Modelling vertical and lateral seed bank movements during
mouldboard ploughing
Nathalie Colbach
a,*, Jean Roger-Estrade
b, Bruno Chauvel
a, Jacques Caneill
caUnite´ d’Agrononomie-Malherbologie,INRA,17 Rue Sully,BV 1540,21034 Dijon Cedex, France bUnite´ d’Agronomie,INRA-INA PG,78850 Thi6er6al-Grignon, France
cDe´partement des Sciences et Techniques Agronomiques,ENESAD,26 Bd du Dr Petitjean,21036 Dijon Cedex, France
Received 19 February 1999; received in revised form 12 August 1999; accepted 27 October 1999
Abstract
The vertical distribution of weed seeds in the soil is of fundamental importance because seedling emergence depends on seed depth. The lateral displacement of the earth during mouldboard ploughing contributes to the dispersal of the weeds inside the tilled field. In order to model vertical and lateral seed displacements during ploughing, an existing model describing soil particle movements for different ploughing characteristics (depth and width) and soil structures was tested on a multilocal field trial. The trials were carried out in 1996 and 1997 and comprised two soil textures and three soil structures; tillage was performed with a mouldboard plough at varying ploughing widths and depths. Seeds were simulated by beads that were introduced immediately before ploughing with an auger at different depths and lateral positions (relative to the future passage of the coulter) within and just below the ploughed horizon. Lateral displacement and the final vertical position of the beads were measured and compared to the simulations obtained with the model. The model correctly simulated the final vertical seed co-ordinate and lateral seed displacement as a function of soil structure, ploughing width and depth and initial seed position, if ploughing depth is lower than ploughing width. If, however, the former exceeds the latter and/or if the furrows are not properly rotated, the model does not simulate the seed movements correctly. The model was then used to calculate seed transfer matrices describing vertical seed movements between seed bank layers for different conditions and plough modes and to determine the optimal ploughing mode for a given seed bank distribution. For instance, if most seeds are located in the top layer ploughing should be as deep as possible, with a low depth to width ratio to maximise soil inversion and seed burial. If, however, the seeds are concentrated in the bottom layer, the model can be used to decide how shallowly to plough in order to avoid disturbing the deeper seeds and what ploughing width to associate to this depth in order to minimise soil inversion and leave as many seeds as possible undisturbed. Ways of improving the model are suggested, particularly the necessity to simulate the effect of a skim coulter. © 2000 Elsevier Science B.V. All rights reserved.
Keywords:Mouldboard ploughing; Soil structure; Weed management; Seed bank; Seed dispersal
www.elsevier.com/locate/eja
* Corresponding author. Tel.: +33-3-80693033; fax: +33-3-80693222. E-mail address:colbach@dijon.inra.fr (N. Colbach).
1. Introduction
One of the most important reasons for soil tillage is weed management (Moss and Clarke, 1994). Among the various possible soil tillage operations, mouldboard ploughing is widely used in most European cropping systems. In weed management, mouldboard ploughing is of special interest because of its important effect on the vertical distribution of the seeds in the soil. The vertical seed bank distribution is of fundamental importance because seedling emergence either de-creases continuously with seed depth (Froud-Williams et al., 1983; Dyer, 1995) or increases with slight burial and then decreases at greater depth (Mohler and Galford, 1997). Simulta-neously, the lateral displacement of the earth dur-ing ploughdur-ing contributes to the dispersal of the weeds inside the tilled field.
