Hubert Du Pontavice
email: hubert.dupontavice@agrocampus-ouest.fr

Didier Gascuel

Gabriel Reygondeau

Aurore Maureaud

William W L Cheung

Climate change undermines the global functioning of marine food webs

Keywords: Marine Food Web, Species Assemblage, Biomass Flow, Trophic Transfer Efficiency, Biomass Residence Time, Climate Change, Trophic Ecology, Ecosystem Modelling

Sea water temperature affects all biological and ecological processes that ultimately impact ecosystem functioning. In this study, we examine the influence of temperature on global biomass transfers from marine secondary production to fish stocks. By combining fisheries catches in all coastal ocean areas and life history traits of exploited marine species, we provide global estimates of two trophic transfer parameters which determine biomass flows in coastal marine food web: the trophic transfer efficiency and the biomass residence time in the food web. We find that biomass transfers in tropical ecosystems are less efficient and faster than in areas with cooler waters. In contrast, biomass transfers through the food web became faster and more efficient between 1950 and 2010. Using simulated changes in sea water temperature from three Earth system models, we project that the mean trophic transfer efficiency in coastal waters would decrease from 7.7% to 7.2% between 2010 and 2100 under the 'no effective mitigation' Representative Concentration Pathway (RCP 8.5), while biomass residence time between trophic level 2 and 4 is projected to decrease from 2.7 to 2.3 year on average. Beyond the global trends, we show that the trophic transfer efficiencies and biomass residence times may vary substantially among ecosystem types and that the polar ecosystems may be the most impacted ecosystems. The detected and projected changes in mean trophic transfer efficiency and biomass residence time will undermine food web functioning. Our study provides quantitative understanding of temperature effects on trophodynamic of marine ecosystems under climate change.

Introduction

In marine ecosystems, temperature is one of the main factors affecting species physiology [START_REF] Cheung | Signature of ocean warming in global fisheries catch[END_REF][START_REF] Pörtner | ECOLOGY : Physiology and Climate Change[END_REF], biogeography (Tittensor et al., 2010), trophic dynamics [START_REF] Boyce | Spatial patterns and predictors of trophic control in marine ecosystems[END_REF][START_REF] Pörtner | Ocean Systems[END_REF], and ecosystem services such as food provision. A growing number of studies have shown that modifications of the natural fluctuation of ocean temperature have caused shifts in the geographic distribution of marine species and phenology from plankton to top predators [START_REF] Beaugrand | Marine biodiversity, ecosystem functioning, and carbon cycles[END_REF][START_REF] Cheung | Projecting global marine biodiversity impacts under climate change scenarios[END_REF][START_REF] Dulvy | Climate change and deepening of the North Sea fish assemblage : A biotic indicator of warming seas[END_REF]Perry, 2005;Pinsky, Worm, Fogarty, Sarmiento, & Levin, 2013;[START_REF] Poloczanska | Global imprint of climate change on marine life[END_REF]. These biogeographical shifts have resulted in reorganization of marine species assemblages in various ecosystems across the global ocean [START_REF] Beaugrand | Synchronous marine pelagic regime shifts in the Northern Hemisphere[END_REF][START_REF] Kortsch | Food-web structure varies along environmental gradients in a high-latitude marine ecosystem[END_REF][START_REF] Kortsch | Climate change alters the structure of arctic marine food webs due to poleward shifts of boreal generalists[END_REF] and influenced the composition of fisheries catches [START_REF] Cheung | Signature of ocean warming in global fisheries catch[END_REF]Stuart-Smith, Edgar, Barrett, Kininmonth, & Bates, 2015).

At the individual scale, warmer temperature results in faster exothermic biogeochemical reactions and higher metabolic rates (Brown, Gillooly, Allen, Savage, & West, 2004a;[START_REF] Bruno | Exploring the role of temperature in the ocean through metabolic scaling[END_REF]. Consequently, warmer temperature conditions may induce an increase in the speed of biomass transfer in the food web and a reduction of the biomass residence time. In addition, higher organism metabolic rates imply larger losses by respiration, and may cause a decrease in the efficiency of biomass transfers by affecting growth [START_REF] Barneche | The energetics of fish growth and how it constrains foodweb trophic structure[END_REF][START_REF] Heilmayer | Growth efficiency and temperature in scallops : A comparative analysis of species adapted to different temperatures[END_REF][START_REF] Palomares | Predicting food consumption of fish populations as functions of mortality, food type, morphometrics, temperature and salinity[END_REF][START_REF] Pörtner | Mechanisms Defining Thermal Limits and Adaptation in Marine Ectotherms : An Integrative View[END_REF].

These changes at the individual level are expected to propagate at the population and hence community levels [START_REF] Barneche | The energetics of fish growth and how it constrains foodweb trophic structure[END_REF]Brown, Gillooly, Allen, Savage, & West, 2004b;[START_REF] Bruno | Exploring the role of temperature in the ocean through metabolic scaling[END_REF]Pinsky, Selden, & Kitchel, 2020;Schramski, Dell, Grady, Sibly, & Brown, 2015).

In particular, changes in species composition induced by warmer waters may result in the selection of species characterized by shorter lifespan and higher respiration rates at every level of the food web, therefore leading to faster and less efficient biomass transfers, respectively. Several studies suggest profound reshuffles of marine communities due to anthropogenic changes in ocean conditions [START_REF] Cheung | Projecting global marine biodiversity impacts under climate change scenarios[END_REF]Pachauri, Mayer, & IPCC, 2015;Pereira et al., 2010;[START_REF] Pörtner | Ocean Systems[END_REF]Rutterford et al., 2015). However, the consequences of ocean warming on properties of biomass flow remain unexplored and unquantified.

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This article is protected by copyright. All rights reserved Here, we used a trophodynamic approach, initially developed by [START_REF] Lindeman | The Trophic-Dynamic Aspect of Ecology[END_REF], to analyse the impact of sea water temperature on biomass flowing in ecosystems, from primary consumer to top predators. Two parameters summarize these biomass transfers through the food web and are expected to change in a warming ocean: the trophic transfer efficiency and the biomass residence time. Trophic transfer efficiency (TTE) is the fraction of energy transferred from one trophic level to the next and summarises all the losses in the food web at each trophic level [START_REF] Jennings | Use of size-based production and stable isotope analyses to predict trophic transfer efficiencies and predator-prey body mass ratios in food webs[END_REF]Libralato, Coll, Tudela, Palomera, & Pranovi, 2008;[START_REF] Lindeman | The Trophic-Dynamic Aspect of Ecology[END_REF][START_REF] Niquil | Reaction of an estuarine food web to disturbance : Lindeman's perspective[END_REF][START_REF] Pauly | Primary production required to sustain global fisheries[END_REF][START_REF] Ricklefs | Metabolic theory predicts whole-ecosystem properties[END_REF][START_REF] Stock | Reconciling fisheries catch and ocean productivity[END_REF][START_REF] Strayer | Notes on Lindeman's Progressive Efficiency[END_REF]. TTE is measured as the ratio between the production rate of two adjacent trophic levels [START_REF] Baumann | A comment on transfer efficiencies[END_REF][START_REF] Libralato | Novel index for quantification of ecosystem effects of fishing as removal of secondary production[END_REF][START_REF] Lindeman | The Trophic-Dynamic Aspect of Ecology[END_REF][START_REF] Pauly | Primary production required to sustain global fisheries[END_REF][START_REF] Ricklefs | Metabolic theory predicts whole-ecosystem properties[END_REF]. This property of the food web has been widely studied [START_REF] Andersen | Trophic and individual efficiencies of sizestructured communities[END_REF][START_REF] Chassot | Global marine primary production constrains fisheries catches[END_REF][START_REF] Irigoien | Large mesopelagic fishes biomass and trophic efficiency in the open ocean[END_REF][START_REF] Jennings | Global-scale predictions of community and ecosystem properties from simple ecological theory[END_REF][START_REF] Stock | Reconciling fisheries catch and ocean productivity[END_REF] and some studies suggest that it spatially varies among biomes or ecosystem types [START_REF] Chassot | Global marine primary production constrains fisheries catches[END_REF][START_REF] Libralato | Novel index for quantification of ecosystem effects of fishing as removal of secondary production[END_REF][START_REF] Ricklefs | Metabolic theory predicts whole-ecosystem properties[END_REF][START_REF] Stock | Reconciling fisheries catch and ocean productivity[END_REF].

Biomass residence time (BRT) is the average amount of time a unit of biomass spends at a given trophic level before trophic transfer to higher trophic levels in the food web through predation [START_REF] Gascuel | Trophic flow kinetics in marine ecosystems : Toward a theoretical approach to ecosystem functioning[END_REF][START_REF] Ricklefs | Metabolic theory predicts whole-ecosystem properties[END_REF]. BRT (expressed in years) is inversely proportional to the speed of biomass transfer across trophic levels. It directly affects the biomass present at each trophic level of the food web (longer residence time results in greater biomass at each trophic level).

