Jérémy Rivière

Cédric Alaux

Yves Le Conte

Yves Layec

André Lozac'h

Vincent Rodin

Frank Singhoff

Frank Singho

Toward a Complete Agent-Based Model of a Honeybee Colony

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Complex systems are commonly referred to systems in which large networks of components with no central control and simple rules of operation give rise to complex collective behaviour [START_REF] Mitchell | Complexity: A Guided Tour[END_REF]. The agent-based approach, because it focuses on the individual to obtain the overall behaviour by emergence, is particularly suited to model and simulate complex systems (e.g. [START_REF] Krichene | Behavioral and informational agents-based modeling and simulation of emerging stock markets[END_REF][START_REF] Bilbao-Castro | Weaver: A multiagent, spatial-explicit and high-performance framework to study complex ecological networks[END_REF] in the past few years).

A honeybee colony, where several tens of thousands of honeybees interact and live together, is a great example of complex system. Indeed, one of the notable characteristics of Apis mellifera L., used in beekeeping, and Apis bee species, is that they live in colonies based on eusocial behaviour patterns [START_REF] Winston | The Biology of the Honey Bee[END_REF]. This social organisation depends on the multiple interactions (e.g. pheromones [START_REF] Traynor | Queen and young larval pheromones impact nursing and reproductive physiology of honey bee (apis mellifera) workers[END_REF], nutrition, communication) occurring between specialized individuals (forager, nurse, builder, etc.) of dierent casts and ages. From these interactions, complex phenomena thus emerge at the system-level (the colony) allowing its self-regulation and self-adaptation, including but not limited to: ⋆ The nal authenticated publication is available online at https://doi.org/10.1007/978-3-319-94779-2_42

Changing roles depending on the needs of the colony [START_REF] Bonabeau | Selforganization in social insects[END_REF]; Thermoregulation and ventilation [START_REF] Sumpter | Shape and dynamics of thermoregulating honey bee clusters[END_REF] and formation of the brood nest [START_REF] Camazine | Self-organizing pattern formation on the combs of honey bee colonies[END_REF]; Selection of the best available nectar sources [START_REF] Seeley | Assessing the benets of cooperation in honeybee foraging: search costs, forage quality, and competitive ability[END_REF][START_REF] Dornhaus | Benets of recruitment in honey bees: eects of ecology and colony size in an individual-based model[END_REF].

Our undertaking is to model these phenomena to simulate a honeybee colony. The objective is twofold. First, we aim at allowing direct interactions with bees via a 3D simulation, for two dierent uses: an educational use (e.g. to learn good beekeeping practices), and a scientic use, to evaluate ecological phenomena (parasites, virus) and anthropogenic factors. Second, investigating these phenomena may lead to identify the core mechanisms behind them, which, from an engineer's point of view, could help to resolve similar issues in other elds.

For example, the bees' ability to detect high protable sources and quickly exploit them before they fade is very ecient, and could inspire new organisation methods in (critic) resource allocation problems. Some of these phenomena may be described at the colony-level by using dierential equations and by not considering bees as individuals [START_REF] Becher | Beehave: a systems model of honeybee colony dynamics and foraging to explore multifactorial causes of colony failure[END_REF][START_REF] Schmickl | Hopomo: A model of honeybee intracolonial population dynamics and resource management[END_REF][START_REF] Russell | Dynamic modelling of honey bee (apis mellifera) colony growth and failure[END_REF]. However, in order to investigate these phenomena and to allow interactions with bees, a bottom-up approach is required to deduce the eects of these micro actions in the short and long run on the colony. Discovering, formalizing and modelling the links between individuals (micro-level) and the behaviour of the system (macrolevel) remain a major issue in complex systems. Population models, because they focus on the macro-level, do not take into account the micro-level and its existing links with the macro [START_REF] Bonabeau | Agent-based modeling: Methods and techniques for simulating human systems[END_REF]. We thus choose to model the honeybee colony following an agent-based approach, where the honeybee is an agent, described by its biological cycle, behaviour, and its interactions with its environment.

We present in this article an agent-based model of foraging bees, and how their interactions and recruitment lead to the selection of the best nectar sources in the surroundings of the colony. Focusing on the hive to allow local actions, such as the removal of a frame, a beekeepers practice, makes the hive the obvious agents' environment, with the need to dene a high-resolution behaviour for the bees within the hive. However, foraging bees go outside the hive to bring back resources (nectar, pollen, water), within a range of approximately 10 km [START_REF] Seeley | The Wisdom of the Hive[END_REF], for an area of 314 km 2 . There is thus great dierences in granularity and scale between the hive (usually 38 x 45 x 31 cm) and the outside environment, making the connection between the two environments dicult.

We tackle this issue by designing an Ecosystem Module. This customizable module is compliant with an agent-based simulation: Forager Agents, described in section 4, interact with this module which rests upon the local weather, the days' length, and the surrounding pollen and nectar sources (see section 3) to simulate the outside trip and bring back resources according to probabilities deduced, adapted or borrowed from previous models in literature.

In the next section, we take a look at some important related works on agentbased simulations of honeybee foraging and recruitment. Preliminary results of experiments conducted under the conditions (weather, sources) of the last three years in Brest (Bretagne, France) with our agent based-model and the Ecosystem Module are presented and discussed in section 5. Finally, we conclude and outline the perspectives of this work in section 6.

2 Agent-Based Models of Foraging and Recruitment As stated by previous works [START_REF] Seeley | Division of labor between scouts and recruits in honeybee foraging[END_REF][START_REF] Seeley | Collective decision-making in honey bees: how colonies choose among nectar sources[END_REF], recruitment is the cornerstone of a selforganization process that leads foraging bees to select the more protable sources in the hive's surroundings. Among foraging bees, the scouts are basically explorers, going outside the hive to discover nectar and pollen sources, forage, and communicate their location and protability (the waggle dance) to unemployed bees, waiting for to be recruited, when coming back at the hive. Surprisingly, the scouts represent a small proportion of the foraging force (around 10% [START_REF] Seeley | The Wisdom of the Hive[END_REF]); and they can only convey the information to a small number of bees, recruiting 0.8 bees on average at each dance [START_REF] Dornhaus | Benets of recruitment in honey bees: eects of ecology and colony size in an individual-based model[END_REF]. Seeley [START_REF] Seeley | The Wisdom of the Hive[END_REF] also noticed that the colony's resources stock leads foraging bees to scout more often and to accept more easily a less protable source when it is low. It is still unclear however how the stock's state is assessed by the bees, although local perceptions may play a role.

Most of agent-based models focusing on foraging are independent models built to investigate precise biological questions [START_REF] Dornhaus | Benets of recruitment in honey bees: eects of ecology and colony size in an individual-based model[END_REF][START_REF] De Vries | Modelling collective foraging by means of individual behaviour rules in honey-bees[END_REF]. For example, Dornhaus et al. [START_REF] Dornhaus | Benets of recruitment in honey bees: eects of ecology and colony size in an individual-based model[END_REF] conducted an experiment based on their model, aiming at quantifying the benets of recruitment according to the size of the colony and the sources quality. This model introduces some interesting probabilities, adapted in our model, and a rst line of approach for the forager agent's behaviour. However, in most cases, these models can hardly be integrated with a model of the colony in the hive because of the dierence between the models' time and spatial scales.

On the other hand, a few agent-based models interact with other models in order to simulate the entire colony. In Beehave [START_REF] Becher | Beehave: a systems model of honeybee colony dynamics and foraging to explore multifactorial causes of colony failure[END_REF], the agent-based model, dedicated to the foraging activity, interacts with two other population-based modules simulating the life of the colony and the propagation of the parasite Varroa destructor in the colony. The agent-based model includes a spatially explicit landscape that the forager agents explore and on which they forage at ower patches. In this module, foragers are super-individuals representing 100 identical foragers. The model is executed once per day, and the time step of the simulation seems to be one minute. These last two parameters make dicult its adaptation to an agent-based model of the colony in the hive.

To conclude this section, we can draw one common characteristic from all these models: they mostly agree on the nature of the hive's environment, made up of nectar and pollen sources and the weather conditions.

The Ecosystem Module

The Ecosystem Module aims at simulating the foraging, at an agent's request, according to the outside environment of the hive. As seen in section 2, two important factors are needed to take into account and evaluate the ecosystem's impact on the colony: a representation of the local climate, and the available pollen and nectar sources at the current time of the year. These two factors are each the target of a dedicated customizable module, the Weather and the Sources Modules.

The trip conditions of foraging bees are strongly inuenced [START_REF] Seeley | The Wisdom of the Hive[END_REF] by (1) the day's length: bees can forage only during daylight hours; and (2) the weather: foraging bees can go outside the hive only when the temperature is above approximately 11°C, and when there is neither rain nor strong wind.

The Weather Module tackles these aspects by, rstly, approximating the time of sunrise and sunset, and secondly, providing real weather data. These aspects are customizable according to the current date and location. The weather data come from the Open Data service (Synop) of the French national meteorological service, Meteo France " . The Synop data are weather records for sixty-two sta- tions in metropolitan France and Overseas territories of France, providing the current temperature, humidity, cloudiness etc. From these records and the time of the day, the Weather Module gives information on whether or not a foraging bee is able to go outside the hive.

The Sources Module allows to represent the surrounding nectar and pollen resources, their distance to the hive, their owering duration and peak, and the sugar concentration of the available nectar, if present. When running a simulation, one can choose to generate a given number of random sources, and can also congure the main local sources. For example, some of the known sources around Brest, in France, and used in the experiment (see section 5), are: the rape, that owers from the 15th of April to the 15th of May, the bramble, from the 15th of June to the 15th of July, but also the sweet chestnut, etc.

