxes per treatment.

The control treatment consisted of bags, containing 20 seeds of each species, to which no microwave treatment was applied. To allow comparison of different microwave treatments with the control treatment, 5 bags of control treatments were randomly distributed at each depth.

The content of each bag (20 seeds) was stuck to double-face plastic films, themselves stuck on tissues (Diatex), which were permeable to 0.2 mm, and placed on a Petri dish (6 cm diameter) on cotton soaked in distilled water. Petri dishes were placed in a growth chambers (Hotcold-GL: 12K lux) with temperature controlled at 25°C day/ 15°C night and a photoperiod of 14h day/ 10h night. Seed germination was monitored every two days, with counting and uprooting of seedling as they germinate to avoid preemption phenomena that could prevent germination of other individuals. The germinations were monitored until no germination was observed, corresponding to 44 days.

The effect of microwave treatment (seven power × duration combinations and control), depth (two) and species (three) and their interaction on germination percentage was tested using logistic regression (binary data).When a significant effect was observed, post hoc comparisons of means were conducted with a Tukey's test. All statistical tests were done using R software (The R Foundation for Statistical Computing, version 3.2.0). Three other parameters were assessed to study the effect of microwave treatment on germination capacity (see Supplementary Material for Method, Results and Discussion) Experiment 2. The aim of the second experiment, conducted on June 30 2015, was to test the effect of three different soil moistures on the effectiveness of microwave treatments to inhibit the germination of the three target species seeds buried at two depths. The soil and experimental set up were the same as in Experiment 1. The four treatments used in this experiment (Table S2) corresponded to two of the treatments that were effective in Experiment 1: 4kW4min and 2kW8min (chosen among the effective treatments because they require less energy), as well as the two non-effective treatments which still reached a temperature above 50°C (2kW4min and 4kW2min; see results), assuming that with different moisture levels they may become effective [START_REF] Bebawi | Effect of microwave radiation on seed mortality of rubber vine (Cryptostegia grandiflora R.Br.), parthenium (Parthenium hysterophorous L.) and bellyache bush (Jatropha gossypiifolia L.)[END_REF].

Three different levels of soil moisture were used: H1, corresponding to the initial soil moisture, H2 and H3 corresponding respectively to an addition of 0.1 L and 0.2 L of water per kg of soil. Wet and dry soil (after drying 120 hours at 105 °C) were weighed to calculate soil moisture (defined as mass water content and expressed as a percentage = ([wet soil massdry soil mass]/dry soil mass)*100) before the experiment on 20 samples.

The pre-treatment soil temperature was 25°C. Temperature of soils, at the periphery and in the middle, were measured with mercury thermometers inserted in the center and at the edge of the soil immediately after microwave treatments in the five replicates of each treatment (Table S2).

To allow comparison of different microwave treatments with the control treatment, 5 bags of control treatments were randomly distributed at each depth for each soil moisture level, in order to have a full factorial design. The germinations were monitored until no germination was observed, corresponding to 39 days.

Logistic regression was performed to test the effect of microwave treatment (four power × duration combinations and control), soil moisture (three), species (three) and depth (two) on germination percentage. Differences in mass water content between the three moistures tested and the moisture of soil used in Experiment 1 was assessed using one-way ANOVA. When a significant effect was observed, post hoc comparisons of means were conducted with a Tukey's test. All statistical tests were done using R software (The R Foundation for Statistical Computing, version 3.2.0).

Results

Experiment 1. Germination percentage was significantly affected by the microwave treatment × depth × species interaction (Table 1). S. gigantea showed a significantly higher germination percentage than D. stramonium and F.× bohemica in the control treatment, whatever the depth (Fig 1). Germination percentage was between 0 and 1% for treatments 2kW8min, 4kW4min, 6kW2min and 6kW4min for all the species, whatever the depth, and significantly lower compared to treatments 2kW2min, 2kW4min, 4kW2min and control (Table 1,Fig 1). For D. stramonium and F.× bohemica, 2kW2min, 2kW4min and 4kW2min treatments had no effect on germination percentage compared to the control treatment, whatever the depth (Table 1,Fig 1). For S. gigantea, 2kW2min treatment had no effect on germination percentage, whatever the depth; 2kW4min treatment significantly reduced germination percentage of seeds located at a 12 cm depth only, and 4kW2min treatment significantly lowered germination percentage particularly for seeds located at a 2 cm depth, compared to control treatment (Table 1,Fig 1).

Experiment 2. Mass water content differed significantly between the three moisture levels tested in Experiment 2 and moisture of soil used in Experiment 1 (Hexp1; F 3 80 = 196.2, P< 0.001), with H1 = 10.2% ± 2.6 < Hexp1 = 13.5% ± 4.4 < H2 = 20.4% ± 1.6 < H3 = 31.4% ± 2.4 (mean ± SE, post-hoc Tukey's test, P< 0.005 ).

Germination percentage was affected by the species × depth × microwave treatment interaction, by the species × depth × moisture interaction and by the depth × microwave treatment × moisture interaction (Table 2).

S. gigantea showed a higher germination percentage than D. stramonium and F.× bohemica in the control treatment, whatever the depth (microwave treatment × depth × species interaction, post-hoc Tukey's test, P< 0.05;

Discussion

Effective treatments to inhibit invasive plant seed germination were, as expected, the power × duration combinations enabling soil to reach 90°C [START_REF] Bebawi | Effect of microwave radiation on seed mortality of rubber vine (Cryptostegia grandiflora R.Br.), parthenium (Parthenium hysterophorous L.) and bellyache bush (Jatropha gossypiifolia L.)[END_REF]Brodie et al. 2007a).

