Correction added on 25 February 2009 after first online publication. On page 2, column 2, paragraph 3, the sentence was changed to ‘Rhizoctonia solani AG2-2 IIIB isolate G6 was . . .’. On page 7, Figures 5a and 5b, ‘Residues’ was removed from the y-axis labels.
The persistence of control of primary infections caused by two soilborne fungal plant pathogens, Rhizoctonia solani and Gaeumannomyces graminis var. tritici, following the incorporation of above-ground parts (AP), below-ground parts (BP) or both (AP+BP) of Brassica juncea into soil was examined through an experiment in controlled conditions. Control was quantified by measuring disease incidence in bioassays where inoculum was introduced at different dates after the incorporation of plant residues. All types of residue showed an unexpected long-term persistence that lasted at least 13 days, while the predominant glucosinolates contained in AP (20·9 µmol sinigrin g−1 dry matter) and BP (2·3 µmol gluconasturtiin g−1 dry matter) were hydrolysed in less than 3 days. Temporal trends in the efficacy of the residues behaved mostly in a quadratic manner, suggesting that the noxious effect of residues may be attributable to the release of isothiocyanates during the first days following incorporation, but that other mechanisms are most likely to contribute to lasting persistence. Across all treatments, AP and AP+BP suppressed R. solani by 54 and 63%, respectively, and G. graminis var. tritici by 40 and 40%, respectively, compared with controls. While BP did not cause any additional detectable effect when combined with AP, they had a significant effect when incorporated alone (approximately 20% suppression of both species), suggesting the existence of a complex interaction between these two types of residue.
Brassica-cover crops are increasingly used as catch crops and/or green manure crops within crop rotations to provide a number of agronomic benefits (e.g. control of nitrogen leaching, increased soil organic matter and improved soil structure). However, they also have the potential to suppress a range of soilborne plant pests and diseases (Muehlchen et al., 1990; Mojtahedi et al., 1991; Snapp et al., 2007). Brassica species contain glucosinolates (GSL), which, upon tissue disruption, are hydrolysed in the presence of water by an endogenous myrosinase enzyme into numerous compounds, notably toxic isothiocyanates (ITC). The detrimental effect of pure ITC to certain fungi has long been known and the potential of Brassica crops to control soilborne pests and pathogens is mainly attributed to these compounds. This process, termed “biofumigation” (Angus et al., 1994), is of increasing interest as it is viewed as an alternative to the use of traditional inorganic soil fumigants in the control of soil pests. However, past studies have reported variable success in biofumigation efficacy of ITC ranging from good disease suppression to no control whatsoever (Johnson et al., 1992) or even to pathogen stimulation (Stephens et al., 1999). Brown & Morra (1997) reviewed the factors contributing to biofumigation efficacy (efficacy of ITC release, susceptibility of the target species, soil moisture content, etc.) and suggested that, as the lifetime of GSL products in the environment was shown to be short (Brown et al., 1991; Morra & Kirkegaard, 2002), “a short residence time places limits on achieving effective control and may contribute to the variability observed in the suppression of soilborne plant pests”. The question concerning the persistence of biological effects of soil amendment with Brassica tissues on soilborne pathogens had, to date, only dealt with the kinetics of disappearance of ITC (Brown et al., 1991; Gardiner et al., 1999; Morra & Kirkegaard, 2002; Gimsing & Kirkegaard, 2006). These studies provided the first insight into understanding some of the mechanisms which might be involved in the persistence of control, but although the disappearance of ITC in soil is rapid, no firm conclusion can be drawn concerning the noxious action of residues after the period of ITC detection has passed.
The above- and below-ground plant components of B. juncea produce different ITC which are expected to show different persistence once the plant residues have been incorporated into the soil. The above-ground, or aerial portion of the plant contains predominately aliphatic GSL such as sinigrin and gluconapin, which produce volatile ITC, while the below-ground, or subterranean parts of the plant contain mainly aromatic GSL such as gluconasturtiin, which produce much less volatile ITC (Kirkegaard & Sarwar, 1998). While, under natural conditions aliphatic ITC are likely to be more toxic than aromatic ITC (Matthiessen & Shackleton, 2005), it is supposed that their biological effect is short-lived because of their volatile nature (Brown & Morra, 1997). Similarly, it is also assumed that the low volatility of aromatic ITC may result in their longer-term persistence in soil (Kirkegaard & Sarwar, 1998).
