François Charles
email: charles@obs-banyuls.fr

Joseph Garrigue

Jennifer Coston-Guarini

Jean-Marc Guarini
email: j.guarini@entangled-bank-lab.org

Estimating the integrated degradation rates of woody debris at the scale of a Mediterranean coastal catchment

Keywords: dead wood, decay dynamics, long-term ecological experiments, land-sea connections, coastal Mediterranean Sea

Woody debris is found in all habitats of the land-sea continuum. While isolated experimental studies of wood degradation exist, few programs have observed the dynamics of wood degradation, in situ across this gradient. Since 2014, we have been conducting a series of long-term observations of wood decay in three characteristic areas of a Mediterranean Sea coastal watershed: forest leaf litter ('Forest'), river bed ('River') and the near-shore marine environment ('Sea'). The study sites are within the Massane River watershed (France) whose headwaters are in a protected beech tree (Fagus sylvatica) dominated forest. Branch sections from a recently fallen beech tree and standardized blocks of Norway spruce (Picea abies) were installed in all three environments. The proportion of remaining mass and volumetric mass of the individual wood samples were determined periodically over 4.2 years. Regardless of wood type, there were marked differences in the decay dynamics. Mass losses at the Forest and River sites were well-described by continuous negative exponential models. At the Sea site, there was a short latency period followed by rapid degradation for the wood fraction exploited by shipworms; in this case, a Weibull-type function was fitted to the data. Integrated mass loss rates at the coastal location were 6 to 20 times faster than in the other two environments. Our study suggests that the early dynamics of wood degradation in a land-sea meta-ecosystem are dominated by the marine invertebrate community. This means woody debris, once it reaches the sea, is likely to break down rapidly within near shore coastal habitats. These results highlight the need to quantify the mass transport dynamics between local ecosystems.

Introduction

Increasingly, it is recognized by decision-makers that coastal systems cannot be managed as disconnected from processes happening upstream in the watershed [START_REF] Gomi | Understanding processes and downstream linkages of headwater systems[END_REF]. Perturbations in local processes and changes in matter fluxes spread from 'source' to 'recipient' ecosystems [START_REF] Soininen | Toward more integrated ecosystem research in aquatic and terrestrial environments[END_REF] through diverse means. Runoff and rivers move dissolved and particulate matter from terrestrial to marine environments. Fluxes can be very important [START_REF] West | Mobilization and transport of coarse woody debris to the oceans triggered by an extreme tropical storm[END_REF] and cross physical barriers that separate adjacent systems [START_REF] Maser | From the forest to the sea: the ecology of wood in streams, rivers, estuaries, and oceans[END_REF]. Moreover, societal pressure for new tools, like carbon-accounting, for mitigating the impacts of different economic activities [START_REF] Keith | Contribution of native forests to climate change mitigation -A common approach to carbon accounting that aligns results from environmental-economic accounting with rules for emissions reduction[END_REF] is increasing. This means that interdependencies between terrestrial, aquatic and marine systems must be known and reconciled to parameterize these tools and make them operational.

Four-fifths of Earth's total plant biomass is in forests [START_REF] Reichstein | Aspects of forest biomass in the Earth system: Its role and major unknowns[END_REF] where the carbon necromass (including a significant proportion of dead wood [START_REF] Delaney | The quantity and turnover of dead wood in permanent forest plots in six life zones of Venezuela[END_REF]) exceeds that of the living mass [START_REF] Pan | The Structure, Distribution, and Biomass of the World's Forests[END_REF]. In unmanaged forests, most standing and fallen woody debris decompose on annual to decadal time scales [START_REF] Freschet | Interspecific differences in wood decay rates: insights from a new short-term method to study long-term wood decomposition: New method to assess wood decay dynamics and rates[END_REF], although it has been reported to occur on centennial scales [START_REF] Daniels | Determining year of death of logs and snags of Thuja plicata in southwestern coastal British Columbia[END_REF]. Some fraction of this mass is exported from the forest floor by diverse transport mechanisms such as fires, debris flows and water currents [START_REF] Lancaster | Effects of wood on debris flow runout in small mountain watersheds: effects of wood on debris flow runout[END_REF]. Along the way, wood debris of all sizes participates in the biogeochemical and ecological processes (e.g. [START_REF] Charles | Ecogeochemical fate of coarse organic particles in sediments of the Rhône River prodelta[END_REF][START_REF] Harmon | Ecology of coarse woody debris in temperate ecosystems[END_REF][START_REF] Leroux | Subsidy hypothesis and strength of trophic cascades across ecosystems: Subsidies and trophic cascades[END_REF][START_REF] Polis | Toward an integration of landscape and food web ecology: the dynamics of spatially subsidized food webs[END_REF][START_REF] Ruiz-Villanueva | Recent advances quantifying the large wood dynamics in river basins: New methods and remaining challenges: Large Wood Dynamics[END_REF][START_REF] Sass | Coarse Woody Debris in Lakes and Streams[END_REF][START_REF] Shumilova | Floating matter: a neglected component of the ecological integrity of rivers[END_REF] by providing new habitats, adding nutrients, and altering the geomorphology and flow of waterways.