In some cases, a temperature equal to or higher than 90°C does not completely inhibit the germination of the seeds and allows 1 or 2% germination. This may be due to uneven temperature distribution in the soil, as sometimes observed between the center and the periphery. Even if the characteristics of the oven favor the good distribution of the waves, the use of a cavity may mean that certain zones receive more energy than others (hotspots). The treatments 2kW4min and 4kW2min showed a strong depth effect at H2, which could be due to the use of a cardboard box for the experiments, leading to energy loss in the open part of the box compared to the closed bottom. Cooling near the surface prevented sufficient heating to kill seeds in the top 2 cm of soil [START_REF] Barker | Inhibition of weed seed germination by microwaves[END_REF]. These results would be different with equipment that does not use a cavity (open structure microwave applicator) or cardboard box.

The capacity of microwave to enable soil to reach 90°C and to totally inhibit seed germination decreased with increasing soil moisture in the range tested. Treatments 2kW4min, 2kW8min, 4kW2min and 4kW4min were all effective at the lower soil moisture level (H1 = 10.2% ± 2.6), but treatments 2kW4min and 4kW2min became ineffective at higher soil moisture levels (Hexp1 = 13.5% ± 4.4, H2 = 20.4% ± 1.6 and H3 = 31.4% ± 2.4); and treatments 2kW8min and 4kW4min remained effective even if their effectiveness tended to decrease at the highest soil moisture level (H3). The more water in the soil, the more energy is needed to achieve the same temperature for a sufficient amount of time to inhibit germination: when the moisture level is higher, a longer processing time and/or higher power are required [START_REF] Mavrogianopoulos | Energy efficient soil desinfestation by microwaves[END_REF][START_REF] Fleming | Efficacy of commercial microwave equipment for eradication of pine wood nematodes and cerambycid larvae infesting red pine[END_REF]. However, this trend may be reversed with very dry or sandy soils that do not allow water retention, because in the absence of water in the soil, microwave treatment does not cause heating . Other types of soil, in terms of texture and organic matter content, should also be tested in future experiments because they influence soil water content and consequently microwave heating (Brodie et al. 2007a). A temperature of 90°C may be considered necessary for the loss of seed viability and thus inhibition of seed germination [START_REF] Barker | Inhibition of weed seed germination by microwaves[END_REF]. However, the question of how long the treatments should last for the soil to reach this temperature and how long the seeds must undergo this temperature to achieve germination inhibition remains. The treatment 2kW8min at the highest moisture level reached a temperature of 90°C but did not damage all the seeds. This may be because at high moisture levels, the time required to reach 90°C is longer and therefore the seeds have undergone this temperature over a shorter duration. Braker and Craker (1991) showed that at least 120s were required to heat the soil above 80°C and that a 30s period of temperatures above 80°C is sufficient to kill seeds.

The species S. gigantea presented the highest germinating capacity but also seems to show the most sensitivity to the tested microwave treatments, which may be due to the small size of its seeds (achenes of 1-1.8 mm length, Weber and Jakobs 2005; seed mass of 0.06-0.074 mg, [START_REF] Kleyer | The LEDA Traitbase: a database of life-history traits of the Northwest European flora[END_REF]) that could make it more susceptible to microwave heating. Seed size seems to be a determining factor to explore further, as our results were not consistent with those of other studies, suggesting that seeds with a higher mass are more susceptible to microwave treatment, perhaps because larger seeds present a larger 'radar cross section' propagating microwave, and thus a higher capacity to absorb electromagnetic energy [START_REF] Bebawi | Effect of microwave radiation on seed mortality of rubber vine (Cryptostegia grandiflora R.Br.), parthenium (Parthenium hysterophorous L.) and bellyache bush (Jatropha gossypiifolia L.)[END_REF]).

Studies on seeds with more contrasting morphologies could shed light on this point.

Microwave soil treatment could potentially be the only method to rapidly and fully inhibit the soil seed bank germination in different types of environments. A major obstacle prohibiting its use is the large amount of energy required to obtain satisfactory results. Our results showed that treatments 2kW8min and 4kW4min, requiring about 3.05kWh.m -2 (1097J.cm -2 ), allowed the relatively efficient inhibition of seed germination under different soil moisture levels (10 to 31.4%) and down to a depth of 12 cm, making this equipment potentially suitable for treating larger soil volumes compared to other equipment described in the various existing experimental works. [START_REF] Mavrogianopoulos | Energy efficient soil desinfestation by microwaves[END_REF] used an open microwave equipment with the waveguide placed vertically on the soil, which required between 7.4 and 24kWh.m -2 (depending on soil moisture: 5.5 or 15%, and initial soil temperature: 20 or 40°C) to reach only 61°C at 10 cm depth in fine sandy loam soil. Brodie et al. (2007b), with a pyramidal horn antenna as a microwave applicator in the soil, report an energy requirement of 0.63kWh.m -2 to inhibit seed germination (germination percentage of 2.5%) in air dried-soil at only 3 cm depth, while it does not allow inhibition of seed germination (germination percentage of 100%) in soil with 37% moisture. According to the results available in Brodie et al. (2007b), 1.875kWh.m -2 would be necessary to totally inhibit seed germination (germination percentage of 0%) in moist soil at 3 cm depth. The experiments of Brodie and Hollins (2015) with horn antenna showed that 3528 J.cm -2 was not sufficient to totally inhibit germination in dry sand, whatever the depth, and 1176 J.cm -2 and 2352 J.cm -2 were required to inhibit germination at 5 cm and 10 cm respectively in sand with 20% moisture. In loam soil (unknown moisture level), a horn antenna applying 1020 J.cm -2 does not allow total inhibition of seed germination, even at low depth (germination percentage of 1.6% at 2 cm burial depth, Brodie and Hollins 2015), while our equipment required only 1097J.cm -2 and enabled treatment of larger soil volumes. In view of the results obtained and in comparison with the experimental work using open microwave equipment placed directly on the soil surface, the development of a mobile continuous conveying tunnel with microwave equipment used in this study will be considered in order to treat infested soil in situ. However the use of this equipment will require to excavate soil and fed it into the tunnel which involves additional energy costs which must be quantified in future work with a field prototype.