It is, therefore, essential to improve our under-standing of the effect of mouldboard ploughing on seed bank movements in order to define effi-cient soil management rules for weed control, leading to a decrease in chemical herbicides. This is the reason why many weed demography models include sub-models illustrating the effect of soil tillage on seed bank dynamics (Aarts, 1986; Doyle et al., 1986; Jordan et al., 1995). Many of these sub-models are either based directly on the work of Cousens and Moss (1990) or developed by similar methods and include a quantification of the vertical seed bank movement during plough-ing. Cousens and Moss divided the seed bank of the tilled horizon into four horizontal sub-layers and estimated the proportion of seeds moved between layers during mouldboard ploughing. This model was deduced from statistical relation-ships observed in one experimental situation. Parameters well known to have a great effect on soil displacement during ploughing such as ploughing depth or width (He´nin et al., 1969; Kouwenhoven and Terpsta, 1972) or pre-tillage soil structure (Coulomb et al., 1993) were not taken into account. It is thus difficult to extrapo-late Cousens and Moss’ model to other soil tex-tures and structex-tures or to variations in tillage depth or width.
No mechanistic model has yet been developed specifically for weed seed movements, but Roger-Estrade and coworkers (Roger-Roger-Estrade, 1995; Roger-Estrade and Manichon, 1998) proposed a model for vertical and lateral movements of soil particles, depending on their initial vertical and lateral position, on ploughing depth and width as well as soil structure. Consequently, the objectives of this paper were: (1) To evaluate the suitability of this model to predict weed seed movements in the soil and, therefore, the distribution of seeds in the seed bank, a multilocal field trial was set up to observe seed movements under various conditions and to compare these observations to the simula-tions obtained with Roger-Estrade’s model. As this model is not limited to the most relevant variable for weed seed position, i.e. vertical seed displacement, but integrates both vertical and lat-eral movements, observations and subsequent evaluations must, of course, take into account both dimensions. (2) To calculate vertical seed
transfer matrices, like those established by
Cousens and Moss (1990), for different conditions and plough modes and to determine the optimal ploughing mode for a given seed bank distribu-tion. This second objective is only feasible if the model is deemed acceptable for weed seed move-ments.
2. Material and methods
2.1. Modelling seed displacement during ploughing (Roger-Estrade,1995; Roger-Estrade and
Manichon, 1998)
In the plane perpendicular to the direction of the plough, the furrow of soil cut by the mould-board plough follows the movement described in Fig. 1. This movement comprises two successive rotations of the furrow and ceases when the fur-row is settled on the previously rotated furfur-row (Fig. 1A). The inclination angle between the fur-row and the plough pan only depends on plough-ing width and depth, i.e. the sine of this angle equates to the ratio of tillage depth to width. Actually, the furrow breaks up during this move-ment and partially falls on the plough pan. This phenomenon is modelled by Roger-Estrade by separating the furrow into slices which slide downwards until they reach the plough pan (Fig. 1B). The number of slices depends on the mechan-ical soil behaviour: it is low in the case of poor fragmentation when the ploughed soil is dry or compacted; and it increases with the
fragmenta-tion of the soil, when ploughing occurs in good
moisture conditions and/or when the ploughed
soil is uncompacted. Using this relationship it is possible to calculate the final vertical and lateral co-ordinates of any point of the furrow as a function of its co-ordinates before ploughing and of ploughing depth and width as well as soil structure.
2.2. The field trials
To evaluate the above described model field trials were set up in two situations: (a) The field chosen at the INRA experimental station in the
Dijon area in 1997 (5°2% E, 47°20% N) was on an
eutric cambisol (FAO). The texture of the ploughed horizon (0 – 30 cm) was: clay 39%, silt 55% and sand 6%. The field had been cropped for several years with small grain cereals that were
Fig. 2. Profile view of the beads introduced with an auger into the ploughed layer and their relative position to the future passage of the coulter. The beads marked are located beneath the ploughed layer and are not moved by the plough.
always sown and harvested in dry conditions, inducing a low risk of compaction. (b) The second field, used in 1996, was located at the INRA
experimental station in Grignon (1°58% E, 48°51%
N). The soil was an orthic luvisol (FAO) and the texture was: clay 26%, silt 58% and sand 16%. For the last two decades the crop rotation had been
maize/winter wheat. Therefore, one harvest in two
took place in autumn when conditions are fre-quently wet, thus inducing a high risk of soil compaction. The aim of this choice was to obtain two contrasted types of soil behaviour during ploughing, with an uncompacted, fragmentary soil structure in Dijon and a compacted structure in Grignon. In order to extend this range of soil structures and mechanical soil behaviours, an ex-treme, severely compacted situation was created on one part of the Dijon field (later on called Dijon II as opposed to Dijon I, i.e. the uncom-pacted part of the field) by rolling the whole area in wet conditions with a heavy tractor, just before ploughing.
