Stéphanie Topoliantz

tel. Jean-François Ponge
email: jean-francois.ponge@wanadoo.fr

Sylvain Ballof

Manioc peel and charcoal: a potential organic amendment for sustainable soil fertility in the tropics

Keywords: Organic farming, Slash-and-burn cultivation, Aluminum, Phosphorus, Earthworm density, Legume, Soil nutrient content

In tropical areas, where crop production is limited by low soil quality, the development of techniques improving soil fertility without damage to the environment is a priority. In French Guiana, we used subsistance farmer plots on poor acidic soils to test the effect of different organic amendments, bitter manioc peel (M), sawdust (Sw) and charcoal (Ch), on soil nutrient content, earthworm abundance and yard-long bean (Vigna unguiculata sesquipedalis) production. The peregrine Pontoscolex corethrurus was the only earthworm species found. Pod production and plant growth were lowest in unamended soil. The application of a mixture of manioc peel and charcoal (M+Ch) improved legume production as compared with other organic mixtures. It combined favourable effects of manioc peel and charcoal. Manioc peel improved soil fertility through its low C:N ratio and its high P content, while charcoal decreased soil acidity and exchangeable Al and increased Ca and Mg availability, thus alleviating possible toxic effects of Al on plant growth. The M+Ch treatment was favourable to P. corethrurus, the juvenile population of which reaching a size comparable to that of the nearby uncultivated soil. The application of a mixture of manioc peel and charcoal, by improving crop production and soil fertility and enhancing earthworm activity, could be a potentially efficient organic manure for legume production in tropical areas where manioc is cultivated under slash-and-burn shifting agriculture.

Introduction

In the tropics, traditional shifting cultivation still supplies food to 300-500 million families (Anonymous 1985). However, in some areas, under increasing population pressure and lack of cultivable land, usually farmers shorten the fallow period [START_REF] Seiler | Estimates of gross and net fluxes of carbon between the biosphere and the atmosphere from biomass burning[END_REF][START_REF] Brady | Alternatives to slash-and-burn agriculture: a global imperative[END_REF]. Biological soil functioning is rapidly perturbed when the balance between plant needs, nutrient availability and decomposer activity is disrupted by the shift from traditional slash-and-burn agriculture towards permanent cultivation [START_REF] Myers | Strategies for management of soil acidity[END_REF][START_REF] Lavelle | Faunal activities and soil processes: adaptive strategies that determine ecosystem function[END_REF]. Without cheap, reliable techniques to maintain the fertility of acid soils under permanent cultivation, crop production rapidly decreases and poverty increases among farmers.

Considering the cost of inorganic, synthetic fertilisers for poor local farmers, and significant leaching losses in sandy soils poor in organic matter, new fertilising techniques in the tropics increasingly rely on the management of soil biota, a key factor in soil fertility [START_REF] Lavelle | Management of earthworm populations in agro-ecosystems: a possible way to maintain soil quality?[END_REF][START_REF] Beare | Agricultural intensification, soil biodiversity and agroecosystem function in the tropics: the role of decomposer biota[END_REF]. Methods using green waste and soil fauna activity were developed to improve crop production by stabilising nutrients and organic matter within soil biogenic structures [START_REF] Sparovek | Influence of organic matter and soil fauna on crop productivity and soil restoration after simulated erosion[END_REF][START_REF] Senapati | In-soil earthworm technologies for tropical agroecosystems[END_REF]. [START_REF] Senapati | In-soil earthworm technologies for tropical agroecosystems[END_REF] improved tomato production in Peru with composted sawdust, reaching the same level as with inorganic fertilizers. Several studies, reviewed by [START_REF] Glaser | Ameliorating physical and chemical properties of highly weathered soils in the tropics with charcoal: a review[END_REF], showed that charcoal, through its positive effects on soil physical and chemical properties, can improve microbial activity and crop production. In the presence of the endogeic earthworm Pontoscolex corethrurus (Glossoscolecidae, Oligochaeta), a species adapted to tropical cultivated soils [START_REF] Lavelle | Adaptive strategies of Pontoscolex corethrurus (Glossoscolecidae, Oligochaeta), a peregrine geophagous earthworm of the humid tropics[END_REF], we previously found that yard-long bean (Vigna unguiculata sesquipedalis L.) production was improved by amendment with manioc peel and to a lesser extent by charcoal. These two amendments, respectively, increased P availability and decreased soil acidity (Topoliantz, unpublished doctorate thesis). In Latin America and Africa, bitter manioc (Manihot esculenta ultilissima Crantz) is widely cultivated for its tubers [START_REF] Guillaumet | Les plantes alimentaires des forêts humides intertropicales et leur domestication: exemple africains et américains[END_REF], and their peel, produced in large quantity, provides a potentially valuable green waste that can be used for vermicomposting despite its cyanide toxicity [START_REF] Mba | Utilization of Eudrilus eugeniae for disposal of cassava peel[END_REF][START_REF] Mba | Treated cassava peel vermicomposts enhanced earthworm activities and cowpea growth in field plots[END_REF]. [START_REF] Tian | Effect of mulch quality on earthworm activity and nutrient supply in the humid tropics[END_REF] found that combining mulches of different quality could help to synchronize nutrient supply with plant needs. The goal of our present study was to test the combined effects of manioc peel, charcoal and sawdust on yard-long bean production, in the true conditions of subsistance farming. Considering the whole agroecosystem plant-soil-fauna, we also determined how mulches affected the soil nutrient content and the earthworm populations as compared with unamended soil. The trial was carried out in the local farming context in order to provide new cheap solutions to improve crop yields in the tropics.

Materials and methods

Site and soil amendment

The experimental study was conducted in French Guiana at Maripasoula (3°39'N; 54°2'W) in a local farmer's field [START_REF] Topoliantz | Effect of organic manure and the endogeic earthworm Pontoscolex corethrurus (Oligochaeta: Glossoscolecidae) on soil fertility and bean production[END_REF]. The soil was an Oxisol with 58% sand, 14% silt, 24% clay, and 3% organic matter in the top 10 cm. Soil preparation for legume culture was carried out according to local practices. In April 2001 the natural herb layer was cut and the soil was hoe-harrowed to 20 cm depth. At the soil surface, rows of different organic mixtures composed of weakly composted manioc peel (M), local home-made charcoal (Ch) and fresh sawdust from a local sawyer (Sw) were applied at the rate of 100 L per row (67 L.m -2 ). The chemical composition of M, Ch and Sw is presented in Table 1. Equal volumes of organic wastes were mixed together and were covered with soil to form mounds, as in traditional practice. There were four mounds amended with M+Ch, M+Sw, Ch+Sw, and M+Ch+Sw and a control mound made of non-amended soil (NoA), each 25 cm wide and 6 m long, placed at 1 m distance from each other, parallel to the gentle land slope.

Lack of space and allowance for traditional methods of cultivation prevented us to impose a randomized block design on the local farmer who kindly accepted to perform the experiment on his own land.

Crop production and plant sampling

Four months after incorporating organic mixtures to the soil, i.e. in October 2001, seeds of yard-long bean (V. unguiculata sesquipedalis) were sowed in the mounds, with pairs of seeds in holes about 40 cm apart. Two months later, i.e. in December 2001, plants were harvested by hand, paying attention to the root system, and the survival rate was measured. Aerial parts were separated from root systems, shoots were dried in newspaper and root systems were preserved in ethyl alcohol until laboratory analysis.

Legume nodules were isolated from roots, then all plant parts (shoots, pods, roots and nodules) were dried at 105°C and weighed. Aphids present on root systems were collected from the fixative and counted.

Earthworm sampling

Earthworms were sampled in the mounds at the time of crop harvesting (December 2001) according to the TSBF method [START_REF] Anderson | Tropical Soil Biology and Fertility. A handbook of methods[END_REF]. Four soil blocks 25 cm x 25 cm x 30 cm were collected 2 m apart on the ridge of each mound, thus totalling 20 samples. Earthworm individuals and cocoons were sorted by hand and counted. Earthworms were also sampled with the same method under adjacent uncultivated herb vegetation. Twelve samples were taken in four rows three-meter long 90 cm apart. All earthworm individuals were identified as P. corethrurus. They were sorted according to their size, as juveniles (newly hatched individuals) and adults (clitellate as well as non clitellate) before being replaced in the soil.

Soil sampling and analyses

In the gaps between the five mounds, a total of eighteen (4 x 4) soil samples were taken for determining the composition of the original soil at the time of soil preparation (April) and checking for gradients of soil fertility in the experimental field (Table 2). At the time of harvest (December) eleven soil blocks per experimental mound, each 7 cm x 7 cm area from 0-10 cm depth, were collected at different places of the ridges, thus totalling 55 samples. The soil was air-dried before transport to the laboratory for chemical analyses: organic C and N according to ISO 10694 and 13878, respectively (Anonymous 1999), soil acidity (pH water and pH KCl ), total P (P tot ) and available P (P av , Olsen method), total K (K tot ), cation exchange capacity (hexamine cobalt extraction), exchangeable K (K ex ), Mg (Mg ex ), Ca (Ca ex ), Na (Na ex ) and Al (Al ex ) according to [START_REF] Baize | Guide des analyses en pédologie[END_REF]. The base saturation of the sorption complex (S/CEC, S=sum of exchangeable K, Mg, Ca and Na) was calculated. Cyanide contents were measured according to NF T90-107 (Anonymous 2001) in soil samples as well as in three samples of weakly composted manioc peel which had been dried for 48h at 105°C.

Statistical analysis

Crop, earthworm and soil chemical data were statistically analysed [START_REF] Glantz | Primer of biostatistics[END_REF].

