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Keywords:

  • arable land;
  • dispersal;
  • Fast Fourier Transforms;
  • probability distribution function;
  • weeds

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

1. To assess the impact of soil cultivation on the horizontal movement of seeds in arable soil, plastic beads and barley or triticale seeds were used as seed models. Different coloured beads were introduced in the field immediately before each of five cultivations: ploughing, two tine cultivations, harrowing and seed drilling. Beads were recovered from 20-cm soil cores divided into four 5-cm deep soil horizons.

2. After a typical cultivation sequence of five operations, beads were found up to 15 m from their source, although most beads were found within 2 m. Most beads were recovered from the surface 5 cm of the soil profile, except for those introduced onto the surface or at 20 cm depth before ploughing, which were concentrated below 10 cm.

3. Regression analysis was used to determine the pattern of bead movement by seed drilling. A novel analysis using Fast Fourier Transforms established the probability distribution functions of the remaining cultivation operations for horizontal movement. Using the final seed distributions, the effects of each cultivation were sequentially deconvoluted and the probability distribution functions smoothed. The proportions of beads moved were also calculated.

4. Ploughing and seed drilling moved seed the least distance compared with other cultivations. The mean distances moved were 0·36 m and 0·26 m, respectively. Tine cultivations moved beads 0·71 m and 1·21 m, while harrowing moved seed a mean distance of 1·58 m. Cultivation sequences based on ploughing are likely to limit seed movement in soil.

5. The Fourier deconvolution approach has potential for predicting future seed distributions and thus the spatial behaviour of weed patches within fields.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

The survival of annual plant species is dependent on the return of viable propagules to situations suitable for germination and growth. Opportunistic plant species, many of which are adapted to dispersal by wind, usually exploit conditions that are only temporarily available, often resulting from disturbance. In contrast, ruderal weed species typical of cultivated arable land often have few adaptations for dispersal and may depend on a persistent bank of dormant seed for survival (Roberts 1981). Both plants and seeds of these arable weed species are often patchily distributed within fields (Marshall 1988; Chauvel, Gasquez & Darmency 1989).

The physical movement of seeds and propagules both within and between fields has important implications for the spatial distribution of species and the persistence of their populations. A spatial population model of Avena sterilis L. demonstrated that inclusion of dispersal and environmental heterogeneity had marked effects on the demography of the weed (Gonzalez-Andujar & Perry 1995). An understanding of the spatial dynamics of arable weed species is therefore likely to be important for their control, for reducing unnecessary use of herbicides (Lutman & Rew 1997), and possibly for the conservation of uncommon cornfield weeds, such as Centaurea cyanus L. (cornflower) in the UK.

Seeds of arable weed species may be dispersed within the field by a variety of means (Marshall & Hopkins 1990). The crop-harvesting machinery may move seed significant distances (Ballaréet al. 1987; Howard et al. 1991). Soil cultivations may also move seed. Studies on the vertical movement of seeds in the soil were made by Moss (1988) and predictive models were used to show differences in cultivation technique on weed seed densities in the soil profile (Cousens & Moss 1990). However, there have been few studies of the horizontal movement of seeds in soil. A study by Fogelfors (1985) indicated that 80% of seed remained within 1·5 m of its source following harrowing. More recently, Mayer, Albrecht & Pfadenhauer (1998) examined the movement of different seeds on a range of tillage implements, demonstrating movement of individual seeds over significant distances and the potential to move in entrained soil from field to field.

The ingress of potential weeds from adjacent habitats into arable crops is also dependent on vegetative growth or on establishment following the dispersal of propagules. The distribution patterns of seedlings in arable fields indicate that some species, particularly those with competitive-ruderal strategies (sensuGrime 1974), disperse from field edges into the crop (Marshall 1989). However, the significance of that spread for the maintenance of populations in the field proper has yet to be established. One factor affecting such processes may be the movement of seed in the soil after shedding.

This paper describes an experiment in which seeds and seed models were used to investigate the effects of different soil cultivations on seed spread. Work by Moss (1988) has demonstrated the similarities of movement in soil between seeds of different species and plastic beads, both of which were used in the work described here.