The use of microwave systems to inhibit the invasive species seed bank germination is promising, and today may be one of the most effective methods available. Results are encouraging enough to justify further experiments to determine the most effective treatments depending on environmental conditions (e.g. types of soil) in order to develop a microwave device to treat efficiently and with reasonable energy requirements large volumes of soil infested by invasive seed bank. However, this technique is not selective and result in the depletion of the entire seed bank, native species included, and may alter the soil conditions through its effect on soil organisms and their activities. Few studies have considered the impact of microwave treatments on soil invertebrates, but [START_REF] Rahi | Effect of moisture on efficiency of microwaves to control plantparasitic nematodes in soil[END_REF] showed their lethal effect on a nematodes species. Responses of key soil micro-organisms and the functional consequences are rather more extensively documented, but results may be contradictory. While some authors demonstrated that fungi are more susceptible than bacteria [START_REF] Wainwright | Effects of 2450 MHz microwave radiation on nitrification, respiration and S-oxidation in soil[END_REF][START_REF] Speir | Effects of microwave radiation on the microbial biomass, phosphatase activity and levels of extractable N and P in a low fertility soil under pasture[END_REF]), Brodie et al. 2015 observed no responses of soil fungi, ciliates, amoeba and flagellates, and a decrease in the bacterial population. (Brodie et al. 2015). [START_REF] Cooper | The effect of microwave radiation and soil depth on soil pH, N, P, K, SO4 and bacterial colonies[END_REF] showed little to no effect of microwave treatment on key soil nutrients and pH, while others showed that soil nutrient content may be modified due to micro-organism cell lyse or the modification of processes due to temperature increase [START_REF] Wainwright | Effects of 2450 MHz microwave radiation on nitrification, respiration and S-oxidation in soil[END_REF][START_REF] Speir | Effects of microwave radiation on the microbial biomass, phosphatase activity and levels of extractable N and P in a low fertility soil under pasture[END_REF]Brodie et al. 2015). These questions therefore remain to be explored for the purposes of the management and restoration of ecosystems affected by biological invasions, as they could influence native and alien plant recruitment and development.

Tables Table 1. Results of Generalized Linear Models testing the effect of microwave treatment, depth and species and their interactions on germination percentage (logistic regression).

Factors

Figures LegendsFigure 1 .

 1 Figures Legends Figure 1. Germination percentage of Solidago gigantea, Fallopia × bohemica and Datura stramonium in control treatment and after different power × duration microwave treatments at two depths in the soil. Top: seed bags placed at 2 cm depth; bottom: seed bags placed at 12 cm depth. Values are expressed as means ± SE of the five replicates. Letters indicate statistically significant differences (microwave treatment × depth × species interaction, post-hoc Tukey's test, P < 0.05).

Figure 2 .

 2 Figure 2. Germination percentage of Solidago gigantea, Fallopia × bohemica and Datura stramonium in control treatment and after different power × duration microwave treatments at two depth in the soil with three different moistures (H1 =10.2% ± 2.6, H2 = 20.4% ± 1.6, H3 = 31.4% ± 2.4). Top: seed bags placed at 2 cm depth, bottom: seed bags placed at 12 cm depth. Values are expressed as means ± SE of the five replicates. Letters indicate statistically significant differences (microwave treatment × depth × moisture interaction, post-hoc Tukey's test, P < 0.05).

Table 2 ,

 2 Fig 2).

	For H1, germination percentage was between 0% (D. stramonium and F.× bohemica) and
	2% (S. gigantea) for the four tested microwave treatments (4kW2min, 4kW4min, 2kW8min
	and 2kW4min), whatever the depth, and were significantly lower compared to control treatment
	(Table 2, Fig 2). For H2, the four microwave treatments significantly lowered the germination
	percentage (germination percentage between 0 and 56%), whatever the depth, compared to
	control treatment (germination percentage between 36 and 68%; Table 2, Fig 2). For seeds
	located at 12 cm depth, germination percentage did not differ between microwave treatments,
	but for seeds located at 2 cm depth, 4kW4min, 2kW8min and 2kW4min treatments reduced
	germination percentage more than 4kW2min. For H3, only 2kW8min and 4kW4min
	significantly lowered germination percentage (germination percentage between 2 and 19%),
	whatever the depth, compared to control treatment.