Wheat and sugar beet crops are often grown in close rotation. Economically important diseases of wheat and sugar beet are, respectively, take-all caused by the soilborne fungus Gaeumannomyces graminis var. tritici, and crown rot caused by Rhizoctonia solani. The epidemiology of take-all is well described (Bailey & Gilligan, 1999). The disease is initiated by primary infection from particulate inoculum, in the form of colonized wheat fragments that survive from a previous crop. The spread of disease continues by secondary infection as the pathogen spreads from root to root. The epidemiology of crown rot on sugar beet is less well understood. The disease is initiated from colonized organic matter residing in the soil or from sclerotia, whilst secondary, plant-to-plant infection, whilst never demonstrated, is not inconceivable. Nevertheless, the importance of particulate inoculum and primary infection is without doubt in both pathosystems.
The aim of this study was to determine the persistence of action of B. juncea residues on the control of disease from particulate inoculum. This was achieved by linking the time at which inoculum was introduced into the soil following the incorporation of B. juncea residues to the disease expression of rhizoctonia root rot of sugar beet and take-all of wheat. As the above-ground parts (AP) and below-ground parts (BP) of the mustard plant are supposed to have different actions on soilborne pathogens and different lifetimes in soil, the objectives were (i) to determine the persistence of action of AP and BP residues and their respective efficacies of control on the two soilborne pathogens and (ii) to determine whether the pattern of control observed when AP and BP were combined in the soil reflected the additive effects of AP and BP when incorporated alone.
Materials and methods
Cultivation of mustard plants
Indian mustard (B. juncea) line 1420 was used in all experiments and was selected for its high level of sinigrin (~115 µmol g−1 seeds), its high in vitro toxicity (Motisi et al., 2007) and its high degree of vigour when grown under field conditions (Lionneton et al., 2004). It is a European-type mustard with brown seeds obtained from the cross-breeding of cv. Musta and cv. Ficita (T. Guinet, ENESAD, France, personal communication).
Mustard was sown at a density of 240 seeds m−2 (equivalent to the planting density used for the purpose of biofumigation under field conditions) in 26-L pots containing natural soil (34% clay, 60% silt, 6% sand) from the Dijon area of France and cultivated to the 10% pod stage in a growth chamber for 10 weeks with a 12-h day at 18°C and a 12-h night at 10°C.
Preparation of inoculum
Rhizoctonia solani AG2-2 IIIB isolate G6 was originally isolated in Seine-et-Marne, France from the necrotic lesion of an infected sugar beet root. Gaeumannomyces graminis var. tritici (G. g. tritici) isolate IV-26/00 was isolated from the root lesion of a plant grown within a fourth consecutive wheat crop in Ille-et-Vilaine, France (Willocquet et al., 2008).
Inoculum consisted of infested barley grains. Barley grains were soaked with water before autoclaving (2 × 1 h at 115°C, with a 24-h interval between autoclavings). The autoclaved barley was inoculated with mycelial plugs removed from the growing margins of 3-day-old (R. solani) or 7-day-old (G. g. tritici) colonies grown on malt agar at 20°C. The inoculated barley grains were then incubated for 3 weeks at 20°C. After incubation, these were air-dried, ground and passed through sieves (>1 mm, <1·6 mm) to obtain a consistent form of inoculum.
Preparation of mustard green manure
Mustard plants were harvested and partitioned into above- (stems, leaves, flowers and pods) and below-ground (roots) components. Four treatments were set up: soil + above-ground parts (AP), soil + below-ground parts (BP), soil + above- and below-ground parts (AP+BP) and bare soil as a control (BS). The quantity of residues incorporated into the soil was adjusted to correspond with the equivalent of 74 t fresh weight (FW) ha−1B. juncea green biomass incorporated to a depth of approximately 10 cm in field soil. In this way, above-ground parts were weighed separately to reach the equivalent quantity (74 g FW L−1 dry soil) and the quantity of below-ground parts was determined by the corresponding roots (4·5 ± 0·7 g FW L−1 dry soil). Plant tissues were ground in a Thermomix blender (Vorwerk) for 15 s, immediately incorporated and carefully mixed with natural soil and filled in 39-mL seedling plant propagation plastic trays (Romberg). A 7-cell tray represented a treatment and each treatment was repeated twice. All of the trays were placed in a growth chamber with a 10-h day at 20°C and a 14-h night at 13°C and the soil moisture was kept to field water-holding capacity to ensure optimal GSL transformation in soil as well as optimal development of both pathogens.