Differences between rows (six) and slope positions (three) in chemical properties of the original soil were tested by two-way ANOVA without replication. The effects of treatments (M+Ch, M+Sw, Ch+Sw, M+Ch+Sw and NoA) on crop, earthworm and soil data were tested by one-way ANOVA (data were log-transformed when necessary) or Kruskall-Wallis rank tests when assumptions of ANOVA were not fully satisfied even after log transformation. Multiple comparisons among means or between groups were done a posteriori using Tukey's test or Dunn's test following ANOVA or Kruskall-Wallis rank test, respectively. The effect of treatments on plant survival was tested by  2 .

Relationships between nodules, pods, shoot, root and aphids were tested by Spearman rank correlation coefficients. Comparisons of cocoon and earthworm abundances between natural fallow and other treatments were made using Dunnett's method. The chemical composition of the initial soil (between mounds) and that of the non-amended mound (NoA) were compared by t-test.

Results

There were no detectable differences between the six rows (four rows between mounds and two outside) in the 15 soil parameters which were measured on the initial (uncultivated) soil (Table 2). Only two out of 15 parameters showed a (weak, although significant at P 0.05 level) slope effect: the P content decreased from 198 to 160 mg.kg -1 from up-to downslope and the base saturation was maximum downslope (67%) and minimum at mid slope (48%). Given the absence of differences between rows and because replication was achieved along the slope within each treatment, we considered that treatments effects were not biased by spatial heterogeneity, despite the absence of block design.

The survival rate of bean (number of shoots living at the time of harvest against number of seeds planted) was only weakly affected by treatments ( 2 = 9.38, P=0.052), although in NoA the observed survival rate was higher than in other treatments. Pod production (per shoot) was higher in M+Ch than in Ch+Sw and NoA treatments where it was nil or near nil (Fig. 1). The effects of treatments on other plant parameters are presented in Table 3. The dry weight of shoots and the shoot:root ratio were higher in the presence of amendments (M+Ch, M+Sw, Ch+Sw, M+Ch+Sw) but did not differ among amendments. The shoot:nodule ratio was higher in M+Ch than in NoA and the root:nodule ratio was not affected by treatments.

Aphid density (number of individuals per g of dry root, 4.2 in average) was not affected by treatments (H= 0.574, P= 0.97).

Figure 2 shows the distribution of cocoons, juvenile and adult/subadult P. corethrurus under each treatment and the natural fallow, at the time of harvest (December). As a consequence of cultivation, a decrease was observed in juvenile densities compared to the natural fallow, except under M+Ch amendment. Only M+Sw decreased cocoon densities compared to the natural fallow. No general decrease and no differential effect of treatments was observed in the adult/subadult population.

At the time of harvest, all soil nutrients except Na were significantly influenced by treatments (Table 4). A higher pH water was found in treatments using charcoal (M+Ch, M+Ch+Sw and Ch+Sw) and the highest pH KCl was observed in the M+Ch treatment. Whatever the method used to measure pH, NoA was the most acidic. The C:N ratio was highest in amendments containing sawdust (M+Sw, Ch+Sw, M+Ch+Sw).

Cation Exchange Capacity (CEC) was lowest in Sw+Ch and M+Sw+Ch treatments and highest in NoA. In this latter treatment, we found the highest rate of exchangeable Al and the lowest rate of exchangeable Mg, Ca and base saturation, the reverse being observed in the M+Ch treatment.

When compared to the composition of the original soil (Table 1), NoA exhibited a lower C:N ratio (t= 4.7, P< 0.001), pH Water (t= 5, P< 0.001) and pH KCl (t= 3.5, P= 0.001) and a higher exchangeable Al level (t= -3.7, P< 0.001). Most cyanide levels were below the detection limit (<0.1 mg.kg -1 ) except for three samples in the M+Sw+Ch treatment which showed a very low cyanide content (0.11, 0.11 and 0.12 mg.kg -1 ) as compared with manioc peel (3.6 mg.kg -1 ).

Discussion

The development of aerial parts of V. unguiculata sesquipedalis L. was improved by amending mixtures as compared with non-amended soil. When nutrients are scarce, plants develop their root system at the expense of shoot growth [START_REF] Taiz | Principles of soil chemistry[END_REF]. Nodulation was reduced by amendment, suggesting a poorer mineral N availability in the unamended soil [START_REF] Salisbury | Plant physiology[END_REF]. In the absence of amendment we also observed a higher soil acidity compared with amended as well as initial soil. A high level of Al, often observed at low pH in the soil solution [START_REF] Nair | Calculations of equilibrium concentration of mono-and polynuclear hydroxyaluminium species at different pH and total aluminium concentrations[END_REF], may be detrimental to cultivated plants by reducing root growth and uptake of P, Mg and Ca by roots [START_REF] Foy | Effects of aluminium on plant growth[END_REF]). The amendments did not exert any depressive effect on aphids, confirming that in this trial these sucking insects drain the sap flow without affecting plant growth [START_REF] Salisbury | Plant physiology[END_REF].

Pod production was highest in treatments with manioc peel, especially when supplemented with charcoal rather than sawdust. This result confirmed those obtained in our previous bioassay [START_REF] Topoliantz | Effect of organic manure and the endogeic earthworm Pontoscolex corethrurus (Oligochaeta: Glossoscolecidae) on soil fertility and bean production[END_REF], in which manioc peel amendment alone was the most productive treatment compared with charcoal, sawdust and nonamended soil. We attribute the beneficial effect of manioc peel to a higher P availability, the effect being reinforced in the presence of P. corethrurus, which stimulates the mineralisation of microbial P [START_REF] Barois | Influence of the tropical earthworm Pontoscolex corethrurus (Glossoscolecidae) on the fixation and mineralization of nitrogen[END_REF][START_REF] Brown | Pedoanthracological contribution to the study of the evolution of the upper treeline in the Maurienne Valley (North French Alps): methodology and preliminary data[END_REF].

Phosphorus and K levels in manioc peel were estimated to 2.26 g kg -1 and 10.3 g kg -1 , respectively, thus higher than in charcoal (0.268 g kg -1 and 5.05 g kg -1 ) and far higher than in sawdust (0.0633 g kg -1 and 0.347 g kg -1 ). However, at harvest time we did not detect any increase in available P in the soil under manioc peel, except when manioc peel were added together with charcoal and sawdust (Table 4). Given that pod production was maximized under manioc peel amendment (Table 3) and that soil collection for chemical analyses (Table 4) was done at harvest, we cannot discard that at least part of the added P (38 g.m -2 ) was mineralized then taken up by crop plants, thus could not be detected in the soil. The negative effect of sawdust on pod production (Table 3) could be due to N immobilization, which has been repeatedly reported to occur in decaying wood [START_REF] Swift | The roles of fungi and animals in the immobilisation and release of nutrient elements from decomposing branch-wood. In Lohm U, Persson T (eds) Soil organisms as components of ecosystems[END_REF][START_REF] Edmonds | Decomposition rates and nutirent dynamics in small-diameter woody litter in four forest ecosystems in Washington, U.S.A[END_REF].

At the time of harvest Al availability in the soil was lowest in the presence of a mixture of manioc peel and charcoal (Table 4). Charcoal, by increasing pH, diminishes mobile forms of Al (Tan 1982). We found that the soil amended with charcoal presented also higher levels of exchangeable Ca and Mg. Several studies previously showed that charcoal as well as its ashes increase the availability of P, K, Mg and Ca and decrease that of toxic elements such as heavy metals (Fe, Mn and Zn) [START_REF] Tryon | Effect of charcoal on certain physical, chemical and biological properties of forest soils[END_REF][START_REF] Kishimoto | Charcoal as soil conditioner[END_REF]Voundi Nkana et al. 1998). This effect can be attributed to the porous nature of charcoal, rather than to a liming effect, given its scarcity in nutrients when compared to manioc peel (Table 1). Charcoal exhibits a high internal surface [START_REF] Brown | Pedoanthracological contribution to the study of the evolution of the upper treeline in the Maurienne Valley (North French Alps): methodology and preliminary data[END_REF] which increases in the course of time and becomes progressively oxidised [START_REF] Chan | Oxidative reactivity of coal chars in relation to their structure[END_REF]. Once chemically activated, charcoal acts as a filter and retains positively as well as negatively charged mineral ions in an exchangeable form [START_REF] Holl | Description of sorption equilibria for ions onto activated barbon using the surface complexation theory[END_REF]. [START_REF] Kishimoto | Charcoal as soil conditioner[END_REF] showed that charcoal also improved soil porosity and moisture holding capacity, which led to better plant and root growth. In our study, lower soil acidity and toxic metals and higher rate of macro-nutrients were observed when charcoal was combined with manioc peel (with a high phosphorus content); this led also to better plant growth. We suspect a synergistic effect of these two amendments due to the high surface area of charcoal that confers a high sorptive capacity for chemical compounds [START_REF] Titoff | Die Adsorption von Gasen durch Kohle[END_REF][START_REF] Zackrisson | Key ecological function of charcoal from wildfire in the Boreal forest[END_REF][START_REF] Wardle | The charcoal effect in boreal forests: mechanisms and ecological consequences[END_REF]microbial communities (Pietikaïnen et al. 2000). Given the low content of swelling clays and organic matter in tropical Oxisols [START_REF] Brady | The nature and properties of soils[END_REF], the existence of a stable, solid component with strong sorptive properties, such as charcoal [START_REF] Skjemstad | The chemistry and nature of protected carbon in soil[END_REF], would help to retain mineral nutrients liberated during the decomposition of organic amendments.

In contrast, soils from treatments with a mixture of manioc and sawdust exhibited at harvest the lowest pH and the same low base saturation as the complete mixture of manioc, sawdust and charcoal. Thus the addition of sawdust to a mixture of manioc and charcoal did not provide any benefit to legume production, even suggesting a negative effect of the three amendments when combined. Fresh sawdust is not palatable to saprophagous biota because of its low nutrient and high phenolic content [START_REF] Tian | Biological effects of plant residues with contrasting chemical compositions under humid tropical conditions: effects on soil fauna[END_REF]. Thus the addition of non-composted sawdust may inhibit manioc peel decomposition. It seems that the positive effect of sawdust amendment on soil nutrient content may appear later than that of manioc peel because of much slower decomposition.

