Modelling the effect of cultivation on seed movement with application to the prediction of weed seedling emergence


A.C. Grundy (fax 01789 470552; e-mail


1. Effective weed control is essential in field vegetables. However, the range of available herbicides has been continually reduced for commercial and toxicological reasons over the last decade. In order to predict the optimum weeding period and to apply alternative control strategies successfully, a realistic estimate is needed of the size, timing and duration of a flush of weed emergence in a crop. The soil weed seed bank is the primary source of future weed populations, and therefore provides a unique resource for predictive management purposes.

2. Models have previously been developed to predict the emergence of weed species from different burial depths and to simulate the vertical movement of weed seeds following seed bed preparation.

3. In this investigation a vertical movement model was extended to include the effects of four cultivation implements on the horizontal displacement of weed seeds. These implements were a rotavator, a spring tine, a spader and a power harrow.

4. The rotavator caused a backward movement of seeds; neither the spring tine nor spader had a significant effect on the horizontal displacement of seeds; whilst the power harrow had the greatest capacity to move seeds forward > 0·5 m in the soil.

5. This investigation combined depth of burial and vertical movement models to simulate the likely outcome of different sequences of spring tine, spader, rotavator and power harrow on subsequent weed seedling emergence. For example, sequences including multiple passes of a spader increased the numbers of emerged seedlings, whilst for those where the rotavator dominated the sequence, a marked reduction in seedling numbers was predicted. The findings of a series of simulations are viewed in the light of existing methods of weed control based on soil cultivation, for example the stale seed bed technique.

6. The combined model provides the basis for a decision support system to aid the control of weeds. Additionally, it provides a research tool to improve understanding of the dynamics of the weed seed bank and the implications of seed bed preparations for future populations. The combined model has helped to identify areas of weed seed ecology requiring further study, essential for the development of true dynamic models.


The horticultural industry faces a continuing decline in the number of available herbicides for use in field vegetables. However, weed control remains essential to maintain crop yield and quality, and there is therefore a need to explore alternative control methods. The soil weed seed bank is the primary source of future weed populations and so provides a valuable resource for predictive management purposes. A greater understanding of the ecology and dynamics of weed seeds in the soil, through modelling and computer simulation techniques, may highlight potential future management strategies.

Vertical gradients in soil microclimate, such as water availability, temperature and light, occur in the field (Heydecker 1973; Fenner 1985), so that one of the major factors influencing the success of weed seed germination and emergence is the seed's position within the soil profile. Chancellor (1982) stated that weed seeds have mechanisms that respond to these gradients to prevent germination at depths from which the seedlings cannot emerge. Many species that require light, such as Matricaria recutita L., tend to germinate at or near the soil surface (Chancellor 1964). It has also been suggested that burial at greater depths increases the presence of toxic and potentially germination-inhibiting gases, thereby reducing germination (Benvenuti & Macchia 1995). Each species has a characteristic emergence response to burial depth and models have been developed that describe the emergence of a range of species (Mohler 1993; Prostko et al. 1997). Recent work has led to the development of preliminary empirical models that predict the emergence of nine common arable weed species over a range of depths of burial in a sandy loam soil (Grundy, Mead & Bond 1996; Grundy & Mead 1998). These depth response models were generated using observations of seeds in narrow bands, validated using data from seeds in evenly mixed broad layers and can be used to predict the emergence for any vertical distribution of seeds in soil.

The distributions of weed seeds in seed banks are spatially heterogeneous both horizontally and vertically. Narrow bands or evenly mixed broad layers of weed seeds represent extremes in distribution not normally observed in a typical horticultural field. Localized seed movement within the soil is due to many agents, including earthworms, mammals, insects, rain and frost. However, the principal source of seed movement and redistribution within the soil is cultivation (Roberts, Chancellor & Thurston 1977). Where subsequent seed return is prevented, different cultivation practices can give rise to distinctive vertical distributions of seeds in the soil profile (Froud-Williams, Chancellor & Drennan 1983). Similarly, after extended periods under a given cultivation regime, the distribution of viable weed seeds can become characteristic of that regime (Roberts & Stokes 1965). A number of studies have described this effect of tillage on seed bank composition and vertical distribution (Roberts 1963; Ball 1992; Clements et al. 1996). Models have been proposed to relate such distributions of seeds to weed emergence in the field (Mohler 1993).

Distributions of weed seeds resulting from cultivation can be quantified through direct soil sampling followed by physical extraction of either weed seeds (Yenish, Doll & Buhler 1992) or plastic or ceramic beads used to represent seeds (Cousens & Moss 1990; Staricka et al. 1990). There are examples of models that predict the horizontal movement of weed seeds (Howard et al. 1991; Brain & Marshall 1996), but few studies have modelled the vertical movement of weed seeds following cultivation. Most notably a transition matrix model was proposed by Cousens & Moss (1990) to simulate the vertical movement of weed seeds within the soil following cultivation by plough and rigid-tine. A similar approach, also incorporating changes in the age distribution, has been developed for Avena fatua (Gonzalez-Andujar 1997). Mead, Grundy & Burston (1998) further developed the transition matrix model approach for implements typical of horticultural seed bed preparation, sampling for both vertical and horizontal displacement of seeds.