The aim of this study is to analyse how the temperature-induced spatial patterns in species composition affect biomass transfers in marine food webs, and how these transfers are expected to change over the 21 st century. We focus on community-level biological responses driven by changes in species assemblages. The study and analysis are performed for the coastal regions of the global ocean which currently support the bulk of fisheries production, and where catch data are used as insights on the features of the marine community structure.

First, we measure TTE and BRT based on fisheries catch species composition over the period 2000-2010 and determine how these two parameters vary along the temperature gradient in the global coastal marine ecosystems. Second, to detect the past changes in biomass transfers and determine if ocean warming has already affected them, we analyse the trends in TTE and BRT between 1950 and 2010 and we compare the observed and modelled trends using sea water temperature data. Finally, we project TTE and BRT by 2100 using simulated changes in sea water

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This article is protected by copyright. All rights reserved temperature based on three Earth system models under two contrasting greenhouse gas emissions scenarios.

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Materials and Methods

Study area and catch data

Since the composition of species assemblages is unknown in many coastal marine ecosystems that we studied, we estimated trophic transfer parameters based on catch data, assuming they can be considered as proxy of the true features of the food web. This assumption will be further discussed and sensitivity analyses were conducted.

Annual reconstructed catch data made available by the SeaAroundUs project from 1950 to 2010 (Pauly and Zeller, 2015) were used. This set of data is spatially disaggregated by taxon on a 1° x 1° spatial grid of the world ocean. The reconstruction is based on the official records from the Food and Agriculture Organization (FAO), with addition of undeclared artisanal and subsidence fisheries, recreational catches, discarded bycatch and illegal and unreported catch (Pauly and Zeller, 2015).

We removed catch of rare taxa representing less than 0.05% of the total catches for each year and catches from unidentified species. Biogeography of coastal and shelf areas were delimited using the distribution of coastal biomes identified by [START_REF] Reygondeau | Dynamic biogeochemical provinces in the global ocean : DYNAMIC BIOGEOCHEMICAL PROVINCES[END_REF] and adapted from [START_REF] Longhurst | Ecological geography of the sea (2nd ed)[END_REF]. To ensure that parameters issued from the catch composition in each grid cell is representative of the food web, we removed grid cells where unidentified species represented more than 50% of the total catch, and cells where one single species represented more than 75% of the catch. Finally, we kept only grid cells where there were more than 10 species excluding rare taxa.

After passing the dataset through the above filters, the final dataset consists of 5,783 (75% of the cells) 1° latitude x 1° longitude grid cells and 1760 taxa in coastal and shelf seas. Each cell was classified as one of the 3 biomes: tropical, temperate and polar biomes. Upwelling ecosystems were added using the biogeographical provinces described by [START_REF] Reygondeau | Dynamic biogeochemical provinces in the global ocean : DYNAMIC BIOGEOCHEMICAL PROVINCES[END_REF] (Figure 1).

Trophic transfer efficiency and biomass residence time calculations

Trophic transfer efficiency (TTE) and biomass residence time (BRT) were estimated within each grid cell using a trophodynamic approach based on two indicators: the efficiency cumulated indicator (ECI) and the time cumulated indicator (TCI). The method to calculate TTE and BRT is summarised in Figure 2.

a. Trophic transfer efficiency (TTE)

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The efficiency cumulated indicator (ECI) developed by [START_REF] Maureaud | Global change in the trophic functioning of marine food webs[END_REF] quantifies the fraction of secondary production transferred from trophic level (TL) 2 to 4, considering only metabolism losses due to respiration and excretion (see partial transfer efficiency (partial TE on Figure 3)). It was calculated for each grid cell i and each year y, as an aggregation from TL = 2 to TL = 4 of the production to consumption ratio (P/Q) τ,i,y which can be defined as the "gross food conversion efficiency" [START_REF] Christensen | Trophic models of aquatic ecosystems[END_REF] at trophic level τ, with the following equations:

𝐸𝐶𝐼 𝑖,𝑦 = 4.0 ∏ 𝜏 = 2.0 ( ( 𝑃 𝑄 ) 𝜏,𝑖,𝑦 )
Eq. 1 P/Q is firstly calculated for each species or taxon j, as the ratio of P/B (Production to Biomass) to Q/B (Consumption to Biomass). For finfish, these taxon-specific ratios are calculated according to the empirical equations of [START_REF] Gascuel | Trophic flow kinetics in marine ecosystems : Toward a theoretical approach to ecosystem functioning[END_REF] and [START_REF] Palomares | Predicting food consumption of fish populations as functions of mortality, food type, morphometrics, temperature and salinity[END_REF] and based on life history traits and thermal habitat (see Supporting Information Appendix S1). The required data (asymptotic weight, Von Bertalanffy growth coefficient, diet type and aspect ratio) were taken from FishBase (http://www.fishbase.org, Froese and Pauly, 2018). For the others species (e.g., cephalopods, crustaceans), the taxon-specific P/B and P/Q ratios were extracted from EcoBase [START_REF] Colléter | EcoBase : A repository solution to gather and communicate information from EwE models[END_REF] (see Supporting Information Appendix S1).

Then, taxon-specific P/Q ratios were transformed into a P/Q trophic spectra [START_REF] Gascuel | The trophic spectrum : Theory and application as an ecosystem indicator[END_REF]. To consider the within-taxon variability of trophic levels, catches of every taxon were distributed over a range of trophic classes (following a lognormal distribution and using classes with a width of 0.1 TL). Trophic spectra were obtained by averaging the taxon-specific P/Q ratios weighted by the resulting catch per taxon and trophic class.

Since the ECI calculation does not account for losses in trophic transfers related to non-predation natural mortality and biomass accumulation, ECI is measuring a partial transfer efficiency, and is likely to overestimate the true trophic transfer efficiency (TTE). To account for such overestimation, partial transfer efficiency was converted into TTE by introducing a correction term based on Ecotrophic Efficiency (EE, [START_REF] Christensen | ECOPATH II -a software for balancing steady-state ecosystem models and calculating network characteristics[END_REF]) and B acc (biomass accumulation rate within each species or taxon). Thus, (EE -B acc ) measures the fraction of the production of a given taxon not transferred to detritus and not accumulated by the taxon, and thus available for trophic transfers through consumption by predators (see theoretical graph on Figure 3). EE and B acc were extracted from coastal Ecopath models (see Supporting Information

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This article is protected by copyright. All rights reserved Appendix S2) included in the EcoBase database [START_REF] Colléter | EcoBase : A repository solution to gather and communicate information from EwE models[END_REF]. The extracted data were then used to calculate a correction factor for each trophic level  and for each ecosystem type  (see Supporting Information Appendix S3). Finally, the two components of TTE -the fraction of loss due metabolism (P/Q) and the non-predation natural mortality and biomass accumulation (EE-B acc ) -are combined. Thus, the trophic transfer efficiency between TL=2 and TL=4, can be estimated as a product of all trophic classes; the estimates, which represent TTE across two trophic levels, is transformed into TTE expressed per trophic level by taking a square root of the term (Eq.2):

𝑇𝑇𝐸 𝑖,𝑦 = [ 4.0 ∏ 𝜏 = 2.0 ( ( 𝑃 𝑄 ) 𝜏,𝑖,𝑦 • (𝐸𝐸 -𝐵 𝑎𝑐𝑐 ) 𝜏, 𝛽 ) ] 1 2
Eq. 2

b. Biomass residence time (BRT)

The BRT, which is called the time cumulated indicator (TCI) by [START_REF] Maureaud | Global change in the trophic functioning of marine food webs[END_REF], was calculated by aggregating the time spent by each unit of biomass within small trophic level classes of   =0.1 TL, when moving into the food web from trophic level 2 to 4. [START_REF] Gascuel | Trophic flow kinetics in marine ecosystems : Toward a theoretical approach to ecosystem functioning[END_REF] showed that the mean speed of the biomass flow passing through a given trophic level can be measured as the production to biomass ratio (P/B). Therefore, as a speed is defined by a distance divided by a time, the time a unit of biomass need on average to cross a trophic class from TL= to TL=+ is equal to /(P/B). Thus, the BRT between TL=2 and TL=4, can be estimated as a sum for all trophic classes, according to:

𝐵𝑅𝑇 𝑖,𝑦 = 4.0 ∑ 𝜏 = 2.0 ∆ 𝜏 ( 𝑃 𝐵 ) 𝜏,𝑖,𝑦 Eq. 3
where BRT is the biomass residence time in the food web, between tropic levels 2 and 4, for cell i and year y. P/B ratio was first calculated by species or taxon (see Supporting Information Appendix S2), and converted into P/B trophic spectra using the above described method, thus providing an estimate for every trophic class.

c. Data used for the calculations TTE and BRT were calculated for each year between 1950 and 2010 in each grid cells. This computation is using the annual catch species composition from the SeaAroundUs database.