Only the mixture of manioc and charcoal did not depress earthworm densities.

In the natural fallow, P. corethrurus juveniles and cocoons were mostly present in the upper 20 cm of the soil and adults tended to live more deeply (Topoliantz, unpublished doctorate thesis). [START_REF] Fragoso | Ecologia general de las lombrices terrestres (Oligochaeta: Annelida) de la region Boca del Chajul, Selva Lancandona, Estado de Chapias[END_REF] already observed the same vertical distribution of P. corethrurus during the dry season. Under cultivation, adults and juveniles were mostly present at greater depths than in the fallow (Topoliantz, unpublished doctorate thesis), suggesting some avoidance effect of mounded soil, which was lessened under mixed manioc-charcoal amendment. Presumably earthworms burrowed deeper in order to avoid desiccation of the superficial soil layers, especially in non-amended cultivated soil. The manioc-charcoal mixture presented as many cocoons and juveniles as the natural fallow, indicating that this amendment did not interfere with P. corethrurus reproduction.

The cyanide content of our manioc peel was very low (3.6 mg.kg -1 ) compared with that reported by [START_REF] Mba | Utilization of Eudrilus eugeniae for disposal of cassava peel[END_REF] in decomposed peel (168.5 mg.kg -1 ). Thus in our study this amendment did not produce cyanide toxicity in the soil. We also observed that soil aggregates 0.2-0.6 cm (mostly earthworm faeces) were negatively correlated with soil acidity (Topoliantz, unpublished doctorate thesis), indicating that charcoal, which increased pH, favoured juvenile earthworm activity. Although P. corethrurus is known to tolerate soil acidity [START_REF] Lavelle | Adaptive strategies of Pontoscolex corethrurus (Glossoscolecidae, Oligochaeta), a peregrine geophagous earthworm of the humid tropics[END_REF], juveniles are apparently more sensitive to this factor, and thus any treatment increasing pH will favour this peregrine species which is able to ingest charcoal and mix it with the original soil [START_REF] Topoliantz | Burrowing activity of the geophagous earthworm Pontoscolex corethrurus (Oligochaeta: Glossoscolecidae) in the presence of charcoal[END_REF].

Under conditions that can be managed by subsistance farmers the combination of charcoal and manioc peel offers a cheap, reliable method to alleviate Al toxicity and to increase the nutrient status of acid tropical soils, through the buffer and filter power of charcoal and the input of P by manioc, thus improving legume production. It also provides favourable conditions for earthworm reproduction, allowing the maintainence of the fragile equilibrium between producers (plants) and decomposers (microbes, soil fauna) under tropical agriculture. As manioc peel are rapidly decomposed by soil biota, this amendment will have to be regularly added, whereas charcoal does not need to be supply repeatedly, being persistent in the soil [START_REF] Glaser | The 'Terra Preta' phenomenon: a model for sustainable agriculture in the humid tropics[END_REF]. Farther, excess of charcoal could even depress plant growth due to a too high alkalinity [START_REF] Kishimoto | Charcoal as soil conditioner[END_REF]. financial support and commodities. We are grateful to Mr Lobbini and his son, local farmers, for their technical assistance on the field. We also thank the Institut Pasteur (Lille, France) for cyanide analyses and the Institut National de la Recherche Agronomique (Arras, France) for mineral soil analyses. One-way ANOVA was followed by comparisons between amendments and natural fallow using Dunnett contrasts.

Legends

Fig. 1 .

 1 Fig. 1. Mean pod production of Vigna unguiculata sesquipedalis (yard-long bean)

Fig. 2 .

 2 Fig. 2. Mean densities of cocoons, juveniles and adults/subadults of the earthworm

  Fig.1

Table 1 .

 1 Chemical composition of the different amendments[START_REF] Topoliantz | Effect of organic manure and the endogeic earthworm Pontoscolex corethrurus (Oligochaeta: Glossoscolecidae) on soil fertility and bean production[END_REF]

				Manioc peels	Wood charcoal	Sawdust
	pH (H 2 O)			6.72	9.60	5.31
	Ashes	(%)		31.9	3.80	2.35
	Total C	(g.kg -1 )	356	905	521
	Total N	(g.kg -1 )	24.2	5.64	5.13
	C:N ratio (g.kg -1 )	14.71	160	102
	Total P	(g.kg -1 )	2.26	0.27	0.06
	Total K	(g.kg	-1 )	10.3	5.05	0.35

Table 2 .

 2 Chemical soil composition of the initial soil in the upper 10 cm (means of 16 replicates ± S.E.).

	1
	2

Table 3 .

 3 Biological parameters of Vigna unguiculata sesquipedalis according to treatments (M: manioc peels, Ch: charcoal, Sw: sawdust, NoA: non-amended soil). Effects of treatments were tested by one-way ANOVA (F) or Kruskall-Wallis rank test (H). Significance levels are indicated by *P < 0.05, ** P<0.01, *** P < 0.001, N.S. not significant. Groups significantly different according to a posteriori multiple comparisons are denoted by different superscript letters. All weights and ratios are based on dry weights of plant parts

	1
	2

Table 4 .

 4 Nutrient contents of the soil at the end of the trial according to treatments (means of 11 samples ± SEM). Otherwise as for Table2.

Acknowledgements

We thank the Mission pour la Création du Parc du Sud de la Guyane, the PPF-Guyane of the Museum National d'Histoire Naturelle and the GIS-Silvolab of French Guiana for


Pierre Oses

Marie-Ange Renault

Rémi Chauvel

Lionel Leroux

Pierre Chevallereau

Cécile Allières

Danièle Daret

Jean-Marie Daniel Lamazière

Pascale Dufourcq

Thierry Couffinhal

Mapping 3-dimensional neovessel organization steps using micro-computed tomography in a murine

Keywords: Animals, Barium, Contrast Media, Disease Models, Animal, Hindlimb, blood supply, Imaging, Three-Dimensional, Ischemia, pathology, surgery, Mesenchymal Stem Cell Transplantation, Mice, Neoprene, Neovascularization, Physiologic, Peripheral Vascular Diseases, pathology, surgery, Tomography, X-Ray Computed, methods

Mapping 3-dimensional neovessel organization steps using micro-computed tomography in a murine model of hindlimb ischemia-brief report

Pierre Oses 1 2 , Marie-Ange Renault 1 , R mi Chauvel However, the classical methods of assessment are not always quantitative, restricted to a limited area of view, evaluate capillary density in 2D sections or report superficial blood flow data . Hence, micro-computed tomography (microCT) can, after the injection of a radiopaque 1 contrast agent, image the vascular network in 3D in an entire organ , and give quantitative data. Several studies have investigated the 2 3 microvascularisation of the kidney, heart, and liver in the rat . Only a few teams have used quantitative tools for studying 4 -6 post-ischemic angiogenesis in the mouse , .

2 3

Here, we used a contrast agent and microCT acquisition procedure dedicated to analyse post-ischemic kinetics of vessel formation and remodelling restricted to arterial network in the mouse hindlimb. We discussed the contribution of these images compared with or in addition to data produced by the conventional laser Doppler and immunolabelling approaches. Our results revealed a predominant arteriogenesis process in the thigh and in contrast a predominant angiogenesis in the tibiofibular region. We showed that neovessel remodelling depends on the restoration of the blood flow. We then provided new data on the mesenchymal stem cell therapy on the feature of vessel formation and organisation.

MATERIALS AND METHODS

Materials and methods related to MSC culture, animal care, model of ischemia, micro-CT data processing and analysis, histological vascularisation quantification appear in the section. supplementary materials and methods

RESULTS AND DISCUSSION

Use of Neoprene latex allows selective arterial filling

We developed and validated a new combination of micronised barium as contrast agent and Neoprene latex as suitable vehicle able to fill only arterial network within a diameter of 20 m. The viscosity property distinguishes latex vehicule from other contrast agent vectors μ which more easily fill the whole vascular network ( section and ). supplementary results and discussion supplementary Fig 1

3D quantification of post-ischaemic arterial vascular growth in the hind limb

For the first time, we demonstrated a significant difference in ischemia-induced vascular growth mechanisms between the thigh and the tibiofibular regions as reported on . mCT analysis demonstrated that the vascular response in the thigh is mostly due to Fig 1 arteriogenesis mechanism as described , . At D15, the number of vessel and connectivity increased slightly, their diameter decreasing 2 3 by two times, with no modification of the total arterial vessel volume in ischemic compared to non ischemic muscle. All these parameters return close to the baseline values by D28 when the perfusion defect was compensated ( ). In summary, microCT Figure 1A and1B uncovered novel arterial remodelling data in the thigh. Other approaches as microangiography were limited by the low spatial resolution and the absence of quantitative volumetric analysis , . Histological examination is rarely carried out in the thigh, because of the 7 8

variability in the degree of ischemia from one muscle to another, of the variations in diameter of medium-calibre arteries detectable only on microCT but not on immunohistochemistry images. Finally, measuring blood flow by laser Doppler is not applicable in this region.