In marine environments, woody debris makes up a relatively small proportion of inner shelf sediments, but occurs across all river-dominated margins [START_REF] Bianchi | Large-river delta-front estuaries as natural "recorders" of global environmental change[END_REF][START_REF] Charles | Ecogeochemical fate of coarse organic particles in sediments of the Rhône River prodelta[END_REF][START_REF] Hedges | What happens to terrestrial organic matter in the ocean?[END_REF][START_REF] Keil | Biochemical distributions (amino acids, neutral sugars, and lignin phenols) among size-classes of modern marine sediments from the Washington coast[END_REF][START_REF] Rabouille | Comparison of hypoxia among four river-dominated ocean margins: The Changjiang (Yangtze), Mississippi, Pearl, and Rhône rivers[END_REF][START_REF] Tesi | Changes in the composition of organic matter from prodeltaic sediments after a large flood event (Po River, Italy)[END_REF]. The bulk of this material arrives seasonally and provides communities of estuarine and coastal organisms a complex mixture of organic compounds with different chemical reactivities [START_REF] Benner | Depletion of 13C in lignin and its implications for stable carbon isotope studies[END_REF]. However, most studies are confined to qualitative approaches, focusing only on one typical habitat or considering only the most reactive part(s) of the total input (e.g. dissolved and sub-millimetric suspended particles). Large wood debris, derived from terrestrial plants and transported by rivers, are mostly ignored by marine biogeochemists [START_REF] Charles | Ecogeochemical fate of coarse organic particles in sediments of the Rhône River prodelta[END_REF][START_REF] Kandasamy | Perspectives on the terrestrial organic matter transport and burial along the land-deep sea continuum: Caveats in our understanding of biogeochemical processes and future needs[END_REF], even if vascular plants have been present on Earth for 450 million years and are recognized globally as significant contributors to marine carbon fluxes and sinks [START_REF] Cragg | Vascular plants are globally significant contributors to marine carbon fluxes and sinks[END_REF].

Quantifying not only the movement [START_REF] Turowski | Decadal carbon discharge by a mountain stream is dominated by coarse organic matter[END_REF] but also the rate of degradation of woody debris [START_REF] Díez | Breakdown of wood in the Agüera stream: Breakdown of wood[END_REF][START_REF] Ruiz-Villanueva | Recent advances quantifying the large wood dynamics in river basins: New methods and remaining challenges: Large Wood Dynamics[END_REF] has become an important part of managing risks associated with wood debris [START_REF] Schmocker | Driftwood: Risk Analysis and Engineering Measures[END_REF]Kramer and Wohl 2016). Whether on land [START_REF] Fravolini | Quantifying decay progression of deadwood in Mediterranean mountain forests[END_REF][START_REF] Freschet | Interspecific differences in wood decay rates: insights from a new short-term method to study long-term wood decomposition: New method to assess wood decay dynamics and rates[END_REF][START_REF] Müller-Using | Decay dynamic of coarse and fine woody debris of a beech (Fagus sylvatica L.) forest in Central Germany[END_REF], in rivers [START_REF] Chauvet | Production de litière de la ripisylve de la Garonne et apport au fleuve[END_REF][START_REF] Díez | Breakdown of wood in the Agüera stream: Breakdown of wood[END_REF], or at sea [START_REF] Björdal | Reburial of shipwrecks in marine sediments: a long-term study on wood degradation[END_REF][START_REF] Charles | Wood decay at sea[END_REF][START_REF] Fagervold | Sunken woods on the ocean floor provide diverse specialized habitats for microorganisms[END_REF], wood degradation takes place over a wide range of spatial and temporal scales. The degradation is the result of a complex interplay between biological, chemical and physical processes that make up the matter and energy cycles of ecological systems [START_REF] Bienhold | How deep-sea wood falls sustain chemosynthetic life[END_REF][START_REF] Björdal | Reburial of shipwrecks in marine sediments: a long-term study on wood degradation[END_REF][START_REF] Cragg | Lignocellulose degradation mechanisms across the Tree of Life[END_REF][START_REF] Fravolini | Soil attributes and microclimate are important drivers of initial deadwood decay in sub-alpine Norway spruce forests[END_REF][START_REF] Harmon | Ecology of coarse woody debris in temperate ecosystems[END_REF][START_REF] Krankina | Coarse woody debris in forest regions of Russia Krankina[END_REF][START_REF] Spänhoff | Breakdown rates of wood in streams[END_REF]. For example, accumulations of wood can act as a refuge or substrate, as a food source and/or as a dispersal vector [START_REF] Carlton | Tsunami-driven rafting: Transoceanic species dispersal and implications for marine biogeography[END_REF]Charles et al., 2020). Woody debris therefore is an important factor in constructing ecological continuity within and between many types of ecosystems.