Each source is ruled by a source factor, giving the accessibility of the nectar and/or pollen resources according to the date. The source factor (SF) is directly inspired by the season factor of the HoPoMo model [START_REF] Schmickl | Hopomo: A model of honeybee intracolonial population dynamics and resource management[END_REF], and is thus dened by the following normalized Gaussian function, where src is the source, nb is the day's number of the year, d is the owering duration and p its peak:

SF (src, nb) = 1 -( 1 d 4 • √ 2•Π • exp(-(nb-p) 2 2• d 4 2
))

Each source has also a protability, computed from its distance to the hive, the nectar's sugar concentration and the quantity of accessible resources. As stated in [START_REF] Seeley | Collective decision-making in honey bees: how colonies choose among nectar sources[END_REF], this protability will impact the recruitment of bees, according to their perception of the colony's resources stocks (see section 4.1).

The nal component of the Ecosystem Module is the Outside Agent, which is the system's interface. We chose to design this interface as an agent to allow our agent-based model to communicate with the Ecosystem Module. The communication protocol lies on the FIPA-ACL standards: a Forager Agent rst sends a request to the Outside Agent to forage at an aimed (ever by recruitment or from its memory) source or at a source it must rst discover. According to the " *https://donneespubliques.meteofrance.fr/ Weather and Sources Modules and the p_death and p_full_return probabilities (see Table 2), the Outside Agent then either refuses to answer the request (because the Forager Agent died, or it has found no source), or accepts. In this latter case, the Outside Agent communicates (1) the pollen and/or nectar quantity the Forager Agent can bring back to the hive, (2) the nectar quality of the source and (3), the travel time, in number of time steps of the simulation (see section 4.4), the Forager Agent has to wait for to simulate its trip. [START_REF] Bonabeau | Agent-based modeling: Methods and techniques for simulating human systems[END_REF] The Agent-Based Model of Foraging Bees As we focus here on the foraging activity, we only consider the foragers, putting the other bees and the interactions with them aside, to be included in the future.

From literature and data gathered by the biologist partners, we thus model the biological cycle of a Forager Agent, its behaviour, and the interactions with its environment. These inputs have also been used to verify and calibrate the model.

Recruitment and Self-Organization Mechanisms

Recruitment and protability are the prime notions on which an ecient source selection lays (as seen in section 2). To reproduce this self-organizing process, we model the recruitment thanks to the following mechanisms:

When coming back at the hive, the agent may communicate (dance ) to unemployed agents the protability and the location of the source they have found, according to:

• this protability value;

• and their perception of the current state of the resources stock.

The state of resources stock in the hive also weights the agent's decision to follow a recruiter or not, and also the probabilities to go scouting (p_scout ) and to go on the dance oor (p_danceoor ).

As presented in the section 5, the preliminary results show that these mechanisms seem sucient to reproduce this self-organization in our model.

Environment

The Forager Agent's environment consists of the hive, the other agents and the Outside Agent (see Table 1). We chose here a minimalist representation of the hive, including only the values of the pollen and the nectar stock. We state that this representation is currently sucient to reproduce the self-organizing process in the foraging activity, but, as said in the introduction, our objective includes a complete spatial representation of the hive. This choice of conception has two consequences. First, the consumption of resources by the bees is simplied and simulated according to the number of bees (foragers, but also larva and other bees) in the hive. Secondly, in a real hive, the perception by the bees of the resources stock's state is a complex

Forager Agent's Behaviour

Because of its simple graphical representation, the state chart presented in Fig. 1 has been the medium to enable an interdisciplinary discussion between biologists, beekeepers and computer scientists, in order to dene the Forager Agent's behaviour. In addition to the interaction table and the table of probabilities and parameters (Table 2), it shows a dynamic view of the agent's behaviour.

In Fig. 1, transitions between states are probabilities and/or conditions veried at each time step by the agent. The Table 2 of the colony's resources stock. A source may be protable (found_source ) but not enough regarding the stocks. When recruiting, it sends a message to a nbr_bees_listening with the name of the source and its protability, then tries to go back outside to the same source if possible.

Implementation and Scheduling

The agent-based model and the Ecosystem Module have been implemented with JADE [START_REF] Bellifemine | Jade a java agent development framework[END_REF] in Java. JADE provides communication mechanisms and a well-suited architecture for our model: behaviours are independent of agents, and can be added or removed following the evolution of the agent's speciality. JADE also oers a FSMBehavior that allows to directly implement the state diagram and its transitions. Finally, this choice of platform also lies on the necessity to implement the model in a standard programming language to maximise code reliability and make it more easily extendible.

Bees being asynchronous entities, as all living beings, we selected a chaotic asynchronous scheduling, in which the agents are activated in a random manner to avoid a bias in the simulation [START_REF] Kubera | How To Avoid Biases In Reactive Simulations[END_REF]. As we deal with agents, though, this activation consists in receiving a message from a Scheduler Agent. However, nothing prevents the environment's scheduler (in our case, the Java Virtual Machine) to favour some agents to make more actions than others. The agents thus have to synchronize themselves at some point or another. This is done by introducing the following policy in the agents' behaviour: Deduced from calibration 1. The Forager Agent waits for the Scheduler Agent's activation message;

2. After reception, it makes n actions;

3. Then, it informs the Scheduler Agent that it has done, and waits again for an activation message.

For its part, the Scheduler Agent waits for all Forager Agents to be done before sending a new activation message, leading to a synchronization of all the agents. The smaller is the value of n, the greater will be the number of messages exchanged. On the other hand, a too great n value can lead to great dierences between the number of actions done by the agents. These actions are dened within the states introduced above, as steps that take in reality approximately one second to be performed by the bee.

Experiments and Preliminary Results

We -H1: The weather inuences the outing of Forager Agents, as stated in [START_REF] Seeley | The Wisdom of the Hive[END_REF];

-H2: Agents select the best available sources in the surroundings of the hive; -H3: Finally, Forager Agents scouting represent an average number of around 10% of the foraging force [START_REF] Seeley | The Wisdom of the Hive[END_REF]. In early March for example, there are some days where the agents cannot go outside at all because of the low temperature or the bad weather. Other days, the average rst foraging hour can be very early in the day (e.g. in June).

As we take a look at the recruitment mechanism, graph (c) shows a correlation between the number of Forager Agents scouting outside (solid line) and the recruited agents (dashed line). In early April for example, a new protable source is discovered by scouts, and, as the weather allows the outing, they recruit a great foraging force toward a source: almost 50% of the total foraging force. This phenomena is explained by the colony's stock low level, that leads the agents to go more easily on the dance oor and to accept less protable sources.

The number of recruits thus rises as only a few scouts remain. These results are found across all runs of the three experiments.

Based on the results over the three experiments, the average proportion of scouts against the total number of Forager Agents (H3) is between 6% and 7%. As the stock is low, we expected to nd a greater value (10%), so more experiments are needed to investigate this point.

Fig. 3 shows the same particular run than the previous gure, to illustrate how the agents select the best available source. Graph (a) shows that, from the 60th to the 80th days, the source S1 (solid line) is the most protable. Then, a second source S2 (dash-dotted line), shorter in duration, becomes the best source for approximately 10 days. Finally, after a quick return of S1, a third source S3

(dashed line) takes over from the 95th day.

In the beginning of the run, the low temperature and the bad weather do not allow the agents to eciently go forage, as we can see in graphs (b) and (c). Three points of interest are then to be noticed. The rst one is around the 75th day (mid-March): scouting agents discover sources S1 and S2, and the recruitment leads the agents to leave S2 for S1 after 3 days. The second interesting point is about source S2, from the 81th to the 98th day, ignored by agents, whereas it is the best available source at this moment. This can partly be explained by the fact that scouting agents missed this source during this duration, maybe caused by a too great concentration of agents on S1 at this time.

Finally, around the 97th day (early April), we nd again the great recruitment described earlier (see Fig. 2). At this point, agents foraging at sources S1 and S2 progressively leave these sources for the third one (S3), as scouting agents discover and communicate about this more protable source. virtual representation of the hive and to integrate visualization and interactions with the colony, which have to be realistic, intuitive and ergonomic.

Conclusion and Perspectives

Fig. 1 .

 1 Fig. 1. State chart of the Forager Agent behaviour.

  have conducted 3 experiments with our agent-based model and the Ecosystem Module, each conducted under the conditions (local weather and sources) of the last 3 years in Brest (Bretagne, France). The experiments run from the 1st of March to the 1st of September of each year. Each experiment consists in 10 runs with the same weather and location of sources, and the same initial state: 500 foraging bees, and rather low resources stock. As the agent-based model does not yet include the queen and the larva, the p_death probability is set to 0. These rst experiments aim at verify our model, by notably verifying the following hypothesis:

Fig. 2 .

 2 Fig. 2. Graph (a) on the top shows the average temperature per day of 2015 in Brest (circles) and the minimum (dash-dotted line) and maximum (dashed line) averages. Graph (b) shows the average rst foraging hour per agent per day (circles), i.e. the time of the day at which the agents go forage for the rst time. Minimum (+) and maximum (x) rst foraging hour per day are also displayed. Graph (c) shows the number of trips done by scouting agents (solid line) and recruiting agents (dashed line) per day.

Fig. 3 .

 3 Fig. 3. Graph (a) shows the protability evolution of three sources between early March and late April 2015. Graph (b) shows the number of trips per day outside the hive according to the same sources displayed on graph (a). The third graph (c) is an enlargement of (b).

Table 1 .

 1 Interaction table of the Forager Agent with its environment.

	Interactions	Forager Agent	Hive	Outside Agent
	Forager Agent Recruitment	Drop resources	Send a request to go outside
	Hive	Stock perception	Pollen and Nectar consumption	-
	Outside Agent	Accept / Refuse the request to go outside	-	-
	phenomena, only partially understood. In this model, this perception is thus
	simplied, computed by each bee from the stock quantities, with a random bias
	to simulate its imprecision.