Table 2 .

 2 The Wald statistic used to test the significance of the parameters, degrees of freedom (df) and p values (P) are indicated. Values in bold indicate significance at P < 0.05. Results of Generalized Linear Models testing the effect of microwave treatment, depth, moisture and species and their interactions on germination percentage (logistic regression). The Wald statistic used to test the significance of the parameters, degrees of freedom (df) and p values (P) are indicated. Values in bold indicate significance at P < 0.05.

	df	Wald statistic (χ 2 )	P

Acknowledgements

This work is part of an FUI (Single Interministerial Fund) research and development project, co-financed by BPI France, Provence Alpes Côte d'Azur (PACA) and Languedoc Roussillon Regions and the Ain local authority. In addition to the authors, the participants in this project also include scientists from EDF, GECO Ingénierie et Travaux, LST&M, NGE, SAIREM. No conflicts of interest have been declared.


François Turlin
email: francois.turlin@univ-lorraine.fr

Clara Deruy

Aurélien Eglinger

Olivier Vanderhaeghe

Anne- Sylvie André-Mayer

Marc Poujol

Abdelali Moukhsil

Fabien Solgadi

A 70 Ma record of suprasolidus conditions in the large, hot, long-duration Grenville Orogen

Petrochronology of magmatic monazite and apatite from a single paragneiss leucosome derived by in-situ partial melting documents the thermal evolution of the Allochthonous Belt of the central Grenville Province. Monazite records suprasolidus metamorphism from ca. 1080 to 1020 Ma under high temperature up to 850°C. Apatite from the same leucosome yields an age of 960 Ma, consistent with cooling of this crustal segment down to subsolidus conditions of ca. 450°C. A pegmatitic granite dyke, with lobate contacts, previously dated at ca. 1005 Ma (Turlin et al., 2017) is interpreted to intrude the paragneisses at a temperature of ca. 650°C close to the wet-solidus. These data document slow cooling at a rate of 2 to 6°C/Ma for the middle crust of this part of the Grenville hinterland marked by protracted suprasolidus conditions for at least 70 Ma. It supports the definition of the Grenville Orogen as a large, hot, long-duration orogen.

1.

INTRODUCTION

The term petrochronology was recently defined to designate geochronological studies that integrate the textural and microstructural position of the dated minerals [START_REF] Engi | Significant Ages -An introduction to petrochronology[END_REF]. Several authors have shown that the use of petrochronological data coupled with thermo-mechanical models can provide new clues to decipher the crustal evolution of orogenic belts (e.g. Brown, 2014;Vanderhaeghe, 2012). The timing and duration of metamorphic processes in a variety of tectonothermal environments are still debated,

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especially for continental collisions marked by high temperature metamorphism (e.g. Johnson et al., 2015;Kohn, 2008). A crucial question is how long the rocks comprising the mid to lower crust remained at suprasolidus temperatures in large, hot, long-duration orogens such as the Himalaya-Tibet Orogen, where the evolution of the Tibetan Plateau is controlled by lateral flow (Jamieson et al., 2004;[START_REF] Nelson | Partially Molten Middle Crust Beneath Southern Tibet: Synthesis of Project INDEPTH Results[END_REF]Vanderhaeghe, 2009).

The exhumed root of the Proterozoic Grenville Orogen, composed of intensely deformed, high-grade metamorphic rocks exposed in southern Canada and the northeastern USA (Fig. 1a), presents an ideal opportunity to investigate the deep crustal processes occurring during a long-lived continental collision. Indeed, the Grenville Province was one of the classic localities for the first studies on mineral cooling ages (e.g. [START_REF] Harper | On the interpretation of potassium-argon ages from Precambrian shields and Phanerozoic orogens[END_REF]. These rocks underwent protracted granulite-facies conditions under an orogenic plateau similar to the present Tibetan plateau (e.g. [START_REF] Indares | Crustal architecture above the high-pressure belt of the Grenville Province in the Manicouagan area: new structural, petrologic and U-Pb age constraints[END_REF]Rivers, 2008;Rivers et al., 2012). In the central Grenville Province in Quebec, suprasolidus growth of monazite has been documented in aluminous gneisses from the mid-to low-pressure segment of the Allochthonous Belt (aM-LP, Fig. 1b) between ca. 1070 and 1020 Ma during a clockwise P-T-t path (Lasalle and Indares, 2014;Lasalle et al., 2014). However, the actual duration of suprasolidus conditions in this aM-LP segment remains unconstrained. In this study, we use U-Th-Pb dating of monazite and apatite from a single leucosome in migmatitic paragneisses from the same area of the central Grenville Province (Complexe de la Plus-Value, Fig. 1c) to better constrain the duration of suprasolidus metamorphic conditions.