Developing a synthetic view of wood degradation dynamics over environmental gradients requires better coordination between field experiments and modelling [START_REF] Kramer | Driftcretions: The legacy impacts of driftwood on shoreline morphology[END_REF]. The present study is part of a long term ecological research program designed to address this knowledge gap. The overall objective is to assess the variability and recycling dynamics of dead wood inputs in three connected habitats of a land-sea continuum (Xyloscope Project, CNRS (Centre National de la Recherche Scientifique), funding program: "Ecosphère Continentale et Côtière"). The aim of the present study is:

(i) to test if wood decomposition rates have different dynamics in each habitat type and (ii) to investigate if variations in decomposition rates may be attributed to the presence of a particular community. To do this, we have been monitoring (since 2014) the changes in sections of beech, Fagus sylvatica L., logs and standardized, reference blocks of Norway spruce, Picea abies (L.) H. Karst, placed within three environments connected by a relatively small river that drains a watershed in the foothills of the eastern Pyrenees Mountains. We report here the first comprehensive analysis of observed degradation rates along this continuum, from the forest to the coast.

Materials and methods

1 Study site

The study sites are in the catchment area of a small, torrential river, called "La Massane", located in the foothills of the French Eastern Pyrenees (Fig. 1). From its source, 968 m above sea level, the river runs through a protected old-growth beech grove (La Réserve Naturelle Nationale de la Forêt de la Massane, 337 ha), then continues, unimpeded, until it empties into the Gulf of Lions at Argelès-sur-Mer (total stream length is 23 km). The nature reserve has recently been designated a site of scientific interest for the conservation of biodiversity (2021, UNESCO World Heritage List of "Primary and ancient beech forests of the Carpathians and other parts of Europe"). La Massane drains a coastal watershed area of 17.2 km². The watershed is characterized by Mediterranean-type precipitation events. These last for short periods from a few hours to days [START_REF] Molinié | Rainfall regime of a mountainous Mediterranean region: statistical analysis at short time steps[END_REF]. The Mediterranean climate is characterized by mild wet winters and warm to hot, dry summers [START_REF] Lionello | The Mediterranean climate: An overview of the main characteristics and issues[END_REF]. We selected three different habitats (Fig. 1 and Table 1) for the experiments: the beech leaf litter of the forest floor; a stretch of the river headwaters; and the coastal seawater of the marina at Argelès-sur-Mer at the river mouth. Average interannual water discharge rates at the gaging station ("Mas d'en

Tourens"; 8.3 km from the river mouth), range from 0.242 to 0.328 m 3 s -1 (average, 0.282 m 3 s -1 , CI 95%, 55 year time series, Water Resources, French Ministry of Ecology, Sustainable Development and Energy, http://www.hydro.eaufrance.fr).

Experimental set-up

In March 2014, a set of sections (150 mm long) were cut from branches (40.4 ± 5.8 mm in diameter) of a recently fallen beech tree, F. sylvatica (L.). Any bark on them was left intact. During the study, we follow the decomposition of two different wood types in three different biotopes. Initially we wished to use a second species of tree present in the Massane Forest Reserve. There are few isolated specimens of yew (Taxus baccata) and black pine (Pinus nigra) but there were insufficient amounts of suitable fallen material (i.e. from a recently fallen tree with similar characteristics of age, size and condition) available at the time the study was under preparation. Therefore, we decided to use a reference block instead. Test or reference blocks are a common practice in marine wood degradation experiments. A block, or plank shape permits X-ray analyses for the detection and measurement of shipworms (e.g.