Trophic levels for each species or taxon were obtained from Fishbase and SeaLifeBase

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This article is protected by copyright. All rights reserved (http://www.sealifebase.org, Palomares and Pauly, 2018). We used sea surface temperature (SST)

to estimate the thermal habitat of fish required to calculate the taxon-specific ratios (see Supporting Information Appendix S1) for every year between 1982 and 2010 from NOAA, using the Optimum Interpolation (OI) V2 dataset derived from in situ and satellite SST's (https://www.esrl.noaa.gov/psd/data/gridded/data.noaa.oisst.v2.html).

Relationships between temperature, trophic transfer efficiency and biomass residence time

In order to understand how the two trophic transfer parameters vary spatially and to determine their relationship to temperature in the recent past, the average values over the period 2000-2010 of TTE and BRT were estimated in each cell. Then, two generalized linear models (GLM), with TTE and BRT per grid cell as the dependent variables and sea water temperature as independent variable, were developed. The models consider an ecosystem type effect (tropical, temperature, polar or upwelling), in order to highlight potential non-temperature related differences in ecosystem structure. The interaction between sea water temperature and ecosystem type is also integrated in the models to take into account the differences in temperature effects among the four ecosystem types.

All statistical analyses were performed with the R free software environment (v.3.4.4, http://cran.r-project.org). The best-fitted family distribution and link function were selected among Gamma distribution (with identity, logarithmic and inverse link function), inverse Gaussian distribution (with identity, logarithmic and inverse link function), and Gaussian distribution (with identity and inverse link function) with log-transformed dependent variable or not. We finally chose to select models based on a Gaussian distribution on log-transformed trophic transfer parameters:

𝑙𝑜𝑔(𝑋) = 𝐼𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 + 𝑆𝑆𝑇 + 𝑒𝑐𝑜𝑠𝑦𝑡𝑒𝑚 𝑡𝑦𝑝𝑒 + 𝑆𝑆𝑇 • 𝑒𝑐𝑜𝑠𝑦𝑡𝑒𝑚 𝑡𝑦𝑝𝑒 + 𝜀 with . 𝜀 = 𝑁(0,𝜎²)
X is TTE or BRT and is the normally distributed error with mean of 0 and variance of σ 2 . 𝜀 Adequacy of the GLMs was evaluated by checking the distribution of model residuals for homoscedasticity, normality, the fraction of deviance explained by the model, and by each variable. The significance of the parameters was assessed using Wald chi-square tests. Laurent's correction was applied to the models to obtain unbiased estimations from log-transformed data [START_REF] Laurent | The Lognormal Distribution and the Translation Method : Description and Estimation Problems[END_REF].

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Past and projected trends in trophic transfer efficiency and biomass residence time

In order to contrast projections over the 21th century against the past variability and trends, TTE and BRT were estimated from 1950 to 2010, based on the fisheries catch species compositions.

These observed past trends were compared to temperature-based estimates using the GLM statistical model. Then, we projected TTE and BRT by 2100 in the four ecosystem types, using yearly values of SST predictions from three Earth System Models, respectively developed by: the

Sensitivity analysis

TTE and BRT time are studied here using post-filtered catch data (see Study area and catch data in Materials and Methods), assuming that the features of the biomass flow of the exploited fraction of marine food webs reflect the features of the biomass flow of the entire marine food web. We recognize that the use of catch data to describe marine ecosystem functioning and structure may lead to biased estimators, due to selective fisheries and changes in the fishing strategies over time and space [START_REF] Branch | The trophic fingerprint of marine fisheries[END_REF][START_REF] Pauly | Fisheries : Does catch reflect abundance?[END_REF]). To evaluate the potential effects of these biases, two sensitivity analyses were conducted (Supporting Information Appendix S4 and S5). First, we tested the robustness of our models by adding the effects of the catch per surface area (as an indicator of the fishing intensity) and the mean trophic level of catch (MTL, as an indicator of the fishing strategy at the ecosystem level). Second, we used a selection of Ecopath ecosystem models to compare the estimates of the trophic transfer parameters based on species assemblages in the ecosystems or in the catch.

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Since we estimated the two trophic transfer parameters from the TL=2 to TL=4 based on catch data, a large fraction of the biomass at lower levels is made up of species such as zooplankton, benthic invertebrates, or larvae not targeted by fishing. Thus, in our catch dataset, species less than or equal to TL of 2.5 represent only between 4 and 8% of the annual global catch. As a consequence, the catch composition between TL=2 and TL=2.5 is unable to reflect the species composition in the ecosystem, what may also lead to bias in our estimates. This potential bias was tested by modelling the temperature effect on the two trophic transfer parameters using only catches between TL=2.5 and TL=4 (Supporting Information Appendix S6).

Our data, TTE and BRT are spatially autocorrelated. This autocorrelation is supposed to be captured by the models. Nevertheless, if a spatial autocorrelation remains in the residuals of the GLMs, the key assumption that residuals are independent and identically distributed is violated, and parameter estimates may be biased. Consequently, we tested the potential spatial autocorrelation bias on our models by comparing the developed models and models based on 100 subsamples with no or a weak spatial autocorrelation (Supporting Information Appendix S7).

Finally, the natural non-predation mortality was taken into account in our analysis by adding a correction which reduces the TTE values. The correction is calculated on the average of ecotrophic efficiency and biomass accumulation by aggregating 72 Ecopath models per ecosystem type. Since these parameters may be modelling dependent and inaccurate in some models, we tested the introduction of this supplementary loss in the model by comparing the sea temperature effect including or not this correction (Supporting Information Appendix S3).

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Results

Relation between sea surface temperature and ecosystem trophodynamics

Trophic transfer efficiency (TTE) and biomass residence time (BRT) over the recent period 2000-2010 differ significantly according to ecosystem type (p-value<0.001). Polar ecosystems exhibit the most efficient but the slowest biomass transfers with a TTE of 10.4% ± 2.7 and BRT of 4.4 years ± 1.3 between trophic level 2 and 4 (Figure 4a andb). In contrast, trophic transfers in upwelling and tropical ecosystems appear faster with 2.8 years ± 2.2 and 1.9 years ± 1.9

respectively but less efficient with 5.9% ± 0.7 and 6.5% ± 0.6. Intermediate values are estimated in temperate ecosystems with 2.8 years ± 0.9 and 8.1% ± 2.4.

The same spatial patterns emerged for the two trophic transfer parameters (see related maps on Figure 5a andb). In the colder coastal waters, for example in the Bering Sea and in the Antarctica coast, TTE and BRT exhibit high values, while in the warmer waters for example along the African coast and in the continental shelf of Southeast Asia, biomass is transferred faster and less efficiently. Some exceptions exist, such as in the Gulf of Mexico, which exhibits high TTE values, and in the Indian Ocean between the area between Seychelles and Mauritius showing a high BRT.

Our models indicate that SST and ecosystem type have both a statistically significant effect on the studied biomass flow parameters. Furthermore, SST explained 34.7% and 48.7% of the total deviance for TTE and BRT respectively, while the interaction between SST and the ecosystem type explained an additional 5.4% and 2.3% for these two parameters (see Supporting Information Appendix S8).

The decreasing relationship between sea temperature and TTE or BRT is consistent across ecosystems types, although the variations in temperature sensitivity of these food web parameters between the ecosystem types were not expected (Figure 4c andd). Temperature sensitivity for TTE is higher in temperate and upwelling zones, followed by polar and tropical ecosystems. In contrast, BRT is more sensitive to temperature in polar and tropical ecosystems followed by temperate and upwelling ecosystems.

Observed past trends in trophic transfer efficiency and biomass residence time Over the period 1950-2010, the observed global mean of TTE, computed from the catch composition, significantly increased from 7.1% to 7.6% (Figure 6a, p-value linear model < 0.001),

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This article is protected by copyright. All rights reserved while BRT decreased from 2.5 to 2.2 years (Figure 6b, p-value linear model < 0.001). The changes in TTE and BRT occurred mainly before the mid-1990s, then TTE stopped its increase and BRT decreased at a slower pace. These increasing TTE and decreasing BRT are observed in every ecosystem type (see Supporting Information Appendix S9) except for TTE in polar ecosystem where the estimates increased from 1950 to 1978 before a steep decrease at the beginning of the 1980s and then an increase until 2010. The outputs of the temperature-based model show that BRT should have decreased at a slower rate than observed, while the TTE should have decreased slightly in place of increasing. Thus, changes in the species composition of the catch have affected the observed parameters which cannot be explained only by the temperature effect. This suggests that faster and more efficient trophic transfers have resulted from direct fishing-induced impacts on species assemblages.

Projections for the end of the century TTE and BRT should decrease until 2040, regardless of the climate scenario or the Earth system model considered (Figure 7a andb). From 2000 to 2040, global averages are projected to decrease slightly by 0.09% for TTE and by 0.09 year for BRT. After 2040, TTE and BRT remain stable in scenario RCP2.6, while the decrease accelerates for both indicators in scenario RCP8.5. Overall, under RCP8.5, we projected a 0.5% loss of TTE (from 7.7 to 7.2%) and a 0.4 year decrease in BRT (from 2.7 to 2.3 years) over the period 2000-2100.