In contrast to the thigh, angiogenesis predominated in the tibiofibular region. In the first 21 days, we showed a dramatic increase in arterial network density (9 fold), volume (6 fold), and vessel connectivity or branching (7 fold) with a decrease of the vessel mean diameter (5 fold). All of these parameters are the hallmark for a dynamic angiogenic process with a very dense and divided arterial network. For the first time, we evidenced a complex arterial vascular remodelling between D15 and D28 in the tibiofibular region, less pronounced in the thigh. The number, connectivity and occupied volume of arterial vessels dropped considerably after D21 ( ) while Fig 1B CD31-positive capillary number and the blood flow gradually improved after 21 days (

). Fig 1C Thus, we propose that the arterial network adapts to tissue perfusion; the precocious development of large-and medium-calibre vessels in the thigh would favour the underlying arterial perfusion and angiogenesis on the tibiofibular region. We then reported after D21, in the tibiofibular region, an arterial neovessel regression while venous and lymphatic capillaries develop as evidenced by immunohistolabelling.

Application to the quantification of an angiogenesis-focused cell therapy

To dissect the mechanisms of mesenchymal stem cell based angiogenic therapy , we examined and quantified by microCT the 9 vascular network in MSC injected vs saline injected hindlimb. MSC graft induced a burst of neo vessels as soon as D8, predominant in the tibiofibular region with an increase in the number, volume and the connectivity of the arterial vessels but with no modification of the mean vessel diameter ( ). Blood flow increased significantly in the mice treated with MSCs (0.205 0.10 vs 0.280 0.17 for Figure 2A and2B ± ± the ischemic/normal limb ratio in control vs MSC-injected animals at D8, respectively, p < 0.05) (not shown). In summary, these observations uncovered a precocious and potent angiogenic role of MSC as soon as D8, showing that MSC therapy acts essentially on angiogenesis.

CONCLUSIONS

é 1 , 2 INTRODUCTION

 12 Lionel Leroux 1 , C cile Alli res As mouse models are largely used to study mechanisms of neovascularisation, vascular repair and growth of collateral vessels , a 1 throughout analysis of the vascular network has gained of interest. Understanding neovessel formation mechanisms requires a complete view of the vascular architecture over the whole of the tissue analysed: size, orientation, branching and organisation of collaterality.

See for a discussionFigure 1 (

 1 Figure 1 (A) Micro-scanner imaging of neovascularisation over time in mice after hindlimb ischaemia on D0, D7, D14, D21, and D28 post-operatively. (B) Quantification of microCT 3D images. Parameters are described in . The results are the mean of n 8 observations for supplemental data = each time point. (C) Arterial density in the tibiofibular region quantified by microCT was compared to the kinetics of blood flow recovery as evaluated by laser Doppler imaging and to capillary density as quantified by immunohistochemistry using the CD31 antibody. The three analyses were performed on the same animals.

Figure 2

 2 Figure 2 MicroCT images (A) and quantification (B) of the effect of mesenchymal stem cell (MSC) therapy on vessel formation. The results are the mean of n 6 observations for each condition.

=


E Roche

O Sename

D Simon

LFT/H ∞ varying sampling control for Autonomous Underwater Vehicles

Keywords: AUV, Robust control, Gain scheduling, Varying Sampling

This paper deals with the robust control of an Autonomous Underwater Vehicle (AUV) subject to communication constraints. The aim is the design of a gain-scheduled varying sampling controller using non periodic measurements from ultrasonic sensors. The contribution of this work lies in a new model formulation of varying sampling discrete-time systems using the Linear Fractional Transformation (LFT) representation. This allows to design, in the LFT context, an H ∞ controller whose matrices are scheduled w.r.t the varying control interval. Moreover the proposed design ensures a performance adaptation when the sampling interval varies. This methodology is developed for AUV and emphasizes important improvements compared with an H ∞ discrete-time control with fixed sampling.

INTRODUCTION

In this paper the H ∞ approach for LPV systems is applied to an Autonomous Underwater Vehicle (AUV) for altitude control. The use of AUV for the exploration of the seabed, and the control of these vehicles has been of large interest for researcher in the past two decades. Many different control laws were studied along the years : decoupling steering, diving, and speed control by PID [START_REF] Jalving | The NDRE-AUV flight control system[END_REF]), coupled PID and anti-windup control [START_REF] Miyamaoto | Maneuvering control system design for autonomous underwater vehicle[END_REF]), sliding mode control [START_REF] Healey | Multivariable sliding mode control for autonomous diving and steering of unmanned underwater vehicles[END_REF]; [START_REF] Salgado-Jimenez | Using a high order sliding modes for diving control a torpedo autonomous underwater vehicle[END_REF]) and H ∞ control [START_REF] Silvestre | Control of the INFANTE AUV using gain scheduled static output feedback[END_REF]; [START_REF] Feng | Reduced order H ∞ control of an autonomous underwater vehicle[END_REF]). The AUV considered in this paper is an Aster X like vehicle, developed by the Ifremer (French Research Institute for Exploitation of the Sea) 1 . In this preliminary study only motions in the vertical plane are considered: the control of the yaw angle and speed are not taken into account.

The measurement of the altitude with respect to the sea floor is made using an ultrasonic sensor. Even if the measurement requests are made periodically, the signal flying time and the time at which the measures are received depend on the distance between the AUV and the sensor's target. This could be viewed as a delay in the reception of the measure, or as a need to apply the control samples in an asynchronous way. Another source of sampling intervals variations may come from sensors scheduling, needed to avoid cross-talking between several ultrasonic devices working in a close area. In this paper this time uncertainty is considered as a gain scheduling parameter for a LPV controller, as in Figure 2. Then the idea is to adapt the control interval with the distance between two samples, so that the controller only acts when a new measurement is available and processed. This approach allows for large measurement time variations because the controller is not only robust to a delay, but also scheduled according to the sampling interval variation. Therefore robust control is necessary to safely perform autonomous missions : in this paper we use the ability of LPV based control to combine the performance specification in the H ∞ framework, and the adaptation of the controller to parameters variations and uncertainties inside a specified range of values provided by the LPV approach.

In [START_REF] Robert | An H ∞ lpv design for sampling varying controllers: Experimentation with a t-inverted pendulum[END_REF] the LPV polytopic approach is used to design a control law with adaptation of the sampling period to account for the available computing resources for an inverted pendulum. In the present paper, the LPV approach relies on the LFT representation to compute the gain scheduled controller. Indeed the main drawback of the polytopic method could be the large number of LMIs to solve when the number of varying parameters increases. This is not the case in the LFT method and, as emphasized in [START_REF] Apkarian | A convex characterisation of gain-scheduled H ∞ controllers[END_REF], it leads to a LMI problem whose solution can directly be implemented. Moreover, this approach allows to consider in the same way varying parameters and uncertainties (adaptation to the parameters and robustness with respect to uncertainties).

The paper is organized as follows. Section 2 presents the non linear model of the AUV considered for the study and the model reduction for the vertical plane motion. Section 3 develops some theoretical background on model discretizing and on keeping the varying period as parameter, and also LPV/LFT control. Finally section 4 contains the control design and simulation results.

AUV MODELS

The model of the vehicle is directly inherited from [START_REF] Roche | Lpv / H ∞ control of an autonomous underwater vehicle (auv)[END_REF].

For the description of the vehicle behavior, we consider a 12 dimensional state vector : X = [η(6) ν(6)] T .

η(6) is the position, in the inertial referential R 0 , describing the linear position η 1 and the angular position η 2 :

η = [η 1 η 2 ] T with η 1 = [x y z] T and η(2) = [φ θ ψ]
T where x, y and z are the positions of the vehicle , and φ, θ and ψ are respectively the roll, pitch and yaw angles.

ν(6) represent the velocity vector, in the local referential R (linked to the vehicle) describing the linear and angular velocities (first derivative of the position, considering the referential transform, see equation ( 2)

) : ν = [ν 1 ν 2 ] T with ν 1 = [u v w]
T and ν 2 = [p q r] T

Non Linear Model

As given in [START_REF] Fossen | Guidance and Control of Ocean Vehicles[END_REF], [START_REF] Santos | Contribution à la conception des sousmarins autonomes : architecture des capteurs d'altitude, et commande référencées capteurs[END_REF], [START_REF] Jalving | The control system of an autonomous underwater vehicle[END_REF], the physical model is given by the following dynamical equation:

M ν = G(ν)ν + D(ν)ν + Γ g + Γ u (1) η = J c (η 2 )ν (2)
where:

-M is the mass matrix which represents the real mass of the vehicle augmented by the "water-added-mass" part, -G(ν) represents the action of Coriolis and centrifugal forces, -D(ν) is the matrix of hydrodynamics damping coefficients, -Γ g correspond to the gravity effort and hydrostatic forces,

-J c (η 2 ) is the referential transform matrix from R(C, xyz) towards R 0 (O, X 0 Y 0 Z 0 ),
-Γ u represent the forces and moments due to the vehicle's actuators. The considered AUV has an axial propeller to control the velocity in Ox direction (forward force Q c ) and 5 independent mobile fins :

• 2 horizontals fins in the front part of the vehicle (controlled with angles β 1 and β 1 ). • 1 vertical fin at the tail of the vehicle (controlled with angle δ).

• 2 fins at the tail of the vehicle (controlled with angles β 2 and β 2 ) inclined with angle ±π/3 w.r.t the vertical fin.

The nonlinear model includes 12 state variables and 6 control inputs. For the computation of the controller, a linear model is proposed. The equilibrium point is chosen as [u v w p q r] = [1 0 0 0 0 0] : all velocities are taken equal to 0, except the longitudinal velocity taken equal to 1m/s, the cruising speed chosen by the operator according to the payload requirements.

Tangential linearization around the chosen equilibrium point yields to a model of the form :

ẋ = Ax(t) + Bu(t) y = Cx(t) + Du(t) where • x stand for the state : x = [x u y v z w φ p θ q ψ r] T • u for the control input u = [β 1 β 1 β 2 β 2 δ 1 Q c ] T
• y for the measured output (here only the altitude z is measured)

All the matrices A, B, C and D depend on the model parameters : hydrodynamical parameters, mass of the vehicle, dimension of fins. . . Note that most of these parameters are uncertain, and that here the control design is proposed for the nominal plant case only.