Steenstrup [START_REF] Steenstrup Kristensen | Observations on growth and life cycle of the shipworm Teredo navalis L. (Bivalvia, mollusca) in the Isefjord, Denmark[END_REF] and has also been adopted as an ad hoc method for monitoring the presence and activity intensity of shipworms in harbors (e.g. [START_REF] Hill | Marine borers and their relation to marine construction on the Pacific coast, being the final report of the San Francisco Bay Marine Piling Committee[END_REF]. We elected to use calibrated blocks of Norway spruce, a species that is foreign to the forest but widespread in Europe, and commonly used in general construction, hence readily available in an untreated format. This choice had the advantage of providing the required number of identical samples representative of a gymnosperm species, even if it did not allow any comparison between the two types of wood because of differences in configuration and condition (e.g. branches vs. blocks). Rectangular blocks of sapwood from Norway spruce (Picea abies (L.) H. Karst), were manufactured in dimensions of: 150(L) × 34(W) × 34(H) mm (L-length, W-width, H-height) from untreated, planed boards (2400 × 34 × 34 mm). Both sets of wood samples had surface to volume ratios of 1.1 to 1.3. Each wood piece was drilled (hole diameter: 7 mm) perpendicular to the longest dimension to provide an attachment point, then they were all oven dried at 50 °C ± 5 °C for five days and individually weighed. On 17 April 2014, 60 wood pieces from each species were arranged by sets of 5 along 12, 1 m long rope lines. These were then installed at each of the three field sites (4 lines per site, 20 pieces total). Each line was labelled (1 to 4) and the position of the wood logs (1 to 5) along each line was recorded. Wood pieces were spaced about 15-20 cm apart so that they would not come into contact once the rope was stretched on the ground or submerged in water. We found this arrangement adequately secured the installation of sample sets at each site, and allowed for efficient sample recovery.

In the beech grove, samples were installed on leaf litter among existing woody debris accumulation.

Each end of a line was secured by two iron bars driven into the forest ground. Samples immersed in the river were connected by their ends to a steel cable wrapped around a large boulder formation. In the marina of Argelès-sur-Mer, lines were attached to a floating pontoon at one end and weighted at the other in such a way that the lines remained entirely submerged at between 1 to 1.5 m below the water surface.

Air temperature (°C) and precipitation (mm) were recorded by the meteorological station of the Réserve Naturelle Nationale of the Massane Forest (42°28'41" N, 3°01'26" E). River water temperature was recorded with a HOBO Pendant® data logger. River flow data are provided by the monitoring program of EauFrance (http://www.eaufrance.fr/). At the Argelès-sur-Mer marina, water temperature and salinity were also measured at each sampling, at 0.6 m below the water surface using a Cond315i conductivity meter (Wissebschaftlich-Technische Werkstätter GmbH, Weilheim, Germany).

Sample processing

The lines at each site were sampled randomly after varying exposure times, depending on the field site, or the wood type. During recovery, each sample was placed in an individual plastic bag and stored at -20 °C until processing. Samples were then freeze-dried and blocks gently brushed to clean loose soil particles, leaf litter and epibiota from the surface. Then, each block was individually weighed.

After analysis, all samples collected in the project are stored in a repository under controlled conditions at the Observatoire Océanologique de Banyuls. They can be made available to other researchers for further analysis if desired (contact the corresponding author).

Data treatment

In this study, wood decay is expressed as the amount of wood remaining after a given time interval. This was calculated as the ratio between the remaining weight of wood and the initial weight of the wood piece. The remaining volume of wood was calculated from the lengths and diameters for the beech branch cylinders, and from the length, width and height for the spruce blocks. The ratio between weight and volume is the change in volumetric mass of a wood piece when the sample was recovered.

Exposure times (Table 1) were different for the Forest and River samples. Thus, differences in degradation rates between sites were tested using an analysis of covariance (ANCOVA) to compare the slopes of linear regressions [START_REF] Zar | Biostatistical analysis[END_REF].

Both

The Sea samples were all recovered at the same time intervals (Table 1). We compared the effects of the exposure duration on the mass loss of the samples with a one-factor analysis of variance. A Pearson's product-moment correlation was used to test the association between the remaining mass and volumetric mass of the wood blocks in all habitats at the time of sample collection. Coefficient values close to 0 indicate that mass loss is related to volume loss, while values close to 1 indicate that mass loss occurs without significant change in the apparent volume of the wood blocks.

Modelling the degradation process

Observed decay rates were estimated by fitting the data with either a negative exponential (Equation 1) or Weibull distribution (Equation 2). For samples exposed to the Forest and River conditions, the negative exponential formulation was expressed as:

𝑚 = 𝑚 0 𝑒 -𝑘𝑡 (1)
where m was the relative mass (dimensionless), t, is the exposure time (year), m0 is the initial mass of the sample, and k is the degradation rate, k (y -1 ).