Methods

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Six 1-m2 plots were located between 5 and 7 m apart in an east–west direction across an arable field near Bristol, UK (51°25′N, 2°40′W; UK National Grid Reference ST 555703). The locations of these plots, which were used as the source of introduced beads and seeds, were surveyed so that they could be re-established precisely after each subsequent soil cultivation. Initially, the six square 1-m2 source areas were excavated to 20 cm and 20 000 plastic yellow beads spread at that depth in each. The soil was replaced, compacted to field level and 20 000 navy blue beads spread on the surface of each plot. The beads, which were the raw material for plastic injection mouldings, were cylindrical with dimensions of c. 1 mm diameter and 3 mm long. Data given by Fogelfors (1985) for a cultivation with a harrow indicated that about 1% of seed might be expected to reach 4·5 m from its origin, giving a bead density of 200 m−2 from the source density used in this experiment. The area was mouldboard ploughed on 11 September 1986 (Table 1). The plots were resurveyed and green plastic beads placed on the soil surface of the source plots prior to spring tine cultivation in a northerly direction. Subsequently, the plots were tine cultivated in the southerly direction with purple beads and seeds of barley (cv. Igri) on the soil surface. Purple beads and seeds of triticale (cv. Lasko) were then placed on the soil, before blench harrowing to the north. The final operation was seed drilling winter wheat to the south on 19 September 1986, prior to which sky-blue beads were placed on the source squares. The five cultivation operations imposed on the area on a north–south axis, comprising ploughing with a reversible mouldboard plough, two spring tine cultivations in opposite directions, one pass with a blench harrow and seed drilling of wheat, were typical of those used to establish winter cereals on loam soils in this area of the UK. Bead and seed numbers were estimated from mean weights (Table 1). Each plot received every cultivation in the sequence, with different coloured beads placed on the soil prior to each. Thus the sky-blue beads were only subject to drilling, but navy beads were subject to all cultivations.

Table 1.  Details of soil cultivations imposed on the study site, with data on plastic beads and crop seeds placed in each 1-m2 source area prior to each cultivation. Beads and seeds were spread evenly across each source area, at a density of 20 000 m–2
Seed modelLocationSeed weight (mg)CultivationDirectionDate
Yellow bead20 cm depth16·03Mouldboard ploughSouth11.09.86
Navy beadSurface 9·32Mouldboard ploughSouth11.09.86
Green beadSurface15·95Spring tineNorth15.09.86
Orange beadSurface15·25Spring tineSouth17.09.86
BarleySurface44·25Spring tineSouth17.09.86
Purple beadSurface11·57Blench harrowNorth18.09.86
TriticaleSurface37·35Blench harrowNorth18.09.86
Sky-blue beadSurface12·07Seed drillSouth19.09.86

Different coloured beads on the soil surface were initially counted in contiguous 10 × 10-cm squares from the centre of the source area in the directions of cultivation (north and south). The counts of beads on the surface were made on 19 September 1986, after the completion of cultivations, to distances of 5 m north and 3 m south of the source area. Beads on the surface were also counted in 0·01-m2 squares in six other directions (W, NW, NE, E, SE and SW) from the edges of the source areas, to assess movement away from the north–south axis (Fig. 1). The numbers of germinated barley and triticale plants were counted in similar quadrats on 24 October 1986, 5 weeks after sowing. At this time, bead and plant densities were low at distances greater than 3 m south and 5 m north from the source. Therefore, they were counted in larger 0·25 × 1·0-m quadrats placed at 0·5-m intervals up to 20 m north and 5 m south of the source area.

image

Figure 1. Layout of surface bead counts in 0·01-m2 quadrats close to the 1-m2 source area and the location of 30 × 30 × 20-cm deep soil samples.