Model Reduction

The complete control of the vehicle is intricate due to the large size of the system. A usual solution is to separate the whole model into three different sub-models with reduced size. This allows for a "decoupling" control synthesis for the three directions Ox, Oy and Oz.

To control the altitude z, the model is reduced to 4 state variables : z, θ (pitch angle) and the corresponding velocity w and q. For the actuation, only 4 fins are needed: the 2 horizontals fins in the front part of the vehicle (β 1 and β 1 ) and the 2 oblique fins at the tail (β 2 and β 2 ). Since the AUV has to stay in the vertical plan, both pairs of fins have to be actuated in the same way (with the same angle) so 2 control variable are chosen as:

β 1 = β 1 and β 2 = β 2 .
Remark : In this paper we focus on the control of the altitude z with adaptation to the sampling period w.r.t. the measurement time, following the bottom referenced altitude control scenario. The other degrees of freedom are controlled using basic (i.e. constant sampling) feedbacks to keep the vehicle in the vertical plane with at the predefined forward velocity. Note that the model built for the control of the longitudinal speed u contains all the dynamics, but can only act on the propeller of the vehicle. To control the yaw angle ψ, the states variables are v, ψ and r.

The actions are the tree fins at the tail of the AUV (corresponding actions δ, β 2 and β 2 ).

A LFT MODEL FOR VARYING SAMPLING PERIOD SYSTEMS

Discrete time model with varying sampling period

This subsection describes the considered model, following the methodology in [START_REF] Robert | An H ∞ lpv design for sampling varying controllers: Experimentation with a t-inverted pendulum[END_REF].

Let us consider a continuous time state space representation of a system of the form :

G : ẋ = Ax + Bu y = Cx + Du (3) with A ∈ R ns×ns
The exact discretization of this system is describe in equation ( 5)

G d : x k+1 = A d x k + B d u k y k = C d x k + D d u k (4)
with Ad ∈ R ns×ns and

A d = e Ah B d = h 0 e Aτ dτ B C d = C D d = D
(5)

The usual numerical method use the exponential of a matrix M :

A d (h) B d (h) 0 I = exp A B 0 0 h (6)
The sampling period is assumed to belong to the interval [h min , h max ] with h min > 0, the sampling period is approximated around the nominal value h 0 as :

h = h 0 + δ with h min -h 0 ≤ δ ≤ h max -h 0 (7)
As explained in [START_REF] Robert | An H ∞ lpv design for sampling varying controllers: Experimentation with a t-inverted pendulum[END_REF] the equation ( 6) in this case becomes :

A d (h) B d (h) 0 I = A h0 B h0 0 I A δ B δ 0 I (8)
In case of an affine model in the variation of the sampling period δ is needed, a Taylor series expansion of order k leads to :

A δ ≈ I + k i=1 A i i! δ i (9) B δ ≈ k i=1 A i-1 B i! δ i (10)
Finally the matrices of the discretized plant are :

A d = A h0 A δ B d = B h0 + A h0 B δ (11)
with A d and B d in an exact or approximate form, depending on the context.

A new LFT Formulation for varying sampling systems

A LFT formulation is proposed in this section to express the system discrete time model by keeping the sampling period as a parameter (i.e. modeled as a system uncertainty).

First, an LPV/LFT model of a system, considering the sampling period as varying parameter is presented, based on the methodology developed in [START_REF] Robert | Contribution à l'interconnection commande / ordonnancement[END_REF]. The objective is to transform the system under the form described in Figure 3. The matrix ∆ represents the uncertainties depending on the sampling period h.

N (z)

∆(k) y u y ∆ u ∆

Fig. 3. System under LFT representation

Two cases are considered below in order to account for varying sampling period :

Unstructured uncertainty case From equations (11) two uncertainties blocks are derived :

∆ 1 = A δ -I ∆ 2 = A h0 B δ (12)
The matrices of the discrete time system (4) are rewritten with these uncertainties :

   x k+1 = [A h0 + A h0 (A δ -I ∆1 )]x k + [B h0 + A h0 B δ ∆2 ]u y = C d x k + D d u
The system is transformed into the form described in Figure 3 by defining :

u ∆ = [u ∆1 , u ∆2 ] T , y ∆ = [y ∆1 , y ∆2 ] T and ∆ = ∆ 1 0 0 ∆ 2
Finally, the LFT form of the model with unstructured uncertainties (with no approximation) is as follows :

       x k+1 = Ax k + B u ∆ u y ∆ y = Cx k + D u ∆ u (13) ∆ = ∆ 1 0 0 ∆ 2 A = A h0 B = (A h0 I B h0 ) (14) C = I 0 C d D = 0 0 0 0 0 I 0 0 D d
The LPV/LFT model of the system is then given by the upper LFT interconnection T u,y = F u (P (z), ∆) = P 22 + P 21 ∆(I -P 11 ∆) -1 P 12 (15)

This approach considers ∆ as a full block diagonal with full matrices ∆ 1 and ∆ 2 . However matrices ∆ 1 and ∆ 2 depend on a single parameter δ, so this uncertainty definition may be too conservative.

Structured uncertainty case

In order to reduce the conservatism the Taylor series expansion of order k (presented in ( 9) and ( 10)) for matrices A δ and B δ is used to obtain a structured uncertainty matrix.

∆ 1 ≈ A δ -I = k i=1 A i i! δ i ≈ Aδ (I + Aδ 2 (I + Aδ 3 (I + . . . )) (16) ∆ 2 ≈ A h0 B δ = A h0 k i=1 A i B i! δ i ≈ A h0 (I + Aδ 2 (I + Aδ 3 (I + . . . )B δ (17)
With this structure of uncertainty, the LFT representation of the system becomes (according to 3) :

∆ = δI 2×k×ns A = A h0 B = (B 1 B 2 B h0 ) (18) C = C 1 C 2 C d D =   D 0 0 0 D D 2u 0 0 D d   (19) B 1 = AaA 0 ns * [ns * (k-1)] B 2 = Aa 0 ns * [ns * (k-1)] (20)
C 1 =     In s . . . . . . In s            k times ; C 2 =     0n s . . . . . . 0n s            k times (21) D =      0n s A 2 . . . 0n s . . . . . . . . . . . . . . . . . . . . . A k 0n s . . . . . . 0n s      D 2u =     B . . . . . . B     (22)
This allows to express the parameter block ∆ as a direct dependence on the varying sampling period δ.

BACKGROUND ON H ∞ / LFT CONTROL DESIGN

The objective is to get an LPV controller taking into account the set of parameter ∆ in the same way as the model, by a lower LFT interconnection :

T zw = F l (K, ∆) := K 11 + K 12 K(I -K 22 ∆) -1 K 21 (23)
The LFT control scheme is presented in Figure 4, where the dependency on the parameters ∆ of the generalized plant P and of the controller K is described in an LFT form.

z ∆ w ∆ z y w u z∆ w∆ ∆(k) P (z) K(z) ∆(k) LPV process LPV controller ∆(t) z w ∆(k) 0 0 ∆(k) P (z) K(z) P (z)

Fig. 4. LFT control scheme

The problem is now to find a discrete controller K for which the system described in Figure 4 is stable and respect some specifications defined by weighting functions set in the control loop (H ∞ design).

The methodology used in this paper for the discrete-time controller synthesis is based on the H ∞ framework, by the resolution of LMIs (derived from the bounded real Lemma), as described in [START_REF] Apkarian | A convex characterisation of gain-scheduled H ∞ controllers[END_REF] and [START_REF] Gauthier | An H ∞ linear parameter-varying (lpv) controller for a diesel engine common rail injection system[END_REF].

To reduce the conservatism due to the presence of uncertainties, the problem is reformulated using some scaling variables L ∆ .

The solution of this problem relies on the bounded real Lemma, as follow :

Lemma Consider a parameter structure Θ, the associated scaling set L Θ = {L > 0 : L∆ = ∆L, ∀∆ ∈ Θ}, and a discrete-time square transfer function T (z) of realization

T (z) = D cl + C cl (zI -A cl )
-1 B cl , then the following statements are equivalent. i) A cl is stable and there exists L ∈ L Θ such that

||L 1/2 D cl + C cl (zI -A cl ) -1 B cl L -1/2 || ∞ < 1.
ii) There exist positive definite solutions X cl and L ∈ L Θ to the matrix inequality

    -X -1 cl A cl B cl 0 A T cl -X cl 0 C T cl B T cl 0 -L D T cl 0 C cl D cl -L -1     < 0 (24)
The main result is as follows.

Theorem 1. Consider a discrete-time LPV plant P ∆ (z) under LF T form. Let N r and N s denote bases of null spaces of (B T 2 , D T θ2 , D T 12 , 0) and (C 2 , D 2θ , D 21 , 0) , respectively. With this notation, the gain-scheduled H ∞ LFT control problem is solvable if and only if there exist pairs of symmetric matrices (R, S) ∈ R na×na and (L 3 , J 3 ) ∈ R n θ ×n θ and a scalar γ > 0 such that

N T r    ARA T -R + B θ J 3 B T θ C θ RA T + D θθ J 3 B T θ C θ RC T θ + D θθ J 3 D T θθ -J 3 C 1 RA T + D 1θ J 3 B T θ C 1 RC T θ + D 1θ J 3 D T θθ B T 1 D T θ1 C 1 RC T 1 + D 1θ J 3 D T 1θ -γI D T 11 -γI    Nr < 0 Ns    A T SA -S + C T θ L 3 C θ B T θ SA + D T θθ L 3 C θ B T θ SB θ + D T θθ L 3 D θθ -L 3 B T 1 SA + D T θ1 L 3 C θ B T 1 SB θ + D T θ1 L 3 D θθ C 1 D 1θ B T 1 SB 1 + D T θ1 L 3 D θ1 -γI D 11 -γI    Ns < 0 R I I S > 0 L 3 Θ = ΘL 3 , J 3 Θ = ΘJ 3 , L 3 I I J 3 > 0
This LMI is then solved using Yalmip interface [START_REF] Lofberg | Yalmip : A toolbox for modeling and optimization in matlab[END_REF]) and Sedumi solver [START_REF] Sturm | Using sedumi 1.02, a matlab toolbox for optimization over symmetric cones[END_REF]).