The initial soil structure was assessed just be-fore ploughing. Three-metre-wide and 50-cm-deep observation pits were dug perpendicular to the tillage direction, and the soil structure of the ploughed layer was described using the method proposed by Manichon (Manichon, 1982, 1987). This method is based on the description of the morphology of the clods created by the action of tillage tools. The clod size, their distribution and internal structural porosity are evaluated in situ. Mean bulk density of the ploughed layer was also
measured with a rubber balloon type density ap-paratus with a piston.
Seeds were simulated by cubic plastic beads (of
about 1 mm3) that are more easily observed and
recovered than weed seeds while being similarly dispersed by ploughing (Ro¨ttele and Koch, 1981; Moss, 1988). Immediately before ploughing, these beads were mixed with soil and introduced with an auger (diameter 5 cm) within and just below the ploughed layer (Fig. 2). Every 5 cm down to a depth of 30 cm in Grignon and 40 cm in Dijon, a different bead colour was used, with a total of six to eight colours depending on the location. Fur-thermore, beads of yet another colour were dis-persed on the soil surface to simplify the recognition of the limits between adjacent furrows after ploughing. Each vertical hole resulting from the auger was considered as a replication and six (Grignon) to eight (Dijon) replications were made (for each structure location), introducing the
beads every w+5 cm (w=plough width) in the
direction perpendicular to the future tillage direc-tion, thus resulting in different lateral positions relative to the future passage of the plough, with only one replication per future furrow. The deep-est beads were not moved by tillage, and marked the initial lateral position of the beads.
in Dijon. Soil moisture at ploughing was mea-sured by randomly choosing a dozen soil samples from the freshly ploughed furrows and calculating the ratio of their dry weight to their fresh weight; mean soil moisture was 30% (S.D. 1.8%) at Dijon and 24% (S.D. 1.5%) at Grignon.
After ploughing, a 50-cm-deep pit was dug perpendicular to the tillage direction, immediately in front of the original position of the beads. The pit covered the complete width of the tilled field. The form and location of the displaced furrows were drawn following the procedure described by Coulomb et al. (1993). The actual ploughing depth was measured for each furrow. The soil was then removed in the direction of the tillage to locate the initial position of the beads, marked by the unmoved beads located below ploughing depth. The actual initial lateral position (relative to the passage of the coulter) was measured for each vertical hole. The removal of the soil was continued to discover the new position of the beads. Lateral displacement and the final vertical position were then measured as shown on Fig. 1 and compared to the simulations obtained with the model. The situation was slightly different in Grignon where all lateral co-ordinates were mea-sured relatively to a common origin and lateral displacements were then deduced.
2.3. Statistics
The model was evaluated, using the formula given by Mayer and Butler (1993) for the coeffi-cient of determination or modelling efficiency:
r2=1−
%(zi−zˆi)2
%(zi−z¯i)2
whereziare observed values (with meanz¯i) andzˆi
simulated values. Another quality indicator which is often used in statistical literature is the mean-squared error of prediction (MSEP); as the data used to evaluate the model were independent of the data used to develop the model, MSEP was estimated as simply the average squared deviation between the model prediction and observations (Wallach and Goffinet, 1987, 1989). To obtain an
error measure of the same unit as both observa-tions and simulaobserva-tions, the square root of MSEP was used.