The standardized form of the decay rate for Sea samples was a function with three parameters, αmin, tc and c, and of time, t, and was expressed as:

𝑚 = 𝑚 0 (𝛼 𝑚𝑖𝑛 + (1 -𝛼 𝑚𝑖𝑛 )𝑒 -( 𝑡 𝑡 𝑐 ⁄ ) 𝑐 ) (2)
where αmin, was the minimum fraction of wood remaining (between 0 and 1). The vector {αmin, tc, c} was optimized so that the sum of the squared residuals (RSS) between actual and estimated values was minimized. Equation 2was fit to the data using the gradient evaluation method from the Python library, SciPy (https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html).

Finally, uncertainty of the parameter estimates in equation ( 2) was deduced from the variancecovariance matrix computed by bootstrapping [START_REF] Efron | An Introduction to the Bootstrap[END_REF]. We generated 200 pseudoreplicates by resampling with replacement the centered residuals of the non-linear regression.

Results

Meteorological conditions

Temperatures ranged from 2.8 to 22.2 °C in the forest, and from 0.1 to 17.9 °C in the river water. High rainfall events were recorded at the beginning of the survey in November 2014 and again in March 2015

with 476 and 289 mm, respectively. Episodes of heavy rainfall matched the 5 river flooding events declared; all these occurred between the end of fall and the beginning of spring. The largest flood event occurred on 30 November 2014 and had a maximum instantaneous water discharge of 60 m 3 s -1 measured at the gaging station. In the marina of Argelès-sur-Mer, water temperature and salinity measured on the sampling dates ranged from 16.0 to 22.8 °C and from 34.9 to 37.4, respectively.

Wood loss rates

Regardless of wood sample type, there were marked differences in the amount of mass loss, as well as in the dynamics of losses between habitats (Fig 2). All curves decreased monotonically. On the forest floor and in the river, dynamics of degradation were well described by a negative exponential function (Table 2). At Sea, the pattern was different. Initially, the degradation rates were slow, then increase rapidly, then they slow again as the fraction of the wood mass accessible to shipworms decreased. On the forest floor and in the river, spruce decayed more slowly than beech wood (ANCOVA test, p<0.05 in both cases). The integrated degradation rate of beech was not significantly different on forest floor and in the river (0.187 y -1 and 0.134 y -1 , respectively (Table 2); ANCOVA test, p>0.05). For spruce, the integrated degradation rate was significantly higher in the river than in the forest (0.079 y -1 and 0.051 y -1 , respectively (Table 2); ANCOVA test, p<0.05).

At the coastal site (Sea), wood mass loss decreased significantly with exposure time (one-way ANOVA, p<0.001; Fig. 2). After 1.1 years of exposure the mass of the wood blocks submerged in seawater was halved (Table 3). Beyond this, the wooden blocks were judged too fragile to continue monitoring the degradation process without risking sample loss. Early wood degradation occurred over the first 7 months in seawater for both wood types (Table 3). Degradation was 6 to 9 times slower for beech in the other two conditions (River, Forest) and from 13 to 20 times slower for the spruce blocks, where the integrated degradation rate on the forest floor was by far the slowest (13.6 y -1 ).

Secondary evidence of the decay process

Visual examination of the samples showed that in forested conditions, the density of fungal hyphae was always much higher on beech logs than on spruce blocks. In the river, the wood samples showed clear signs of erosion (the initially sharp edges were all blunted). The beech samples in the river had completely lost their bark by the second date of sampling. At the other two sites, the percentage of bark at the end of exposure was always greater than 65% of the initial bark coverage (Fig. 3). In the forest, the underside of spruce blocks in direct contact with the soil layer, developed ridges and hollows following the alternating earlywood and latewood layers.

Fig. 3.

Relative amount of bark remaining on beech cylinders after each exposure period, in each of the three conditions (Forest, River, Sea). Corresponding exposure times are listed in Table 1.

Wood samples submerged at the marine site had an increasing number of holes with the time of exposure. Beech wood samples only had visible holes where the surface of the wood was not covered with bark. Attacks by shipworms were visible on all sides of the spruce blocks.

Depending on the habitat and wood type, the degree of dependence between mass loss and density of the samples was either close to 0 or close to 1. This suggests that mass loss was either related to volume loss or occurred without significant change in the apparent volume of the wood blocks (Fig. 4 A andB).

For beech wood, the correlation was high for samples placed directly on the forest floor (r²=0.959, n=18, p<0.001) and in the marine conditions (r²=0.964, n=18, p<0.001) (Fig. 4A). For spruce, the two variables were significantly correlated only for samples at sea (r²=0.968, n=18, p<0.001) (Fig. 4B). For the remaining conditions, the Pearson's correlation coefficient was between 0.05 for spruce on the forest floor and 0.15 for beech immersed in the river water.