H ∞ CONTROL DESIGN FOR AUVS

LFT model of the AUV

An LPV/LFT model of the AUV considering the sampling period as varying parameter, using the methodology previously described is built. The Taylor series expansion described in equation ( 16) and ( 17) is made at order k = 2. Here the Bode diagram of this LPV/LFT system is presented on Figure 5, using the structured case uncertainties :

∆ = δI 2×k×ns (25)
According to the sampling period variation, this Bode Diagram shows a variation on the system gain and also on the bandwidth.

Structure and weighting function

The method is based on the H ∞ control design. The first step is to choose a control structure and weighting functions that will be placed in the control loop for setting some specifications (response time in closed loop, tracking error...).

We choose the following classical structure, with :

• W e a weight on the tracking error, for fixing specifications on the controlled outputs y (here only the altitude z has to be controlled). The varying sampling period considered for the controller synthesis imposes a parametrized discretization of weights. This allows the adaptation of the performances with respect to the current sampling period, as explained in [START_REF] Robert | An H ∞ lpv design for sampling varying controllers: Experimentation with a t-inverted pendulum[END_REF]. So W e is defined with the following state space system, with the frequency f = 1/h :

ẋ = (a × f )x + (a × f -b × f )u y = x + u ( 26
)
This weight is then discretized to obtain discretetime representation :

W d (z) : x k+1 = A d x k + B d u k y k = x k + u k (27)
A d = e af h = e a B d = (af ) -1 (A d -I)bf = a -1 (A d -I)b (28)
The simplification between h and f leads to discrete LTI representation of the weight.

The elements a, and b are chosen for obtaining :

• a good robustness margin.

• a tracking error less that 1%.

• a settling time of 5 seconds. • W u is chosen to account for actuator limitations (all action where normalized, so we choose the identity matrix of size 4 for W u ).

Then the augmented plant (P in Figure 4) is built containing the model of the system and the weighting functions.

LFT controller

A LPV/LFT controller is computed for the control of the altitude z, by considering the the previous structure and weights.

The interval of variation of the sampling period for the controller design is : h ∈ [0.05; 0.3]s

Similarly to the Bode diagram of the system, the controller Bode diagram varies according to the sampling period, as seen in Figure 7. The sampling period clearly affects the controller bandwidth, this in accordance with the system bandwidth variation.

SIMULATION RESULTS

We consider as a mission to follow the sea bottom at constant height and move at constant speed (require for a good interpretation of the results).

The complete linearized model of the AUV is used for the following simulations. We focuses in the sequel on the control of the altitude z. An independent discretetime controller control the cruising speed u which start at 0 and stay constant and equal to 1m/s during all the simulation (its design will not be detailed here; it is a simple H ∞ discrete-time controller, with a sampling period of 0.1s).

H ∞ Discrete controller

First, a H ∞ controller is synthesized and serves as reference (using dhinflmi function of the LMI Control Toolbox). This controller is designed for a single sampling period (not gain scheduled) so could not adapt to sampling period variation. However the robustness brought by the method should allow little variation around h = 0.1s.

LPV control with sampling period as varying parameter

The controller synthesized in the previous section is used for the control of the system. Different sampling period variation scenarios will be considered, corresponding to different measurement time acquisition.

Test 1: Constant sampling period Both controllers are tested on the AUV model, with no variation of the sampling period. The simulation is done with h = 0.1s, namely the period considered for the H ∞ controller design. The LFT controller is adapted to this period via the ∆ matrix. Simulation results are presented in figure 9. Test 2: Sinusoidal variation of the sampling period h For this simulation, the sampling period varies in a sinusoidal way. The step on altitude reference is done at minimal and maximal value of the sampling period , but h changes (in a sinusoidal way) during the step on z. Results are presented in Figures 10 and11.

In the same case the discrete-time controller leads to worst results (in particular for h = 0.3) :

The LFT controller gives good results : the system remain stable whatever the sampling period h. Moreover the adaptation of the performances w.r.t h is also visible : when the sampling period is high (h = h max = 0.3s) the response time is low, and inversely. The discrete-time H ∞ controller leads to poor performances especially when Test 3: Step variation of the sampling period h Now we consider two successive step variations of the sampling period on extreme value of the sampling period variation interval. A step on the altitude reference is done at the same time, to see the influence of the sampling period on the response. Results are presented on Figures 12 and13.

In the same case the discrete-time controller leads to instability of the system.

The LPV/LFT controller still leads to good results (almost unchanged w.r.t the previous case).

CONCLUSIONS AND PERSPECTIVES

In this article, we have presented a new formulation for LPV systems, considering the sampling period as varying parameter into an LFT form. During the control design step, the definition of a varying weighting function allows for performance adaptation w.r.t the current sampling period. The main advantage is the robustness of the LPV/LFT method with respect to the variation of the sampling period, considered here as the varying parameter. By adaptation of the controller to the current sampling period, the LFT controller leads to good results whereas the simple discrete-time controller could give instability of the system.

In our work here presented, a unique varying parameter as been considered (the sampling period). In the future, thanks to the LFT formulation, other parameter could be easily added, as for example the forward speed u (to consider different mission scenarios). In the same way, uncertainties can also be added in the ∆ matrix.

Finally this controller can be integrated in a global structure of control, to study the interaction between the three decoupled controller in the three dimensions.

Fig. 1 .

 1 Fig. 1. The Aster X AUV operated by Ifremer

Fig. 2 .

 2 Fig. 2. Sensor acting on the sampling period of the controllerThe control of underwater vehicles is made difficult by numerous non-linearities, due to cross-coupled dynamics and hydrodynamic forces subject to large uncertainties.

FigFig. 6 .

 6 Fig. 5. Bode diagram of the system

Fig. 7 .

 7 Fig. 7. Bode diagram of the LPV/LFT controller The sensitivity function S is presented in Figure 8. The

Fig. 9 .

 9 Fig. 9. Test 1: Altitude z with discrete time H ∞ and LFT controllers (Te=0.1s)The H ∞ controller gives better results than the LFT one in term of response time but the LFT controller present a smaller overshoot. Both controllers have no tracking error.

Fig. 10 .

 10 Fig. 10. Test 2: altitude z with LPV/LFT controller, h sinusoidal

Fig. 12 .

 12 Fig. 12. Test 3: Altitude z with LPV/LFT controller, step variation of h

This work is supported by the FeedNetBack Europeen project (FP7 IST 223866) and CONNECT ANR. 1 http://www.ifremer.fr/fleet/r&dprojets.htm


Stéphanie Topoliantz

tel. Jean-François Ponge
email: jean-francois.ponge@wanadoo.fr

Charcoal consumption and casting activity by Pontoscolex corethrurus (Glossoscolecidae

Keywords: Slash-and-burn, Forest, Fallow, Tropical earthworms, Population origin, Soil ingestion

The endogeic earthworm Pontoscolex corethrurus (Glossoscolecidae) is a peregrine species commonly found in tropical lands cleared by man for cultivation. We compared the charcoal consumption and casting activity of a population of P. corethrurus from a cultivated area under repeated slash-and-burn (fallow population) with that of a population living in a field cultivated after recent burning of a mature forest (forest population). Their cast production was measured in containers in the presence of pure charcoal, soil of fallow and forest origin, or a mixture of charcoal and soil. The forest population defecated less in pure charcoal than in forest soil, whereas the reverse was observed in the fallow population. When living in fallow soil, both populations defecated more at the surface of a mixture of charcoal and soil than at the surface of pure soil (x 2 and x 3 with fallow and forest population, respectively). In forest soil, both populations showed an increased charcoal consumption (x 12). In the light of these experiments, we hypothesized that an adaptation of P. corethrurus to charcoal and fallow soil exists, supporting the observed distribution of this earthworm species in tropical open lands.

Introduction

Slash-and-burn cultivation, currently practised in tropical rain forests, transforms the pre-burn biomass into fertile ashes and charcoal [START_REF] Fearnside | Tropical forest burning in Brazilian Amazonia: measurement of biomass loading, burning efficiency and charcoal formation at Altamira, Pará[END_REF][START_REF] Graça | Burning of Amazonian forest in Ariquemes, Rondônia, Brazil: biomass, charcoal formation and burning efficiency[END_REF]. Under heavy rain, fertile ashes are rapidly lost through leaching and surface runoff whereas charcoal remains in the soil for centuries, constituting with charred plant material an important sink of carbon and a source of persistent soil organic matter in burnt soils [START_REF] Seiler | Estimates of gross and net fluxes of carbon between the biosphere and the atmosphere from biomass burning[END_REF][START_REF] Glaser | The 'Terra Preta' phenomenon: a model for sustainable agriculture in the humid tropics[END_REF]. Charcoal is also an efficient adsorbent of soluble organic and mineral compounds leached from litter and can support microbial communities, due to its high internal surface area made of interconnected micropores [START_REF] Pietikäinen | Charcoal as habitat for microbes and its effect on the microbial community of the underlying humus[END_REF]. Through its sorptive properties, charcoal enhances the degradation of litter phenolic compounds which may biochemically interfere with plant germination, thus playing a fundamental role in forest regeneration. This has been especially demonstrated in boreal forests [START_REF] Zackrisson | Key ecological function of charcoal from wildfire in the Boreal forest[END_REF][START_REF] Wardle | The charcoal effect in boreal forests: mechanisms and ecological consequences[END_REF].