3. Results and discussion
3.1. E6aluation of ploughing model
3.1.1. Description of furrows after ploughing and choice of model input 6ariables
Observations and measurements of the initial soil structure verified that the produced experi-mental situations indeed ranked as wished, i.e. with the most compacted structure at Dijon II, the less compacted one in Dijon I and Grignon being intermediate. In Dijon II the soil structure appeared homogeneous, massive, without any ap-parent structural porosity; mean bulk density was
1.49 Mg m−3 with an S.D. of 0.03. Because of
this compacted soil structure the furrows were nearly unfragmented. Therefore, only two transla-tion slides were used in the simulatransla-tions. In Dijon I the soil structure was fragmentary, characterised by the dominance of fine earth with some clods of which the diameter did not exceed 5 cm; mean bulk density was significantly lower than in Dijon
II (1.29 Mg m−3, with an S.D. of 0.10). Furrow
fragmentation was high enough to obtain a smooth soil surface and little void between adja-cent furrows; therefore, five translation slides were used for the simulations. The Grignon profile showed a spatially variable soil structure: frag-mentary zones alternated with compacted soil vol-umes. The degree of fragmentation of the furrow and soil surface roughness were intermediate be-tween Dijon I and II. Consequently, simulations were performed with three translation slides.
this large ploughing depth (relative to the plough-ing width) the average inclination angle was close to 90° (sin A close to 1). At Dijon I the ploughing depth, ranging from 33 to 37 cm, exceeded in some furrows the ploughing width. In this treat-ment the furrow inclination angle was close to 90° in most of the furrows. However, some furrows did not complete their first rotation, either be-cause the depth was too great to accomplish that movement or because their rotation movement was blocked by their too-deeply ploughed neigh-bour furrow. This situation probably resulted from the fact that the plough worked in a very compacted clayey soil, so that the actual working depth of the plough was very difficult to control. The input value for ploughing width was 40 cm for the Grignon data and 35 cm at Dijon. What-ever the location, the input value for tillage depth in the model was the measured ploughing depth of each furrow when this value was lower than the ploughing width. When this was not the case the depth to width ratio exceeded 1 and it was impos-sible to calculate the sine; the inclination angle in the model was then set at 90°.
By removing the soil in the direction of the soil tillage the furrows could be observed at various longitudinal positions. No supplementary fissures or variations in the inclination angle or in the degree of fragmentation of the furrows at the level
of auger penetration were observed. Therefore, the use of an auger to introduce the beads did not seem to influence furrow rotation and distortion.
3.1.2. Analysis of model performances
At a first look, the final vertical co-ordinate (the distance to the plough pan) and the lateral displacement were not excessively well simulated
by the model (Table 1): modelling efficiency (r2)
was only slightly higher than 0.6, mean error
(MSEP) was rather large, even compared to the
observed range of variations. No systematic over-or under-estimation (mean of residuals close to zero) was found. Fig. 3, comparing observed and simulated values for the final vertical co-ordinate and the lateral displacement respectively, rein-forces this first impression, showing large
dis-crepancies between simulated and observed
values, even though the points were generally distributed around the equation representing equality of simulated and observed values.
If however, the replications located in those furrows identified by the above described analysis of furrow characteristics (i.e. too deeply ploughed furrows or furrows that had been rotated by less than 90°) were eliminated, the model performance increased dramatically (Table 1): in that case modelling efficiency was high, mean error consid-erably decreased and again, there still was neither
Table 1
Evaluation of Roger-Estrade’s model by analysing prediction accuracy of lateral displacement and final vertical coordinate of displaced beads. Synthesis of three situations: Dijon I, Dijon II (1997) and Grignon (1996)a
MSEP
Number of
Case Evaluated output Mean of r2
points variable residuals (cm) (cm)
All points 155 Lateral −1.1 0.69 12.0
displacement
Final vertical –0.5 0.63 8.2 coordinate
Lateral −1.4 0.85
Elimination of furrows with ploughing depth 73 8.7
\width and without completed 1st rotation displacement
Final vertical –1.1 0.85 4.4 coordinate
aResidual=zˆ
i−zi, whereziare observed values (with meanz¯i) andzˆisimulated values; modelling efficiency r2= 1−((zi−zˆi)2/ (zi−z¯i)2) (Mayer and Butler, 1993); MSEP=(zi−zˆi)2/nwithn=number of observations (Wallach and Goffinet, 1987, 1989);",
Fig. 3. Comparison of final vertical seed coordinates (A) and of lateral seed movements (B) simulated by the mouldboard plough model (Roger-Estrade, 1995) and observed on three field trials. Each point represents beads of a given colour and replication.