Studies of seedling emergence from different depths and of the vertical distributions of seeds in different tillage systems are important. However, these two related areas of weed biology need to be combined (Forcella 1997). Jordan et al. (1995) used a transition matrix approach to develop a population-projection model for depth-structured weed seed populations of Abutilon theophrasti and Setaria viridis. However, there are few other examples.

The present paper describes the linking of a model that predicts emergence as a function of depth (Grundy & Mead 1998) with a model simulating the effect of typical horticultural cultivation implements on the movement of weed seeds in soil (Mead, Grundy & Burston 1998). The model system could be applied to both improving the prediction of seedling emergence from a known weed seed bank, and to identifying how different cultivation sequences could be used to modify weed seed distribution and subsequent emergence.

Materials and methods

The effect of burial depth on emergence

Grundy & Mead (1998) describe in detail the experiment to determine the response of weed seeds to burial depth. A series of artificial seed banks was constructed using cylinders filled with sterilized loam. Weed seeds were collected from the experimental fields at Horticulture Research International, Wellesbourne, UK (HRI). Three-hundred weed seeds of each of nine species abundant in the local weed flora, were either buried in narrow bands or thoroughly mixed with an appropriate quantity of sterile loam to form broad layers between the surface and known depths. The species chosen for study were: Polygonum aviculare L., Chenopodium album L., Solanum nigrum L., Tripleurospermum inodorum (L.) Schultz-Bip., Veronica persica Poiret, Stellaria media (L.)Vill., Capsella bursa-pastoris (L.) Medic, Veronica arvensis L. and Thlaspi arvense L. Weed emergence was recorded on an approximately weekly basis, with seedlings being removed and discarded once they had been recorded.

A single probit model did not provide an adequate description of the emergence response to increasing burial depth observed for the nine species, as previously discussed by Grundy, Mead & Bond (1996). Three alternative models, based on a known population size, were considered; a standard two-parameter probit model, a ‘control mortality’ probit model, and a quadratic probit model (Grundy & Mead 1998). This last model allowed for an overturning response, with the maximum probability of emergence occurring below the soil surface. Algebraically, all three models can be expressed within a single framework:

p=θ(1−Φ(a+b ln(depth)+c(ln(depth))2))(eqn 1)

where p is the proportion emerged and Φ is the cumulative normal distribution function. The standard two-parameter probit model is obtained when θ is one and c is zero. Similarly the control mortality probit model has θ less than one and c equal to zero, and the overturning, quadratic probit model has θ equal to one and c greater than zero. For the standard and ‘control mortality’ probit models, parameter b takes a positive value, whilst for the overturning probit model parameter b is negative. Estimated parameter values for the best-fitting models for each of the nine species are given in Grundy & Mead (1998, their Table 2).

Seed movement

Mead, Grundy & Burston (1998) previously described in detail the experimental procedure used at HRI to simulate the incorporation of weed seeds. Plastic beads (Moss Plastic Parts Ltd, Oxford, UK) were used to mimic weed seeds and the movement caused by four implements. The implements used were the spring tine (Kongskill, variable width from 1·4 to 2·0 m), rotavator (Dodswell, 2·0 m width), spader (Tomlin, 1·8 m width) and power harrow (Lely, 1·8 m width). Beads of different colours (3000 of each colour per plot) were either placed on the soil surface or buried at each of six depths (16·5, 13·5, 10·5, 7·5, 4·5, 1·5 cm). Sampling of the experiment was made on a grid. Three soil cores (diameter 8·5 cm) were taken at 0, 0·25, 0·5, 0·75, 1·0, 2·0, 3·0 and 4·0 m ahead of the line of impact. Cores were similarly taken at 0·25 and 0·5 m behind this line to account for beads being thrown backwards. At each distance from the line of impact, the three cores were taken spaced 0·25 m apart, the middle core being taken at the mid-point of the plot width. Immediately before each core was taken, the beads visible on the surface were recorded and removed. Each soil core was divided into a series of 3-cm sections: 0–3 cm, 3–6 cm, 6–9 cm, 9–12 cm, 12–15 cm and 15–18 cm. Sections of the soil core taken from the same depth, from each of the three cores at a given distance, were bulked together. The beads from each of these soil samples were extracted in the laboratory. The recovered beads, together with the 10 surface samples per plot, were separated into colours, counted and recorded.

Based on the proportion of each colour recovered from each depth and averaging across horizontal distance, simple transition matrices were developed to describe the pattern of vertical movement caused by each implement (Mead, Grundy & Burston 1998). The transition matrix for each implement contains the probabilities of seed movement between any pair of layers. The vertical distribution of seeds after cultivation by a particular implement can then be obtained by premultiplying a vector containing the numbers of seeds in each layer before cultivation by the appropriate transition matrix:

image(eqn 2)

where pij is the probability of moving from layer i to layer j, ni,t is the number of seeds in layer i before cultivation, ni,t+1 is the number of seeds in layer i after cultivation, and with the surface, 0–3 cm, 3–6 cm, 6–9 cm, 9–12 cm, 12–15 cm and 15–18 cm layers labelled as layers 1–7, respectively.

An initial assessment of the effect of each implement on the horizontal dispersion of beads was obtained by calculating the mean and standard deviation of the number of each colour of bead recovered at each horizontal sampling position.