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During the early summer of 1987, buried beads were retrieved from soil samples taken at 1-m intervals to distances 15 m north and 5 m south from the first four plots only, involving the transport of in excess of 1·7 t of soil. Three samples were removed from each 1-m2 source area, one from the centre and two at 0·5 m from the centre, straddling the north and south edges of the source area (Fig. 1). Samples were taken by hammering a 30 × 30-cm open steel box into the ground. One side of the box was removed and four soil samples excavated in 5-cm deep sections to a depth of 20 cm. Samples were washed out over sieves and the beads recovered and counted. In July 1987, the numbers of barley and triticale inflorescences were counted in 0·25-m2 quadrats, at 1-m intervals away from four of the plots. As severe lodging had occurred, counts were made from 2 m either side of the source areas.

Statistical analysis

As the bead densities recorded at different distances from the source are the result of a series of superimposed separate operations, a novel method of quantifying the effects of individual cultivations was required. This was possible for overall lateral movement but not for vertical movements, where sequential operations might move seeds up or down.

The effect of a cultivation can be quantified in terms of the proportion of seeds reaching any chosen distance from the source. This defines the probability distribution function (p.d.f.) of the distance a seed is moved by a cultivation. Various statistics can be derived from this, such as the mean distance moved and the distance from the source that will contain 50% of the beads.

Two separate approaches were required: first, for the bead profiles resulting from the last cultivation (the sky-blue beads), and secondly, for the other coloured beads that had been subject to more than one cultivation. The aim in both cases was to estimate the p.d.f. of the distance a seed is moved by a cultivation.

Estimating the p.d.f. for the final cultivation

The effect of the last cultivation, seed drilling, could be investigated directly using the final positions of the sky-blue beads. The observed distribution of the sky-blue beads at distance d, g(d), is the convolution of the initial distribution of beads (evenly spread within a 1-m square) at distance d, h(d), and the p.d.f. of the distance, x, moved by drilling [denoted by f (x)]. Thus if h(d) is the initial density of beads at distance d from the centre of the 1 m square, then:

  • image(eqn 1)

where A is the bead density per unit length of a transect of a chosen width. The convolution of f(x) and h(d) predicts g(d) generally as:

  • g(x) = ∫h(df (d-v)dv.(eqn 2)

For the specific h(d) above, g(x) is given by:

  • image(eqn 3)

A reasonable assumption is that a proportion, p, of the beads is moved, and the distance they are moved has an exponential distribution (i.e. the probability of a bead moving a given distance decreases with the distance moved). This was specifically chosen as a description of the dispersion process as it assumes that after a bead has been moved any chosen distance, the p.d.f. of the distance left to move is still exponential with the same mean, thus incorporating a ‘lack of memory’ property which we think is likely to hold in practice. Then the p.d.f. of the distance moved, x, denoted by f(x), is:

  • f (x) = (1-p) × δ(x) + p × λex, x ≥ 0(eqn 4)

where δ(x) is the Kronecker delta function, having a value of 1 at x = 0 and 0 otherwise, p is the proportion of beads moved by the cultivation, and λ is the reciprocal of the mean distance moved by the ‘mobile’ beads. This is in contrast to Rew & Cussans (1997), who assumed that all seeds in their experiment moved but that the distance moved had the log-normal distribution. When the distribution in equation 4 is substituted in the convolution equation 2 above, the final observed distribution of beads, g(d), is as below:

  • image(eqn 5)

where d is the distance moved by the cultivation.

The parameters λ, p and A (the number of ‘sown’ beads in a strip of width 2Δ[Δ = 15 cm] in the original 1-m2 area) were estimated by fitting equation 5 to the observed profile where the fitted counts in the soil core at distance d (with a width of 2Δ) are given in Table 2. The observed counts were assumed to have a Poisson distribution and fitted using maximum likelihood, using Genstat (Genstat Committee 1993).

Table 2.  Equations used to predict counts of sky-blue beads at different distances for soil cores of width 2Δ
Distance (x)Predicted bead count/A
  1. A = Number of beads on a rectangular patch of width 2Δ and length 1 m.

  2. p = proportion of seeds moved by the cultivation.

  3. λ = 1/(mean distance moved of moved beads).