The geographical distributions of the projected changes in TTE and BRT under RCP8.5 scenario show that the two trophic transfer parameters should decrease everywhere by the end of the 21 st century (2100), with the largest changes expected at high latitudes (Figure 4g andh). In polar, upwelling and temperate ecosystems, the projected losses in TTE are around 0.8% by 2100, while they are much lower around 0.2% in tropical ecosystems (Figure 7c). The BRT will be more affected by ocean warming in polar ecosystems than in others, with more than a 1.0 year decrease by 2100, compared to 0.4 year (~5 months) in tropical ecosystems, 0.2 year (~2 months) in temperate ecosystems, and almost no effect in upwelling ecosystems, on average (Figure 7d).

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Discussion

Our results provide estimates of average TTE and BRT in coastal marine food webs, at the global scale and per ecosystem type. We show that human-induced changes in species assemblages may already have affected the functioning of coastal marine food webs and are expected to have greater impacts over the 21th century. Specifically, the trophodynamics of coastal marine ecosystems have already changed and are expected to amplify their rate of change in the coming decades.

Less efficient and faster transfers in warm waters

Our study shows that sea water temperature significantly influences biomass transfers through the food web in global coastal marine ecosystems. The warmest coastal ecosystems are characterised by low-efficient and fast biomass transfers through the food web. These characteristics indicate that species assemblages are dominated, at each trophic level, by species with low TTE because of large energy losses due to their metabolism processes that scale with temperature (Brown et al., 2004b;[START_REF] Ricklefs | Metabolic theory predicts whole-ecosystem properties[END_REF]. Also, the BRT is shorter in tropical coastal ecosystems so the biomass transfer between a prey and its predator is faster at each trophic level. These trophic functioning properties may be explained by species assemblages where communities may be dominated by short-living and fast-growing species. In contrast, in polar and temperate ecosystems, biomass is transferred more efficiently and slowly, where a unit of biomass spends more time in the food web. Such trophodynamic properties may be explained by species assemblages dominated by long-living and slow-growing species in colder waters as suggested by several authors in polar ecosystems (e.g., [START_REF] Murphy | Understanding the structure and functioning of polar pelagic ecosystems to predict the impacts of change[END_REF][START_REF] Peck | A Cold Limit to Adaptation in the Sea[END_REF][START_REF] Pörtner | Constraints and trade-offs in climatedependent adaptation : Energy budgets and growth in a latitudinal cline[END_REF]. As the biomass transfer indicators are calculated using trophic spectra, the observed contrasts between warm and cold waters do not result from the distribution of long or short-living species among food webs (more predator and less prey in cold waters), but from differences occurring at every trophic level (longer living preys and predators in cold waters in contrast to warm waters).

The natural non-predation mortality is an additional factor reducing TTE by introducing supplementary losses, although it appeared to have little effect on the differences in TTE between the ecosystem types (Appendix S3). Finally, the low TTE in upwelling is consistent with the literature (Coll, Libralato, Tudela, Palomera, & Pranovi, 2008;[START_REF] Libralato | Novel index for quantification of ecosystem effects of fishing as removal of secondary production[END_REF] and may be due to the highly variable productivities of upwelling ecosystems. This lack in stability, which

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This article is protected by copyright. All rights reserved characterises immature or disturbed ecosystems (sensus [START_REF] Odum | The Strategy of Ecosystem Development[END_REF], is likely to result in a weakly structured food web with fast and inefficient biomass transfers.

Robustness of the analysis

As we use catch data to study TTE and BRT, fishing effort, in addition to temperature, might affect trophic flow in marine ecosystems. The assessment of the potential effects of the confounding factors from fishing shows that the temperature sensitivity of these indicators remains supported (Appendix S4 and S5). First, we found that the fishing intensity (catch per km 2 ) and the fishing strategies (MTL) have only a small effect on TTE estimates while BRT estimates are more sensitive to fishing intensity (Information Appendix S4). However, the effects of sea water temperature and ecosystem type on BRT remained highly significant and qualitatively unchanged even after accounting for the effects of fishing. Secondly, based on data from the selected Ecopath models, the absolute values of BRT and TTE are overestimated and underestimated, respectively, when using catch data instead of biomass data (Appendix S5). However, here too, qualitative results regarding the temperature effect and the variability among ecosystem types remained consistent.

Furthermore, it appeared that the exclusion of the lowest trophic levels affects mainly cold waters and upwelling ecosystems, decreasing the estimated TTE and increasing BRT (Appendix S6).

However, the variations due to the lower trophic levels of the food web do not modify the order of magnitude and the trends regarding sea water temperature and ecosystem type effects.

The potential bias due to the spatial autocorrelation is low for TTE with a slight effect in tropical ecosystems (Appendix S7). Regarding BRT, the effect is a bit stronger, suggesting that we underestimated BRT in temperate and tropical ecosystems (greater values without the spatial autocorrelation) and we underestimated the temperature effects in polar and tropical ecosystems (greater slopes without the spatial autocorrelation).

The introduction of the natural non-predation mortality as an additional loss in TTE estimates by adding a correction factor (Supporting Information Appendix S3) has a rather low effect on the GLMs outputs. It induces an overall decrease in TTE but that does not change substantially neither the temperature effect nor the differences between the ecosystem types. Even if it is imperfect especially because we use potentially biased modelled parameters, we consider that the inclusion of the correction is better than ignoring the additional losses.

Accepted Article

This article is protected by copyright. All rights reserved More generally, the observed temperature effects and predicted changes in trophic transfer are likely to be underestimated because our study is taking into account only the effect of community structure on the ecosystem functioning. Additional ocean warming effects at individual and population level are also expected to change the trophic transfer in marine food webs.

Towards faster and less efficient trophic transfers

The global decrease in BRT and increase in TTE over the period 1950-2010 is likely partly driven by the global increase in fishing pressure as previously shown by [START_REF] Maureaud | Global change in the trophic functioning of marine food webs[END_REF], who focused on quantifying the fishing effects on trophodynamics over the Large Marine Ecosystem.

Majorities of fishing activities tend to select the targeted large and long-living species causing a decrease in their abundance compared to small species with fast life histories [START_REF] Cheung | Intrinsic vulnerability in the global fish catch[END_REF][START_REF] Jennings | Structural change in an exploited fish community : A consequence of differential fishing effects on species with contrasting life histories[END_REF]Planque et al., 2010;[START_REF] Shephard | Size-selective fishing drives species composition in the Celtic Sea[END_REF]. Our results suggest that the same fishing effects occur within each trophic class leading to shorter biomass residence time and less efficient energy transfer in marine food webs. Such a trend may be considered as an adaptive reaction to the fishing pressure [START_REF] Maureaud | Global change in the trophic functioning of marine food webs[END_REF], leading to more efficient, but simplified and potentially less resilient food web.

The global decreasing trend of TTE estimated using the modelled temperature-based GLM (Figure 6a) is not consistent with the observed TTE over the period 1950-2010. The opposition between observed and modelled trends can be derived from the dominant fishing pressure. The decrease in the modelled TTE is driven by ocean warming, while the increase in the observed TTE between 1950 and the mid-1990s can likely be attributed to the growing amount of fishing pressure [START_REF] Maureaud | Global change in the trophic functioning of marine food webs[END_REF][START_REF] Pauly | Catch reconstructions reveal that global marine fisheries catches are higher than reported and declining[END_REF]. Following [START_REF] Pauly | Catch reconstructions reveal that global marine fisheries catches are higher than reported and declining[END_REF], global fishing catch reached its maximal value in 1996 and stabilized until now. Therefore, the stabilization of TTE trend from the mid-1990s can be assumed to be caused by the effects of constant fishing catch over already exploited system and the growing effect of ocean warming [START_REF] Beaugrand | Prediction of unprecedented biological shifts in the global ocean[END_REF]. In parallel, the decreasing trend in BRT between 1950 and the mid-1990s is consistent with the observed BRT (Figure 6b). However, the decrease in observed BRT is steeper between 1950 and the mid-1990s. That can be also attributed to the increasing fishing pressure. As for TTE, the trend in observed BRT stabilized between 2000 and 2010 probably due to the decreasing fishing effects and the growing effect of ocean warming.

In the coming decades, as ocean warming is expected to intensify and by hypothesising that global fishing pressure will stabilize, the trend in TTE may reverse and decrease (Figure 7a andc) while

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This article is protected by copyright. All rights reserved BRT may globally continue to decrease (Figure 7b andd). Consequently, the greater losses of production between every trophic level due to the decrease in TTE and BRT in the food web may lead to a decrease in biomass and production at each trophic level.

Our projections of changes in trophic transfer functioning only result from the expected modifications in species assemblages induced by warming. At the species level, responses to warming may differ from one species to the other, depending on their thermal tolerance and life histories (Perry et al., 2010;[START_REF] Pörtner | Climate change effects on fishes and fisheries : Towards a cause-and-effect understanding[END_REF], and leading to changes in their own productivity and/or biogeographical shifts of their spatial distribution. In addition, indirect effects due to changes in species interactions can enhance the changes in marine community structure and functioning [START_REF] Bruno | Exploring the role of temperature in the ocean through metabolic scaling[END_REF].