According to the literature, the lifetime of ITC and GSL in soil was shown to be 6 and 8 days, respectively, at the most (Gimsing & Kirkegaard, 2006). As the purpose of this study was to determine the time when the effect of ITC would shut down, it was decided to work on a fine timescale of 13 days. Thus, fungal propagules were incorporated into the soil at different times (t = 0, 1, 3, 5, 7, 9, 11 and 13 days) after the incorporation of green manure. At each time, one propagule of R. solani or five propagules of G. g. tritici were placed into the soil at a depth of 1 cm and at a distance of 1 cm from the right edge of the 4-cm-diameter cell. In controls, no fungal propagules were incorporated into the soil.
Assessment of inoculum survival
Fifteen days after the incorporation of mustard residues, seeds from the respective host plants were sown 1 cm from the left edge of the cell on the basis of one seed per cell (in total 14 seeds per treatment were sown). Sugar beet cv. Alpage and wheat cv. Talent were used to assess the survival of R. solani and G. g. tritici, respectively. Host plants were cultivated in a growth chamber for 1 month with a 14-h day at 25°C and a 10-h night at 18°C to ensure optimal development of R. solani and with a 10-h day at 20°C and a 14-h night at 13°C to ensure optimal development of G. g. tritici. The infectivity of inoculum of R. solani was estimated from changes in the number of beet seedlings with damping-off over time. Seeds of non-emerged plants were examined for infestation by the pathogen. For G. g. tritici, the roots of wheat seedlings were examined visually, following washing, for the presence of root necrosis (stellar discoloration) after 1 month. Disease incidence (i.e. the number of diseased plants) was measured for both fungi.
Kinetics of GSL disappearance in residues
To determine whether the kinetics of ITC formation was linked to disease incidence after the incorporation of B. juncea residues into soil, the quantity of the remaining GSL within the residues was measured at each date of soil infestation (described above under ‘Soil infestation’). After grinding the residues, nylon bags containing either 10 g AP or 0·75 g BP were prepared. At t = 0, one nylon bag of each AP and BP residues were immediately plunged into liquid nitrogen in order to arrest enzyme activity and then stored at −80°C. The remaining bags were placed in moist vermiculite to allow the hydrolysis of GSL by myrosinase. After t = 1, 3, 5, 7, 9, 11 and 13 days, one bag of each AP and BP residues were randomly removed from vermiculite and placed in liquid nitrogen and stored at −80°C. The quantity of GSL prior to grinding was determined using three entire mustard plants partitioned into AP and BP after uprooting and submerged in liquid nitrogen and stored at −80°C. One week after the final sampling date, all bags were dried in a freeze-dryer for 3 days, placed in dry ice and sent to CETIOM (France) to quantify the contents of sinigrin (SIN) and gluconasturtiin (GST), the dominant GSL of B. juncea found in AP and BP, respectively (Kirkegaard & Sarwar, 1998). Analyses were carried out using high performance liquid chromatography of desulphated derivatives (ISO 9167-1 method). Identification of the GSL was achieved by UV spectra and comparison with pure standards of desulphoglucosinolates (DS-GSLs) (Watheket et al., 2004).
The experimentation was repeated twice. Each experiment was arranged in a randomized complete block design including two blocks and 64 treatments (8 dates, four modalities of green manure incorporation, two modalities of inoculum) for each fungus.
As there was no significant effect of repetition on the incidence of R. solani (P = 0·92) and G. g. tritici (P = 0·09), all calculations were done on the combined data from the two experiments.
Calculation of disease incidence was performed for each green manure treatment as follows: for R. solani, disease incidence =∑ diseased plants/∑ germinated seeds; and for G. g. tritici, disease incidence =∑ diseased plants/∑ emerged plants.