Discussion

Our multi-year survey of wood degradation suggests the dynamics of wood decomposition differ by up to two orders of magnitude between the three different conditions (Forest, River, Sea) investigated along a land-sea continuum. To the best of our knowledge, only one other similar study [START_REF] Ferrer | Contribution of fungal and invertebrate communities to wood decay in tropical terrestrial and aquatic habitats[END_REF] reports on a synoptic comparison of wood recycling kinetics in different habitats of a tropical region. There are very few reports presenting integrated studies on wood production, degradation and transfer from the forest to the coastal sea. Hypothetically, such a study would start by developing a global approach, incorporating progressively processes quantified in all the environments that are crossed by the wood debris, including terrestrial, freshwater and marine biotopes. Quantities of wood transported would be a function of the wood debris mass available when transport processes are active (like flooding events on a river). This makes it important to quantify hydrological conditions as well as biomass production and degradation processes in each of the environments to be represented in a quantitative framework.

Variability in degradation rate estimates

The most striking result of our study was how much faster wood mass loss occurs under marine conditions, with the presence of shipworms. No difference in degradation rate was detected between the two wood types. In the beech wood samples, shipworms entered on the cut ends and the few places where the bark had disappeared. While the spruce blocks had entry holes on all sides. This suggests there may be variability in substrate colonization by shipworm species but that is undetected by our method. Even if we did not assess the net effect of shipworms on the wood here, the tunneling of these marine bivalves contributed to the nearly 50% of wood mass loss within 7 months. This suggests that wood boring invertebrates degrade wood much faster in the marine environment than has been reported for terrestrial environments [START_REF] Seibold | The contribution of insects to global forest deadwood decomposition[END_REF].

Among the three sites, the Forest samples are the only blocks to have experienced at least two distinct micro-environments because one side is in direct contact with the soil surface, while the other sides are exposed [START_REF] Tatti | What does 'lignoform' really mean?[END_REF]. In the sloping, irregular forest floor habitat, not all pieces of wood had strictly identical conditions, especially for humidity. This could account for the dispersion of values for the beech samples. The beech blocks were all covered with fungal hyphae while, by comparison, the surface of the spruce blocks remained nearly bare.

For River-exposed samples, the spruce degraded significantly faster than the Forest samples. However, the difference between them remained small, and decay rates were among the lowest recorded in the study. Conifer species tend to have lower decay rates than angiosperms [START_REF] Harmon | Release of coarse woody detritus-related carbon: a synthesis across forest biomes[END_REF].

Compositional differences, like the absence of large vascular vessels, a generally higher proportion of lignin, and a less diverse carbohydrate composition [START_REF] Pettersen | The chemical composition of wood[END_REF] may explain why gymnosperm wood decomposes differently than angiosperm wood [START_REF] Díez | Breakdown of wood in the Agüera stream: Breakdown of wood[END_REF][START_REF] Freschet | Interspecific differences in wood decay rates: insights from a new short-term method to study long-term wood decomposition: New method to assess wood decay dynamics and rates[END_REF].

Concerning beech wood, our results indicate no significant difference in degradation rates between conditions on the forest floor and in the river water. Nevertheless, the highest mass losses were measured on the forest floor for beech. In the river, loss of mass was more regular and the values for a given exposure duration was less scattered than for samples from the forest floor.

Decay processes

Mass loss and visual estimates of degradation only provide a non-specific, empirical estimate of wood degradation. In other words, our measurements cannot differentiate between all the ecological, biochemical and physical processes involved. It is thus important to consider what we can learn from the necessity of having to use two different formulations to fit the observations. For observations from the Forest and River sites, decay was described by a negative exponential model, which is a not only a common but also a minimal formulation [START_REF] Díez | Breakdown of wood in the Agüera stream: Breakdown of wood[END_REF][START_REF] Freschet | Interspecific differences in wood decay rates: insights from a new short-term method to study long-term wood decomposition: New method to assess wood decay dynamics and rates[END_REF][START_REF] Müller-Using | Decay dynamic of coarse and fine woody debris of a beech (Fagus sylvatica L.) forest in Central Germany[END_REF][START_REF] Spänhoff | Breakdown rates of wood in streams[END_REF]. This simple linear process suggests that the material decomposes over time at the same relative rate, and hence there is no variation imposed by any external factors, but only a single dependence of the substrate composition and its availability. In the marine environment, the strong non-linearity of the formulation suggests that, on the contrary, there are components involved that are not accounted for (e.g. the shipworm community). The change of relative rate in the decay can be attributed to change in the shipworm community composition, abundance and/or activity rate.