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MONAZITE-APATITE CRYSTALLIZATION AND COOLING IN ANATECTIC ALUMINOUS GNEISSES

P-T-t record of the central Grenville Province

The Grenvillian Orogeny has been described as a two-phase late-Mesoproterozoic to early-Neoproterozoic continental collision involving the Laurentian and Amazonian cratons (Jamieson et al., 2007;Rivers, 2008;Rivers et al., 2012). The older Ottawan phase, for which ages spread from ca. 1090 to 1020 Ma, is interpreted as a long-lived period of a large hot orogeny. During the Ottawan period, the Allochthon Boundary Thrust (ABT) is inferred to have played the role of a shallow-dipping crustal scale ramp accommodating lateral extrusion of the ductile mid-crust parallel to the orogenic belt (Rivers, 2008;Rivers et al., 2012). In the aM-LP segment south of the Manicouagan Reservoir, the Ottawan high-grade peak of metamorphism is recorded as a moderate-gradient P-T path, up to sillimanite-grade with P-T conditions of ca. 950 MPa and 850°C interpreted to represent the thermal peak (Lasalle and Indares, 2014;Rivers et al., 2012). Two studies have investigated the timing of the Ottawan phase in this area by U-Pb dating of monazite from anatectic gneisses (metapelites and aluminous gneisses, Fig. 1c, Dunning and Indares, 2010;Lasalle et al., 2014). Yakymchuk et al., 2017). These younger ages are coeval with the Rigolet tectonic phase attributed to crustal thickening at ca. 1005-960 Ma (Jannin et al., accepted;Rivers, 2008;Rivers et al., 2012;van Gool et al., 2008) recorded in the underlying Parautochthonous Belt with a high-grade peak of metamorphism up to 1250-1500 MPa and 815-850°C (Jordan et al., 2006). The 10 to 20 Ma hiatus in ages in the Grenville Province has been interpreted to correspond to the transition from post-Ottawan orogenic gravitational collapse to renewed crustal thickening during the Rigolet tectonic phase (Rivers, 2008).

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Petrochronology of monazite and apatite from migmatitic paragneisses

Migmatitic paragneisses from the Complexe de la Plus-Value of the central Grenville

Province sampled for this study (Fig. 1c) have deposition ages comprised between ca. 1.6 and 1.5 Ga (U-Pb on detrital zircon cores and on zircon from the intrusive Bardoux Plutonic Suite, [START_REF] Augland | Pinwarian to Grenvillian magmatic evolution in the central Grenville Province: new constraints from ID-TIMS U-Pb ages and coupled Lu-Hf S-MC-ICP-MS data[END_REF]Lasalle et al., 2013;Moukhsil et al., 2014). They are composed of cm-size leucosomes and melanosomes underlining the syn-migmatitic foliation (Fig. 2a,b).

They are intruded by a 1005±4.4 Ma (U-Pb dating on magmatic monazite, Turlin et al., 2017) pegmatitic granite dyke (PGD) (Fig. 2a). The walls of the dyke do not correspond to fractures cutting across minerals of the migmatitic paragneiss but are rather lobate suggesting intrusion in a ductile rock. Moreover, the paragneisses do not show evidence for contact metamorphism (Fig. 2a). These features indicate a close to wet-solidus temperature of the latter at that time (Vanderhaeghe, 2001), i.e. above ca. 650-700°C in such metapelites (e.g.

Yakymchuk and Brown, 2014). Investigated monazite and apatite grains were sampled from a single leucosome of this migmatitic paragneisses.

Leucosomes show a magmatic texture (Fig. 2b,c) and are composed of a coarse grained (1-5 mm) assemblage of subhedral to euhedral and undeformed quartz and plagioclase with peritectic K-feldspar and garnet (45:35:15:5, Figs. 2c,d). In addition, some biotite show a corroded, nearly skeletal, texture and are separated from garnet by K-feldspar (Fig. 2d). As identified by Lasalle et al. (2014), subhedral, uncorroded and inheritance-free monazite grains (100-300 µm) are found (i) as inclusions in peritectic garnet (Fig. 2e) and Kfeldspar, and (ii) in the matrix. These monazite grains have homogeneous compositions with significant components of cheralite and xenotime end-members (Table S1), consistent with

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1049±25 Ma (2 , Fig. 3a, Table 1). No inherited ages were identified in the isotopic ratios, consistent with the homogeneous and unzoned character of the grains.

Apatite grains (300-600 µm) occur as stubby and euhedral to subhedral grains in the leucosome matrix (Fig. 2c,f). Along with their shape, the lack of inherited cores/domains or dissolution/precipitation textures, and their homogeneous compositions (Table S2), provide evidence for the crystallization of apatite grains in equilibrium with the residual melt (Fig. 2c,f). Since apatite generally exhibit a low radiogenic-Pb/common-Pb ratio, the data were plotted in a Tera-Wasserburg diagram (Tera and Wasserburg, 1972), in which the variable 206 Pb/ 207 Pb ratios define a discordia line with a lower intercept of 960±10 Ma (MSWD=1.11, Fig. 3b, Table 2) and an initial 206 Pb/ 207 Pb ratio of 0.90 consistent with the model evolution of Stacey and Kramers (1975). The closure temperatures of these crystals were calculated between 526±24 and 459±22°C, using the equation of Dodson (1973) and data from Cherniak 3).

et al. (1991) (Table

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the biotite dehydration-melting reaction. Monazite grains shielded within peritectic Kfeldspar and garnet (Fig. 2e) formed, respectively, by the incongruent melting of muscovite at ca. 700-750°C and the partial incongruent melting of biotite at ca. 800-850°C. Evidence for the latter are given by some biotite grains that are separated from garnet by K-feldspar and that show a corroded texture, nearly skeletal (Fig. 2d). This feature is expected during biotite

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channel flow (Rivers, 2008) that was, however, inferred to have terminated by ca. 1050 Ma.