The efficacy of disease control was firstly investigated by modelling the temporal trends. First, the most likely temporal trends in the incidence of the controls were determined by comparing the three simplest types of models: a null model (constant incidence), a linear model (incidence~t) and a quadratic model (incidence~t2+t). The best model (i.e. the most parsimonious) was determined by AIC (Akaike, 1974). If linear or quadratic trends were selected, then the corresponding linear or quadratic slopes were tested by t-tests. Secondly, the most likely temporal trends in the efficacy of each treatment were determined. Efficacy was calculated as follows:
where IRi is the disease incidence with residue i and IC is the fitted disease incidence without residue (i.e. control). Then, as described above for the incidence of the controls, the most parsimonious model fitting the data was determined: a null model (constant efficacy), a linear model (efficacy~t) or a quadratic model (efficacy~t2+t). The model fitting accounted for estimation uncertainty by weighting efficacies by the inverse of the variance between replicates. The selected linear or quadratic slopes were tested by t-tests.
Finally, the global efficacies of the disease control obtained with the different types of residue were compared. Global efficacy was determined as follows:
where IRit was the disease incidence with residue i at date t, and ICt was the disease incidence without residue (i.e. control) at date t.
Persistence of action of the different types of residue on disease incidence
The incorporation into soil of the above-ground parts alone (AP) or the above-ground parts combined with the below-ground parts (AP+BP) reduced the infectivity of inoculum of both R. solani and G. g. tritici at every date at which inoculum was added to soil over the 13-day period of assessment (Fig. 1a,c and Fig. 2a,c). The effect of adding the below-ground parts alone (BP) was less, but nevertheless, disease incidence was significantly reduced for seven of the eight times at which inoculum was added (Fig. 1b and Fig. 2b).
Temporal trends in efficacy of disease control of the different types of residue
The efficacies of control of R. solani and G. g. tritici by B. juncea residues changed over time (Fig. 3). For R. solani, the most parsimonious model fitting the efficacy of the three types of residue was the quadratic model (convex). The quadratic slope was significantly positive for AP (P = 0·002) and BP (P = 0·009), but not for AP+BP (P = 0·128). For all three types of residue, efficacy was high at t = 0 (70·3, 24·2 and 79·3% for AP, BP and AP+BP respectively), then decreased until the fifth day to 42·0, −7·7 and 36·2% for AP, BP and AP+BP respectively and then increased until the thirteenth day up to 59·1, 51·8 and 70% for AP, BP and AP+BP respectively. For G. g. tritici, the most parsimonious model describing the efficacy of AP residues was the null model, while for AP+BP and BP residues, the quadratic model was the most parsimonious (convex for AP+BP and concave for BP). The quadratic slope was significantly negative for BP (P = 0·006) and not significantly different from 0 for AP+BP (P = 0·215). For AP, efficacy seemed to be constant to a quite high average of 54·6% whereas for BP efficacy was negative at t = 0 (−9·5%), then increased until the ninth day up to 40·9% and then decreased until the thirteenth day to 19·8%. For AP+BP, efficacy was high at t = 0 (69·4%), then decreased until the ninth day to 29·2% and did not increased very much until the thirteenth day (36·3%).
Comparison of global efficacies of disease control by AP, BP and AP+BP
BP was approximately half as effective at controlling either R. solani or G. g. tritici as AP; the combination of both AP and BP residues did not increase significantly the efficacy of disease control compared to AP (P = 0·18 for R. solani and P = 0·96 for G. g. tritici) (Fig. 4). Comparisons between the two pathogens showed that AP residues were 27% less effective in controlling disease incidence caused by G. g. tritici than in controlling disease incidence caused by R. solani, while BP residues appeared to have the same global efficacy (approx. 20%) on both fungi (P = 0·73).
Kinetics of disappearance of GSL in residues after grinding
AP and BP residues varied with respect to the type and quantity of GSL (Fig. 5). Sinigrin (SIN) was predominant in AP (20·9 µmol g−1 dry matter compared with 0·8 µmol gluconasturtiin (GST) g−1 dry matter), whereas gluconasturtiin was more prevalent in BP (2·3 µmol g−1 dry matter compared with 1·4 µmol SIN g−1 dry matter). For both types of residue, grinding resulted, in the first instance, in a dramatic decrease of GSL; in AP and BP residues, respectively, SIN content was diminished by 85 and 96% and GST content by 89 and 97%. The majority of the release of both types of GSL occurred within the first day in AP residues and shortly after grinding for BP residues.