systematic over- nor under-estimation. If the residuals were analysed separately for each loca-tion it appeared that the errors for lateral dis-placement were significantly higher at Grignon
(mean of absolute residual values=7.9 cm) than
at Dijon (4.5 cm). However, this particularity was probably related to the different measurement system used at Grignon where, whatever the
beads, all lateral co-ordinates were established relative to one common origin, with an error risk increasing with the distance from this origin.
ploughing depth is lower than ploughing width.
If, however, the former exceeds the latter and/or if
the furrows are not properly rotated, the model cannot be used. This restricts the possible use of the proposed model, but admittedly, under field conditions, ploughing is usually performed with a ploughing depth lower than the ploughing width. The model gives the position of the seeds imme-diately after ploughing. At least in compacted structures the soil settles considerably later on, either because of superficial tillage for soil bed preparation or because of climatic interference such as alternation of dry and humid or cold and warm conditions. The seed displacement model for ploughing must, therefore, be completed by a further model describing the degradation and compression of the furrows after tillage.
3.2. Using the model for simulation of the 6ertical weed seed distribution
3.2.1. Determination of 6ertical seed transfer
matrixes
As shown by the model evaluation, Roger-Estrade’s model can be used to simulate seed movements and final seed positions immediately after tillage. Most existing weed demography
models are only dealing with vertical seed trans-fers and positions as they do not simulate hori-zontal movements (Colbach and Debaeke, 1998). Among the few authors who attempted to quan-tify the effects of soil tillage on vertical seed movements, Cousens and Moss (1990) proposed a compartmental model. In this model the tilled horizon is divided into four 5-cm-thick horizontal layers that are considered as compartments. The
seed content of one compartment j of the
post-tillage seed bank can be predicted from the seed content of the four layers of the initial seed bank and a vertical seed transfer matrix. Each coeffi-cient of this matrix represents the proportion of
seeds of layerimoved to layerjduring soil tillage.
Roger-Estrade’s model can be used to deter-mine such vertical seed transfer matrices. In order to compare the result with the model of Cousens and Moss, similar tillage conditions, i.e. settled soil (resulting from a high number of translation slides), a plough depth and width of 20 and 30.5 cm, respectively, are used for the simulation. Table 2 gives the proportions of seeds moved between layers during soil tillage for the matrices presented by Cousens and Moss and calculated with Roger-Estrade’s model. It appears that this model predicts a homogeneous distribution of the seeds of each layer among the four tilled layers whereas Cousens and Moss’ model foresees that a large proportion of the initially superficial seeds is buried in the two deepest layers. This is not surprising as these authors added a skim-coulter to their mouldboard plough, thus ensuring that superficially located seeds, residues and soil clods are buried close to the plough pan, whereas sim-ply ploughing tends to distribute seeds more or less homogeneously among the layers (Fig. 4). This appears to be an interesting strategy in the case of a field with a superficial soil layer heavily infested by weed seeds where the aim is to limit immediate seedling emergence. Therefore, the de-scription of the soil and seed movements due to a skim-coulter should necessarily be added to Roger-Estrade’s model.