  In this case, it assesses the protability of the conveyed source according to its biased perception of the colony's resources stock. If the source seems protable enough, it will try to go outside to forage at this aimed source. In other cases, and if the agent has waited too long, it may also go scouting according to the p_scout probability. TripOutside: this state simulates the agent's trip outside the hive to bring back resources. It is in this state that it communicates with the Outside Agent and interacts with the Ecosystem Module.

	tired || unable		tired || unable
	|| 1 -p_dancefloor
				Recruitment
		Resting	found_source	!(tired || unable)
			&& dance
		p_dancefloor
			EmptyReturn
				1 -p_full_return
	tired || unable	OnTheDanceFloor	FullReturn
			(Nectar Delivery and
			Pollen Storage)
	! found_source &&
		1 -p_scout	( found_source && ! dance ) ||	p_full_return
			p_scout
	WaitingForToBeRecruited
	! recruited		"Trip" Outside
		( time_out	&& p_scout )	p_death
			|| recruited
	Recruitment: the agent, after a successful trip outside, goes back to the dance
	oor and may try to recruit (dance ) other agents in the WaitingForToBeRe-
	cruited state according to the protability of the source and its perception

gives the values of the probabilities used by the Outside Agent (p_full_return and p_death) and by the Forager Agent. It also shows the values of the Forager Agent's parameters, which may have a random deviation, in order to introduce variability between the agents. The Forager Agent thus follows the behaviour dened by this state chart, made of seven states. The most important states are:

OnTheDanceFloor: this state is the crossroad of many transitions. The agent can come from the Resting state, in order to either wait for to be recruited by another agent or go outside as a scout (p_scout probability). The agent can also come from outside, bringing back resources or not (FullReturn and EmptyReturn states). WaitingForToBeRecruited: the agent is ready to receive a message from a recruiting agent (Recruitment state).

Table 2 .

 2 Probabilities and parameters used by the Outside and the Forager Agents . Each value is given according to the ratio simulation time step

	real time that can be weighted by the colony's resources stock are represented with a *. = 1 1000 . Probabilities
	Probability/Parameters	Value	Adapted from
	Outside Agent
	p_death	0.0108	[11]
	p_full_return	0.43 when scouting	[16]
		0.93 when recruited	[16]
	Foraging duration	[5.41; 11.37]min. for 650m [15]
	Max. quantity in one trip:
	-of nectar	[14.6; 16]mg	[7]
	-of pollen	25mg	[7]
	Flight speed	1.29m.s -1	[15]
	Nectar consumption in ight 0.0083mg.m -1	[14]
	Forager Agent
	p_scout *	0.00825	[7]
	p_danceoor *	0.001	Deduced from calibration
	max_outing_on_a_row	[20; 30] trips in a row.	[14]
	min_go_out_temp max_go_out_temp	11°C + -1 40°C + -1	[14] [14]
	nbr_bees_listening	[0; 3] agents per dance	[7]
	wait_recruit_time	30min.


Jean Barr

Gilles Chabriel
email: chabriel@isitv.univ-tln.fr-barrere@isitv.univ-tln.fr

BLIND WAVE SEPARATION BY SPATIAL OVERSAMPLING

This paper is a contribution to the problem of the separation of propagating source signals recorded simultaneously by a s e t of receivers. We propose to use a small-sized sensor array so that the waves are spatially oversampled. Sensors are assumed to be directional, to have the same complex frequency response and to be di erently oriented in space. Under these assumptions, sources are received on each sensor with di erent attenuations and with di erent time delays. When the dimensions of the array are chosen so that time delays are small in comparison with the coherence time of each source, we s h o w that the array outputs can be approximated to a particular model of instantaneous mixtures involving the sources and their rst derivative with respect to time. Because sources are statistically dependent to their rst derivative, this problem does not appear as a classical Blind Source Separation (BSS) problem. We present then a matched second-order blind identi cation algorithm in order to estimate this particular mixing system. The validity of the proposed model and of our algorithm is con rmed by computer simulations in the case of audio sources.

GENERAL MODEL

It is assumed that a set of N independent colored signals x 1 (t) : : : x N (t) are propagating in an echo-free environment. These signals are recorded on M sensors without any additive noise (presence of noise will be treated in the full paper). The observation satisfy the equation model below: y 1 (t) = x 1 (t) + x 2 (t) + : : : + x N (t) y i (t) = j=N X j=1 c i j x j (t ; i j ) i = 2 : : : M (1) where i j and c i j represent respectively the relative delay and the relative amplitude of source x j (t) observed on the i th sensor versus the rst observation y 1 (t). We'll show in the full paper that in case of a compact sensor array, delays are su ciently small when:

2 i j << 1 2 2 2 M 8i j
where M is the maximum frequency present in the observations. In this case, an approximation for the observations y i (t) ( i = 2 : : : M ) using an order one Taylor expansion can be considered:

y i (t) c i 1 x 1 (t) ; c i 1 i 1 dx 1 (t) dt + c i 2 x 2 (t) ; c i 2 i 2 dx 2 (t) dt + : : : + c i N x N (t) ; c i N i N dx N (t) dt :
(2) Let consider the observation vector y(t) = y 1 (t) y 2 (t) : : : y N (t)] T . Using approximation (2) in (1), the set of equations (1) can be rewritten as: and the components of vector _ x(t) are the rst derivatives of each source.

y(t) M 1 x(t) + M 2 _ x(t):
We can use the following matrix and vector notation:

y(t) M 1 M 2 x(t) _ x(t) : (3)
Matrix M = M 1 M 2 (M 2N) is called the instantaneous mixing matrix for small delays.

Equation [START_REF] Tong | Indeterminacy and identi cability of blind identi cation[END_REF] shows that when the di erent w aves are spatially oversampled ( 2 i j << 1 2 2 2 M 8i j) the sensor array delivers a set of instantaneous mixtures involving sources and their rst derivatives. For each source signal, original source and its rst derivative are dependent signals but uncorrelated at the same time. This last property will be exploited to identify the instantaneous mixing system M.

An other important result to be pointed out is: when delays become small, the dimension of the signal sub-space de ned by the array outputs tends towards 2N. So, to simplify here the summary, w e'll take M = 2 N (twice as much sensors than sources) and we'll assume that, in that case, M is a regular matrix (case M > 2N will be treated in the full paper with the noisy case).

IDENTIFICATION OF THE INSTANTANEOUS MIXING MATRIX FOR SMALL DELAYS

The BSS problem consists in estimating a separating matrix S such as: SM = DP, w h e r e D is a regular diagonal matrix, P is a permutation matrix. The product of S with the observations leads to: z(t) = DP x(t) _

x(t)] T , representing the sources and their rst derivatives except for one permutation and a scaling factor.

Because of the spectra di erences of sources, the problem can be solved adapting classical blind identi cation methods for instantaneous mixtures using second-order statistics of the observations (see Tong's AMUSE 1] 2], SOBI 3] , IMISO 5] o r 4 ] : : : ).

Consider the spatial covariance matrix R yy ( ) = E y(t)y(t + ) T ]. With expression (3), R yy ( ) reads: R yy ( )

M E " x(t) _ x(t) x(t + ) _ x(t + ) T # M T M R xx ( ) R x _ x ( ) R _ xx ( ) R _ x _ x ( ) M T : (4)
With a lag = 0, each source x i (t) and its rst derivative _ x i (t) are uncorrelated. Matrices R x _ x (0) and R _ xx (0) are then null matrices. Because sources are uncorrelated, matrices R xx (0) and R _

x _

x (0) are diagonal matrices. Thus, we can write for spatial covariance R yy (0): R yy (0) = MD 0 M T [START_REF] Fety | M ethodes de traitement d'antenne adapt ees aux radiocommunications[END_REF] where D 0 is a diagonal matrix.

Let's linearly lter with the impulse response h(t) each member of expression (4):

R h yy ( ) M R h xx ( ) R h x _ x ( ) R h _ xx ( ) R h _ x _
x ( ) M T where R :: h ( ) = h R :: ( ):

The entries of the function matrix R x _ x ( )(= R _ xx ( )) are odd functions. If the impulse response h(t) i s c hosen even, t h e e n tries of R h

x _

x ( )(= R h _ xx ( )) are still odd functions. Taking = 0 assures these previous matrices to benull.

Matrices R h

xx (0) and R h _ x _

x (0) being diagonal, the ltered spatial covariance matrix R h yy (0) can be factorized as: R h yy (0) = MD h 0 M T [START_REF] Cavassilas | S eparation autodidacte de sources temporellement corr el ees (m elange instantan e)[END_REF] where

D h 0 = R h xx (0) R h x _ x (0) R h _ xx (0) R h _ x _
x (0) is a diagonal matrix.

Because matrix R yy (0) is regular, we can introduce the matrix: R = h R yy (0) i ;1 R h yy (0):

Then from ( 5) and ( 6), it comes: R = h M T i ;1 h D 0 i ;1 h D h 0 i M T : We can show t h a t ; M T ;1 can be estimated except for one diagonal matrix and one permutation matrix from the eigenvector matrix of R.

SIMULATIONS Array and source con guration:

Two audio signals propagating in the air are detected by an half spherical sensor array (see g. 1). In this case of two sources mixed, only four sensors are used they are plotted in bold on g. 1. Distance between center of close sensors is 2cm. Sphere radius is 17 cm. Each sensor have the same complex frequency response and the same cosine beam pattern (this for any frequency in the sensor bandwidth). The rst audio source is an Beethoven fragment and the second is a swept sine. Each source is sampled at 5.5 KHz and is 6 seconds long (32768 samples). Fig. 2 shows Power Spectral Density (PSD) of the sources. The performance of our method is measured using the criterion introduced by Shobben and al in 6]. The quality of separation of the j th separated output is de ned as:

S j = 1 0 l o g E (z j xj ) 2 ] E ( P i6 =j z j xi ) 2 ] !
where z j xi is the j th output when only x i is active.

For our numerical experiments the performance measures can be found in the following

CONCLUSION

A method to separate propagating sources has been presented. This approach needs to record the waves with a compact discrete antenna so that propagation delays become small in comparison to the signal coherence time (spatial oversampling). Let point out that this notion of compactness depends both on the spectra of sources but also on the propagation velocity. For example in sub-marine propagation, the dimensions of antenna be higher than in aerial propagation.