The effect of horizontal dispersion on vertical seed movement

In the present study an initial model combining the effects of each implement on the horizontal and vertical movement of beads was produced. The effect of horizontal movement was summarized by the proportions of beads of each colour moved forwards, remaining at the point of impact or moved backwards. For each of these three subsets of the data (where appropriate), transition matrices were produced as described in Mead, Grundy & Burston (1998). In addition, for each of the three subsets of the data (where appropriate), diagonal matrices were produced containing the probabilities of horizontal movement from each of the layers. These probabilities are simply the proportions of beads of each colour moved forwards, remaining at the point of impact or moved backwards. The overall probabilities of beads being moved backwards from one layer to another are then obtained by postmultiplying the transition matrix for beads moved backwards by the diagonal matrix for backward movement (equation 3), with similar constructions for the other forms of horizontal movement:

image(eqn 3)

where bi is the probability of the horizontal movement backwards from layer i, pij is the probability of vertical movement from layer i to layer j for beads moved backwards, and bpij (equal to pij multiplied by bi) is the probability of movement backwards from layer i to layer j.

The vertical and horizontal distribution of seeds after cultivation by a particular implement can be obtained by combining the initial distribution with the three transition matrices as calculated in equation 3. Mathematically this is expressed by premultiplying a vector containing the numbers of seeds in each layer, at a particular horizontal position before cultivation, by each of the three transition matrices. The resulting values can be conveniently shown in a 7-row by 3-column matrix:

image(eqn 4)

where [bpij], [npij] and [fpij] are the vertical transition matrices for movement backwards, no horizontal movement and movement forwards; ni,t is the number of seeds in layer i before cultivation, and nib,t+1, nin,t+1 and nif,t+1 are the numbers of seeds in layer i after cultivation that have been moved backwards, remained at the point of impact or been moved forwards, respectively.

Combining the models of seed movement and the effect of depth of burial

Having produced the two separate models, linking them is straightforward. Because the movement model predicts the numbers of seeds in each 3-cm layer (and on the soil surface), the probabilities of emergence from each of these layers need to be obtained from the depth of burial model. These can be obtained by calculating the mean proportion emergence over the 1·25-mm bands contained in each of these layers as described in Grundy & Mead (1998). The surface layer is assumed to consist of the uppermost 1·25-mm band. The expected emergence for each species after a single pass of an implement is calculated by multiplying the probability of emergence from each layer by the number of seeds in that layer after cultivation. To assess the effect of a sequence of cultivations, the appropriate transition matrix for each implement is applied in the order that the implements are used in the field:

Final distribution = Tn*. .*T3*T2*T1* Initial distribution(eqn 5)

where TI is the transition matrix for the ith cultivation operation.

A computer implementation of the combined model was produced in matlab (matlab is a registered trademark of The MathWorks Inc., Natrick, MA), allowing the combined effects of various sequences of cultivation implements to be simulated. The effects of these sequences could then be assessed both in terms of the movement of seeds, and concerning the impact on seedling emergence for each of the nine species studied.


Depth of burial models for emergence

As shown in an earlier study (Grundy & Mead 1998), three of the species (C. album, P. aviculare, S. nigrum) displayed a non-monotonic response, with the greatest probability of emergence observed from a band other than the surface. For these species, and T. arvense, the quadratic probit model was found to give the best fit. The control mortality probit model gave the best fit for both V. persica and S. media, whilst a standard probit model gave the best fit for T. inodorum, C. bursa-pastoris and V. arvensis (Grundy & Mead 1998).

Vertical movement of seeds

Using the transition matrices developed earlier (Mead, Grundy & Burston 1998), it was possible to predict the vertical distribution after a single cultivation with each of the four implements, for any initial vertical distribution of seeds. The simplest initial distribution would be for all seeds to be on the surface of the soil. Hypothetically this could occur immediately after seed shedding onto a sterile soil. For each of the four implements, Fig. 1 shows the characteristic distributions produced following a single pass. Similarly, for another scenario, where the seeds are evenly distributed between the seven layers, each cultivation implement produces a characteristic redistribution of seeds between the original layers (Fig. 2). The effect of a sequence of cultivation passes on the vertical distribution of seeds can also be predicted by combining the appropriate transition matrices, as demonstrated in Mead, Grundy & Burston (1998).

Figure 1.

Simulated vertical distribution of 10 000 beads initially sown on the soil surface following one pass of (a) spader, (b) rotavator, (c) spring tine and (d) power harrow.

Figure 2.

Simulated vertical distribution of beads initially sown evenly down the soil profile (2000 beads at each sowing depth) following one pass of (a) spader, (b) rotavator, (c) spring tine and (d) power harrow.

General horizontal movement of seeds

The overall patterns of horizontal movement for the four cultivation implements are shown in Fig. 3. The results indicated that the majority of beads were recovered close to the point of impact, with, for example, 82% of those from the spring tine plots being recovered from the samples collected at the point of impact. Two of the implements, rotavator and power harrow, resulted in a considerable proportion of beads being recovered from behind the point of impact (81% and 42%, respectively), and for implements other than the spring tine beads were recovered at least 1 m beyond the point of impact.

Figure 3.

Observed horizontal distribution of beads sown evenly down the soil profile (3000 beads at the soil surface and each of 1·5, 4·5, 7·5, 10·5, 13·5, 16·5 cm below the soil surface) following one pass of (a) spader, (b) rotavator, (c) spring tine and (d) power harrow.