However, despite this deficiency,
Roger-Estrade’s model has several advantages over Cousens and Moss’ model: in contrast to the latter, the first uses ploughing depth and width as
Table 2
Proportion of seeds moved from layer i to layer j by a mouldboard plough (depth 20 cm; width: 30.5 cm) in case of a seedbank divided into four 5-cm-thick horizontal layers
Final Initial layerI 4 (bottom) 0.24 0.24 0.24
aAccording to Cousens and Moss (1990).
bAccording to the plough model (Roger-Estrade, 1995) in
Fig. 4. Seed distribution after ploughing in the case of a soil with a superficial weed seed infestation. Simulations were performed with the vertical transfer matrixes proposed by Cousens and Moss (1990) or calculated with Roger-Estrade’s model (Roger-Estrade, 1995).
well as soil structure as input variables and is not restricted to a 20-cm-deep four-layer seed bank. Indeed, not only can different ploughing modes such as deeper or wider ploughing be simulated, but, much more importantly, the seed bank can be divided into more numerous, thinner layers. This is essential if the plough model is to be introduced into models describing the
demogra-phy of species such as blackgrass (Alopecurus
myosuroides Huds.) for that only seeds located close to soil surface can successfully emerge and give rise to seedlings and seed-producing adults (Barralis, 1968; Naylor, 1972) whereas seed germi-nation and mortality rates vary considerably with seed depth (Barralis, 1970; Horng and Leu, 1978; Ballare´ et al., 1988; Cussans et al., 1996).
The separation of the seed bank into horizontal layers is easy in the case of highly fragmented soil where the post-tillage soil surface is smooth. But this separation is considerably more complicated if the soil structure is compacted and the ploughed soil surface rough, i.e. when furrows are poorly fragmented. In this case (as on the Grignon and Dijon II trials), the layers are
defined as shown on Fig. 5, i.e. depending on the distance of the seeds to soil surface. The layers are thus almost horizontal in the case of highly frag-mented soil structure (Fig. 5A), they appear to be more ‘zigzagged’ when the fragmentation is lim-ited (Fig. 5B). This procedure of subdividing the seed bank appeared more relevant as most physi-cal conditions that are important for weed seed evolution depend on the distance to the surface. For instance, for many weed species (Barralis, 1970; Bouwmeester and Karssen, 1989; Bai et al., 1995; Benvenuti, 1995; Jensen, 1995) and even some cropped species occurring as volunteers (Pekrun et al., 1997a,b; Pekrun and Lutman, 1998), the amount and quality of light is essential for the onset of germination and these factors were shown to decrease with depth (Benvenuti, 1995).
3.2.2. Simulations
In the case of an initial superficial seed infesta-tion, if the aim is to bury as many seeds as possible, then ploughing is, of course, advised instead of superficial tillage or direct drilling, but soil structure influences the efficiency of this oper-ation via its effects on the final vertical seed distribution: in the case of a fragmented structure (Fig. 6A) ploughing distributes the seeds homoge-neously among the ploughed layers, regardless of ploughing width. Hence, the proportion of seeds found at a given depth only depends on tillage depth; the deeper the ploughing, the less seeds are found at a given depth (and, therefore, close to the soil surface). The situation is not as simple in the case of a compacted structure (Fig. 6B) where ploughing width also influences seed distribution and both tillage depth and width must be rea-soned together. Indeed, Fig. 6B shows that the deepest ploughing does not necessarily result in the lowest superficial seed content and that, in fact, a high ratio of ploughing width to depth (with a high inclination of the furrow) is necessary to bury superficial seeds. In contrast, in the case of a low width to depth ratio (with a low inclina-tion of the furrow) the superficial seed concentra-tion after deep tillage can be as high as that after a more shallow tillage with a high width to depth ratio.