  : 1 : : : 1 c 2 1 : : :c 2 j : : :c 2 N . . . . . . . . . c M 1 : : :c M j : : :c M N M 1 : : :c M j M j : : :c M N M N

Figure

  Figure 1: Sensor Array

Figure 3 :

 3 Figure 3: DSP of estimated sources

table :

 : Figure 2: DSP of sources Fig.3 presents the PSD of the estimated sources which are similar to those of g. 2.

	10
	5						PSD of Estimated Source #1
	0	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
	20
	10						PSD of Estimated Source #2
	0	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
	30
	20					PSD of Estimated
	10						first derivative of Source #1
	0	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
	30
	20					PSD of Estimated
	10						first derivative of Source #2
	0	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
						Normalized frequencies
				Estimated Source ]1 S 1 = 3 9 d B Estimated Source ]2 S 2 = 4 0 d B
	10
	8
	6
	4						PSD of Source #1
	2
	0	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
	20
	15
	10						PSD of Source #2
	5
	0	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
						Normalized frequencies

We s h o wed that in previous conditions, the problem can be seen of a BSS problem of statistically dependent sources. Inversion of the mixing system is obtained with a matched algorithm based on the second-order statistics of waves. Simulation of the extraction of two audio sources in aerial propagation recorded with a feasible discrete sensor array h a ve been provided. Good results obtained prove the practical interest of our approach.


D Amendola

M Mutema

V Rosolen

V Chaplot

Soil hydromorphy and soil carbon: A global data analysis

Keywords:

Introduction

Wetlands are transitions from aquatic to dry land (upland) habitats and they occur in areas where soils are inundated/saturated by water due to high groundwater or ponding surface water during a part or all of the year [START_REF] Neue | Factors and processes controlling methane emissions from rice fields[END_REF]. Globally, wetlands cover over 2.1 million km 2 (Ramsar Convention, 2016), representing about 6% of the earth's surface [START_REF] Zhang | Modeling spatiotemporal dynamics of global wetlands: comprehensive evaluation of a new sub-grid TOPMODEL parameterization and uncertainties[END_REF]. Even though wetlands provide a wide range of ecosystem services of great social and economic values, their rate of deterioration is faster than that of any other ecosystem [START_REF] Davidson | Earth observation for wetland inventory, assessment and monitoring[END_REF]. For example, US wetland area was reported to have declined by about 25,200 ha between 2004[START_REF] Fritsch | Organic complexation and translocation of ferric iron in podzols of the Negro River watershed. Separation of secondary Fe species from Al species[END_REF](US Fish and Wildlife Services, 2011). Wetlands are also a highly threatened ecosystem type in New Zealand with only < 10% of their original extent remaining nowadays [START_REF] Myers | Wetland management in New Zealand: are current approaches and policies sustaining wetland ecosystems in agricultural landscapes?[END_REF].

All wetland soils are characterized by excess water on momentary to permanent bases (EPA, 2017). The excess water induces reduction processes [START_REF] Vepraskas | Morphological indicators of soil wetness[END_REF] resulting in generally low soil chroma and value (< 2). Additionally, the lack of oxygen lessens organic matter mineralization with subsequent accumulation of organic carbon (C) in the soils [START_REF] Vaughan | Evaluating large-scale effects of Bacillus thuringiensis var. israelensis on non-biting midges (Chironomidae) in a eutrophic urban lake[END_REF]. [START_REF] Gorham | The biogeochemistry of northern peatlands and its possible responses to global warming[END_REF] and [START_REF] Zhang | Modeling spatiotemporal dynamics of global wetlands: comprehensive evaluation of a new sub-grid TOPMODEL parameterization and uncertainties[END_REF] estimated worldwide wetlands' C storage to range from 150 to 535 Gt C, which makes wetlands a key component of the global C cycle. The capability of wetlands to accumulate organic C varies with climate, soil properties and hydrological regime [START_REF] Zhang | Organic carbon accumulation capability of two typical tidal wetland soils in Chongming Dongtan, China[END_REF][START_REF] Wang | Five-year changes in soil organic carbon and total nitrogen in coastal wetlands affected by flow-sediment regulation in a Chinese delta[END_REF]. Accumulation of C in wetlands is a balance between net primary productivity and decomposition mediated by microbial processes [START_REF] Stemmler | Microbial activity as a major factor in the mobilization of iron in the humid tropics[END_REF][START_REF] Zerva | Short-term effects of clear felling on soil CO 2 , CH 4 , and N 2 O fluxes in a Sitka spruce plantation[END_REF], decomposer community, environmental conditions and substrate litter quality [START_REF] Werker | Treatment variability for wetland wastewater treatment design in cold climates[END_REF][START_REF] Koide | Fungal succession and decomposition of Camellia japonica leaf litter[END_REF][START_REF] Urakawa | Wetland management using microbial indicators[END_REF].

Wetlands of cold regions have the greatest C accumulation potential due to low temperatures, high humidity and weak microbial activities [START_REF] Tockner | Riverine flood plains: present state and future trends[END_REF] with, for example, boreal peatlands containing 270-370 Gt C [START_REF] Fan | The response of soil organic carbon of a rich fen peatland in interior Alaska to projected climate change[END_REF], compared to tropical wetlands which stock only 89 Gt C [START_REF] Page | Global and regional importance of the tropical peatland carbon pool[END_REF] because of higher temperatures and microbial activities. The boreal and temperate wetlands are C sinks [START_REF] Moore | Peatlands. Elek Science[END_REF] and they accumulate peat layers at rates regulated by climate, vegetation and topography [START_REF] Armentano | Patterns of change in the carbon balance of organic soilwetlands of the temperate zone[END_REF]. The total organic C pool in the permafrost zone is composed of C frozen at depth in peatlands and C intermixed with mineral soils [START_REF] Schuur | Vulnerability of permafrost carbon to climate change: implications for the global carbon cycle[END_REF]. The northern permafrost zone alone is estimated to store 1672 Pg C; 277 Pg C of that in peatlands and 1024 Pg C in the 0-3 m permafrost-zone, representing a large fraction of global soil C stocks [START_REF] Schuur | Vulnerability of permafrost carbon to climate change: implications for the global carbon cycle[END_REF]. Thawing of the permafrost, which results in decomposition of previously frozen organic C, constitutes a significant feedback from terrestrial ecosystems to the atmosphere [START_REF] Schuur | Vulnerability of permafrost carbon to climate change: implications for the global carbon cycle[END_REF] with approximately 100 Pg C set to be released from thawing permafrost by 2100 if temperature increases by 4 °C [START_REF] Gruber | The vulnerability of the carbon cycle in the 21st century: an assessment of carbon-climate-human interactions[END_REF]. The collapsing permafrost generates fens in hydromorphic zones and bogs in the drier zones. [START_REF] Trumbore | Carbon cycling in boreal wetlands: a comparison of three approaches[END_REF] showed that different decomposition rates give rise to the greatest C accumulation in the intermediate zone. Accumulation of C in the bogs and fens is low due to low inputs matched by low outputs and high productivity matched by high respiration, respectively. The collapse of permafrost wetlands also changes plant and microorganism communities with, for example, increasing organic C degraders in Alaska [START_REF] Chapman | Soil microbial community composition is correlated to soil carbon processing along a boreal wetland formation gradient[END_REF].

On the other hand, tropical wetlands are the largest natural source of atmospheric C with organic substrate quality the main control of decomposition [START_REF] Miyajima | Anaerobic mineralization of indigenous organic matters and methanogenesis in tropical wetland soils[END_REF]. Substrate quality is important in both anaerobic decomposition and methanogenesis, and correlate strongly with lignin content [START_REF] Miyajima | Anaerobic mineralization of indigenous organic matters and methanogenesis in tropical wetland soils[END_REF][START_REF] Hoyos-Santillan | Quality not quantity: organic matter composition controls of CO2 and CH 4 fluxes in neotropical peat profiles[END_REF]. [START_REF] Hoyos-Santillan | Quality not quantity: organic matter composition controls of CO2 and CH 4 fluxes in neotropical peat profiles[END_REF] reported high CO 2 and CH 4 emissions under anoxic conditions in tropical peatlands, which strongly correlated to lignin content, long chain fatty acids and polysaccharides concentrations. Unlike temperate and boreal peatlands which come from more degradable sphagnum mosses and sedges (Yavitt and Williams, 2015a), tropical peatlands come from high lignin tree litter. Although decomposition rates are generally faster in lower C:N ratio substrates, C:N ratio had no limit on mineralization in tropical wetlands (Yavitt and Williams, 2015b). However, [START_REF] Sjogersten | Organic matter chemistry controls greenhouse gas emissions from permafrost peatlands[END_REF] showed no link between organic chemistry of arctic and subarctic peatlands and CH 4 emission under flooded and non-flooded conditions. The emission was limited by availability of specific substrates i.e. sugars and low molecular weight organic acids, which ferment to acetate, a precursor for CH 4 production. Unlike high latitude wetlands with relatively stable water levels [START_REF] Junk | Brazilian wetlands: their definition, delineation, and classification for research, sustainable management, and protection[END_REF], neotropic peatland C losses follow water level drawdown and litter quality [START_REF] Bridgham | Mechanisms controlling soil respiration (CO2 and CH 4 ) in southern peatlands[END_REF][START_REF] Laiho | Decomposition in peatlands: reconciling seemingly contrasting results on the impacts of lowered water levels[END_REF]. The neotropic wetland hydrology, characterized by river flooding and groundwater table fluctuations [START_REF] Junk | The flood pulse concept in river-floodplain systems[END_REF], modifies the chemical and physical properties, degree of anoxia, sediment properties and soil pH, which subsequently reflect in the decomposition rates of organic materials [START_REF] Webster | Vascular plant breakdown in freshwater ecosystems[END_REF].