The effect of initial vertical position on the horizontal movement of seeds

The mean numbers (and standard errors) of beads of each colour (sowing depth) recovered from each of the 10 horizontal sampling points were calculated (Table 1). Overall, the recovery of beads for each of the implements was 9·0%, 6·7%, 4·2% and 4·4% for the spring tine, rotavator, power harrow and spader, respectively. The 30 soil cores sampled from each plot represented 3·4% of the total possible plot area.

Table 1.  The total number of beads recovered at each sampling distance from the point of impact from initial sowing depths, including the surface (3000 beads sown at each initial sowing depth). The data represent means and standard errors (in parentheses) from 30 soil cores (8·5 cm diameter) on each plot, following a single cultivation with a spader, rotavator, spring tine and power harrow
Depth sown (cm)
distance recovered from
point of impact
Surface 1·5 4·5 7·5 10·5 13·5 16·5 
–0·50 m0(0·0)0(0·0)0(0·3)1(0·5)0(0·0)1(0·3)0(0·3)
–0·25 m0(0·0)0(0·3)1(0·8)1(0·4)1(0·7)9(7·2)0(0·3)
0·00 m0(0·0)13(7·8)89(34·6)252(54·4)198(31·1)88(30·8)48(24·0)
0·25 m1(0·8)47(15·1)42(22·9)12(5·7)13(4·9)9(2·7)11(9·7)
0·50 m3(2·0)15(10·2)11(4·9)2(0·9)8(4·7)2(0·7)1(0·7)
0·75 m1(0·7)7(4·5)5(1·3)3(0·9)2(0·9)1(0·5)0(0·0)
1·00 m4(1·6)2(0·6)4(1·6)3(0·9)3(1·7)1(0·7)0(0·3)
≥ 2·00 m4(1·6)2(1·3)0(0·3)0(0·0)0(0·0)0(0·0)0(0·0)
–0·50 m12(6·4)24(20·1)27(23·0)17(16·3)17(16·0)3(2·8)0(0·0)
–0·25 m141(16·0)127(30·7)98(35·6)100(29·4)112(27·6)297(103·4)160(66·4)
0·00 m25(6·3)23(6·8)29(7·3)22(9·7)18(3·9)15(3·1)9(1·6)
0·25 m12(2·3)12(3·0)7(1·7)10(3·4)14(4·5)8(2·1)2(0·9)
0·50 m9(2·1)5(1·7)6(1·3)5(1·8)9(3·3)5(1·5)2(1·1)
0·75 m5(1·7)3(0·5)2(0·3)4(1·9)7(1·7)1(0·6)0(0·3)
1·00 m3(1·5)3(1·0)2(0·6)0(0·3)2(0·3)1(0·7)1(0·5)
≥ 2·00 m0(0·0)0(0·0)0(0·0)0(0·0)0(0·0)0(0·0)0(0·0)
Spring tine
–0·50 m1(0·3)0(0·0)0(0·0)0(0·0)0(0·0)0(0·0)0(0·0)
–0·25 m7(3·2)2(1·1)0(0·3)0(0·0)0(0·0)0(0·0)0(0·3)
0·00 m186(59·8)164(19·1)108(21·2)185(67·8)276(111·7)330(113·0)311(106·7)
0·25 m124(13·9)111(26·8)33(10·5)8(4·3)16(2·3)18(5·9)15(5·6)
0·50 m4(1·5)1(0·8)1(0·3)1(0·3)1(0·5)0(0·3)2(1·3)
0·75 m0(0·0)0(0·0)0(0·0)0(0·0)0(0·0)0(0·0)2(1·5)
1·00 m0(0·0)0(0·0)0(0·0)0(0·0)0(0·0)0(0·0)0(0·0)
≥ 2·00 m0(0·0)0(0·0)0(0·0)0(0·0)0(0·0)0(0·0)0(0·0)
Power harrow
–0·50 m1(0·5)2(0·3)1(0·3)0(0·3)0(0·0)0(0·0)0(0·0)
–0·25 m26(4·5)79(26·2)144(81·5)92(76·0)24(10·5)6(1·9)5(5·0)
0·00 m20(4·1)8(2·2)5(0·6)22(4·4)59(16·2)104(38·7)111(26·6)
0·25 m8(2·6)3(1·6)2(1·0)2(0·9)4(1·7)20(2·9)30(5·3)
0·50 m13(4·0)10(2·9)5(2·4)0(0·0)0(0·0)1(0·5)14(3·3)
0·75 m12(3·7)6(1·0)7(0·9)0(0·0)0(0·3)1(0·3)4(1·6)
1·00 m15(1·3)11(1·9)5(2·9)0(0·3)0(0·0)1(0·3)0(0·3)
≥ 2·00 m10(2·5)5(0·7)2(0·8)0(0·3)0(0·0)0(0·0)0(0·0)

For the spader, beads originally in the lower four layers were generally recovered at the point of impact (particularly so for those sown at 7·5 and 10·5 cm). In contrast, those in the upper three layers were more likely to be moved forward. Overall, less than 1·5% of the recovered beads were found behind the point of impact. Recovered beads that had been sown on the surface were evenly distributed across the horizontal sampling range, with some moving as much as 4 m, but the total recovery represented less than 0·5% of the number sown.