In contrast, data presented here are suggestive of persistence of a melt fraction in the Ottawan channel for at least ca. 70 Ma (Fig. 5a,b). This thermal-tectonic evolution, comparable to the one inferred for the Cenozoic Himalaya-Tibet orogenic belt [START_REF] Nelson | Partially Molten Middle Crust Beneath Southern Tibet: Synthesis of Project INDEPTH Results[END_REF]Royden et al., 1997Royden et al., , 2008;;Searle et al., 2011;Vanderhaeghe and Teyssier, 2001), is tentatively interpreted to reflect the impact of a long-lived thickened orogenic crust associated with delamination or retreat of the lithospheric mantle.

Subsolidus thermal history

The youngest Grenvillian metamorphic ages reported in this aM-LP segment range from 987±11 to 995±3 Ma and were obtained on titanite from (i) pre-Grenvillian metatuffs and metagranite (protolith ages of ca. 1410 Ma, Dunning and Indares, 2010, and ca. 1200 Ma, [START_REF] Indares | Crustal architecture above the high-pressure belt of the Grenville Province in the Manicouagan area: new structural, petrologic and U-Pb age constraints[END_REF], and from (ii) a syn-Ottawan metagranite (protolith age of ca.

1065 Ma, Dunning and Indares, 2010). They are interpreted as a signal of a late-Grenvillian magmatic/metamorphic/deformation event under semi-brittle conditions, consistent with the subsolidus closure temperature of titanite at ca. 550-650°C (Fig. 4, Dunning and Indares, 2010; [START_REF] Indares | Crustal architecture above the high-pressure belt of the Grenville Province in the Manicouagan area: new structural, petrologic and U-Pb age constraints[END_REF]Schoene and Bowring, 2007 and references therein;Yakymchuk et al., 2017). Apatite grains from the leucosome crystallized in equilibrium with the residual melt as indicated by their textural setting, their homogeneous compositions, and their lack of inherited cores/domains or dissolution/precipitation textures (Fig. 2c,f, Table 2,S2). Their crystallization ages at 960±10 Ma (Fig. 3b) along with their estimated closure temperature between 526±24 and 459±22°C (Table 3) support the conclusion that this aM-LP crustal segment remained above 450-500°C for at least ca. 110 Ma (Figs. 4,5c).

We propose to integrate the thermal evolution of the central Grenville Province described in this study at the lithospheric scale. This geodynamic model, following Rivers

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(2012) and Corriveau and Morin (2010), invokes asthenospheric upwelling beneath the Grenville belt as recorded by coeval mantle and crustal derived magmatism from ca. 1050 to ca. 960 Ma (Fig. 5). We favour a model of lithospheric thinning by slab retreat but it should be mentioned that delamination by convective removal would also account for these features.

Similar scenarios have been proposed for the magmatic record of the Variscan belt [START_REF] Moyen | Collision vs. subduction-related magmatism: Two contrasting ways of granite formation and implications for crustal growth[END_REF][START_REF] Moyen | Collision vs. subduction-related magmatism: Two contrasting ways of granite formation and implications for crustal growth[END_REF] and for the Indosinian Songpan Ganze terrane (de Sigoyer et al., 2014).

Data from this study coupled with results of Dunning and Indares (2010), Indares andDunning (2004), Lasalle et al. (2014) and Lasalle and Indares (2014) in the Allochthonous Belt of the central Grenville Province allowed the estimations of cooling rates from the early-Ottawan initiation of suprasolidus conditions to the post-Ottawan cooling down to subsolidus conditions (Table 4). The estimated cooling rates are (i) 2.3 to 4.4°C/Ma for the Ottawan period and (ii) 1.8 to 7.5°C/Ma for the post Ottawan period (Table 4), with most data consistent with a narrower range of 2.7 to 6.1°C/Ma. Post-Ottawan rates are similar to those reported for aM-LP rocks of the southwestern Grenville Province determined from 40 Ar/ 39 Ar of hornblende, muscovite, biotite and K-feldspar (see Rivers et al., 2012 and references therein) and more generally for ca. 1 Ga old orogens (Dunlap, 2000). These data indicate that the central Grenville Province exposes the exhumed mid-to lower-part of a large, hot and long-duration orogen that recorded protracted HT metamorphism in the presence of melt for at least ca. 70 Ma followed by a slow cooling history (Figs. 4,5).

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Table 3. Closure temperature of investigated apatite calculated on the basis of their stubby and euhedral to subhedral, crystal diameters of 300 and 600 µm, and a range of typical lateto post-Grenvillian and ca. 1 Ga orogens cooling rates of 1°C/Ma, 3°C/Ma, 5°C/Ma and 7°C/Ma (e.g. Rivers et al., 2012;Dunlap, 2000). Table 4. Grenvillian cooling rates calculated using data from the literature coupled with the data presented in this study on a single leucosome from migmatitic paragneisses of the central Grenville Province. Note the similar cooling rates obtained for both Ottawan and post-Ottawan orogenic phases suggesting a continuum of cooling from the former through to the latter. Post-Ottawan 960±10 3 437 4 3.9-7.5 6 550 5