If most seeds are, however, located in the deeper soil layers (Fig. 6C and D), then shallow ploughing (or even superficial tillage) is advised to limit superficial seed content, whatever the soil structure. Again, seeds are distributed homoge-neously among the ploughed layers in the case of the fragmented structure whereas the seed profile is highly irregular for the compacted structure with, moreover, an influence on the ploughing width. However, in contrast to the above de-scribed situation with an initially superficial seed concentration, ploughing depth remains the most important factor, even for compacted structures. Indeed, if the layers containing the weed seeds are not disturbed it is unlikely that these seeds are carried back to the soil surface, except that some movement can take place as a result of soil fauna activity for instance, albeit on a small scale. If though shallow tillage is not a possible option, then at least ploughing with a low width to depth ratio should be attempted to decrease the propor-tion of exhumed seeds.
In this discussion the aim of ploughing was to minimise seed content close to the soil surface to limit weed seedling emergence immediately after tillage (Yenish et al., 1992). This is, however, not always the objective of tillage, even when its ultimate aim is weed control. If ploughing pre-cedes the seeding of a crop by several months (as in the case of clay soils to be sown with spring
crops) in some cases it can be more advantageous to maximise superficial seed content in order to make as many seeds as possible emerge before crop seeding and thus deplete the seed bank, i.e. the stale seedbed technique (Leblanc and Cloutier,
1996). Such a strategy would, of course, only work with relatively non-dormant seeds (such as
Poa annua L., Orlando et al. (1995)) that respond to tillage by emerging immediately. This strategy would, on the other hand, be disastrous in the
Fig. 6. (Continued)
case of species such as Polygonum persicaria L.
(Orlando et al., 1995) that emerge predominantly in spring; the seed bank dormancy would have decreased between tillage and seeding and the seeds concentrated in the top layers would just be ready for emergence at crop seeding.
4. Conclusion
The evaluation of Roger-Estrade’s model
and to quantify soil tillage effects for a variety of soil structures and ploughing modes. However, this model does not foresee the use of a skim-coulter, a tool that would considerably improve the burial of initially superficial weed seeds. Fur-ther studies are, Fur-therefore, currently being under-taken by the authors to model the effects of this additional implement to the mouldboard plough. Another necessary addition to this ploughing model describing seed positions immediately after tillage concerns the long-term seed movements under the influence of superficial soil tillage and climate. This especially concerns compacted soil structures where important soil and, therefore, weed seed movements occur when the formerly compacted furrows break up and the soil settles on the plough pan.
Despite these considerations the model can al-ready be used to optimise soil tillage for weed management by indicating the optimal ploughing depth and width, depending on the soil structure and the initial vertical seed distribution in the soil, as shown by the various simulations. Further-more, due to the quantification of the soil tillage effects on vertical seed positions and to the model ability to distinguish layers of varying numbers and thicknesses, Roger-Estrade’s model can be used to manage by soil tillage weed species with contrasting germination and emergence require-ments. To optimise this weed management the soil tillage model should be combined with further models describing biological processes such as seed mortality, dormancy and seedling emergence. These processes not only depend on vertical seed position, but also on soil properties such as tem-perature, humidity, light penetration, oxygen con-tent, etc., which are also influenced by soil tillage (Mohler and Galford, 1997).
The range of possible soil tillage solutions could, of course, also be increased by proposing other techniques such chisel ploughing or various superficial interventions. To evaluate the relative performances and advantages of these different tillage options, models similar to the ploughing model would then be necessary for these other tillage implements.
Roger-Estrade’s model also constitutes a first step on the way to weed demography models
integrating intra-field variability as, besides verti-cal seed movements, lateral displacements are de-scribed. Therefore, it is now already possible to build models describing lateral (perpendicular to the direction of the soil tillage) intra-field variabil-ity and thus describe lateral weed dispersal and variations in weed densities. To accomplish com-plete horizontal variability, both in the direction and perpendicular to the direction of tillage and other agricultural interventions, it is, however, necessary to tackle longitudinal seed movements during tillage.
Acknowledgements
The authors thank Jacques Troizier, Head of the Experimental Centre at Grignon, and his team, and Luc Biju-Duval and his colleagues of the Experimental Station of INRA-Dijon, for conducting the field trials.
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