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:
r
2
= 1 −
z
i
− zˆ
i 2
z
i
− z¯
i 2
where z
i
are observed values with mean z¯
i
and zˆ
i
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 simulations, 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 simulations. 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.
At Grignon the tillage depth was a uniform 25 cm and the furrows had been properly rotated so
that the inclination angle of the furrows angle A in Fig. 1 was about 40° as foreseen by the model.
At Dijon the measurements of the actual plough- ing depth performed for every furrow showed that
the ratios of ploughing width to depth varied between furrows. Consequently, furrow inclina-
tion also varied considerably. At Dijon II the tillage depth ranged from 29 to 33 cm. Because of
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 r
2
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 r
2
Mean of Evaluated output
points variable
residuals cm cm
All points 155
Lateral 12.0
− 1.1
0.69 displacement
Final vertical 8.2
0.63 –0.5
coordinate Lateral
0.85 −
1.4 Elimination of furrows with ploughing depth
73 8.7
\ width and without completed 1st rotation
displacement Final vertical
4.4 –1.1
0.85 coordinate
a
Residual = zˆ
i
− z
i
, where z
i
are observed values with mean z¯
i
and zˆ
i
simulated values; modelling efficiency r
2
= 1−
z
i
− zˆ
i 2
z
i
− z¯
i 2
Mayer and Butler, 1993; MSEP = z
i
− zˆ
i 2
n with n = number of observations Wallach and Goffinet, 1987, 1989; , mean significantly different from zero at a = 5.
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. These results show that Roger-Estrade’s model
correctly simulates the final vertical seed co-ordi- nate as well as lateral seed displacement as a
function of soil structure, ploughing width and depth and, of course, initial seed position, if
ploughing depth is lower than ploughing width. If, however, the former exceeds the latter andor 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 layer i moved to layer j during 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 layer I
1 2
Layer j 3
4 A
a
0.02 0.21
0.37 1 top
0.29 0.10
2 0.26
0.11 0.27
0.12 0.20
0.30 0.40
3 0.46
0.21 0.18
4 bottom 0.48
B
b
0.24 0.24
0.24 1 top
0.24 0.26
0.26 2
0.26 0.26
3 0.26
0.26 0.26
0.26 0.24
4 bottom 0.24
0.24 0.24
a
According to Cousens and Moss 1990.
b
According to the plough model Roger-Estrade, 1995 in the case of a fragmented soil structure ten translation slides.
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.
Roger-Estrade’s model was then used to calcu- late vertical transfer matrices for 30-cm-deep seed
banks divided into 1-cm-thick layers. These ma- trixes were calculated for different soil structures
as well as ploughing depths and widths and then applied to various initial seed distributions.
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
Fig. 5. Subdivision of seed bank into layers before and after ploughing, depending on soil structure. Each layer comprises all the points located at equal distance from the soil surface which is defined as the nearest part of the contour of the furrow. Thus, each
layer has the shape of the surface of the freshly ploughed field: horizontal in case of a highly fragmented soil or rough ‘zigzagged’ when fragmentation due to the plough is poor.
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. Seed distributions before and after ploughing based on simulations performed with the vertical transfer matrixes calculated with Roger-Estrade’s model Roger-Estrade, 1995. A Case of a highly fragmented soil structure with a superficial weed seed
infestation. B Case of a highly compacted soil structure with a superficial weed seed infestation. C Case of a highly fragmented soil structure with a deeply located weed seed infestation. D Case of a highly compacted soil structure with a deeply located weed
seed infestation.
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