Following cultivation with the rotavator, the majority of beads (81%) were recovered behind the point of impact, with more horizontal movement, in general, from the upper layers.

For the spring tine the majority of beads (82%) remained at the point of impact. The only appreciable horizontal movement was from the upper three layers, but this forward movement was only over short distances (< 1 m). Again only a small percentage of recovered beads (0·5%) were found behind the point of impact.

The effect of the power harrow was to move large numbers of beads to positions both behind and in front of the point of impact (42% and 21%, respectively). However, patterns of horizontal movement from the different sowing depths were more complex than those seen for the other implements. Beads from the lower two layers generally remained at the point of impact with some forward movement. In contrast, those sown at 1·5 or 4·5 cm tended to be moved backwards but with some beads moved a substantial distance forward (13% and 4% > 1 m, respectively). Beads sown at 7·5 and 10·5 cm showed an intermediate response, either remaining at the point of impact or being moved a small distance backwards. Finally, beads sown on the surface were spread across the whole horizontal range.

A simple approach to summarizing the horizontal movement from each layer was to consider the proportions of beads moved either backwards or forwards, or remaining at the point of impact (Table 2). Because, as described above, the spader and spring tine resulted in negligible backward movement, this category was combined with no movement for these implements.

Table 2.  Probabilities of horizontal movement within each of the seven layers and overall
 Vertical position (cm)SpaderRotavatorSpring tinePower harrow
Surface– 0·74– 0·26
0–3– 0·77– 0·66
3–6– 0·74– 0·85
6–9– 0·76– 0·79
9–12– 0·72– 0·28
12–15– 0·92– 0·04
15–18– 0·92– 0·30
Overall– 0·81– 0·42
No horizontal movement

Effect of horizontal movement on vertical transition matrices

Incorporating the effects of horizontal movement using the three categories described above has further developed the transition matrix model presented in Mead, Grundy & Burston (1998). The resulting transition matrices are shown in Table 3. The highlighted diagonal in each transition matrix indicates the probability of no vertical movement from each layer, with the upper ‘triangle’ containing the probabilities of upward movement and the lower ‘triangle’ those of downward movement.

Table 3.  Transition matrices (see equation 3) for the vertical movement of seeds for a specified direction of horizontal movement. Values expressed as probabilities. Within each matrix, figures in each column give the probabilities of movement from a given initial depth, and those in each row give the probabilities of movement to a given final layer. Initial depths from left to right are: surface, 1·5 cm, 4·5 cm, 7·5 cm, 10·5 cm, 13·5 cm and 16·5 cm. Final layers from top to bottom are: surface, 0–3 cm, 3–6 cm, 6–9 cm, 9–12 cm, 12–15 cm and 15–18 cm
Direction of horizontal movementSpaderSpring tine
No horizontal movement  
Forward horizontal movement  
 RotavatorPower harrow
Backward horizontal movement  
No horizontal movement  
Forward horizontal movement  

Comparison of the transition matrices for the spader indicated a greater tendency for upward movement from the lower layers where forward movement had occurred, and a greater tendency for downward movement from the upper layers where no horizontal movement had occurred. As surface sown beads were only recovered forwards of the point of impact, there was no information about the vertical movement of these beads when no horizontal movement had occurred.

The transition matrices for the spring tine show that beads were more likely to stay in the same vertical position or move up the profile where there was no horizontal movement, and were more likely to move down the profile where there was forward movement.

For the rotavator, the probability of upward movement from the bottom two layers was low for beads moved backwards and high for those moved forwards, with beads left at the point of impact showing an intermediate response. Conversely, the probability of downward movement from the upper or middle layers was greater for beads moved backwards than for those either left at the point of impact or moved forwards.

For the power harrow two distinct patterns were apparent. For the lower five layers, beads that were moved backwards tended to stay in the same vertical position or move down one layer, whilst those that were moved forward tended to move up the profile. Those that remained at the point of impact showed an intermediate response. Beads from the upper two layers showed a greater tendency for downward movement when moved forward or left at the point of impact.

Linking models for movement and depth of burial

The effects of a single pass of each cultivation implement on the subsequent weed seedling emergence for both of the simple initial seed distributions considered earlier (Figs 1 and 2) and for each of the nine species studied, are presented in Table 4. For most species, where seeds were initially only on the soil surface, a single pass of any implement resulted in a dramatic reduction in emergence compared with the predicted response following no cultivation (Table 4). For the four species (P. aviculare, C. album, S. nigrum and T. arvense) modelled using the quadratic probit function (Grundy & Mead 1998), however, the simulation suggested that cultivation would often result in an increase in emergence. Where an initial uniform vertical distribution was assumed, the effect of cultivation was less pronounced, but generally resulted in a reduction in emergence. Again, the main exceptions were for those species showing an overturning emergence response to depth (Table 4). It should be noted that the predicted emergence in Table 4 was based purely on the position of seeds following cultivation and therefore does not account for any direct effect that cultivation may have on germination/emergence. In addition it is assumed that sequences of cultivations are additive, or that successive cultivations are performed with a significant interval between them.