Polar ecosystems: the more affected ecosystems?

Ocean warming effects on the trophic transfer parameters exhibit substantial differences between ecosystem types. TTE and BRT in polar ecosystems are projected to strongly decrease by 2100 due to its high sensitivity to temperature (Figure 4). Such a high thermal sensitivity of TTE and BRT in polar ecosystems is likely due to the narrow thermal window of the polar species that inhabit in stable ecosystem [START_REF] Peck | Extreme sensitivity of biological function to temperature in Antarctic marine species[END_REF][START_REF] Pörtner | Ocean Systems[END_REF]Sunday, Bates, & Dulvy, 2011). The changes in biomass transfer may be also exacerbated by the reshuffling of polar ecosystems structure induced by the observed and projected poleward shifts in species distribution and the expansion of subpolar/boreal communities with faster and less efficient biomass flow properties [START_REF] Cheung | Projecting global marine biodiversity impacts under climate change scenarios[END_REF][START_REF] Frainer | Climate-driven changes in functional biogeography of Arctic marine fish communities[END_REF][START_REF] García Molinos | Climate velocity and the future global redistribution of marine biodiversity[END_REF][START_REF] Kortsch | Climate change alters the structure of arctic marine food webs due to poleward shifts of boreal generalists[END_REF]. In addition, although the complexity and the diversity of the planktonic food web in polar ecosystems is equivalent to temperate ecosystems [START_REF] Michel | Biodiversity of Arctic marine ecosystems and responses to climate change[END_REF][START_REF] Smetacek | Polar ocean ecosystems in a changing world[END_REF], the relatively low coastal marine biodiversity of high trophic level species (Tittensor et al., 2010;Worm & Lotze, 2016) may accelerate the rate of decline of polar species. Such declines of endemic and sea ice dependent species are already observed at some locations (e.g., krills in the Southern Ocean, [START_REF] Atkinson | Long-term decline in krill stock and increase in salps within the Southern Ocean[END_REF]. Besides, the effects of temperature may be also abrupt in polar ecosystems due to more frequent and extreme marine heatwaves [START_REF] Frölicher | Marine heatwaves under global warming[END_REF].

Species inhabiting in tropical ecosystems has also a relatively narrow thermal window that could explain the high thermal sensitivity of BRT [START_REF] Poloczanska | Responses of Marine Organisms to Climate Change across Oceans[END_REF]. However, TTE in tropical ecosystem exhibits a low thermal sensitivity and thus a moderate projected decrease by 2100. The

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This article is protected by copyright. All rights reserved higher biodiversity in tropical ecosystem may help buffer the warming effects on biomass transfer at lower latitudes. Therefore, in tropical ecosystem the BRT is expected to largely decrease but the losses in production between each trophic level may be weakly impacted. However, as our projections are based on current temperatures, we likely underestimate the effects of ocean warming on tropical ecosystems since these ecosystems will experience unprecedentedly observed temperature level associated with more frequent and extreme marine heatwaves [START_REF] Frölicher | Marine heatwaves under global warming[END_REF].

BRT in temperate ecosystem exhibits a low thermal sensitivity to ocean warming probably due to the wide thermal window of the marine species living in temperate regions, as the result of the high seasonal variability (Sunday et al., 2011). However, TTE is highly sensitive to temperature leading to a high projected decrease in TTE while BRT is projected to decrease moderately.

In summary, our results show that biomass transfers in marine food webs have globally become more efficient and faster over the period 1950-2010, which may be explained, at least partially, by the past increase in global fishing pressure. Such changes may have compensating effects on the whole ecosystem biomass, as faster transfers imply less biomass per trophic level while more efficient transfers is reducing the losses. We also found that temperature plays a key role to determine the properties of the biomass flow in marine coastal ecosystems. While warm coastal ecosystems are characterised by less efficient and fast biomass transfers, in colder coastal ecosystems, biomass transfers are slower and more efficient. Our model projections suggest that the increase in sea temperature is expected to shift the global ocean towards faster and less efficient biomass transfers by 2100 with especially drastic changes in polar ecosystems. These changes in trophic functioning have cumulative effects and will likely lead to a decrease in biomass through increasing losses of production at each trophic level, and decreasing BRT in the food web. Ultimately, they may severely affect the catch potential of fisheries across the globe by the end of the century. Figure 2: Synthetic schematic representation of the method to calculate trophic transfer efficiency and biomass residence time focused on the data that we used and the levels of ecological organisation (from species to trophic level to ecosystem). n represents the number of species. 1 (Froese and Pauly, 2018), 2 [START_REF] Colléter | EcoBase : A repository solution to gather and communicate information from EwE models[END_REF], 3 [START_REF] Gascuel | Trophic flow kinetics in marine ecosystems : Toward a theoretical approach to ecosystem functioning[END_REF][START_REF] Palomares | Predicting food consumption of fish populations as functions of mortality, food type, morphometrics, temperature and salinity[END_REF], 4 (Pauly and Zeller, 2015). RCP 2.6 (e,f),and RCP 8.5 (g,h).

Accepted Article

List of legends

Figure 1 :

 1 Figure 1: (a) Map of the coastal areas represented in the dataset and associated to ecosystem types. The colours refer to the ecosystem types: polar (in blue), temperate (in orange), tropical (in red) and upwelling (in green). The four graphs (b), (c), (d), and (e) show the past reconstructed trends in sea surface temperature (SST) and the predicted trends under RCP8.5 scenario (business as usual scenario). Temperature is represented by mean values of SST coming from the three Earth System Models used in the study and described in Materials and Methods.

Figure 3 :

 3 Figure 3: Schematic representation of biomass flow parameters between two trophic levels. Black arrows represent energy transfers or losses. The prey has a trophic level τ and the predator has a trophic level (τ+1). The partial transfer efficiency (partial TE) (Pτ+1/Qτ+1) and trophic transfer efficiency (Pτ+1/Pτ) are indicated (derived from[START_REF] Gascuel | Trophic flow kinetics in marine ecosystems : Toward a theoretical approach to ecosystem functioning[END_REF][START_REF] Maureaud | Global change in the trophic functioning of marine food webs[END_REF].

Figure 4 :

 4 Figure 4: The effect of temperature on the two trophic transfer parameters. The violin plots on the top panels represent the distribution of the mean values of the two trophic transfer parameters: (a) trophic transfer efficiency (TTE) and (b) biomass residence time (BRT) in each ecosystem type over the period 2000-2010. The colours refer to the ecosystem types: polar (in blue), temperate (in orange), tropical (in red) and upwelling (in green). In both panels (c) and (d), coloured solid lines represent the predicted values (i.e., the temperature effect) of TTE and BRT respectively, provided for each ecosystem type by the GLM model. The black dashed lines represent the predicted values of TTE and BRT by an additional GLM model considering only SST as a covariate. The shaded areas refer to the mean predicted value confidence intervals (95%). 5783 grid cells were used to calculate the trends.

Figure 5 :

 5 Figure 5: Trophic transfer efficiencies and biomass residence times in the coastal regions of the global ocean. The panels (a) and (b) represent the observed values over the period 2000-2010 while the other panels exhibit the predicted values from the General Linear Model for: the period Accepted Article

Figure 6 :

 6 Figure 6: Past trends of trophic transfer parameters over the period 1950-2010. The dashed lines represent global mean values of the observed trophic transfer efficiency (TTE) (a) and biomass residence time (BRT) (b). Shaded areas refer to bootstrap confidence intervals at 95%. Solid black lines represent theoretical global mean trends of TTE and BRT, computed using the GLM temperature-based model. Light grey lines are trends calculated using three Earth System Models (GFDL: Geophysical Fluid Dynamics Laboratory, MPI: Max Plank Institute, IPSL: Institut Pierre Simon Laplace). 2253 grid cells were used to calculate the trends.

Figure 7 :

 7 Figure 7: The expected changes of trophic transfer at the global scale over the 21st century. Panel (a) shows the projections of trophic transfer efficiency (TTE) and panel (b) shows the projections of biomass residence time (BRT) in the coastal ecosystems between 2000 and 2100 under two climate change scenarios, RCP2.6 and RCP8.5 in green and red, respectively. The dark lines are the mean values of the trophic transfer parameters and the light lines are the values of each general circulation model. Panels (c) and (d) focus on RCP8.5 scenario (the business as usual scenario) and represent the changes in TTE (c) and BRT (d), relative to 2000-2010 for each ecosystem type. 4608 grid cells were used to calculate the trends.Accepted Article

Acknowledgment

We wish to thank the Nippon Foundation-UBC Nereus program for supporting the collaboration between Agrocampus Ouest, Rennes, and the University of British Columbia, Vancouver. Hubert du Pontavice, William W.L. Cheung and Gabriel Reygondeau acknowledge funding support from the Nippon Foundation-UBC Nereus Program. Aurore Maureaud has received funding from the VILLUM Foundation (research grant attributed to Martin Lindegren, No. 13159). This study was made possible by Vicky Lam who provided disaggregated SeaAroundUs data. We further thank Jerome Guitton for his technical support.