However, there are discrepancies in wetland C storage for any given region because decomposition in the wetlands is a complex aerobicanaerobic process regulated by physical, chemical, and biological processes [START_REF] Kayranli | Carbon storage and fluxes within freshwater wetlands: a critical review[END_REF]. Landscape diversity also contrasts wetlands by influencing vegetation growth and C storage capacity [START_REF] Heinselman | Landscape evolution, peatland types, and the environment in the Lake Agassiz peatlands natural area, Minnesota[END_REF]. In similar Brazilian climatic conditions, for example, [START_REF] Martins | Caracterização físico-química do covoal do cÓrrego da fortaleza, chapada oeste do triângulo mineiro[END_REF] pointed to maximum SOC content (SOC C ) of 41 g C kg -1 , while [START_REF] Bardy | Micromorphology and spectroscopic characteristics of organic matter in waterlogged podzols of the upper Amazon basin[END_REF] and [START_REF] Rosolen | Contamination of wetland soils and floodplain sediments from agricultural activities in the Cerrado biome (state of Minas Gerais, Brazil)[END_REF] estimated maximum values of 455 and 537 g C kg -1 , respectively. [START_REF] Chaplot | Soil carbon storage prediction in temperate hydromorphic soils by using a morphologic index and Digital Elevation Model[END_REF] and [START_REF] Rosolen | Contamination of wetland soils and floodplain sediments from agricultural activities in the Cerrado biome (state of Minas Gerais, Brazil)[END_REF], amongst others, also reported on large differences in SOC C of a single wetland, which may be associated with differences in soil saturation by water and hydromorphy. The results of [START_REF] Chaplot | Soil carbon storage prediction in temperate hydromorphic soils by using a morphologic index and Digital Elevation Model[END_REF] showed the highest SOC C of 460 g C kg -1 at the valley bottom and a lowest of 100 g C kg -1 at the footslope in the Armorican Massif of western France.

Relationships between flooding duration and frequency and decomposition rates in wetlands are still not well understood due to great variability in wetland types [START_REF] Brinson | Primary productivity, decomposition and consumer activity in freshwater wetlands[END_REF][START_REF] Neiff | Leaf litter decomposition in three wetland types of the Paraná River floodplain[END_REF]. The present study aimed at (i) reviewing existing works that assessed SOC C levels in wetland soils at a global scale and (ii) investigating the links between SOC C and soil hydromorphy and the main soil and environmental factors of control. These objectives were achieved by gathering quantitative data from various natural wetlands in different environments worldwide. Such quantitative analysis is important for land managers concerned with understanding the potential impact of change in wetland hydromorphy through, for instance drainage, on C losses from the soils. It might also help in estimating the C sequestration potential of degraded wetland soils in the framework of international programs such as the '4 per mille Soils for Food Security and Climate', which was launched at the COP21 with an aspiration to increase global soil organic matter stocks. The results could in particular inform on ways to render certain wetlands more efficient in sequestrating atmospheric C. Finally, quantitative information on the links between, for instance, climate or soil clay content and wetland SOC C could constitute an important tool for the spatial prediction of wetland soil C.

Materials and methods

Study setup

The study was based on data collected from electronic reserves and databases containing field experiment reports performed on wetlands or waterlogged sites. The literature data search targeted information from soil profiles developed under different wetland types e.g. floodplains, swamps and peatlands. The search used key words and phrases such as "water-logged soil", "soil hydromorphy", "hydromorphic features", "Gleysols", and "SOC". A number of electronic databases such as Google, Google Scholar, Web of Science and Science Direct were searched for the data. The methods used in organizing the database and statistical treatments of the data were according to [START_REF] Mutema | Annual water, sediment, nutrient, and organic carbon fluxes in river basins: a global meta-analysis as a function of scale[END_REF].

Many papers were downloaded but gaps in data on SOC C and/or information on the intensity of soil hydromorphy led to omission of some papers from the current analysis. Other important soil parameters sought included iron (Fe), aluminum (Al), clay content and Munsell soil color (Hue, Value and Chroma). In addition to these parameters, the data sources also needed to provide site locational and climatic information. Boreal and temperate wetlands were not included the current study because they accumulate very large amounts of C and would behave as outliers when put together with other environments. Outliers are values that shift the median and mean up. The final database consisted of 27 published ISI papers and two masters' theses, totalizing 122 soil profiles from different sites across the world. Amongst these accepted data sources, 12 came from Brazil, 3 from Germany, two from China and USA, and one from each of Switzerland, Bangladesh, Italy, India, Mexico, Bolivia, Russia, South Africa, and France (Fig. 1) with sites spanning a latitudinal range from 30°15′ S to 47°57′ N.

The database captured information on author name(s), years the papers were published, paper titles, experimental site characteristics such as geographical location, climatic parameters, dominant land use, number and descriptions of the studied soil profiles. The data on SOC C , Clay, Fe and Al, collected from the data sources, were in different units but mainly presented in terms of mass (e.g. g kg -1 , mg g -1 and percentage %). The data were normalized to g C kg -1 for SOC C and % for Fe, Al and Clay. Other site characteristics recorded include longitude (LONG), latitude (LAT) in degrees, 30-year mean annual precipitation (MAP) and temperature (MAT). Table 1 presents a summarized version of the database.

Definitions of variables

Climatic factors

The climatic factors considered in the present study were MAP and MAT. They were grouped into categories (Table 2) following [START_REF] Mutema | Annual water, sediment, nutrient, and organic carbon fluxes in river basins: a global meta-analysis as a function of scale[END_REF]. MAP was categorized into 120-800, 800-1200 and 1200-2200 mm year -1 , while MAT was grouped into 6-15, 15-22 and 22-30 °C year -1 .

2.2 Soil properties.

Soil properties, such as soil clay content, intensity of soil hydromorphy, soil Munsell Value and Chroma, soil pH and soil depth also varied greatly from one site to another and were grouped into three categories each (Table 2). Soil clay content categories were adopted from [START_REF] Mutema | Annual water, sediment, nutrient, and organic carbon fluxes in river basins: a global meta-analysis as a function of scale[END_REF], namely 0-25%, 25-50% and > 50%. Chroma was grouped into 0-4, 4-7 and 7-10, and value into 2-4, 4-6 and 6-8. The Hydromorphic Index HI [START_REF] Chaplot | Soil carbon storage prediction in temperate hydromorphic soils by using a morphologic index and Digital Elevation Model[END_REF] was grouped into three categories, namely 0-15 for low intensity of soil [START_REF] Chaplot | Soil carbon storage prediction in temperate hydromorphic soils by using a morphologic index and Digital Elevation Model[END_REF][START_REF] Franzmeier | Color patterns and water table levels in some Indiana soils[END_REF]. Soil depth was also grouped into three domains, namely 0-40, 40-80 and 80-120 cm. The SOC, Al and Fe contents used in the current analysis referred to average values obtained from amounts present in horizons A and B of the soil profiles.

Data analyses

The sample size (N) for each environmental factor and response variable was first determined, and then summary statistics, described by minimum, maximum, median, standard deviation (SD), skewness, 25th quartile (Q1) and 75th quartile (Q3), kurtosis and coefficient of variation (CV%), generated (Table 3). Variability and distribution of the datasets for the different factor categories were elucidated using boxplots (Figs. 23). Each box-plot shows the minimum, maximum, median, Q1 and Q3 values after outliers were checked and removed from the box-plots. Spearman correlation analyses (Table 4) were performed to evaluate the one-on-one relationships between controlling factors and response variables. Finally, principal component analysis was used to depict the multiple relationships between the controlling environmental factors and response soil variables (Fig. 4). A principal component analysis (PCA) is a powerful tool that visually presents linear relationships between variables by converting non-linear variables into related linear components [START_REF] Jambu | Exploratory and Multivariate Data Analysis[END_REF].

Results

Variability of environmental factors and soil variables

The summary statistics in Table 3 indicated that the environmental and biogeochemical parameters from the wetland soil profiles varied widely across the different locations. MAP ranged from minimum 127 mm year -1 in USA [START_REF] Thompson | Hydrologic and edaphic characteristics of three mountain wetlands in southeastern Kentucky, USA[END_REF] to maximum 3833 mm year -1 in a Bolivian tropical forest [START_REF] Schawe | Soil development along an altitudinal transect in a Bolivian tropical montane rainforest: podzolization vs. hydromorphy[END_REF], with an average of 1316 mm year -1 . MAT varied from minimum -1.6 °C year -1 in temperate Russia [START_REF] Sorokin | Microbial complexes of hydromorphic soils in the Selenga River delta (Baikal region)[END_REF] to 30.15 °C in tropical Brazil [START_REF] Schiavo | Characterization and classification of soils in the Taquari River basin -Pantanal region, state of Mato Grosso Do Sul, Brazil[END_REF]. Soil pH was very acidic with a value of 2.5 in an alluvial wetland in Italy [START_REF] Ferronato | Chemical and pedological features of subaqueous and hydromorphic soils along a hydrosequence within a coastal system (San Vitale Park, Northern Italy)[END_REF], while the other extreme was the basic soil with a pH value of 8.9 in a floodplain of a tropical forest in Brazil [START_REF] Guimaraes | Characterization and classification of gleysoils on the floodplain of the Solimoes river (Iranduba and Manacapuru), Amazonas, Brazil[END_REF]. Soil clay content varied from a minimum of 0.20% at a site in Brazil [START_REF] Martins | Caracterização físico-química do covoal do cÓrrego da fortaleza, chapada oeste do triângulo mineiro[END_REF] to a maximum of 83% in Bangladesh [START_REF] Brinkman | Surface-water gley soils in Bangladesh[END_REF]. The overall average soil clay content was 21%. Soil color also showed high variability with a respective coefficient of variation of 33% for Value and 75% for Chroma. Chroma ranged from 0 for some sites in Brazil, USA and China [START_REF] Skorupa | Assessing hydric soils in a gallery forest in the Brazilian Cerrado[END_REF][START_REF] Vepraskas | Interpreting morphological features in wetland soils with a hydrologic model[END_REF][START_REF] Kölb | Accelerated soil formation due to paddy management on marshlands (Zhejiang Province, China)[END_REF] to a maximum of 10 for a site in Brazil [START_REF] Schiavo | Characterization and classification of soils in the Taquari River basin -Pantanal region, state of Mato Grosso Do Sul, Brazil[END_REF]. Value varied from a minimum of 2 at sites in the US, Germany, Brazil and China [START_REF] Vepraskas | Interpreting morphological features in wetland soils with a hydrologic model[END_REF][START_REF] Fiedler | Linking soil classification and soil dynamics ± pedological and ecological perspectives[END_REF][START_REF] Nascimento | Podzolization as a deferralitization process: a study of an Acrisol-Podzol sequence derived from Palaeozoic sandstones in the northern upper Amazon Basin[END_REF][START_REF] Kölb | Accelerated soil formation due to paddy management on marshlands (Zhejiang Province, China)[END_REF] to a maximum of 8 reported for a site in Brazil [START_REF] Martins | Relações solo-geoambiente em áreas de ocorrência de ipucas na planície do médio araguaiaestado de Tocantins. R. Árvore[END_REF]. Soil variables varied more widely than environmental controlling factors with coefficients of variation of 265, 147 and 236% for SOC C , Fe and Al, respectively. Minimum SOC C was 0.1 g C kg -1 in South Africa [START_REF] Olaleye | Wetlands in Khalong-la-Lithunya catchment in Lesotho: soil organic carbon contents, vegetation isotopic signatures and hydrochemistry[END_REF] and a maximum of 540 g C kg -1 was observed in Germany's Black Forest, located in humid temperate climate [START_REF] Fiedler | Linking soil classification and soil dynamics ± pedological and ecological perspectives[END_REF]. The lowest Fe and Al contents of close to 0% were found in Russian [START_REF] Sorokin | Microbial complexes of hydromorphic soils in the Selenga River delta (Baikal region)[END_REF]. The highest soil Fe content was 17% found in Italy [START_REF] Ferronato | Chemical and pedological features of subaqueous and hydromorphic soils along a hydrosequence within a coastal system (San Vitale Park, Northern Italy)[END_REF], while the highest Al content of 38% was reported in Brazil by [START_REF] Fritsch | Organic complexation and translocation of ferric iron in podzols of the Negro River watershed. Separation of secondary Fe species from Al species[END_REF].