At sea, wood is removed and damaged as shipworms tunnel into and grow within the wood mass, hollowing out the structure from the interior and leaving unchanged the external dimensions. This leads to (for both wood types) a relatively rapid reduction in the mass of wood without an apparent decrease in volume. At the marine site, shipworms are known to occur quickly after the installation of wood samples [START_REF] Charles | Wood decay at sea[END_REF]. The dynamics of degradation depend on the seasonality of fallen wood production and the timing and frequency of new dead wood arrivals at the coast. In marine environments, there are also fungal and bacterial decomposers present [START_REF] Björdal | Reburial of shipwrecks in marine sediments: a long-term study on wood degradation[END_REF][START_REF] Ferrer | Contribution of fungal and invertebrate communities to wood decay in tropical terrestrial and aquatic habitats[END_REF]. The effects of these groups are expressed more slowly but probably favored by the increase in the surface-volume ratio resulting from the creation of an extremely dense network of galleries by the bivalves. We cannot exclude the hypothesis that degradation in the other two habitats could eventually catch up, given a longer observation time.

In the river, the volumetric mass of wood blocks did not change significantly during exposure regardless of the type of wood. This does not mean an absence of effect of other processes, but suggests instead that physical processes of erosion on the external edges of the blocks were the main cause. For example, the beech branches quickly lost their bark after the first flood event (November 30, 2014) which was also the largest event over the entire monitoring period. Bark affects the dynamics of wood decomposition in sometimes antagonistic ways, depending on the species, size of the woody debris, and position [START_REF] Dossa | The cover uncovered: Bark control over wood decomposition[END_REF]. However, our study does not allow us to draw any important conclusions on this matter. We can only report that the loss of bark into the river accounts for the erosion effect of the water current and suspended materials, while the persistence of bark on samples exposed to the marine environment may have acted as a barrier to shipworms.

Volumetric mass of the beech wood that stayed the longest in the river was on average lower than the rest of the series. It is thus possible that for the beech samples, degradation processes other than surface erosion were active. No similar effect was detectable for the spruce blocks. At the Forest site, the beech wood blocks had a relatively constant volume, while losing mass throughout the study period.

Fungi hyphae covered the entire surface of some blocks. The mass of the spruce blocks on the forest floor changed little and few scattered fungal hyphae could be observed on them. The main deterioration factor appeared to be erosion of the block surfaces that were in direct contact with the soil.

Influence of the experimental context

Studies on wood decay differ in terms of tree species used, size of the wood debris and how they are installed in the environment. The climatic context as well as the species involved are considered particularly important for wood degradation [START_REF] Edman | Warming effects on wood decomposition depend on fungal assembly history[END_REF][START_REF] Pietsch | Wood decomposition is more strongly controlled by temperature than by tree species and decomposer diversity in highly species rich subtropical forests[END_REF][START_REF] Ulyshen | Wood decomposition as influenced by invertebrates: Invertebrates and wood decomposition[END_REF].

Our estimated decay rates in each of the three habitats were consistent with data on wood degradation on soil, in riverine water and at sea as reported in the literature dealing with the same tree species under the same latitudes [START_REF] Charles | Wood decay at sea[END_REF][START_REF] Díez | Breakdown of wood in the Agüera stream: Breakdown of wood[END_REF][START_REF] Müller-Using | Decay dynamic of coarse and fine woody debris of a beech (Fagus sylvatica L.) forest in Central Germany[END_REF][START_REF] Spänhoff | Breakdown rates of wood in streams[END_REF]. In the comparable synoptic study in a tropical zone, [START_REF] Ferrer | Contribution of fungal and invertebrate communities to wood decay in tropical terrestrial and aquatic habitats[END_REF] showed that regardless of the habitat conditions, wood decayed at similar rates. [START_REF] Mackensen | Decomposition rates of coarse woody debris-A review with particular emphasis on Australian tree species[END_REF] reported significant inverse relationships between sample size and decomposition rate.

Therefore, [START_REF] Díez | Breakdown of wood in the Agüera stream: Breakdown of wood[END_REF] suggested that direct comparison must be limited to similar sizes and types of wood. In other studies, litter bags have been used to monitor the degradation of wood blocks to prevent the material under study from becoming dispersed in the environment. The disadvantage is that these bags partially isolate the sample from the environment [START_REF] Seibold | The contribution of insects to global forest deadwood decomposition[END_REF], thus limiting interactions with biotic and abiotic factors. At the risk of losing the material, we chose not to put any physical barrier between the wood and the environment, which allowed us to monitor all environmental effects (including surface erosion) on the wood.

Conclusion

Woody debris transferred to the sea is largely absent from studies of the global carbon [START_REF] Ciais | Carbon and other biogeochemical cycles[END_REF]). Yet, large accumulations of plant and tree remains are visible in many habitats of the land-sea continuum. The fluxes of this pool of organic carbon are considered negligible compared to fluxes of terrestrially derived dissolved and particulate organic carbon [START_REF] Bianchi | The role of terrestrially derived organic carbon in the coastal ocean: A changing paradigm and the priming effect[END_REF]. There are, however, no estimates of the flux, or stock of wood debris discharged into the sea available.