Accepted Article

Accepted Article

This article is protected by copyright. All rights reserved Perry, A. L. (2005). Climate Change and Distribution Shifts in Marine Fishes. Science, 308(5730), 1912Science, 308(5730), -1915. https. https://doi.org/10.1126/science.1111322 Perry, R. I., Cury, P., Brander, K., Jennings, S., Möllmann, C., & Planque, B. (2010). Sensitivity of marine systems to climate and fishing : Concepts, issues and management responses. Journal of Marine Systems, 79(3-4), 427-435. https://doi.org/10.1016/j.jmarsys.2008.12.017 Pinsky, M. L., Worm, B., Fogarty, M. J., Sarmiento, J. L., & Levin, S. A. (2013). Marine Taxa Track Local Climate Velocities. Science, 341(6151), 1239-1242. https://doi.org/10.1126/science.1239352 Pinsky, Malin L., Selden, R. L., & Kitchel, Z. J. (2020). Climate-Driven Shifts in Marine Species Ranges : Scaling from Organisms to Communities. Annual Review of Marine Science, 12(1). https://doi.org/10.1146/annurev-marine-010419-010916 Planque, B., Fromentin, J.-M., Cury, P., Drinkwater, K. F., Jennings, S., Perry, R. I., & Kifani, S.

Accepted Article

This article is protected by copyright. All rights reserved Stuart-Smith, R. D., Edgar, G. J., Barrett, N. S., Kininmonth, S. J., & Bates, A. E. (2015). Thermal biases and vulnerability to warming in the world's marine fauna. Nature.


Michelle Valente

Cyril Joly

Arnaud De

La Fortelle

Deep Sensor Fusion for Real-Time Odometry Estimation

Cameras and 2D laser scanners, in combination, are able to provide low-cost, light-weight and accurate solutions, which make their fusion well-suited for many robot navigation tasks. However, correct data fusion depends on precise calibration of the rigid body transform between the sensors. In this paper we present the first framework that makes use of Convolutional Neural Networks (CNNs) for odometry estimation fusing 2D laser scanners and mono-cameras. The use of CNNs provides the tools to not only extract the features from the two sensors, but also to fuse and match them without needing a calibration between the sensors. We transform the odometry estimation into an ordinal classification problem in order to find accurate rotation and translation values between consecutive frames. Results on a real road dataset show that the fusion network runs in real-time and is able to improve the odometry estimation of a single sensor alone by learning how to fuse two different types of data information.

I. INTRODUCTION

Self-localization of an intelligent vehicle is still a challenging and ongoing task for the autonomous driving development. A reliable localization is necessary for intelligent vehicles to be able to take important decisions like overtaking another vehicle or simply defining a trajectory. To address this task, methods known as Simultaneous Localization and Mapping (SLAM) allow to localize the vehicle in a previously unknown environment while concurrently mapping the environment. Different types of sensors can be used for this purpose, such as cameras, laser scanners and radars. Each sensor has its own particular limitations and advantages and, for this reason, a single sensor cannot reliably be used alone; thus it is necessary to perform the fusion of different sensors to increase the accuracy of various tasks. One of the main difficulties to perform the fusion is to have a common data format and an accurate calibration between the different sensors.

It is very popular the usage of 3D laser scanners for autonomous driving research, however because of its cost it has become a major drawback for automobile manufacturers to be able to maintain a reasonable price for the future vehicles. Moreover, the amount of data provided by 3D laser scanners requires large computational resources making it difficult to have real-time localization methods. Considering this, we chose to focus on a solution for vehicles equipped with low cost 2D laser scanners. On the other hand, since {michelle.valente, cyril.joly, arnaud.de_la_fortelle}@mines-paristech.fr only a 2D slice of the surrounding environment is detected at each scan, some situations can be challenging if we only rely on this sensor. To address this problem, we propose to fuse the 2D laser scanner with a mono-camera, that can detect more information about the environment and increase the accuracy of the localization method.

In the last years, Deep Learning methods have received attention in the field of autonomous driving. The most common applications use cameras or laser scanners for tasks such as obstacle detection [START_REF] Li | 3d fully convolutional network for vehicle detection in point cloud[END_REF] and classification [START_REF] Zhao | Deep reinforcement learning with visual attention for vehicle classification[END_REF]. These tasks are mainly in the field of environment understanding and mapping. However, the localization of the vehicle and the fusion of different sensors is still a task that has not yet been extensively explored by machine learning techniques. The use of Neural Networks for this purpose could not only make the task faster, but also eliminate the need of a precise calibration between the sensors.

Considering this, we propose a complete Deep Learning approach to use CNNs to extract the features of two different sensors, a 2D laser scanner and a mono-camera, and sequentially fuse them in order to estimate the odometry of the vehicle. A schematic of the proposed approach is presented in Figure 1. We also present a new method to transform the odometry estimation regression problem into an ordinal classification that facilitates the training of the network. The solution can be run in real time and tests in real road scenarios shows competitive results compared to other deep learning approaches.

The remainder of the paper is organized as follows. First, we present the related work in Section II; the proposed method and the design of the network is presented in Section III; experimental results are presented in Section IV; finally conclusion and perspectives are given in Section V.

II. RELATED WORK

The application of Deep Learning techniques has presented impressive results recently in tasks such as object detection and classification by the use of camera images. To obtain these results, a large amount of datasets has become available in the last years. In the context of intelligent vehicles, interesting work has emerged in different fields: mapping [START_REF] Wirges | Object detection and classification in occupancy grid maps using deep convolutional networks[END_REF], trajectory prediction [START_REF] Altché | An LSTM network for highway trajectory prediction[END_REF], control [START_REF] Devineau | Coupled Longitudinal and Lateral Control of a Vehicle using Deep Learning[END_REF] and even end-to-end approaches [START_REF] Jaritz | End-to-end race driving with deep reinforcement learning[END_REF].

At the same time, localization, which is still a very challenging problem for robotic systems, is not yet well explored by deep learning methods. The most common approaches are based on the use of camera images for odometry estimation. They are inspired by the classic methods for Visual Odometry (VO) [START_REF] Mur-Artal | ORB-SLAM: a versatile and accurate monocular SLAM system[END_REF][10], which consists in estimating the camera's motion by finding geometry constraints from a sequence of images. The use of machine learning for this purpose allows to deal with challenging environments and camera parameters difficulties. The first method proposed was PoseNet [START_REF] Kendall | Posenet: A convolutional network for real-time 6-dof camera relocalization[END_REF], which it is based on the use of CNNs to estimate the 6-DoF pose using only RGB images. More recently, Wang et al. [START_REF] Wang | Deepvo: Towards end-to-end visual odometry with deep recurrent convolutional neural networks[END_REF] introduced the DeepVO method, which uses RCNNs with the same goal. The same authors also presented the method UndeepVO [START_REF] Li | Undeepvo: Monocular visual odometry through unsupervised deep learning[END_REF], which proposes an unsupervised deep learning method to estimate the pose of a monocular camera. However, the classic VO methods still outperform deep learning based methods published to this date, considering the accuracy in the pose estimation.

Laser scanners are also popular for classic pose estimation because of its accuracy. Classic approaches for this problem consist in trying to match two point clouds and estimate the transformation between them, this solution is known as Iterative Closest Point (ICP) [START_REF] Besl | Method for registration of 3-D shapes[END_REF]. Since then, more robust and complex algorithms were presented to achieve the same objective. LOAM [START_REF] Zhang | LOAM: Lidar Odometry and Mapping in Real-time[END_REF] is currently one of the most popular method because of its high accuracy and ability to achieve real-time processing by running two different algorithms in parallel.

The application of deep learning techniques for this purpose using laser scanners is still considered as a new challenge and only few papers have addressed it. Nicolai et al. [START_REF] Nicolai | Deep learning for laser based odometry estimation[END_REF] were the first to propose to apply 3D laser scanner data in CNNs to estimate odometry. Their approach provides a reasonable estimation of odometry, however still not competitive with the efficiency of state-of-the-art scan matching methods. Later, Velas et al. [START_REF] Velas | CNN for IMU assisted odometry estimation using velodyne LiDAR[END_REF] presented another approach for using CNNs with 3D laser scanners for IMU assisted odometry. Their results were able to get high precision and close results compared to state-of-the-art methods, such as LOAM [START_REF] Zhang | LOAM: Lidar Odometry and Mapping in Real-time[END_REF], for translation, however the method is not able to estimate rotation with sufficient precision. Considering their results, the authors propose that their method could be used as a translation estimator and use together an Inertial Measurement Unit (IMU) to obtain the rotation. Another drawback is that, according to the KITTI benchmark, even using CNNs the method is slower than LOAM.