Variation of SOC C as a function of soil and environmental factors

Box-plots in Fig. 2 show the variability of SOC C as a function of hydromorphic index (HI), soil Value, soil Chroma and soil depth. SOC C showed a tendency to increase with HI (Fig. 2A). On the basis of median values, SOC C increased from 5.5 to 20 g C kg -1 (an increase of 263%) as HI increased from 0 to 15 to 15-30 (Fig. 2A). This was followed by a further 55% increase to 31 g C kg -1 for the 20-50 HI range. In contrast, SOC C tended to decrease with soil Value, soil Chroma and soil depth. The decrease from Value range 2-4 to 4-6 was from 9.5 to 3.1 g C kg -1 and this was followed by a further decrease of 2 g C kg -1 from 4 to 6 to 6-8 (Fig. 2B). SOC C also showed a general decrease with increase in soil Chroma (Fig. 2C). It decreased from 9.1 to 6.0 g C kg -1 from 0 to 4 to 4-7 Chroma, and to 3.5 g C kg -1 for 7-10 Chroma. The decrease of SOC C from the top (0-40 cm) to subsurface (40-80 cm) layer was greater than from the subsurface to deeper (80-120 cm) soil layer (Fig. 2D). The SOC C decreased by 48% from the top to subsurface layer (i.e. from SOC C = 20 to 9.2 g C kg -1 ), followed by 45.6% decrease from the subsurface to the deeper horizon.

Spearman Rank Correlations (r s ) in Table 4 show that LAT significantly correlated with SOC C (r s = 0.15) implying higher SOC C at higher latitudes. Surprisingly, MAP showed no significant correlation with any of the soil variables investigated in the current analysis but MAT correlated significantly and negatively with SOC C (r s = -0.14) and Fe (r s = -0.35). Soil pH correlated significantly and positively with soil Clay, Chroma and Value (0.18 ≤ r s ≤ 0.23) but negatively with SOC C (r s = -0.24). The Clay-Chroma correlation was significantly positive (r s = 0.19); however, the negative correlation between Clay and SOC C (r s = -0.35) was rather surprising. It was also surprising that both Chroma and Value correlated significantly but negatively with SOC C with respective r s of -0.26 and -0.42. However, SOC C was positively correlated to Fe (r s = 0.21), while in turn Fe was also positively correlated to Al (r s = 0.62).

These results also suggest that, unlike SOC C , soil Clay and Al contents tended to decrease with the intensity of soil hydromorphy. Indeed, both soil clay (Clay, %) and aluminum (Al, %) content showed a general decrease with the hydromorphy index (HI) (Fig. 3A-B). In Fig. 3A, Clay decreased from 27 to 6% (i.e. by 60%) from HI range of 0-15 to 15-30, and this was followed by a further 59% decrease from 15 to 30 to 20-50. Interestingly, the 0-15 and 15-30 HI ranges showed much greater variability of Clay content than the 20-50 range. In the case of Al concentration (Fig. 3B), the decrease from 0 to 15 to 15-30 was by 50% (from 2.2 to 1.1%), while the decrease from 15 to 30 to 30-50 HI range was by only 36%. Variability of Al was greatest in the 15-30 range, and least in the 20-50 range.

Variation of HI as a function of climatic factors

HI correlated highly with SOC C and it could, thus, be used as a proxy for SOC C spatial prediction, the latter being potentially rendered easier by the use of ancillary data such as MAP or MAT because of their worldwide availability. Moreover, trends could inform on the mechanisms involved in the formation of soil hydromorphic features. In general, HI tended to decrease with increase in both MAP (Fig. 3C) and MAT (Fig. 3D). HI decreased from 25 to 16 from MAP range of 120-800 mm year -1 to 800-1200 mm year -1 , and to 7 at MAP 1200-220 m yr -1 . HI varied greatly within the MAP ranges, but variability was greater at 120-800 and 1200-2200 mm year -1 than at 800-1200 mm year -1 . In the case of MAT, HI varied greatly in all the three MAT categories but there was a trend for higher HI to occur at lower MAT values. HI decreased from 14.8 for 6-15C year -1 to around 8.5 for 15-22 and 22-30 °C year -1 MAT ranges.

Multivariate analysis

The two major PCs of the PCA (Fig. 4) explained 70.6% of the dataset variability, with PC1 and PC2 accounting for 47.2% and 23.4%, respectively. PC1 was closely associated with HI, MAP and soil depth; but HI showed negative coordinates while MAP and soil depth had positive coordinates on this axis. PC2 was closely associated with MAT and Clay with both of them showing negative coordinates along this axis. The results in this PCA suggest a general increase of SOC C with increasing HI, and decreasing MAP and soil depth. In contrast, there was a tendency for soil clay content and MAT to have very little impact on both soil hydromorphy and SOC C .

Discussion

Links between SOC C and soil hydromorphy

The study results showed a general increase of SOC C with HI (Fig. 2A and Fig. 4), which was consistent with results from many studies across the world (e.g. [START_REF] Chaplot | Soil carbon storage prediction in temperate hydromorphic soils by using a morphologic index and Digital Elevation Model[END_REF][START_REF] Jungkunst | Groundwater level controls CO 2 , N 2 O and CH 4 fluxes of three different hydromorphic soil types of a temperate forest ecosystem[END_REF][START_REF] Maljanen | Greenhouse gas balances of managed peatlands in the Nordic countriespresent knowledge and gaps[END_REF][START_REF] Wang | Soil organic carbon of degraded wetlands treated with freshwater in the Yellow River Delta, China[END_REF]. This relationship could be explained by the impact of soil saturation on the stability of organic C. Saturation of soils by water creates reducing conditions where microbial activities are also suppressed due to very low free O 2 levels. Decomposition of soil organic matter (SOM) decreases to very low rates in the absence of microbial activity because lack of O 2 reduces the metabolic activities of the aerobic soil organisms responsible for decomposing the SOM. In their study of soil CO 2 effluxes, [START_REF] Freeman | Export of dissolved organic carbon from peatlands under elevated carbon dioxide levels[END_REF] explained that higher CO 2 effluxes from soil C pools under drier conditions were a result of greater decomposition rate. [START_REF] Jungkunst | Groundwater level controls CO 2 , N 2 O and CH 4 fluxes of three different hydromorphic soil types of a temperate forest ecosystem[END_REF], who evaluated CO 2 effluxes from seasonally saturated soils due to variation of the groundwater table, confirmed this with their results indicating higher CO 2 emissions when the soils were relatively drier. The highest concentrations of dissolved CO 2 occurred in waterlogged soils [START_REF] Jungkunst | Groundwater level controls CO 2 , N 2 O and CH 4 fluxes of three different hydromorphic soil types of a temperate forest ecosystem[END_REF].

The accumulation of organic C in waterlogged soils induces typical changes in soil color [START_REF] Schoeneberger | Field Book for Describing and Sampling Soils (Ver. 1.1)[END_REF][START_REF] Vepraskas | Redoximorphic Features for Identifying Aquic Conditions[END_REF][START_REF] Vepraskas | Interpreting morphological features in wetland soils with a hydrologic model[END_REF][START_REF] Vepraskas | Morphological features of seasonally reduced soils[END_REF], especially lower Munsell Value and Chroma. The long periods of water saturation also reduce soil metallic elements, e.g. Fe and Al, to forms that exhibit dark to greyish colours (USDA- NRCS, 2006) which are also associated with low Value and Chroma (Munsell codes for soil color often used as indicators for soil hydromorphy). Transfer of Fe from soils is a mechanism for soil evolution controlled by water regime, which create reducing conditions. While hydromorphic environments favour dissolution of Fe out of soil systems [START_REF] Fekiacova | Inferences from the vertical distribution of Fe isotopic compositions on pedogenetic processes in soils[END_REF], the transfer of Fe may not be a definitive loss because the mottled horizons, especially those formed by water level fluctuations, tend to develop localized Fe accumulation structures [START_REF] Wilson | Rewetted industrial cutaway peatlands in western Ireland: prime location for climate change mitigation?[END_REF]. Moreover, the Fe depleted structures may also result in geochemical degradation of ferruginous matrices [START_REF] Beauvais | Geochemical balance of lateritization processes and climatic signatures in weathering profiles overlain by ferricrete in Central Africa[END_REF]. [START_REF] Guimaraes | Characterization and classification of gleysoils on the floodplain of the Solimoes river (Iranduba and Manacapuru), Amazonas, Brazil[END_REF] also used similar processes to explain the occurrence of Gleysol profiles in the Brazilian Amazon floodplains. It is, however, still important to point that soil color is also influenced by transformation and accumulation of SOM and that SOM accumulation occurs in both biologically active soils with well humified OM and poorly active acidic environments with slow humification [START_REF] Zaiets | Micromorphology of organic matter and humus in Mediterranean mountain soils[END_REF].