  • image
  • image
 
  • image
  • image
  • image
  • image
  • image

Estimating the p.d.f. for the other cultivations

The distributions of the beads, other than the sky-blue that is produced by drilling alone, are the result of increasing numbers of operations. The distribution of purple beads is that produced by harrowing and drilling, that of orange beads by drilling, harrowing and one tine cultivation, and so on. We denote the p.d.f. of the observed distances away from the centre of the initial square after i cultivations by gi(d), where d is distance from the centre of the square to the north or south. We assume that the ith cultivation will have an associated probability distribution function (p.d.f.) describing the probability of a bead reaching a particular distance, x, denoted by fi(x). Then the p.d.f. of the distribution of beads after i cultivations, gi(d), is the convolution of the distribution after (i – 1) cultivations, and the ith cultivation effect, that is:

  • image(eqn 6)

Brain & Marshall (1990) developed a novel technique using Fast Fourier Transforms to deconvolute this integral numerically using the pairs of observed profiles, to give point estimates of the underlying cultivation effect p.d.f.s fi(x). This relied on the property that if the Fourier Transform of a function is denoted by f*(s) then:

  • gi*(s) = f *(s) × g*i-1(s)(eqn 7)

so that the Fourier Transform of the cultivation p.d.f., f*(s), is simply (g*i(s)/g*i – 1(s)). Their technique is presented in more detail in Brain & Marshall 1999). The Fourier Transform of each observed pattern was made, then the Fourier Transform of the cultivation effect could be calculated by dividing the later pattern by that for the earlier one, and the result back-transformed to give an estimate of the underlying cultivation effect. All calculations were made using Mathcad (Anonymous 1993). When these p.d.f.s were plotted against distance moved they often oscillated wildly for distances moved in a negative direction, i.e. in the opposite direction to the cultivation, a counter-intuitive result (examples are given in Fig. 2). This is an artefact of the estimation process in the presence of variation, as for negative distances the p.d.f. is effectively zero. The oscillating estimates are thus random variables with an overall mean of zero. However, it is possible to ‘smooth’ these p.d.f.s by multiplying the Fourier Transform of the estimated p.d.f. by a smoothing function before back-transforming. This smoothing effectively takes the average of the p.d.f. over an interval of S either side of the observed point, i.e. by estimating:

image

Figure 2. Examples of estimated p.d.f.s derived from Fast Fourier deconvolutions of four different cultivations. Initial p.d.f.s are shown without smoothing and subsequently with smoothing. Arrows show direction of cultivation.

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  • image(eqn 8)

rather than f (x). Typical smoothed p.d.f.s are given in Fig. 2, and show that the smoothing has largely removed the oscillations. The exponential distribution, which had worked well for the seed drilling results, generally showed evidence of lack of fit, so the Gamma distribution was used instead, which has the form:

  • image(eqn 9)

with the mean being (β/α), and standard deviation (Üq1β/α). The estimated means and standard deviations of the distribution are presented in the results for the experiment covered here. The Gamma distribution was chosen as it is a generalization of the exponential distribution, with similar properties to the log-normal distribution used by Rew & Cussans (1997). The log-normal distribution, by contrast, does not include the exponential distribution as a special case. It has been noted previously that the exponential distribution has a ‘lack of memory’ property, so that the probability of a bead being deposited in any time interval is only dependent on the length of the time interval; the Gamma distribution has a similar interpretation, but with several independent exponential stages, corresponding to, for instance, the initial dispersal by the first tine of a harrow, followed by dispersal by a successive tine, etc. The Gamma distribution gave a good description of the harrowing and tining cultivation p.d.f.s for this experiment. In all cases the estimated proportion of the beads not moved by the cultivation was estimated.