The use of 2D laser scanners instead of 3D laser scanners could reduce considerably the price of future intelligent vehicles and the need of high computational resources. The authors of this work presented in [START_REF] Valente | An LSTM Network for Real-time Odometry Estimation[END_REF] a solution that relies only on a 2D laser scanner for odometry estimation using Recurrent Convolutional Neural Networks (RCNNs). The method showed promising results along with a very fast computational time. However, one of the main difficulties encountered by this approach was that sometimes in challenging environments the 2D laser scanner could not detect many obstacles and it would generate inaccurate results. Considering this, in this work we propose a new solution to improve the odometry estimation by fusing mono-cameras and 2D laser scanners using only Convolutional Neural Networks.

The fusion between laser scanners and cameras is commonly used in tasks such as object recognition and navigation of mobile robots [START_REF] Valente | Fusing Laser Scanner and Stereo Camera in Evidential Grid Maps[END_REF] [START_REF] Gleichauf | Sensor Fusion of a 2D Laser Scanner and a Thermal Camera[END_REF]. The use of Deep Learning with sensor fusion is not yet extensively explored; Most of the existing deep sensor fusion solutions are based on object detection, like in [START_REF] Xu | Pointfusion: Deep sensor fusion for 3d bounding box estimation[END_REF] where the authors fuse 3D laser scanners and camera images to predict object's bounding boxes. There are also methods that use sensor fusion for end-to-end learning [START_REF] Patel | Sensor modality fusion with CNNs for UGV autonomous driving in indoor environments[END_REF], where the input is the data of different sensors and the output is directly steering commands.

We present the first deep learning method for odometry estimation based on the fusion of a 2D laser scanner and a camera. The proposed network is able to provide a real-time solution that overcome the difficulties enconter by one sensor alone. We also present how to transform the odometry regression problem into a into a series of simpler binary classification subproblems, known as ordinal classification. Finally, we explore this solution in outdoor environments, training and testing it with the KITTI [START_REF] Geiger | Are we ready for autonomous driving? the kitti vision benchmark suite[END_REF] dataset, which contains sequences on different types of scenarios.

III. METHOD

The proposed approach consists in finding the vehicle displacement by estimating the transformation between a sequence of camera images and laser scanner acquisitions. From two consecutive observations, where each observation is a 360 • set of points measured during one laser rotation and one camera image, the network predicts the transformation T = [∆d, ∆θ ], which represents the travelling distance ∆d and the orientation ∆θ between two consecutive laser scans (s t-1 , s t ) and camera images (c t-1 , c t ). Therefore, the goal is to learn the optimal function g(.), which maps the fusion between (s t-1 , s t ) and (c t-1 , c t ) to T at time t:

T t = g((s t-1 , s t ), (c t-1 , c t ))
(1) Fig. 2: Architecture of the proposed network. Each block of the illustration presents the size of the tensors considering that the input is the raw sensor data pre-processed as presented in subsection III-A.

Once we learn these parameters, we can obtain the 2D pose (x t , y t , θ t ) of the vehicle in time t as follow:

x t = x t-1 + ∆d sin (∆θ ) y t = y t-1 + ∆d cos (∆θ ) θ t = θ t-1 + ∆θ (2)
In this way, we can accumulate the local poses of the vehicle and estimate the global position of the vehicle at any time t. Since the algorithm does not perform any sort of loop closure, drift can be also accumulated, thus reducing the accuracy of the vehicle's localization. The main goal is to explore the use of CNNs to match laser scans and camera images between two consecutive frames for odometry estimation, and especially, to prove that the fusion between the two of them for this purpose is possible to be executed by neural networks.

The following subsections will present in details the proposed method. First, we show how the raw data of the sensors are pre-processed. Sequentially, we present the configuration of the network and the specifics of the training process.

A. Data Pre-processing

The raw data coming from the two sensors need to be prepared before they can be used as an input for the neural network. For the laser scanner we use the same data encoding of our previous work [START_REF] Valente | An LSTM Network for Real-time Odometry Estimation[END_REF], where the sensor point set is encoded into a 1D vector. The vector is created by binning the raw scans into bins of resolution 0.1 • . Since many points can fall into the same bin, we calculate the average depth value. Finally, considering all the bins of a 360 • rotation range, we store the depth values into a 3601 size vector, where each possible bin angle average depth is represented by the elements in the vector.

After two sequential laser scans are encoded as 1D vectors, we concatenate them to create the input of the laser scanner network. The idea is to create a sort of image of size (2, 3601), allowing to use standard convolutional layers to extract the features detected by the sensor in the surrounding environment.

For the camera raw data we only resize the images in order to reduce the computational time. We tested different sizes so that the accuracy of the method was not reduced but we would still be able to produce faster results. Considering this, the best match for accuracy and time was achieved with the image size (416, 128). After resizing them, two consecutive image are stacked together, in the same way of the scans, to form a tensor that represents two camera acquisitions. This format allows us to feed the two images to the same sequence of CNNs to extract the features.

B. Network Architecture

In Figure 2 the architecture of the proposed network is presented. The input consists in the pre-processed raw data from the two sensors as explained in the previous subsection, while the rest of the network can be separated in the three main parts explained bellow: the laser scanner (CNN-Laser), the camera (CNN-Cam) and finally the fusion.

1) CNN-Laser: Two pre-processed laser scanner acquisitions, represented as a one dimension vector of size 3601, are concatenated to create the input tensor of the network. Sequentially, the tensor is fed into the sequence of 1D convolutional and average pool layers to learn the features between the two acquisitions. We use the same CNN configuration of our previous work [START_REF] Valente | An LSTM Network for Real-time Odometry Estimation[END_REF]. It consists of 6 1D convolutional layers, where each layer is followed by a rectified linear unit (ReLU) activation. Between each sequence of two convolutional layers, there is also one average pool layer to reduce computation complexity. The difference from the previous work is the extra layer, the linear layer, after the sequence of CNNs to reduce the tensor size before the fusion. The goal is to input the same amount of information from both of the sensors to the fusion part of the network.

2) CNN-Cam: The configuration of the camera network is the CNN part of the RCNN proposed by DeepVO [START_REF] Wang | Deepvo: Towards end-to-end visual odometry with deep recurrent convolutional neural networks[END_REF]. However, we use a smaller input as explained before in the pre-processing. In the same way of the CNN-Laser, we added an extra linear layer to reduce the tensor size before the fusion. Therefore, the input is two raw camera images and the output is the reduced features detected by the sequence of CNNs to be then fused with the features detected at the CNN-Laser.

3) Fusion: After extracting features from consecutive laser scans and camera images using the previous described CNNs, we concatenate their outputs in order to estimate the pose of the vehicle. The concatenated features are fed to two different sequence of linear layers. We tested the use of same linear layers for both rotation and translation estimation together, however better results were found once we separated them. In order to avoid the overfitting, the two linear layers are preceded by Dropout layers.

C. Training

The training of the network was performed in two steps; First, we trained the single sensor CNNs separately to find the best pre-trained weights possible for those networks. For this purpose, we connected them to two separate linear layers, one for the rotation and one for the translation. After it, the pre-trained CNNs are connected to the fusion part of the network and we perform the final training step.

In [START_REF] Valente | An LSTM Network for Real-time Odometry Estimation[END_REF], we prove that the CNN network get better results if we reformulate the problem as a classification task for the rotation, and continue it as a regression one for the translation. Considering all the possible variation of angles between two frames, we created classes for the interval ±5.6 • with 0.1 • resolution, resulting in 112 possible classes.

In this work we propose to not only treat the rotation as a classification task, but also the translation in order to facilitate the training. We observed that in all the possible sequences of the KITTI dataset the maximum translation between two frames is around 2.6 meters and the minimum 0.0. Therefore, we created 270 classes for this interval considering the resolution of 0.01 meters. Results showed that it became easier for the network to converge and the accuracy was not reduced by this transformation.

The main problem of transforming the rotation and translation in a classification task is that no order about the data is learned by the network. This happens because machine learning methods for classification problems commonly assume that the class values are unordered. For example, it would not be possible to understand that a difference of 2 degrees was higher than only 0.1 degrees. In [START_REF] Li | Ordinal regression by extended binary classification[END_REF] the authors introduce a simple method that enables standard classification algorithms to make use of ordering information in class attributes, known as ordinal classification. The idea is to transform the ordinal regression problem into a series of simpler binary classification subproblems. Inspired by this work, the authors of [START_REF] Niu | Ordinal regression with multiple output cnn for age estimation[END_REF] applied this idea solving the simpler binary classifications for age estimation by the use of CNNs.