Grenvillian orogenic

1.8 6 -4.3 1 : Temperature and timing of the peak metamorphism from Lasalle and Indares (2014). 2 : Close to wet-solidus temperature of the migmatitic paragneisses at the time of intrusion of the pegmatitic granite dyke (Turlin et al., 2017). 3 : Subsolidus timing of apatite isotopic closure (this study). 4 : Minimum closure temperature of investigated apatite grains (this study). 5 : Maximum closure temperature of investigated apatite grains (this study). 6 : Extreme values. Cooling rates are predominantly in the range 2.7 to 6.1°C/Ma.

  the observations of Lasalle et al. (2014). Plotted on a Concordia diagram, U-Th-Pb isotopic data spread along the Concordia curve with 208 Pb/ 232 Th ages ranging between 1077±26 and

  Monazite grains investigated in this study share (i) microstructural settings and (ii) a range of U-Th-Pb ages similar to the ca. 1080-1020 Ma monazite grains from aluminous gneisses of this aM-LP segment reported by Dunning and Indares (2010) and Lasalle et al.(2014). Accordingly, we infer that the studied migmatitic paragneiss records similar P-T-t conditions at ca. 950 MPa and 850°C between ca. 1070-1050 Ma (Fig.4) and represents a suitable sample to investigate the retrograde P-T-t path.Reaction sequences for the clockwise P-T path published by Lasalle and Indares (2014) involve three main partial melting reactions for these paragneisses: (i) the consumption of free aqueous fluid, (ii) the muscovite dehydration-melting reaction, and (iii)

  dehydration melting, a melt-producing reaction(Kriegsman and Alvarez-Valero, 2010). As proposed byLasalle et al. (2014), these grains grew during prograde heating and partial melting between ca. 700 and 850°C(Kelsey et al., 2008; Yakymchuk and Brown, 2014) and thus correspond to prograde suprasolidus monazite(Yakymchuk, 2017).Accordingly, data obtained on monazite from this study along with data reported by Dunning andIndares (2010) andLasalle et al. (2014) point to the crystallization of monazite (i) during the prograde P-T path as early as ca. 1080 Ma under temperatures of at least 700-750°C, with (ii) a maximum temperature of 850°C between ca. 1070 and 1050 Ma, and (iii) down to ca. 1020 Ma, during the retrograde P-T path (Fig.4). The assumption that younger monazite ages between ca. 1010-990 Ma(Lasalle et al., 2014) are coeval with greenschistfacies conditions is reappraised on the basis of the textural relationships between the investigated paragneisses and the intrusive PGD at ca. 1005Ma (Fig. 2a, Turlin et al., 2017).The lobate contact of the PGD with its host paragneisses in this aM-LP segment imply limited or negligible thermal exchange and thus a close to wet-solidus (ca. 650-700°C) temperature of the host rock at the time of intrusion(Figs. 2a, 4, Turlin et al., 2017).These features are consistent with a long-duration, mid-crustal residence of this aM-LP segment under suprasolidus conditions between ca. 1080 and 1005 Ma in the central Grenville Province, i.e. suprasolidus conditions lasted for at least 70 Ma(Figs. 4, 5a,b). A key point to explain such a long residence at HT may be found in the proposition of a syn-Ottawan extrusion of ductile mid-to low-crust over the ABT associated with some form of

  separation from peritectic garnet by K-feldspar. The suprasolidus, or close to suprasolidus, retrograde T-t path is recorded by monazite from the matrix and down to ca. 1005 Ma as evidenced by the intrusion of a pegmatitic granite dyke into paragneisses which lobate contact with no evidence of contact metamorphism nor thermal exchange with the host evidence for the close to wet-solidus temperature of the host. The retrograde T-t path is recorded by titanite from the same segment and dated between ca. 1000 and 975 Ma, and by apatite from the matrix of the investigated leucosome dated at ca. 960±10 Ma with isotopic closure temperatures of ca. 440-550°C. Abbreviations: Ap = apatite; Bt = biotite; Mnz = monazite; Ms = muscovite; PGD = pegmatitic granite dyke; Tc = isotopic closure temperature.

Figure 5 .

 5 Figure 5. Schematic cross sections illustrating the thermal evolution of the high and mid

Table 1 .

 1 U-Th-Pb dating of monazite from a leucosome of migmatitic allochthonous paragneisses from the central Grenville Province.