To give increased flexibility in estimating the proportion unmoved it was assumed that the ‘unmoved’ beads could be slightly perturbed by a very small random distance in either direction, with the p.d.f. of this random distance being assumed normal with a zero mean and a very small variance. Thus, the p.d.f. of the distance moved by the ‘unmoved’ beads has the p.d.f. fU(x), where:

  • image(eqn 10)

which gives a zero mean movement with a spread of movement around this mean distance with standard deviation of size σ. In most cases the value of σ was set to be infinitesimally small, when the ‘smoothed’ distribution takes the form of a step of fixed width, i.e. has a value of 1/(2S) for |x| < S, and 0 otherwise.

Denoting the p.d.f. of the Gamma distribution as fE(x), the final cultivation p.d.f. is given by:

  • f (x) = (1-pfU(x)+pfE(x)(eqn 11)

where p is the proportion of beads moved; the smoothed distribution could be readily derived from this. The smoothed p.d.f., fS(x), was fitted directly by least squares, using Genstat (Genstat Committee 1993). In many of the cases there was no evidence that p was less than one, i.e. there was evidence that all beads had moved; where there was evidence of non-movement the proportion of beads moved was estimated. For the ploughing treatment there was no evidence of movement, so the parameters of the Gamma distribution could not be estimated. Instead the parameters of the normal distribution, corresponding to a slight perturbation of the beads, were estimated where possible.

Simulated bead dispersal using the model

As well as giving point estimates of the cultivation p.d.f., equation 4 can be used to give post-cultivation maps of bead density. The precultivation bead distribution (gi−1(x)) is evaluated on a regular grid with a spacing small compared with the mean distance moved by the cultivation; in this experiment we used a grid spacing of 2 cm. The effect of using a fine grid is to give an almost identical result as that which would have been obtained if the simulation had been carried out analytically. The estimated cultivation p.d.f. (f (x)) (in this case a Gamma distribution with a probability spike at distance zero) is then evaluated at a set of distances with the same spacing. The Fourier Transforms of both functions are evaluated, and equation 4 is used to give the Fourier Transform of the post-cultivation distribution. This is then back-transformed to give the required post-cultivation map. This process can be repeated several times to reproduce the effect of the successive cultivations.

Results

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Surface counts

North–south axis

Mean bead densities on the soil surface are illustrated in Fig. 3. Drilling (sky-blue beads) towards the south moved most beads only a short distance, none being found beyond 1·8 m from the edge of the source area. Blench harrowing (purple beads) to the north moved more beads to greater distances. Tine cultivations (orange, barley seeds and green beads) appeared to move beads intermediate distances. The patterns of orange beads on the surface and the barley plant densities were similar, although more barley plants than beads were recorded, perhaps as a result of germination from below the surface. Few yellow beads were counted (after ploughing) but were present up to 3·8 m northwards and 0·8 m southwards. No beads were found further than 4·5 m to the south of the plots, while single beads and barley plants were found 20 m northwards.

image

Figure 3. Mean densities (m–2) of barley plants and plastic beads on the soil surface after a series of cultivations. The colour of the beads, and their associated cultivation are: (a) sky-blue, drilled; (b) purple, harrow + drill; (c) orange, tine + harrow + drill; (d) barley (seeds), tine + harrow + drill; (e) green, tine + tine + harrow + drill; (f) yellow, ploughed up + tine (× 2) + harrow + drill. The direction of cultivation is shown by an arrow in each figure. Data represent densities in 0·01-m2 samples from –3 m to 5 m and in 0·25-m2 samples at greater distances. Arrows show direction of last cultivation.

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Lateral spread

Surface counts in directions other than north and south are represented in Fig. 4, as mean densities in successive 0·01-m2 squares. The results show some spread in the east–west axis, although almost no beads were counted beyond 0·5 m from the edge of the source area and few beyond 0·2 m. Orange and green beads (tines) showed more lateral spread than purple (blench harrow) or sky-blue (seed drill) beads. The location of the barley and triticale plants in the autumn and spring indicated only limited lateral spread. An uneven distribution was found with yellow beads, which were only found to the west of the source area (recall that yellow beads were buried at 0·2 m in the source area before being ploughed up and cultivated). The plough furrows were laid to westwards and the pattern of yellow beads showed displacement in that direction.

image

Figure 4. Densities of plastic beads (m–2) recorded on the soil surface in the other major compass directions (NE, E, SE, SW, W and NW) after cultivations.