The quantity of GSL released into the soil and actually in contact with either one propagule of R. solani or five propagules of G. g. graminis during the 13 days period of incubation was plotted (Fig. 6). After 13 days of incubation, each fungal propagule had been exposed to 1·5 µmol SIN and 0·04 µmol GST in AP treatments and 2·6 × 10−3µmol SIN and 3·1 × 10−3µmol GST in BP treatments.
Given the relatively rapid disappearance of ITC from the soil (Brown et al., 1991; Morra & Kirkegaard, 2002), the persistence of action of B. juncea residues on the infectivity of particulate inoculum of the pathogens R. solani and G. g. graminis was longer than expected. Residues formed from both above- and below-ground components of B. juncea reduced the infectivity of inoculum of G. g. tritici and R. solani for a period at least 13 days. The original definition of biofumigation is the suppression of soilborne pests and diseases by biocidal products (particularly ITC) released from incorporated tissues or rotation crops of GSL-containing plants, notably Brassica spp. (Matthiessen & Kirkegaard, 2006). Hence, it is commonly supposed that the most important suppressive effect of soilborne diseases is an ITC-based biofumigation effect (Brown & Morra, 1997). However, the persistence of ITC in soil after the grinding and incorporation of Brassica residues was shown to be short, and according to previous studies, no longer than 3 days (Gardiner et al., 1999; Morra & Kirkegaard, 2002) to 6 days (Gimsing & Kirkegaard, 2006), significantly shorter than the persistence of residue action observed in the present study.
The persistence of action of B. juncea residues might be expected to be shorter still in the present experiment since the residues were incorporated into a clay soil (Price et al., 2005). Besides the fact that the structure of clay soils (small pore space and increased tortuosity) is supposed to lead to a slow diffusion of ITC (Price et al., 2005), reduction of bioactive ITC may be caused by ITC adsorption to soil organic carbon (Borek et al., 1995). In addition, the incubation temperature (10-h day at 20°C/14-h night at 13°C) was quite warm, shown to be a factor that decreases the aliphatic ITC half-life in soil (Borek et al., 1995). Hence, according to these data, the persistence of action of B. juncea residues in the present study should have been much shorter than that observed, of the order of less than 3 days for above-ground parts residues and 1 day for below-ground parts residues.
Larkin & Griffin (2007) observed that a reduction of Rhizoctonia disease was not always associated with GSL level and biofumigation potential of Brassica residues incorporated into soil. In addition, Tsao et al. (2000) found that bran of mustard had an enhanced nematicidal activity over pure ITC. This suggests that factors other than early-liberated ITC may be of importance in reducing soilborne diseases. Persistence of action of B. juncea residues may be caused by the persistence of unhydrolysed GSL in soil which could be detected for 5–8 days after residue incorporation (Gimsing & Kirkegaard, 2006). As myrosinase activity can be detected in soils with no recent history of cultivation of GSL-containing plants (Gimsing et al., 2006) GSL can potentially be hydrolysed (by extracellular microbial myrosinase) several days after residue incorporation, depending on environmental conditions (Al-Turki & Dick, 2003). Alternatively, non-ITC-related effects are highly likely to occur. Several non-GSL-derived volatile S-containing compounds, such as sulphides and thiols, are formed by microbial degradation of Brassica residues in soil (Bending & Lincoln, 1999). These compounds are known to be toxic to a range of organisms and are likely to contribute to biofumigation by acting in association with ITC. In a recent study, Mazzola et al. (2007) demonstrated that the suppression of R. solani AG-5 by B. juncea seed meal amendment was associated with the release of allylisothiocyanate in the first day, but that long-term control (4 weeks after amendment) was attributed to an increase in populations of Streptomyces spp. known to be antagonistic to R. solani (Cohen et al., 2005). In the same way, Yulianti et al. (2007) showed that the saprophytic and pathogenic behaviour of R. solani AG2-1 after soil amendment with Brassica nigra was affected in the long term (6 months after residue incorporation). Those authors suggested that as the impact of ITC seems to be short-term (days), an increase in microbial activity or a release of compounds from the green manures over a long time period are more likely to be the dominant factors affecting R. solani activity. This supports the present results on the temporal changes in the efficacy of disease control by B. juncea residues. The following explanation for the trends observed in the present experimentation is proposed: that the convex quadratic trends describing changes in the control of R. solani over time for AP and BP were the result of (i) an initial decrease in efficacy (during the first 5 days) resulting from the fast disappearance of the ITC released by the residues and (ii) a subsequent increase caused by a delay in the activation of microbial communities (because of the initial detrimental effect of ITC) responding to the incorporation of additional organic matter. In contrast, the ability of BP residues to control G. g. tritici showed a concave quadratic trend, although this may also be explained by similar mechanisms if it is considered that G. g. tritici is globally less sensitive to B. juncea residues than R. solani, as shown in Fig. 3. It can be hypothesized that if G. g. tritici is insensitive to ITC released by BP residues, then its growth might be favoured by the nutrients contained in BP residues incorporated in soil. The subsequent increase of the efficacy of disease control then could be the result of a delayed increase of the native microbial populations, as suggested for R. solani.