Table 4.  Simulated seedling emergence over a 1-year period for nine weed species following one pass of a spader, rotavator, spring tine or power harrow or after no cultivation. Data presented as a percentage of the number of seeds sown
 SpaderRotavatorSpring tinePower harrowNone
10 000 seeds sown initially on the soil surface
Veronica persica2·63·716·313·544·2
Stellaria media3·65·522·919·651·7
Tripleurospermum inodorum2·53·314·811·751·8
Polygonum aviculare0·30·51·91·80·6
Veronica arvensis2·12·615·011·164·4
Chenopodium album1·22·06·26·02·5
Solanum nigrum7·210·220·120·32·3
Capsella bursa-pastoris2·43·110·98·933·7
Thlaspi arvense1·01·56·45·46·6
14 000 seeds evenly distributed between the seven layers (2000 seeds per layer)
Veronica persica4·03·05·65·88·5
Stellaria media5·94·48·38·510·8
Tripleurospermum inodorum3·72·75·05·19·2
Polygonum aviculare0·50·40·80·80·5
Veronica arvensis3·22·24·44·510·4
Chenopodium album2·01·62·72·81·8
Solanum nigrum10·17·911·711·67·6
Capsella bursa-pastoris3·32·54·24·36·7
Thlaspi arvense1·61·22·22·33·2

The simulated vertical distributions of seeds, following four contrasting sequences of implements, are shown in Fig. 4. Each simulation started with 10 000 seeds on the soil surface. A suggested sequence (spader, rotavator, spader, spring tine) that might be used in horticultural practice (J. Brandreth, personal communication) produced the distribution shown in Fig. 4b. This sequence left 53% of the seeds in the top 6 cm of the soil profile, and moved only 24% of the seeds to below 12 cm. The power of the simulation approach is illustrated with the other three hypothetical sequences. These sequences were chosen to illustrate how this approach can be used to identify potential management strategies. The distribution shown in Fig. 4a left a greater percentage (61%) in the top 6 cm and moved only 12% below 12 cm. Such a sequence could be used within a stale seed bed strategy. In contrast, the other two sequences (Fig. 4c,d) reduced the percentage of seeds left in the top 6 cm (47% and 31%, respectively), simultaneously increasing the percentage below 12 cm (23% and 41%, respectively). These sequences suggest possible control strategies for weed species that are not persistent within the seed bank.

Figure 4.

Final simulated vertical distributions of weed seeds following four contrasting sequences of implements. The four sequences are (a) spader, spader, spader; (b) rotovator, power harrow, power harrow, spring tine; (c) spader, rotovator, spader, spring tine; and (d) spader, rotovator, rotovator, rotovator, spring tine. Subsequent predicted seedling emergence from each final vertical distribution of 10 000 seeds, initially shed on the soil surface only, is given for nine weed species. Percentage change refers to increase or decrease in total weed emergence relative to sequence (b).

For each of the sequences, the predicted numbers of seedlings emerging from each vertical layer for each of the nine species modelled are presented alongside the distributions (Fig. 4). Where the number of seeds present in the top 6 cm was reduced, this was accompanied by a corresponding decrease in the number of emerged seedlings for all species. The reductions in emergence seen when comparing sequences (b) and (d) with the worst-case scenario (a) were achieved through a consistent decrease in seedling emergence from the top three layers. However, a comparison of sequences (a) and (c) showed little variation in the emergence from both the surface and 3–6 cm layer, the overall reduction in emergence in sequence (c) being almost entirely attributable to the dramatic reduction in emergence from the intervening layer.

The contrasting effects of different cultivation sequences on different species were highlighted by the responses for V. arvensis and S. nigrum. Veronica arvensis showed the largest percentage increase (28%) in seedling emergence when comparing sequences (a) and (b), only a small percentage decrease (10%) when comparing sequences (c) and (b), and the equal largest percentage decrease (42%) when comparing sequences (d) and (b). In contrast, S. nigrum had a much smaller percentage increase (16%) for the first comparison and a much smaller decrease (36%) for the third. This marked difference in predicted seedling emergence was caused by the difference in the shape of the depth of emergence response curves for the two species (Grundy & Mead 1998).


Emergence depth response

Two basic patterns of decrease of emergence in response to increasing depth have been found in previous studies on the effect of seed burial, as reviewed by Mohler (1993). It was noted that, whilst half conform to a monotonic decrease in emergence with increasing depth, the others have a non-monotonic response in which shallow burial increased emergence but deep burial reduced emergence. Bliss & Smith (1985) observed this non-monotonic response in C. album, where germination increased in response to covering with 2 mm of soil. These observations would appear to be in agreement with the findings of Grundy, Mead & Bond (1996) and Grundy & Mead (1998). Prostko et al. (1997) suggest that the Fermi–Dirac distribution function could be used to describe the emergence response to depth for Bromus tectorum L., Sorghum halepense (L.) Pers. and Malva pusilla Sm. This function is a reparameterization of the logistic function and effectively has the same shape as the standard probit curve used in Grundy & Mead (1998).