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Location of buried beads

Beads were recovered from four sections of the soil profile, 0–5 cm, 5–10 cm, 10–15 cm and 15–20 cm, from four replicate plots only, as logistics limited the amount of soil that could be handled. Mean bead densities (m–2) from the four depths for each colour are illustrated in Fig. 5. The bulk of yellow and navy beads, which were ploughed up and ploughed down, respectively, were recovered from the 15–20 cm profile. In both cases, few beads were found further than 1 m from the source area. In contrast to the ploughed beads, the majority of the remaining coloured beads were recovered from within 10 cm of the soil surface. Most green and orange beads, which received tine cultivations, harrowing and drilling, remained within 3 m of the source area. Purple beads were only found northwards but were moved greater distances. The bulk of the purple beads were recovered up to 6 m from the source, although small numbers were found as far as 14 m. Sky-blue beads were only moved by drilling, few moving further than 0·5 m southwards from the edge of the source area.

image

Figure 5. Mean bead densities (m–2) recovered from four soil depths (0–5, 5–10, 10–15, 15–20 cm), at increasing distance from 1-m2 source areas, after a series of soil cultivations. The colour of the beads, and their associated cultivation, are: (a) sky-blue, drilled; (b) purple, harrow + drill; (c) orange, tine + harrow + drill; (d) green, tine + tine + harrow + drill; (e) navy, ploughed down + tine (× 2) + harrow + drill; (f) yellow, ploughed up + tine (× 2) + harrow + drill. Arrows show direction of last cultivation.

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Effects of individual cultivations

The patterns of bead recoveries from the soil, presented above, are those after increasing numbers of sequential cultivations. Regression analysis was used to describe the movement of sky-blue beads. For the remaining beads, a novel use of Fast Fourier Transforms of the total numbers of beads recovered from each distance allowed the deconvolution of bead distributions. The results were obtained for individual cultivations on four replicate plots. As noted in the Methods, the proportion of the beads that were not moved could be estimated by assuming that the unmoved beads were slightly perturbed around the source according to the normal distribution. The mean distances moved by beads for each of the replicates, together with the proportion moved, are presented in Table 3. For the ploughing cultivation, there was no evidence that any of the beads were moved according to the Gamma distribution, so in this case the normal distribution was used to describe the distribution of movement.

Table 3.  The estimated proportion of beads moved (p), their mean distance moved, and the standard deviation of distance moved (SD) (figures in parentheses), estimated for cultivation p.d.f.s for individual replicates  
Proportion moved (p)Mean distance moved of proportion moved (SD) (m)
CultivationRep. 1Rep. 2Rep. 3Rep. 4MeanRep. 1Rep. 2Rep. 3Rep. 4Mean distanceMean distance moved
  1. (+) Normally distributed disturbances.

Seed drilling (sky-blue)0·030·97  0·979·640·27   0·26
Blench harrowing (purple)0·430·960·871·000·822·47 (1·10)2·00 (1·08)1·08 (0·44)2·38 (2·82)1·981·58
Tine cultivation (orange)0·191·000·450·230·471·59 (1·32)1·46 (0·83)1·56 (0·73)1·62 (0·72)1·560·71
Tine cultivation (green)1·001·000·591·000·901·26 (0·94)1·84 (0·87)1·29 (0·76)1·461·21
Ploughing (navy) (+)00000·00– 0·23 (0·059)0·33 (0·010)0·32 (0·002)1·02 (0·050)0·36
Seed drilling

The decline in the sky-blue bead counts with distance from the source was well described by equation 2, apart from plot 1, which appeared to behave very differently from the other three plots. The equation was fitted to the observed soil core counts as described previously; the results are given in Table 3. The equation did not appear to describe plot 1 at all well; for the other plots there was evidence that the estimated number of beads ‘sown’ varied from plot to plot, but no evidence that either the proportion moved, p, or the mean distance moved by beads that were moved (1/λ), varied between the plots. Comparisons of plots 2, 3 and 4 showed that there was evidence of overdispersion, but no evidence of lack of fit of the equation when this overdispersion was taken into account. Estimated recovery rates for plots 2, 3 and 4 ranged from 86% to 103% that for plot 1 was 58%. The mean distance a bead was moved (if it moved at all) was 0·27 m for plots 2, 3 and 4, but was over 9 m for plot 1.