Hence, the persistence observed in the present study cannot be explained by an ITC-related pathway alone, and many other phenomena are highly likely to contribute to the persistent effect of Brassica residues on the infectivity of soil inoculum.
Given this unexpected persistence of the effects of both types of residue on R. solani and G. g. tritici, it could not be concluded that BP residues provided more persistent control of soilborne inoculum than AP residues. However, these results provide valuable insight into the relative efficacy of control afforded by AP and BP residues, both separately and in combination. BP residues were globally less effective than AP residues on both fungal species, but considering the small amounts of material added and the GSL released into the soil after incorporation of BP residues, the suppressive capacity of BP residues is remarkable. Although 2-phenylethyl ITC (aromatic ITC principally produced by below-ground tissues) and 2-propenyl ITC (aliphatic ITC principally produced by above-ground tissues) exhibit similar in vitro toxicity to several pathogens including R. solani and G. g. tritici (Kirkegaard et al., 1996), differences in the ability of the residues to reduce the infectivity of inoculum may be explained by the nature and the behaviour of the ITC released in the soil. Matthiessen & Shackleton (2005) demonstrated that even though aromatic ITC were more biologically active in vitro against a model soil insect (whitefringed weevil) than were aliphatic ITC, this tendency was reversed in natural conditions. However, it is still unclear whether this would inactivate their contact toxicity to soilborne fungi, and the notable efficacy of BP residues in the present study could be attributed to (i) effective contact toxicity of aromatic ITC (Borek et al., 1995) or other hydrolysis products released as roots decay, along with (ii) the effects of other organic-matter-induced changes discussed above.
If differences in the ability of AP and BP residues to control inoculum can be easily explained, the behaviour of the combination of both types of residue is less obvious. The combination of AP and BP residues was no more effective than AP residues incorporated alone, i.e. less effective than would be expected from a simple additive effect of the two types of residue. This suggests that either (i) AP or BP lost a part of their initial control efficacy when incorporated together or (ii) the level of control obtained with AP was the maximum attainable through biofumigation on primary inoculum and primary infections at this stage of residue decomposition. Results obtained by Snapp et al. (2007) exhibited diverse interactions between above- and below-ground residues of B. juncea, ranging from a gain of efficacy in in vitro and field experiments to a loss of efficacy in controlled environments. The exact cause of this phenomenon is unknown, but it suggests that environmental conditions determine diverse and complex interactions between above- and below-ground residues of B. juncea.
The results of the present study suggest that disease suppression by Brassica amendments does not derive solely from ITC or other GSL-related compounds, but from other chemical or biological changes in the soil microbial profile which can influence disease expression. However, biofumigation efficacy and microbial activity in the field are likely to be lower than those of the present experiments because Brassica green manures are generally incorporated into the first 10 cm of the topsoil, so that the volume of soil which is effectively treated in the field is different from that in small-scale experiments. Furthermore, as was shown by Kirkegaard et al. (2000), other epidemiological factors (inoculum survival, disease development and expression ... ) must be taken into account at the field scale as they are likely to restrict the benefits of biofumigation to specific seasonal conditions.
This paper is apparently only the second to compare Brassica above- and below-ground plant components and a combination of both, and the first to show the non-additive effect of AP and BP residues when combined. Field experimentation to add to these results and support the associated hypotheses described in this paper is underway.
We thank E. Lemarchand, S. Bensidhoum and C. Lacroix for their technical assistance and data collection, M. Krouti and J. Dechambre at CETIOM for the analyses of GSL, D. Bailey, M. Gosme, Y. Bas and anonymous referees for their useful comments. This work was partly funded by the Institut Technique français de la Betterave industrielle.