	Analysis no.	Concentrations			Isotopic ratios				Ages/Ma
		Pb (ppm) U (ppm) Th (ppm)	206 Pb/ 238 U	2	208 Pb/ 232 Th	2	206 Pb/ 238 U 2	208 Pb/ 232 Th 2
	Mnz-03	2568	5657	35563	0.1754 0.0046	0.0538	0.0013	1042 25	1058 25
	Mnz-04	2874	10542	28447	0.1744 0.0046	0.0534	0.0013	1036 25	1051 25
	Mnz-06	2365	7613	26481	0.1746 0.0046	0.0535	0.0013	1038 25	1054 25
	Mnz-07	2748	6731	37166	0.1753 0.0047	0.0533	0.0013	1041 26	1049 25
	Mnz-08	3577	17411	23848	0.1752 0.0047	0.0536	0.0013	1041 26	1055 25
	Mnz-09	2586	5887	35691	0.1767 0.0048	0.0542	0.0013	1049 26	1066 25
	Mnz-10	2583	5744	36107	0.1769 0.0048	0.0541	0.0013	1050 26	1066 25
	Mnz-11	2878	6435	40465	0.1757 0.0048	0.0540	0.0013	1044 26	1062 25
	Mnz-12	2495	6866	30822	0.1781 0.0049	0.0548	0.0013	1057 27	1077 26
	Mnz-13	2584	6776	34297	0.1737 0.0048	0.0537	0.0013	1032 27	1057 25
	Mnz-14	3187	6099	48278	0.1758 0.0049	0.0540	0.0013	1044 27	1062 26
	Mnz-15	2378	6356	31272	0.1753 0.0049	0.0536	0.0013	1041 27	1056 25
	Mnz-16	2384	6332	31314	0.1764 0.0050	0.0538	0.0013	1047 27	1059 26
	Mnz-17	3078	9311	37637	0.1750 0.0050	0.0536	0.0013	1040 27	1055 26
	Mnz-18	2465	6522	32261	0.1771 0.0051	0.0542	0.0013	1051 28	1066 26
	Mnz-19	2650	7494	34203	0.1760 0.0052	0.0534	0.0013	1045 28	1051 26
	Mnz-20	3080	10383	34931	0.1742 0.0052	0.0540	0.0014	1035 28	1063 26
	Mnz-21	3043	7898	40976	0.1760 0.0053	0.0540	0.0014	1045 29	1063 26
	Mnz-22	4040	17441	34861	0.1765 0.0053	0.0538	0.0014	1048 29	1058 26
	Mnz-23	2946	8983	35659	0.1793 0.0055	0.0538	0.0014	1063 30	1059 26
	Mnz-24	2416	5590	34395	0.1796 0.0055	0.0538	0.0014	1065 30	1060 26

Table 2 .

 2 U-Pb dating of apatite from a leucosome of migmatitic allochthonous paragneisses from the central Grenville Province.

	Analysis no.	Concentrations		Isotopic ratios
		Pb (ppm)	U (ppm)	238 U/ 206 Pb	2	207 Pb/ 206 Pb	2
	Ap-1	3.5	18	4.77	0.16	0.2487 0.0031
	Ap-2	3.3	20	5.02	0.17	0.2281 0.0028
	Ap-3	2.5	35	5.61	0.19	0.1476 0.0019
	Ap-4	3.0	57	5.82	0.19	0.1290 0.0014
	Ap-5	3.0	58	5.86	0.20	0.1295 0.0018
	Ap-6	3.8	54	5.68	0.19	0.1470 0.0018
	Ap-7	27	179	5.14	0.17	0.2106 0.0028
	Ap-8	17	90	4.98	0.17	0.2458 0.0033
	Ap-9	25	318	5.64	0.19	0.1469 0.0017
	Ap-10	50	149	4.37	0.15	0.3082 0.0050
	Ap-11	71	419	4.68	0.16	0.2776 0.0041
	Ap-12	14	102	5.03	0.17	0.2109 0.0033
	Ap-13	3.2	5.8	3.41	0.13	0.4336 0.0085
	Ap-14	3.5	5.4	3.21	0.11	0.4878 0.0098
	Ap-15	4.8	33	5.04	0.17	0.2119 0.0028
	Ap-16	5.7	38	5.08	0.18	0.2227 0.0036
	Ap-17	6.4	44	5.04	0.18	0.2213 0.0039
	Ap-18	9.1	40	4.56	0.16	0.2833 0.0049
	Ap-19	7.3	94	5.83	0.20	0.1534 0.0028
	Ap-20	7.8	93	5.63	0.19	0.1568 0.0019
	Ap-21	7.4	88	5.59	0.19	0.1554 0.0016
	Ap-22	7.2	100	5.83	0.19	0.1465 0.0017
	Ap-23	5.9	30	4.89	0.17	0.2461 0.0030

  Calculated using the Dodson (1973)'s equation with data fromCherniak et al. (1991)

	Crystal diameter	Cooling rate	Closure temperatures 1	±
	(µm)	(°C/Ma)	(°C)	(°C)
	300	1	459	22
	600	1	485	23
	300	3	479	23
	600	3	507	24
	300	5	489	23
	600	5	518	24
	300	7	497	24
	600	7	526	24
	1 :

ACKNOWLEDGMENTS

This work was funded by the Labex Ressources 21 (supported by the French National Research Agency) through the national program "Investissements d'avenir", reference ANR-10-LABX-21-LABEX RESSOURCES 21 and the Région Grand-Est, and benefited from the Accepted Article This article is protected by copyright. All rights reserved. framework of the DIVEX "Rare earth element" research program. Authors are grateful to the Ministère de l'Énergie et des Ressources naturelles (Québec) for technical and financial support for field work and analyses, to Alexandre Crépon, Frédéric Diot (GeoRessources, Nancy), Emmanuel Davy (CRPG, Nancy), Andreï Lecomte and Jean Cauzid (GeoRessources, Nancy) for their help in field work, sample preparation and SEM imaging, respectively, to Anthony Pochon (Géosciences Rennes) for his help in handling closure temperatures of apatite, to Flavien Choulet for his constructive comments on a previous version of the manuscript, and to Félix Gervais for our discussions on the geodynamic context of the Grenvillian Orogeny. The authors also thank Toby Rivers, an anonymous reviewer and the associate editor for their careful review that significantly improved the manuscript, and Klaus Mezger for his constructive comments and editorial handling. This contribution is the Ministère de l'Énergie et des Ressources naturelles du Québec (Canada) publication n° 8449-2017-2018-03.

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