Blench harrowing

The estimated proportion of beads moved for plots 2, 3 and 4 ranged from 87% to 100%, with plot 1 again appearing atypical, with only 43% moved. The mean distances moved by the proportion of beads that did move ranged from 1·1 m to 2·38 m; when the proportion that did not move was also included, the mean distance moved was 1·58 m.

Tine cultivation

Both orange and green beads were used with tine cultivation, although in opposite directions. A sensible p.d.f. for replicate 1 for tine cultivation in a northerly direction could not be fitted, so is omitted from further comments. For the other replicates, the estimated proportions moved ranged from 19% to 100%, with corresponding mean distances for the moved beads ranging from 1·26 m to 1·84 m. Over the four replicates tined in a southerly direction, the mean distance moved by beads that moved was 1·56 m; over the three replicates tined in a northerly direction, the mean distance moved by beads that moved was 1·46 m. When the proportion not moved was also included, these mean distances were reduced to 0·71 m and 1·21 m, respectively.

Ploughing

Yellow beads, which were ploughed up rather than starting on the soil surface, were excluded from the analysis because the numbers recovered were low. The analysis of the navy beads, which were ploughed under, indicated that beads were only moved a small distance from their original position, with the mean perturbation being 0·36 m, ranging from –0·23 m to 1·02 m across the four replicates.

Modelling weed patch behaviour

The p.d.f.s. derived from the data have potential uses in modelling the behaviour of patches of weeds within fields. If control methods, particularly herbicide application, can be targeted to where weed patches occur, there is potential for reductions in agrochemical use (Rew et al. 1996). Cultivations may have significant effects on seed movement in soil and thus on weed patch behaviour. This potential is illustrated in the simulation shown in Fig. 6, where a simulated patch of a uniform seed distribution is blench harrowed three times in one direction. The simulation was carried out in Mathcad (Anonymous 1993) as described in the Methods, using the estimated Gamma p.d.f. with a probability spike at distance zero, for plot 1 (a proportion (p) 0·43 of the beads moved a mean distance 2·47 m, with the standard deviation of the distribution of the moved beads being 1·10). It can readily be seen that the seed distribution is smeared in the direction of cultivation.

image

Figure 6. Modelled seed distributions after one, two or three tine cultivations, using the cultivation p.d.f. for blench harrowing (plot 1) (a proportion of 0·43 of the beads moving a mean distance 2·47, with the standard deviation of the distance moved being 1·10), on a patch with weed seeds initially uniformly distributed.

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Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

The bead distributions in the north–south directions gave consistent results showing differences between the different cultivation methods. Limitations in the approach used were associated with the soil sampling procedure. With decreasing densities of beads with distance away from the source area, sample size needed to be large. However, as large amounts of soil had to be excavated for processing, sampling was limited to the north–south directions. Surface counts indicated that there was some spread from the source area in other directions (Fig. 4), but this was limited and of little significance in comparison with the main axis. The surface bead patterns indicated some trend for greater lateral spread with spring tine cultivations, rather than with harrowing or drilling. Overall surface patterns indicated least movement with drilling and most with harrowing, the tine cultivations giving intermediate seed movement.

Soil sampling was delayed to the early summer following autumn cultivations to allow the barley and triticale to mature. During this period, it is possible that some vertical redistribution of beads could have occurred, particularly downwards. However, this seems of minor significance as most beads were found within 10 cm of the surface. Likewise, it is possible that some lateral displacement may have occurred. However, as the field was flat, water movements were likely to have been small. The process of sampling could also have moved a small number of beads down the profile, but the probable proportion of beads involved will have been small, as evidenced by the concentration of beads in the upper soil profile.