Links between soil hydromorphy and other soil properties and feedbacks to SOC C

Soil matrix chroma is a property used for characterising hydrological regimes and boundaries of wetlands [START_REF] Atkinson | Use of created wetland delineation and weighted averages as a component of assessment[END_REF]. While wetland environments are generally expected to have soils with low Value and Chroma (i.e. dark colours) [START_REF] Vepraskas | Redoximorphic Features for Identifying Aquic Conditions[END_REF], the high Value and Chroma values observed in some of the wetland profiles used in the current analysis were of young Gleysols impacted on, for example, by river pulses. Considerable time is required for hydric soil indicators to develop [START_REF] Atkinson | Use of created wetland delineation and weighted averages as a component of assessment[END_REF][START_REF] Campbell | A comparison of created and natural wetlands in Pennsylvania, USA[END_REF]. The high soil Value and Chroma categories were associated with low SOC C (Fig. 2A and C, respectively) pointing to possible enrichment of these soil profiles by high activity clay minerals low in SOC. Such soils when impacted on by river pulses tend to exhibit dark colours despite being generally freely-drained and oxidized environments [START_REF] Vepraskas | Albic neoskeletans in argillic horizons as indicators of seasonal saturation[END_REF].

Despite the positive impact of HI on SOC C , the HI correlated negatively with soil properties such as clay (Fig. 3A) and chemical elements Al and Fe (Fig. 4). The decrease of soil clay content with HI indicates the existence of at least two pedogenetic processes causing loss of clays in the wetlands, (i) ferrolysis and (ii) physical weathering. Ferrolysis is a geochemical destruction process pertaining to the removal of Fe hydroxides during water movement along soil macro pores. The clay particles may be removed together with Fe hydroxides and be elluviated (through argilluviation) to lower horizons [START_REF] Wilding | Pedogenesis of soils aquic moisture regimes[END_REF]. The other process is still linked to ferrolysis in that clay particles are decomposed during ferrolysis in acidic and seasonally wet soils [START_REF] Van Ranst | Evaluation of ferrolysis in soil formation[END_REF]. This process is based on alternating reduction and oxidation of Fe. Mineralogical instability occurs in seasonally wet-dry conditions because the acids produced by decomposing organic matter, (under reducing conditions) generate soluble Fe 2+ which moves through the soil and precipitates as Fe(OH) 3 [START_REF] Espiau | Etude du phénomène d'échange et mise en évidence du role catalytique des minéraux argileux[END_REF]. Aluminum is also dissolved out of soil systems in the same way because its solubility is highly dependent on pH [START_REF] Bloom | Aluminum organic matter in acid soils: buffering and solution aluminum activity[END_REF]. The Al is mobilized into the aqueous form under acidic conditions, but precipitate to form amorphous Al hydroxides, Al-silicate secondary minerals, and/or Al-organic complexes under high pH conditions [START_REF] Li | Relationships among pH, aluminum solubility and aluminum complexation with organic matter in acid forest soils of the Northeastern United States[END_REF]. Interactions between Al and SOM are directly linked to acidic functional groups on SOM surfaces [START_REF] Bloom | Aluminum organic matter in acid soils: buffering and solution aluminum activity[END_REF]. The Al can be available for co-precipitation with silica to form Al silicates, which correspond with negative correlations between SOC C and Al. In general, seasonally waterlogged soil pH decreases in the oxidized phase and rises in the reduced phase [START_REF] Brinkman | Ferrolysis, a hydromorphic soil forming process[END_REF]. The strongly positive correlation between soil clay content and pH (r s = 0.21; Table 4) cements the role of ferrolysis, which becomes dominant under acidic conditions, in the destruction and transfer of clay particles. This also makes the positive correlations between soil clay and Al in the study results plausible because Al elevates soil pH through the presence of Al 3+ and H + [START_REF] Machado | Comportamento do carbono orgânico em área úmida do cerrado: Estudo de caso em uma área úmida do Córrego Beija-Flor[END_REF].

While our results point to negative correlations between SOC C on one hand and Fe and Al on the other (Table 4), some study results are contrary to this (e.g. [START_REF] Wagai | Sorptive stabilization of organic matter in soils by hydrous iron oxides[END_REF][START_REF] Kaiser | The role of DOM sorption to mineral surfaces in the preservation of organic matter in soils[END_REF][START_REF] Wilson | Rewetted industrial cutaway peatlands in western Ireland: prime location for climate change mitigation?[END_REF][START_REF] Akter | Control of Fe and Mn availability on nitrogen mineralization insubtropical paddy soils[END_REF]. They explain that Fe hydroxides in water saturated soils play a role in stabilizing SOM through complex stabilization mechanisms by sorptive processes, or by the formation of organo-mineral complexes including SOM-Fe oxide-clay associations [START_REF] Kaiser | The role of DOM sorption to mineral surfaces in the preservation of organic matter in soils[END_REF]Guggenberger, 2000, Wagai and[START_REF] Wagai | Sorptive stabilization of organic matter in soils by hydrous iron oxides[END_REF]. [START_REF] Wilson | Rewetted industrial cutaway peatlands in western Ireland: prime location for climate change mitigation?[END_REF] also pointed that strongly crystalline Fe hydroxide features are able to sequester OM in Fe-SOM complexes via encapsulation at the core of the Fe nodules. The anaerobic bacteria in waterlogged soils were also reported to increase the bond between Fe hydroxides and SOM [START_REF] Akter | Control of Fe and Mn availability on nitrogen mineralization insubtropical paddy soils[END_REF]. Similar results relating to Al are also available in literature; however, poorly crystalline Fe and Al hydroxides are more important than strongly crystalline mineral hydroxides for the stabilization of SOM [START_REF] Spielvogel | Soil organic matter stabilization in acidic forest soils is preferential and soil-typo-specific[END_REF]. This meta-analysis points to relatively low impact of organic CeFe bonds on C accumulation in hydromorphic soils.

Factors controlling soil hydromorphy: towards better understanding of C stabilization in wetland soils

While soil hydromorphy would generally be anticipated to increase with precipitation due to amount of available water, our results show negative correlations between HI and climatic factors (Figs. 3 and4). This may be explained in terms of weathering and its impact on drainage properties of soils. In general, high precipitation and temperature enhance weathering processes giving rise to well-structured soils with good drainage properties, which may explain their low hydromorphic intensity. In addition to climate, many other interactive controls of a geologic, geomorphologic and pedogenetic nature influence the development of aquic conditions and hydromorphy in soils. On the basis of topography, hydromorphic soils are normally found in valleys surrounded by hills with no permeable subsoil horizons to allow lateral flow and seepage downslope [START_REF] Bouma | Use of soil survey data to select measurement techniques for hydraulic conductivity[END_REF]. The aquic conditions may also be due to lithogenic discontinuity [START_REF] Putzer | The geological evolution of the amazon basin and its mieral resources[END_REF], denudational events [START_REF] Sombroek | Soils on a Warmer Earth: The Tropical Regions[END_REF] and geochemical equilibrium between dissolution and precipitation during soil evolution [START_REF] Dubroeucq | Evolution des couvertures pédologiques sableuses à podzols géants d'Amazonie (Bassin du haut Rio Negro)[END_REF]. Geochemical landscape denudation over extensive geological periods in tectonically stable areas can cause soil surfaces to approach the top of, for example, a regional groundwater table leading to prolonged water saturation. Tectonic factors may also reduce soil drainage efficiency by promoting relative rises in base levels through tilting [START_REF] Dubroeucq | Les couvertures pédologiques à Podzols du bassin du haut rio Negro (Amazonie)[END_REF] and/or subsidence of large spatial extent.

Latitude is also an important factor controlling C stability in wetlands because landscape position and climate change control waterlogging conditions resulting in distinct SOM decomposition. For example, climate change induced thawing of permafrost in high latitudes is causing partially and/or seasonally waterlogged soils exposing previously frozen C to aerobic decomposition under more elevated temperatures, which increase CO 2 and CH 4 emissions by > 5 times in comparison to the same soil under anaerobic conditions [START_REF] Gruber | The vulnerability of the carbon cycle in the 21st century: an assessment of carbon-climate-human interactions[END_REF][START_REF] Schuur | Vulnerability of permafrost carbon to climate change: implications for the global carbon cycle[END_REF]. In the lowlands, the dissolved and particulate C exported by erosion from thawed soils can be deposited in aquatic environments [START_REF] Walter | Methane bubbling from Siberian thaw lakes as a positive feedback to climate warming[END_REF].

Considerable fluctuations in soil spatial patterns due to differing drying rates following high rainfalls have also been reported [START_REF] Guo | Unification of soil feedback patterns under different evaporation conditions to improve soil differentiation over flat area[END_REF]. Soil drying is highly influenced by evaporation conditions (air temperature, humidity and wind speed) and its topographical location. Soil properties change due, for example, to changes in chemical element content, type and quantity of organic compounds [START_REF] Vepraskas | Albic neoskeletans in argillic horizons as indicators of seasonal saturation[END_REF][START_REF] Peterschmitt | Yellowing, bleaching and ferritisation processes in soil mantle of the western Ghâts, South India[END_REF][START_REF] Montes | Syste`mes sols ferrallitiques-podzols et gene`se des kaolins[END_REF] and may also alter the hydric systems. Such processes may involve lateral soil transformation where the hydromorphic properties develop in matrices of lateritic soils triggered by sharp structural, textural and mineralogical changes.