In tropical earthworm communities, post-burn environmental changes lead to the disappearance of specific forest species and the establishment of peregrine species commonly found in open land like the geophagous earthworm Pontoscolex corethrurus [START_REF] Standen | Oligochaetes in fire climax grassland and conifer plantations in Papua New Guinea[END_REF][START_REF] Römbke | About earthworm communities in a rain forest and an adjacent pasture in Peru[END_REF]. This earthworm species is highly adapted to tropical cultivated soils through its capacity to live and reproduce over a wide range of soil moisture and acidity conditions and its consumption of low-quality organic matter [START_REF] Lavelle | Adaptive strategies of Pontoscolex corethrurus (Glossoscolecidae, Oligochaeta), a peregrine geophagous earthworm of the humid tropics[END_REF]. Although many experiments have been conducted to study the cast production of P. corethrurus [START_REF] Barois | Transformation of the soil structure through Pontoscolex corethrurus (Oligochaeta) intestinal tract[END_REF][START_REF] Hallaire | Soil structure changes induced by the tropical earthworm Pontoscolex corethrurus and organic inputs in a Peruvian ultisol[END_REF], no published paper mentions the casting activity of this earthworm species in the presence of charcoal. In a previous paper [START_REF] Topoliantz | Burrowing activity of the geophagous earthworm Pontoscolex corethrurus (Oligochaeta: Glossoscolecidae) in the presence of charcoal[END_REF], we observed that P. corethrurus ingested charcoal and then incorporated it into the soil through defecation. Black and grey aggregates, originating from earthworm casts partly or totally made of powdered charcoal, were found in tropical soils under shifting cultivation [START_REF] Topoliantz | Réponse fonctionnelle de la pédofaune à la mise en culture itinérante et permanente des sols du sud-ouest de la Guyane française[END_REF].

The aim of our study was to quantitatively analyse the behaviour of P. corethrurus when allowed to eat and defecate on soil, charcoal or charcoal-enriched soil. Two populations were compared, one from a mature forest which had been recently burnt for cultivation (forest population) and the other from an area repeatedly cultivated under slash-and-burn with short fallow duration (fallow population). This allowed us to detect possible shifts in choice and casting behaviour of this peregrine species which could have developed in the course of time under repeated cultivation.

Materials and methods

Experimental design

The surface cast production and the growth rate of P. corethrurus were studied in plastic containers (11x 8.5x 4 cm) in the presence of soil and charcoal. Charcoal was prepared from charred wood taken from the surface of the fallow soil. The animals were collected from soil under shifting cultivation in French Guiana (South America). The first population, living in a field recently opened by burning a mature forest (3°26'11''N; 53°59'01''W), was called FOR (forest) population, and the other one, living in a 3-yr old fallow setting in a wide slash-and-burn cultivated area with short fallow duration and frequent burning, around the village of Maripasoula (3°39'17'' N; 54°02'21'' W), was called FAL (fallow) population. FOR and FAL soils did not differ to a great extent. Both were Oxisols, acidic (pH < 5) and sandy (60-65% sand). The size of the experimental boxes was considered suitable for this small endogeic species, on the basis of previous observation [START_REF] Topoliantz | Réponse fonctionnelle de la pédofaune à la mise en culture itinérante et permanente des sols du sud-ouest de la Guyane française[END_REF].

In the first experiment, the surface casting activity of both earthworm populations was studied in polystyrene containers, in which one half of each was filled with powdered charcoal and the other with soil of FOR or FAL origin. The FOR soil was collected in mature forest (more than 50-yrs old) in the immediate vicinity (< 50 m) of the recently burnt field where the FOR population was sampled, and the FAL soil at the same location as the FAL earthworm population. Both soils were taken from the top first 20 cm. Soils and charcoal were dried in open air immediately after collection then they were kept and transported to the laboratory in polythene bags. Once at the laboratory charcoal was ground in a ball mill then soils and powdered charcoal and soil were sieved at 2 mm. Grinding of charcoal and sieving of soil and charcoal were judged necessary to fill our containers with homogeneous substrates. A piece of cardboard was inserted at the middle part of each container. The two compartments thus delineated were filled to 1 cm from the top with sifted soil or charcoal. The cardboard was removed, then both compartments were progressively moistened by spraying deionized water until all the substrate was uniformly moist. These conditions were maintained throughout the experiment, by weighing containers and adding water when necessary. For both populations and both soils, one subadult P. corethrurus was weighed then gently positioned by hand at the top middle part of each container (5 replicates for each combination). Containers were then kept covered throughout the experiment. Before the experiment worms of each population were kept alive in their original soil, without any additional food. In the second experiment, containers were filled on one side with FAL soil and on the other side with a 3:2 (w:w) mixture of charcoal and FAL soil (CHAR+soil), then one subadult P. corethrurus was introduced (6 replicates for each population).

Table 1 shows some chemical features of the soil and charcoal substrates used for the experiments, after sieving and homogenizing. In both experiments, containers were maintained at 25°C in an forced-air chamber for 20 days.

Casts produced at the soil or charcoal surface were removed daily for 20 days and sorted according to colour: brown (colour of the original soil), brown-grey (with a low content of charcoal), dark grey (with a medium content of charcoal) and black (with a high content of charcoal). Casts were oven-dried for 24 h at 105°C, then weighed. At the end of each experiment all worms were weighed individually. All worms were found alive at the end of each experiment.

Statistical analyses:

In experiment 1, the influence of earthworm population and soil origin (FAL or FOR) on total surface cast production and colour was analysed by two-way ANOVA. The influence of substrate (soil or charcoal) on surface cast production (total and sorted by colour) was tested separately for each earthworm population by two-way ANOVA. When necessary, data were log-transformed before ANOVA. When residuals did not follow a normal distribution after log-transformation, groups were compared by Kruskall-Wallis rank test [START_REF] Sokal | Biometry[END_REF].

In experiment 2, the effects of population (FAL or FOR) and substrate (soil or CHAR+soil) on total cast production were analysed by two-way ANOVA. Means were compared by Tukey a posteriori tests. Casts produced on soil and CHAR+soil, sorted by colour, were compared for each population (6 replicates) by t-test or Mann-Whitney rank test when data were not normally distributed.

Results

First experiment: surface cast production in the presence of pure charcoal

All introduced earthworms survived and grew during the experiment. The mean individual fresh weight increased from 0.28±0.01 g at the the start to 0.45±0.02 g at the end of the experiment.

The growth rate of P. corethrurus was not influenced either by population origin or by soil. Figure 1 shows the mean cast production per day per earthworm. The highest and the lowest total surface cast production were obtained when the FAL population was reared in the FAL soil and the FOR soil, respectively. The FAL population produced 1.6 times more surface casts than the FOR population, when all substrates were combined (Table 2). Total surface cast production was twice more in FAL soil than in FOR soil, when the two earthworm populations were combined. Cast production was 3.6 times higher with FAL soil than with FOR soil at the surface of the soil substrate. No influence of population or soil origin was detected at the surface of charcoal.

Brown casts averaged 69.7±3.3 % of the total surface cast production, while brown-grey casts, dark grey casts and black casts averaged 27.8±3.2 %, 1.7±0.4 % and 0.8±0.3 % of the total surface cast production, respectively. When earthworm populations were combined, 4.5 times more brown casts were produced at the soil surface in the presence of FAL soil than of FOR soil (Table 3), and 12.3 times more dark grey casts were produced at the charcoal surface in the presence of FOR soil than of FAL soil. The FAL population produced 4.1 times more brown-grey casts at the charcoal surface than the FOR population. Black cast production was not influenced by soil or population origin.

As shown in Figure 1, more total casts were produced at the soil surface than at the charcoal surface except by FAL earthworms when in the presence of FOR soil (ANOVA, interaction population X soil, F = 4.56, P < 0.05). However, when casts were sorted by colour, black and dark grey cast production did not differ between soil and charcoal. In the presence of FAL soil, the FAL population produced more brown casts (t = -3.82, P < 0.01) and the FOR population more brown-grey casts (t = -3.02, P < 0.05) at the soil surface than at the charcoal surface.

3.2. Second experiment: cast production in the presence of a mixture of charcoal and FAL soil Like in previous experiment, all individuals survived and grew, irrespective of population origin and soil. The mean individual fresh weight increased from 0.42±0.03 g at the the start to 0.54±0.03 g at the end of the experiment. Figure 2 shows the mean cast production per day per earthworm. The FAL population produced 2.4 more total casts (7.04±1.31 g.d ) when substrates were combined (Mann-Whitney, T = 53, P < 0.05). Cast production was 2.7 times higher at the CHAR+soil surface (7.28±1.33 g.d -1

) than at the soil surface (2.70±0.67 g.d -1

) when populations were combined (T = 55, P < 0.01). Brown casts displayed the same significant trends as total casts, but black, dark grey and brown-grey cast production did not differ between both substrates and populations.

When substrates were combined, brown casts were the most abundant category (87.0±3.7 %), followed by brown-grey casts (10.3±3.4 %), dark grey casts (1.7±1.0 %) and black casts (0.9 ± 0.4 %, mean ± SEM), corresponding to a decreasing order of soil content.