We observed that once woody material reaches the waters of the Mediterranean Sea, the integrated early degradation occurs at rates of 6 to 20 times faster than on the forest floor or when submerged in a river. Counter-intuitively, the results show that although woody debris continues to perform the same ecological functions and ecosystem services as in its source ecosystem where it originates, woody materials in marine environments cannot be considered part of the degradation-resistant organic carbon pool. At the level of the meta-ecosystem, because the location of the fast degradation is different from the location of the wood debris production, our study suggests that the limiting factor of the wood degradation process is the transfer between local ecosystems at the regional scale. The transfer rate between local ecosystems would constrain wood borer community dynamics and diversity.

This limitation on the local system highlights how some limiting ecosystem functions and processes may be obscured in large-scale accounting approaches attempting to represent carbon cycles (e.g. [START_REF] Ward | Representing the function and sensitivity of coastal interfaces in Earth system models[END_REF].

Fig. 1 .

 1 Fig. 1. Geographic location and spatial extent of the watershed. The three considered habitats are indicated by the circles. The Massane Forest Nature Reserve (Réserve Naturelle Nationale de la Forêt de la Massane) is indicated in the gray-shaded area, and the dashed line encompasses the watershed of the Massane River.

Fig. 2 :

 2 Fig. 2: Degradation observed of wood blocks during the first four years of exposure. Solid lines correspond to the fit of the regression models to the observations for beech cylinders (A) and Norway spruce blocks (B). The horizontal dashed line indicates the proportion equivalent to 50% of the initial wood mass.

Fig. 4 .

 4 Fig. 4. Relationship between the proportion of remaining wood mass and volumetric mass of beech wood (A) and Norway spruce wood (B) at the time the samples were collected. Straight lines indicate the existence of a significant correlation between the two variables on the Forest floor (solid line) and at the Sea site (dotted line).

Table 1

 1 Position, elevation, description and exposure duration at each of the three habitats

	Habitat	WGS 84 coordinates	Elevation (m)	Description	Exposure (year)	Wood type
	Forest	42° 29' 34" N 03° 01' 57'' E	698	litter of the beech grove	0; 0.3; 2.1; 3.1; 4 0; 0.3; 0.8; 3.2; 4	Beech Spruce
	River	42° 29' 18" N 03° 01' 42" E	648	head of the watershed	0; 0.3; 2.1; 3.1; 4.1 0; 0.3; 2.1; 3.2; 4.2	Beech Spruce
	Sea	42° 32' 34" N 03° 03' 08" E	-1	marina at the river mouth	0; 0.3; 0.4; 0.6; 1.1

Table 2

 2 Estimates of the decay rates (k) and the time, in years, needed to reach 50% of mass loss (t50) for the two types of wood exposed to forest and river habitats. Strength (R²) and statistical significance (p-value) of the relationships between the negative exponential model and the observations.

	Wood type	Habitat	R 2	p-value	k (y -1 )	SE	t50 (y)	t50 -range (y)
	Beech	Forest	0.6	***	0.187 0.029	3.7	3.3 -4.5
		River	0.9	***	0.134 0.007	5.2	4.9 -5.5
	Norway spruce Forest	0.8	***	0.051 0.006	13.6	12.3 -15.7
		River	0.9	***	0.079 0.006	8.8	8.2 -9.6

Table 3

 3 Optimized

	Wood type	𝛼min(SE)	tc (SE)	c(SE)	RSS	t50 (SE)
	Beech	0.48(0.01)	0.52(0.01)	6.77(0.99)	0.033	0.61(0.02)
	Norway Spruce 0.46(0.01)	0.51(0.01)	4.26(0.31)	0.012	0.64(0.01)

parameters of the curve fitting to the observations made for blocks from both wood types exposed to seawater; 𝛼min, proportion of the wood block mass that remained unavailable to wood-borers; tc, time (in year) required for the borers to consume half of their total consumption; and c, rapidity of mass loss in the vicinity of the inflection point of the fitted curve. Residuals sum of squares (RSS) is given as an estimate of the good of fit; t50 is time, in year, needed to reach 50% of the initial mass. SE account for standard errors.

Acknowledgements

This work was supported by the French CNRS (Centre National de la Recherche Scientifique) through their funding program EC2CO (Ecosphère Continentale et Côtière) with the DEFLAM and XYLOSCOPE projects. We thank the referees whose thoughtful reviews considerably improved the quality of the manuscript.