Seed movement and incorporation

Mapping of seed banks can be used to identify patches of future weed infestations and thus help target control strategies. However, within patches there can be a large variation between samples (Deassaint, Chadoeuf & Barralis 1991) and there can be a significant lack of correlation between the seed bank and resulting weed emergence. For example, the relationship between seed banks and seedling emergence can vary over time and space (Cardina, Sparrow & McCoy 1996). A major factor is that weed seeds are spatially distributed both vertically and horizontally. Where there is greater soil disturbance there is generally less correlation between the seed bank and seedling emergence, possibly due to increased mixing and burial of seeds (Cardina, Sparrow & McCoy 1996). While several models have been developed to simulate the vertical distribution of seeds following cultivation (Cousens & Moss 1990; Staricka et al. 1990; Gonzalez-Andujar 1997) many do not incorporate a horizontal movement element within the simulation. Similarly, Marshall & Brain (1999) have developed a model for the horizontal movement of seeds following cultivation, but vertical movement has not been included. Extending models to include both the horizontal and vertical movement of seeds may have future implications for the understanding of the development and stability of patches of weeds. For example, a three-dimensional model, based on the matrix of Cousens & Moss (1990) has been developed to study the spatial redistribution of tubers of yellow nutsedge Cyperus esculentus (Schippers et al. 1993).

Mayer, Albrecht & Pfadenhauer (1998) have demonstrated the importance of collecting data over a wide sampling range in order to assess the potential for horizontal movement, where seeds were found to be transported as far as 23 m. A number of models have been developed to simulate this horizontal movement through cultivation implements, and these can be used to assess the spread of species. For example, the effect of cultivation using a rotary harrow on the dispersal of Bromus sterilis L. and Bromus interruptus (Hackel) Druce, has been quantified using mathematical models (Howard et al. 1991). Similarly, Fourier transforms have been used to map patch development following successive cultivations (Brain & Marshall 1996). However, these models do not quantify vertical movement. The original model of Mead, Grundy & Burston (1998) assumed that averaging over horizontal position gives a realistic estimate of the probability of a seed moving from one vertical position to another. It is evident from the present study that the probabilities of vertical movement do not remain constant over horizontal distance. Rew & Cussans (1997) observed that surface sown seeds moved further following cultivation than those buried 10 cm below the soil surface, following sequences of implements (including rotary power harrow, drill and tine). This is in general agreement with the findings of the present study. Rew & Cussans (1997) also found that the majority of seeds were detected between the point of impact and 1 m forward of this point. In the present study, however, substantial numbers of beads were recovered behind the point of impact for both rotavator and power harrow. Rew & Cussans (1997) used seed germination to determine seed movement, i.e. their data would represent surface and 1·5-cm depth data in our studies; their work consequently provides an underestimate of the true response. In addition Rew & Cussans (1997) were not able to determine the depth from which seedlings had emerged, while in our study both the initial and final depths of the beads could be identified. For the rotavator and power harrow many of the beads recovered behind the point of impact were raised from deeper initial layers than those used in the Rew & Cussans (1997) experiment. It should be noted, however, that our model assumed an additive effect of multiple cultivations, whereas this has been demonstrated not to be the case in some situations (Rew & Cussans 1997). Rew & Cussans (1997) also found that there were species differences in the magnitude of seed movement, with smaller seeds moving further than larger seeds. However, Soriano et al. (1968) found no difference in the vertical distribution of seeds from two species specifically chosen for their dissimilarities in seed coat and geometry.

Combining models for systems

A wide range of different weed seed bank distributions and compositions can be generated using a range of different tillage operations (Feldman et al. 1997). We have demonstrated how our model for the vertical movement of seeds following cultivation can be combined with a model for the effect of depth of burial on emergence to manipulate the seed bank to our advantage. One example of where this could be useful is in the stimulation of emergence using the stale seed bed technique (Johnson & Mullinix 1995). Manipulation of the vertical distribution of weed seeds could also be used to target specific problematic species or even populations within a species, through exploiting dissimilarities in emergence characteristics. For example, Kremer & Lotz (1998) have studied differences in the emergence characteristics of two biotypes of S. nigrum in order to manage for triazine resistance selectively. In the present study, in contrast to many of the other species, the predicted emergence of S. nigrum was significantly increased following one pass of either the spring tine or power harrow compared with leaving the seeds at the soil surface. Webster, Cardina & Norquay (1998) have also demonstrated how no-tillage and the mouldboard plough can be used to modify emergence of A. theophrasti. Alternatively, cultivation operations could be used to reduce weed emergence by placing seeds in the lower part of the profile (Froud-Williams 1983).

Future developments

Presently the transition matrix model requires expansion to include other implements and soil types and the possible differential effects on seeds of different sizes. It will also be necessary to combine it with other aspects of weed dynamics, including competition both within weed species and between crops and weeds (Aikman et al. 1995), efficacy of different control measures, seed return and seed persistence. The current studies were performed on a sandy loam soil. However, to enable the depth of emergence model to have wider application, it needs to be adaptable to different soil types and conditions. Physiologically based models may offer scope for universal application across a range of soil types, such as those relating burial depth, soil penetration resistance and seed weight to pre-emergence growth (Vleeshouwers 1997). Similarly, Prostko et al. (1997) suggest that the shape of the Fermi–Dirac distribution could be correlated with abiotic effects such as soil moisture and soil texture.

Seed return is arguably the greatest variable factor in any model attempting to understand the dynamics of seed banks. Even small numbers of weeds surviving at the end of the season and allowed to set seed have the potential to quickly ‘restock’ the seed bank. Jordan et al. (1995) have included within their simulation studies density-dependent matrices specifically for seed production.