Each rank receives a label to an angle or translation In order to transform our rotation and translation classes into a series of binary classification subproblems it is necessary to change how we label the dataset. Instead of labeling directly with a class that represents the ground truth value, the samples are labeled by an ordinal scale called the rank. Considering k the number of possible classes, we are going to transform the problem into k -1 simpler binary classification subproblems. Specifically, for one sample i each subproblem receives a label l k i ∈ 0, 1 indicating if the sample class l i is larger than r k as follow,

l 1 i l 2 i l 3 i l 4 i l 5 i l 6 i l k i … 1 1 0 0 0 0 … 0 Ordinal Classification Labeling 0 ≤ l i ≤ 112 -5.6 ∘ ≤ θ ≤ 5.6 ∘ r k 0.0 ≤ t ≤ 2.7 r 1 r 2 r 3 r 4 r 5 r 6 r k r 1 r 2 r 3 r 4 r 5 r 6 r k 1 1 1 1 0 0 … 0 r 1 r 2 r 3 r 4 r 5 r 6 r k (l k -5.1 ∘ , l k -5.
l k i = 1, if (l i > r k ) 0, otherwise. (3)
The rank format allows the network to learn the order of the classes by showing that one value is smaller or larger than other. A summary of the ordinal classification labeling process is presented in Figure 3.

To solve the binary classification subproblems we calculate the Binary Cross Entropy between the target and the output for rotation and translation and we sum them as follow:

L = L BCE ( d, d) + β L BCE ( θ , θ ) where L BCE (x, y) = -∑ k y k log (x k ) + (1 -y k ) log (1 -x k ) (4)
d and θ are relative ground-truth translation and rotation rank labels, and d and θ their output of the network counterparts. d and θ pass by a Sigmoid function before the loss function for numerical stability. We use the parameter β > 0 to balance the scale difference between the rotation and translation loss values. ) RMSE drift on trajectory lenghts of 100 to 800 meters, along with the computation time per frame, for the proposed approach and the DeepVO [START_REF] Wang | Deepvo: Towards end-to-end visual odometry with deep recurrent convolutional neural networks[END_REF] method.

The network is implemented on the framework PyTorch and the Adam optimizer is applied with learning rate 0.0001. As recommended in [START_REF] Wang | Deepvo: Towards end-to-end visual odometry with deep recurrent convolutional neural networks[END_REF], during the pre-training of the CNN-Cam we initialize it with pre-trained FlowNet model weights to reduce the training time.

IV. RESULTS

For validation we use the KITTI dataset [START_REF] Geiger | Are we ready for autonomous driving? the kitti vision benchmark suite[END_REF], which provides several sequences in different conditions for outdoor environments. To simulate a 2D laser scanner data, we extracted one 360 • layer from the Velodyne data, while for the camera we use the RGB raw images provided by the dataset. We use the 11 sequences from the KITTI odometry dataset which contain ground truth values to train and test the proposed method. Among the 11 sequences, we separate 8 for training and 3 for testing. We use for training the sequences 00, 02, 03, 04, 05, 06, 08 and 09 and for testing the sequences 01, 07 and 10. We chose these three sequences because they are not very long, leaving more data for the training, but they can still be challenging and present the potential of the proposed method. In the previous work [START_REF] Valente | An LSTM Network for Real-time Odometry Estimation[END_REF], we could not evaluate the sequence 01 because the vehicle is in a highway where the 2D laser scanner could not detect obstacles most of the time, making it impossible for a laser-only network to predict the odometry. For this reason, we add this sequence specially to observe if the fusion could improve the results.

In order to validate our method and compare to the solution DeepVO, we calculated the drift according to the KITTI VO [START_REF] Geiger | Are we ready for autonomous driving? the kitti vision benchmark suite[END_REF] evaluation metrics, i.e., averaged Root Mean Square Errrors (RMSEs) of the translation and rotation error for all subsequences (100, 200,..., 800 meters). However, we need to adapt our 2D results to be able to compare to the 3D errors of DeepVO, therefore we create 3D poses from our 2D values by giving 0.0 to the values we do not estimate (lateral and longitudinal angles and translation in the vertical axis).

Table I presents the translation and rotation error score for the testing sequences 07 and 10 and we compare these values between the proposed approach and the method DeepVO, along with their computational times. Even though we transform our results to 3D, it is important to mention that the results are not yet directly comparable, but we can still have an estimation if the order of error is around the same and we can compare the computation time of both methods. For the translation error the comparison is easier to perform since the global translation in the vertical axis is very small and not significant compared to the other axes. On the other hand, for the angles comparison, since most of the time the 3 angles are around 0 degree (the only high rotation rates are on z axis during turns, which represent a very small part of a complete trajectory), all their drifts are in the same order of magnitude and should be relevant for the comparison; For this reason, it is expected that the DeepVO method has a rotation error around three times more than our solution. As a result of these difficulties in the comparison of the two methods, we can only really extract from these results that the errors are around the same order of magnitude but we are still providing a solution that is 10 times faster using no GPU acceleration (2,6 GHz Intel Core i5, Intel Iris 1536 MB), and can be as fast as 0.01s with GPU acceleration (4,0 GHz Intel Core i7, GeForce GTX 1060). This faster processing is mainly due to the fact that we resize the images for smaller sizes and we use only CNNs instead of a RCNN.

We can observe in Figure 4 that even with the eventual errors in the odometry estimation, we can still obtain a trajectory close to the ground truth. However, since the proposed approach does not perform any sort of loop closure, and does not even use temporal information by recurrent neural networks (as in the DeepVO method), one eventual large error can be accumulated over time, generating a large drift like the one we have by the end of sequence 10. For this reason, a better way to understand the accuracy of the proposed approach is presented in Table II and in Figure 5. Table II shows the average rotation absolute error σ r and the average translation absolute error σ t for the single sensor CNNs and the CNN-Fusion. We can observe that in all the cases the result of the fusion was equal or better than the result of the single sensor network. Specially for the rotation estimation, the fusion of the features was able to increase the accuracy in all of the sequences, which proves that the network was able to learn how to perform the fusion of the two sensors. In the sequence 01, which is the hardest sequence because of the vehicle's velocity and lack of features to detect, it is clear how the laser was not able to estimate the angles because of the few detected points, but after the fusion with the camera the network was able to estimate more accurate angles. However, the translation was still inaccurate because this is the only sequence in the training dataset where the vehicle has a high velocity, therefore there were not other samples for it to learn the translation classes for this case.

Figure 5 presents the odometry estimation (rotation and translation) together with the ground truth for each frame of the sequences 07 and 10. These values present how the network can most of the time estimate accurate odometry, however there are still some difficult cases that can result in inaccurate values. For example, in the sequence 10 we can notice that the highest angle was not properly estimated, this probably happened because there are not a lot of samples for this type of rotation, making it hard for the network to learn this rotation class. We can expect that training this type of network with a larger dataset, with more samples for the challenging cases, could possibly resolve this type of problems and increase the accuracy.

The results show how promising is the fusion between sensors by the use of CNNs, and that the proposed method could be used as a complement to traditional localization methods for intelligent vehicles or any mobile robot. It is also important to mention that we trained the network with a relatively small dataset compared to other deep learning classification tasks, therefore the result could be considerably improved using more sequences for training.

V. CONCLUSION AND FUTURE WORK

In this paper we presented the first Deep Learning approach for sensor fusion to odometry estimation. We used as input only 2D laser scanner data and camera images to match their features in order to determine the translation and rotation of the vehicle using sequences of CNNs. The proposed network presents that the fusion between the sensors is possible by applying a purely CNN method and we can obtain good accuracy using only low cost sensors. We also introduced a new form of treating the odometry problem in deep learning methods by transforming the regression task into smaller binary classification subproblems that facilitates the training of the network.

We evaluated the results using the KITTI odometry dataset, making it possible to compare to other approaches. The results showed competitive accuracy, however classic approaches can still provide better results and a better understanding of the quality of their outputs. In spite of that, the proposed approach could be an interesting complement for classic localization estimation methods, since it can be run in real-time and could give relatively accurate values in systems where no wheel encoder data is provided or GPS signal is absent. Moreover, the proposed method presents that the use of Neural Networks is possible to perform the fusion between 2D laser scanners and mono-cameras, and this method could be used for other tasks in robotic systems. In the future work, better results could be obtained by training on larger datasets, specially with samples where the vehicle is moving in high speed and when there are sharp turns, and by exploring the use of temporal information or loop closure methods.

Fig. 1 :

 1 Fig. 1: Overview of the proposed system. Consecutive laser scans and camera images are used, first in two separate networks and sequentially in a common network, in order to estimate the pose of the vehicle between consecutive frames.

Fig. 3 :

 3 Fig. 3: Summary of the ordinal classification labeling with an example for the angle classification.

Fig. 4 :

 4 Fig. 4: Trajectories of two test sequences (07 and 10) applying the proposed CNN-Fusion. The blue lines represent the ground truth trajectory, while in red the predicted one.

Fig. 5 :

 5 Fig. 5: Results of rotation and translation estimation for the testing sequences 07 and 10. The ground truth values are presented in blue and in red the output of the Fusion-CNN network.

TABLE I :

 I Average translation (%) and rotation ( • /100m

TABLE II :

 II Average rotation absolute error σ r (degrees) and the average translation absolute error σ t (meters) results for the single sensor CNNs, CNN-Cam and CNN-Laser, and the result after CNN-Fusion.