There are also anthropogenic factors which contribute to climate change and subsequently influence evapotranspiration potential and hydrology [START_REF] Sombroek | Soils on a Warmer Earth: The Tropical Regions[END_REF]. Soil use may be considered a sensitive factor of color change associated with organic matter; for example, that land uses related with artificial hydromorphic soils such as rice cultivation keep high soil C levels due to the reducing character credited to long artificial flooding. Mineral soils of wetlands may also not have the organic horizon due to annual tillage operations [START_REF] Ewing | Changes in wetland soil morphological and chemical properties after 15, 20, and 30 years of agricultural production[END_REF]. These interferences contribute to the development of hydromorphic environments that result in increased water saturation and temporary immersion which reduce decomposition rates of organic matter in soil developed in topographical depressions.

Conclusions

In this study of 122 soil profiles from 29 studies performed under temperate, humid, sub-humid, tropical and sub-arctic conditions, our main objective was to evaluate the global variations in wetlands SOC content (SOC C ) and to relate this to key soil and environmental factors such as soil texture, intensity of soil hydromorphy, content in metals and climate. Three main conclusions can be drawn. The first one is that SOC C whose average was 53.5 ± 15.8 g C kg -1 showed a range between 1 and 540 g C kg -1 . The second conclusion was that soil carbon content in wetland soils highly increase with increase in soil hydromorphy. The third one was that intensity of soil hydromorphy and thus SOC C decreased with increasing mean annual precipitation. This was surprising as high precipitation would induce a greater occurrence of soil saturation by water but could be the result of greater oxygen input to the system or a greater soil drainage as rock weathering is enhanced. These results on the global variations in SOC C in wetlands soils could inform land use planners and policy makers on the level of SOC C to expect in a wetland of a given environment and thus the sequestration potential of degraded wetlands or the potential losses from natural wetlands when submitted to changes in land use or management. There were however several limitations to this study which were inherent to data availability. First of all, despite numerous studies on wetland soil carbon, there were very few studies simultaneously reporting on SOC C and soil hydromorphy and more needs to be done to report on other important factors such as land use, geological bedrock and topographic conditions for a more holistic assessment of the controls of SOC C level in wetland soils.

Fig. 1 .

 1 Fig. 1. Global distribution of the study sites used in this meta-analysis.

Fig. 2 .

 2 Fig. 2. SOCc as function of (A) soil hydromorphy (HI index), (B) soil Value, (C) Chroma and (D) Depth.

Fig. 3 .

 3 Fig. 3. (A) Clay and (B) Al as function of HI, and HI as a function of (C) MAP and (D) MAT index.

Fig. 4 .

 4 Fig. 4. Principal Component Analyses (PCA) of environmental factors (MAP: mean annual precipitation; MAT: mean annual temperature; SD: soil depth; DH: depth of hydromorphy in the soil profile) and soil parameters (Clay: soil clay content, SOC C : soil organic carbon content, Chroma and Value, pH and, Al and Fe content).

Table 1

 1 Compilation of references included in the database for analysis of the factors controlling SOC in hydromorphic soils.

	Author(s)	Country	LONG	LAT	MAP	MAT	SOC C			Clay	Chroma	Value
			°mm year -1	°C year -1	g C kg -1			%
							Mean	Min	Max
	Bardy et al. (2008)	Brazil	-1.87	-61.60	2000.00	26.00	319.80	165.00	455.00		1.57	3.32
	Brinkman (1977)	Bangladesh	90.09	24.50	2923.00	23.90	2.63	0.20	6.50	7.20	1	6.44
	Bullinger-Weber et al. (2014)	Swiss	8.60	47.56	870.00	10.10	20.19	1.10	56.20	0.70	-	-
	Chaplot et al. (2001)	France	5.3	47.5	1000.00	10.8	56.86	1.2	460	1.87	2.77	4.17
	Ferronato et al. (2016)	Italy	12.24	44.51	600.00	13.50	18.61	1.10	118.10		1.13	3.75
	Fiedler et al. (2002)	Germany	8.12	47.12	785.00	8.30	209.06	2.00	540.00	18.84	3.08	4.45
	Fiedler and Kalbitz (2003)	Germany	47.12	8.12	1600.00	6.00	157.57	5.00	430.00	11.40	-	-
	Fritsch et al. (2009)	Brazil	-1.87	-61.60	2000.00	26.00	3.20	1.65	4.55		-	-
	Gangopadhyay et al. (2015)	India	23.02	91.58	2150.00	18.70	8.35	0.50	24.30	38.90	1.71	4.88
	Guimaraes et al. (2013)	Brazil	-3.17	-60.50	2000.00	25.00	7.36	0.18	36.27	21.40	7.36	5.07
	Jungkunst et al. (2008)	Germany	47.95	8.12	1600.00	6.00	274.53	23.00	500.00	25.74	-	-
	Kölb et al. (2014)	China	30.17	121.23	1325.00	13.60	7.93	1.40	30.00	28.94	2.53	4.02
	Machado (2014)	Brazil	-19.36	-48.00	1474.00	22.55	89.00	17.77	175.88	57.36	-	-
	Martins et al. (2006)	Brazil	-49.50	-10.66	1750.00	24.00	29.13	0.30	121.10	29.88	3.17	5.52
	Martins (2014)	Brazil	-19.22	-48.06	1474.00	22.55	13.44	1.42	41.27	56.96	2.09	5.3
	Mello et al. (2015)	Brazil	-16.50	-56.17	1150.00	25.00	13.51	6.40	23.83		-	-
	Nascimento et al. (2004)	Brazil	-1.87	-61.60	2000.00	26.00	19.35	0.60	54.30	8.48	2.33	6
	Nascimento et al. (2010)	Brazil	-16.80	-48.68	1440.00	23.00	12.64	0.69	40.86	2.50	-	-
	Neto et al. (2015)	Brazil	-29.75	-50.50	1309.00	19.50	46.77	1.90	453.00	18.45	2.38	3.76
	Olaleye et al. (2014)	South Africa	-28.88	-28.78	464.00	15.50	6.35	3.63	8.89	3.83	1.62	2.91
	Orozco et al. (2014)	Mexico	19.64	-101.59	919.00	16.80	26.14	4.00	66.00	26.21	2.42	2.69
	Rosolen et al. (2015)	Brazil	-18.93	-47.83	1516.00	23.00	31.62	5.00	116.00	537.6	2.59	3.88
	Schawe et al. (2007)	Bolivia	-16.15	-68.92	3833.30	13.30	120.36	11.00	447.00	14.64	-	-
	Schiavo et al. (2012)	Brazil	-18.99	-56.60	1433.00	30.15	7.95	0.10	110.50	7.47	3.52	4.52
	Skorupa et al. (2013)	Brazil	-48.02	-15.75	1594.00	21.20	41.11	3.00	190.00	34.42	3.06	3.44
	Sorokin et al. (2006)	Russia	106.36	57.28	244.00	-1.60	19.59	2.50	41.20	9.11	-	-
	Thompson et al. (2007)	USA	-83.40	36.80	127.00	12.50	27.18	2.0	65.00		1.14	4.37
	Vepraskas and Caldwell (2008)	USA	35.57	-77.44	1260.30	16.40	22.06	2	71		2.11	4.17
	Wang et al. (2011)	China	37.58	-118.55	552.00	12.10	57.93	35.40	107.50		-	-

Table 2

 2 Environmental factors, soil variables and their classes as used in the current paper.

	Environmental factor	Symbol	Remarks Class definition Class name
	Mean annual precipitation	MAP	120-800	Semi-arid
	(mm year -1 )		800-1200	Humid
			1200-2200	Wet
	Mean annual temperature	MAT	6-15	Cold
	(°C)		15-22	Warm
			22-30	Hot
	Soil clay content (%)	Clay	10-25	Sandy loam
			25-50	Sandy Clay
			50 >	Clay
	Chroma	Chroma	0-4	Low
			4-7	Medium
			7-10	High
	Value	Value	2-4	Low
			4-6	Medium
			6-8	High
	Hydromorphic index		0-15	Low
			15-20	Medium
			20-50	High

Table 3

 3 Summary statistics of the environmental and soil variables.

	Statistic	Controlling factors

Table 4

 4 Spearman rank correlations between environmental factors and soil variables.

		LONG	LAT	MAP	MAT	pH	Clay	Chroma	Value	SOC C	Fe	Al
	LONG	1.00
	LAT	0.36 ⁎	1.00
	MAP	-0.17 ⁎	-0.31 ⁎	1.00
	MAT	-0.47 ⁎	-0.74 ⁎	0.51	1.00
	pH	-0.09 ⁎	-0.14 ⁎	-0.09	0.05	1.00
	Clay	-0.01	-0.08	0.03	0.09	0.21 ⁎	1.00
	Chroma	0.09 ⁎	-0.05	0.06	0.03	0.18 ⁎	0.19 ⁎	1.00
	Value	-0.01	-0.08	0.04	0.06	0.23 ⁎	-0.03	0.39 ⁎	1.00
	SOC C	0.034	0.15 ⁎	-0.02	-0.14 ⁎	-0.24 ⁎	-0.36 ⁎	-0.26 ⁎	-0.42 ⁎	1.00
	Fe	-0.00	0.13	-0.12	-0.35 ⁎	-0.11	-0.04	0.17	-0.01	0.21 ⁎	1.00
	Al	0.09	-0.10	-0.09	-0.06	0.05	0.19	0.67 ⁎	0.22	0.19 ⁎	0.62 ⁎	1.00

⁎ Significant correlation at p < 0.05.

Acknowledgements

The authors acknowledge the funding from FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo -Proc. N°2014/001131-4 and 2017/14168-1).