Currently the depth of emergence model described only gives an estimate of the proportion of emerged seedlings from a given depth of burial, and does not include information on the fate of those seeds that do not emerge as seedlings. In particular, the effect of burial and burial depth on dormancy is extremely species specific. In the species Hordeum murinum L. dormancy was not affected by burial depth (Popay & Sanders 1975), while Zorner, Zimdahl & Schweizer (1984) showed that persistence of Kochia scoparia, which was regulated by dormancy retention, increased with burial depth. An approach to modelling the effect of depth on persistence could be achieved via models for the viability of seed stored under different environmental conditions (Ellis & Roberts 1980; Mead & Gray 1999). Existing studies relating seed weight and persistence could also be utilized to enhance the dynamics of a future model (Thompson, Band & Hodgson 1993).

Another fate of weed seeds relating to burial depth is lethal germination. Sanchez Del Arco, Torner & Fernandez-Quintanilla (1995) demonstrated that lethal germination of Avena sterilis ssp. Ludoviciana accounted for a significant proportion of the seed bank depletion of this species. The proportion of seed bank depletion due to lethal germination increased with increasing depth. Similarly, depth of burial may affect the probability of a seed coming into contact with hazards such as predators. For example, in no-tillage systems, where seeds are left on the soil surface, the likelihood of predation increases (Andersson 1998). In the present study, it is not possible to differentiate whether the reduction in emergence of C. album and S. nigrum observed at the soil surface was due to poor conditions for germination, a reduction in the number of viable seeds available for germination through lethal germination or predation. These examples emphasize the importance of the effect of seed position within the soil profile on seed bank dynamics and the potential for management opportunities.

Differences in crop–weed competition are dependent on the distribution of seeds over depth. This is due to the effect of burial depth on the pre-emergence time–course and hence the relative emergence times of crop and weeds (Håkansson 1979; Vleeshouwers 1997). Consequently, crop–weed competition models could benefit from improved knowledge of the vertical distribution of weed seeds within the soil profile.

The model currently assumes that all weed emergence occurs after the final cultivation, i.e. only cumulative emergence in a season. This is a simplification of reality, where, if conditions are suitable, emergence may occur between cultivations, depending on the season and species concerned. For example, the light sensitivity of many species is seasonal (Milberg & Andersson 1997). It is also possible that where conditions are not conducive to germination, there can be considerable delays in the flush of weed emergence. Delays in weed emergence of up to 13 weeks following cultivation have been observed where the prevailing weather has been exceptionally dry (Bond & Baker 1990). It is therefore important that the model includes information about the timing of cultivation with respect to environmental conditions. This information would also be essential in improving predictions/simulations, because the prevailing weather and the relative timing and frequency of multiple passes of an implement could have significant effects on the magnitude of seed movement due to changes in soil moisture and texture. Rew & Cussans (1997) observed that multiple cultivations made within a short period of time did not have an additive effect on seed movement owing to each pass of an implement altering the tilth encountered by each subsequent pass.

Mohler & Galford (1997) have demonstrated that the action of cultivation itself can have a stimulatory effect, independent of the direct effects of burial depth. Their studies, however, only considered the direct effect of the interaction between cultivation and depth on the emergence response through using pregerminated seed, and not any similar effects of these factors on germination. There are several examples of how cultivation can directly affect the soil structure in such a way as to promote germination and emergence. For example, the destruction of clods can provide better soil–weed seed contact. therefore producing conditions conducive to germination (Johnson & Mullinix 1995). Pareja, Staniforth & Pareja (1985) have hypothesized that this increase in germination is linked with a breaking of dormancy as seeds are released from within clods. In contrast, Cussans et al. (1996) suggest that emergence is enhanced by coverage with coarser aggregates due to increased access to light and air. Jensen (1995) demonstrated the relationship between the number of cultivations and increased levels of emergence.

Both the direct and indirect effects of cultivation discussed here need to be quantified so that they can be included in the interaction between the seed movement model and that for the effects of depth of burial on emergence. It is clear that although a number of models have been developed to target specific processes in the incorporation and distribution of weed seeds and the subsequent seedling emergence, few presently attempt to combine the processes involved. However, there is the danger that over-complication through multiple linking of models could potentially also lead to greater capacity for error. Jordan et al. (1995) state that the numerous and diverse processes involved in seed banks make the study of weed population dynamics a daunting challenge; future models may be most useful when developed as conceptual schemes allowing the study of events, processes and interactions on their effect on the seed bank. For example, when considering the complex factors involved following cultivation, seed depth may be the single most important element in population dynamics (Buhler, Harzler & Forcella 1997). As the suite of models described is developed further, it will be important to test the sensitivity of the system and to compare simulated results with field observations.

The model system presented in this study is intended to serve two purposes. First, the system has the potential to be used as a decision support aid. Secondly, it provides a research tool that can be used to help target our future investigations appropriately and to identify areas of weed seed ecology requiring further study, thus leading to the development of true dynamic models.


This research was funded by the Ministry of Agriculture, Fisheries and Food. The authors wish to thank W. Bond for his advice, K. Dent for her help during sampling and J. Brandreth for his skilful use of the cultivation implements that made the experiment possible.