Discussion

P. corethrurus ingested powdered pure charcoal but in small amounts compared with soil.

Less than 1% (in weight) of total cast production was black (made of pure or near pure charcoal). The low amount of black casts produced can be explained by the low bulk density of charcoal (0.60 g.cm -³)

as compared to soil (1.35 g.cm -³) in our containers. Indeed, [START_REF] Buck | Influence of mulch and soil compaction on earthworm casts properties[END_REF] demonstrated that cast production increased with soil bulk density. In our experiments, when charcoal was mixed with soil, black casts had a higher density [START_REF] Topoliantz | Réponse fonctionnelle de la pédofaune à la mise en culture itinérante et permanente des sols du sud-ouest de la Guyane française[END_REF], thus they were thought to contain more soil than in the presence of pure charcoal. Thus the low production of black casts could result from the low bulk density of charcoal, through which earthworms could force their way without ingesting the substrate [START_REF] Topoliantz | Burrowing activity of the geophagous earthworm Pontoscolex corethrurus (Oligochaeta: Glossoscolecidae) in the presence of charcoal[END_REF]. However, it should be noticed that other colour categories than brown casts were characterized by the presence of charcoal mixed with soil [START_REF] Topoliantz | Réponse fonctionnelle de la pédofaune à la mise en culture itinérante et permanente des sols du sud-ouest de la Guyane française[END_REF]. The production of dark grey and brown-grey casts exemplifies the mixing effect of P. corethrurus on topsoil components [START_REF] Barois | Transformation of the soil structure through Pontoscolex corethrurus (Oligochaeta) intestinal tract[END_REF]. This biological process may explain the building of 'Terra Preta' Amazonian soils, where charcoal has been demonstrated to be a source of stable carbon [START_REF] Glaser | The 'Terra Preta' phenomenon: a model for sustainable agriculture in the humid tropics[END_REF]. In field conditions, charcoal and partly charred plant material, which are let at the soil surface after burning the forest, are ingested by P. corethrurus, which is able to grind and mix them with the mineral soil, depositing dark casts at the soil surface like in our experiments [START_REF] Topoliantz | Réponse fonctionnelle de la pédofaune à la mise en culture itinérante et permanente des sols du sud-ouest de la Guyane française[END_REF].

The cast production of P. corethrurus was higher on a mixture of charcoal and soil than on the original fallow soil. Inasmuch as cast production can be taken as a measure of habitat suitability [START_REF] Topoliantz | Burrowing activity of the geophagous earthworm Pontoscolex corethrurus (Oligochaeta: Glossoscolecidae) in the presence of charcoal[END_REF], our results suggest that the mixture of charcoal and soil was preferentially used as living substrate. Earthworms possess a high chemosensitivity to acidity [START_REF] Laverack | Tactile and chemical perception in earthworms. II-Responses to acid pH solutions[END_REF][START_REF] Magdoom | Studies on chemosensitivity of the megascolecid earthworm Lampito mauritii[END_REF]. Although P. corethrurus is known to live in a wide range of soil acidity [START_REF] Lavelle | Adaptive strategies of Pontoscolex corethrurus (Glossoscolecidae, Oligochaeta), a peregrine geophagous earthworm of the humid tropics[END_REF], by mixing soil (pH 4) with charcoal (pH 7) it may decrease the acidity of its immediate environment. This process can complement buffering properties of external mucus [START_REF] Schrader | Influence of earthworms on the pH conditions of their environment by cutaneous mucus secretion[END_REF].

The two studied populations consumed similar amounts of charcoal but their behaviour towards forest or fallow soil differed strongly between them. The fallow population produced more casts on charcoal in the presence of forest soil, while the casting activity of the forest population was higher on soil whatever the soil origin (fallow or forest). Although P. corethrurus is probably indigenous to the rain forest of the Guiana plateau [START_REF] Righi | Pontoscolex (Oligochaeta, Glossoscolecidae) a new evaluation[END_REF], few reports have been made on its abundance in tropical forest soils. [START_REF] Martinez | Comunidades de lombrices de tierra (Annelida: Oligochaeta) en un bosque siempre verde y un pastizal de Sierra del Rosario, Cuba[END_REF] found that the earthworm population of an evergreen forest in Cuba was dominated by P. corethrurus, and [START_REF] Zou | Changes in earthworm density and community structure during secondary succession in abandoned tropical pastures[END_REF] observed the presence of this species at all stages of vegetation succession after abandonment of pastures in Puerto Rico. From our results, it appears that the forest population is suited to forest as well as to fallow soils, and thus is able to colonize habitats created by slash-and-burn agriculture. Such behaviour was not shown by the fallow population, which seemed to be more restricted in its requirements. We cannot discount the possibility that other factors than management could explain the observed differences between the forest and the fallow population, since they were geographically separated along the Maroni river (see Materials and methods). However, we must emphasise the fact that both populations were living in acid, sandy soils, the only difference being the richness of the forest soil in organic matter (Table 1).

Both populations produced more brown casts in the presence of the fallow soil compared with the forest soil, probably because of low nutrient quality of the former (34% less C, 36% less N). It is known that turnover of the soil by earthworms increases when the quality of soil organic matter decreases [START_REF] Flegel | Importance of food quality on selected enzyme activities in earthworm casts (Dendrobaena octaedra, Lumbricidae)[END_REF]. The fallow population produced more than twice the amount of casts produced by the forest population, without increasing its growth rate [START_REF] Topoliantz | Réponse fonctionnelle de la pédofaune à la mise en culture itinérante et permanente des sols du sud-ouest de la Guyane française[END_REF]. This difference in cast production can be considered as a compensatory mechanism, the higher ingestion rate of the fallow soil compensating for its low nutrient content.

It has been suggested that soil fertility and soil biological activity might decrease under repeated slash-and-burn cultivation with short fallow periods [START_REF] Kleinman | The ecological sustainability of slash-and-burn agriculture[END_REF]. By elsewhere,

Pontoscolex corethrurus, which thrives after deforestation of neotropical rain forests [START_REF] Römbke | About earthworm communities in a rain forest and an adjacent pasture in Peru[END_REF], is sometimes considered as a pest in Amazonian pastures, where coalescence of its surface casts forms a compact crust which prevents infiltration of water and penetration of roots [START_REF] Chauvel | Pasture damage by an Amazonian earthworm[END_REF]. However, we demonstrated that in the presence of charcoal this species improved soil properties, by increasing pH and incorporating stable carbon to the mineral soil [START_REF] Topoliantz | Réponse fonctionnelle de la pédofaune à la mise en culture itinérante et permanente des sols du sud-ouest de la Guyane française[END_REF][START_REF] Topoliantz | Burrowing activity of the geophagous earthworm Pontoscolex corethrurus (Oligochaeta: Glossoscolecidae) in the presence of charcoal[END_REF]. To the light of our results, we suspect that P.

corethrurus was the chief agent of the formation of the fertile Terra Preta in Brazil [START_REF] Glaser | The 'Terra Preta' phenomenon: a model for sustainable agriculture in the humid tropics[END_REF].

Natural populations living in fallow soil have been used in bioremediation experiments using charcoal and manioc peels at Maripasoula [START_REF] Topoliantz | Effect of organic manure and the endogeic earthworm Pontoscolex corethrurus (Oligochaeta: Glossoscolecidae) on soil fertility and bean production[END_REF]. The increased casting activity of the fallow (FAL) population of P. corethrurus in the presence of charcoal and soil may help to explain how this species, which is present at low densities in the mature forest, may benefit from repeated cultivation.

We demonstrated that charcoal/soil mixture was more attractive than soil itself (Fig. 2). Thus, the incorporation of charcoal to the mineral soil, in the form of casts of varying charcoal content, from brown-grey to black [START_REF] Topoliantz | Réponse fonctionnelle de la pédofaune à la mise en culture itinérante et permanente des sols du sud-ouest de la Guyane française[END_REF], may act as a positive feed-back on the earthworm population.

Figure captions

Fig. 1 .

 1 Fig. 1. Experiment 1. Mean daily cast production by Pontoscolex corethrurus from fallow and forest populations in the presence of fallow and forest soil and pure charcoal.

Fig. 2 .

 2 Fig. 2. Experiment 2. Mean daily cast production by Pontoscolex corethrurus from fallow and forest populations in the presence of fallow soil and a mixture of charcoal and fallow soil.

Table 1

 1

		Chemical features (pH. total C and N content) of incubating substrates
		sieved at 2 mm
		Substrate	pH	C (g.kg	-1 ) N (g.kg	-1 ) C:N ratio
		Fallow soil	4.63	28.8	2.15	13.40
		Forest soil	4.16	43.7	3.37	12.97
		Wood charcoal	7.06	675	8.63	78.14
	1	Mixture charcoal+soil	6.90	395	2.99	132.07
	2

  Effect of earthworm population, soil origin and population x soil interaction on surface cast production (g.day -1 .ind -1Mean±S.E.M. is given for each group -5 replicates) and F value of ANOVA is given for each factor.Significant differences among groups are mentioned by stars: * P<0.05, ** P<0.01; *** P<0.001. The origin of earthworm populations and soils is abbreviated as following: fallow (FAL), forest(FOR)

		Table 2
		FAL Experiment 1. Earthworm population FOR Total cast production	F value	FAL Soil	FOR	F value	Interaction Population x Soil F value
		On charcoal surface	0.10±0.02	0.06±0.02	2.67	0.07±0.02	0.10±0.02	1.78	2.71
		On soil surface	0.23±0.06	0.15±0.03	2.92	0.30±0.05	0.08±0.01	23.28***	4.56*
	1	On total surface	0.33±0.04	0.21±0.03	5.23*	0.36±0.04	0.18±0.02	12.20**	1.04
	2

Table 3

 3 Experiment 1. Effects of earthworm population, soil origin and population x soil interaction on surface production of brown, brown-grey and dark grey casts (mg.day-1.ind-1). Mean±S.E.M. is given for each group (5 replicates) and F value of ANOVA is given for each factor.Significant differences among groups are mentioned by stars: * P<0.05, ** P<0.01; *** P<0.001. The origin of earthworm populations and soils is abbreviated as following: fallow (FAL), forest(FOR)

	Interaction Population x Soil

Acknowledgements

We thank the SOFT Program of the French Ministry for the Environment and the GIS-SILVOLAB of French Guiana for their financial supports and we are grateful to Jean-Pierre Rossi for his help in earthworm sampling in French Guiana.