Our results showed that mean distances moved by the beads were of the order of 1·6 m for blench harrowing and about 1·0 m for tining. In comparison, Rew & Cussans (1997) observed mean distances of about 0·6 m for spring tining on beans and barley seeds, which are of a similar order of magnitude. They did not include an estimate of the proportion of beads that were unmoved; this may account for the disparity in the estimates. Data from a range of horticultural (Mead, Grundy & Burston 1998) and arable cultivations (Mayer, Albrecht & Pfadenhauer 1998) largely confirm the patterns of seed movement reported here.

The effects of tine cultivations on soils have been examined elsewhere (Kouwenhoven & Terpstra 1979). These types of cultivator have two main actions, sorting and throwing. During sorting, larger particles move to the surface and finer particles fall. Unattached seeds, being fairly small, would be expected to descend within the soil profile. When soil is thrown, it moves forwards and to the side of the tines. Surface particles also move further than those at lower levels (Kouwenhoven & Terpstra 1977). The harrow used in this experiment was a blench harrow with downward-directed tines mounted on a steel frame. While working, there was some accumulation of thrown soil in front of the leading frame. Some beads trapped in this soil may have moved considerable distances. Ploughing resulted in distributions in which most beads were found more than 10 cm below the soil surface. Few navy or yellow beads were counted on the surface or recovered from 0–10 cm soil layers. There was evidence of lateral displacement by the mouldboard plough, so it is possible that samples along the north–south axis could have underestimated bead densities. However, as soil displacement would only have been approximately 35 cm, the width of the ploughshare, soil cores would have still been sampled from within the displaced source area (Fig. 1), which was 1 m2. The use of a wide uniform distribution of beads as a source allowed this displacement, but also contributed to reducing variability in the results. The source area can be considered as a series of abutting narrow lines of beads so that the observed results are the sum of the results for the individual bands. This effectively increases the replication of the experiment, with the cost of an increase in the complexity of analysis. However, the proposed technique is not difficult to implement practically, so its complexity is not a major drawback. In contrast, the use of narrow sown bands of beads may itself cause bias in the estimates of the distances moved, as they are equivalent to narrow patches.

Seed on the soil surface is buried by ploughing (Fig. 5), with little lateral displacement. A small proportion of seed present as a layer at 20 cm was brought to the surface by ploughing, which could be moved by subsequent cultivations. However, few beads were recovered at any distance from the source. These data indicate that cultivation sequences based on regular ploughing may tend to preserve patchy distributions of weeds within fields. Cultivations based on tines, discs and harrowing, or non-inversion tillage machines (cf. Tebrügge 1993), may tend to move seed greater distances.

The results have produced probability distribution functions that should further our understanding of the spatial effects of cultivations on weed populations. Mean distances that seeds were moved were less than 2 m, with ploughing and seed drilling moving seed less than 1 m on average. The results confirm those of Fogelfors (1985), who showed that after harrowing most seed remained within a few metres of starting locations. On that basis, Fogelfors also indicated that field edges were unlikely to be significant sources of weed seed for the adjacent field area. Direct observation of weed seedlings at the field edge indicates that this is probably the case for most plants of field margins (Marshall 1989), with some important exceptions, such as Anisantha sterilis (L.) Nevski and Galium aparine L. Within the main arable field, Marshall (1988) noted that weeds are patchily distributed and Wilson & Brain (1991) have shown that patches of Alopecurus myosuroides Huds. remain remarkably constant within a farm over 10 years. This is despite regular cultivations that move seed in the soil. However, in the 10-year study the sampling grid used was large, rendering it difficult to assess the size, behaviour and fate of individual weed patches. A more fruitful approach will be to include the p.d.f.s generated by this study in stochastic models of the spatial dynamics of weed populations. Initial attempts to include dispersal and spatial dynamics in crop–weed models indicate that there can be significant interactions between dispersal power and environmental heterogeneity on weed population dynamics (Perry & Gonzalez-Andujar 1993; Gonzalez-Andujar & Perry 1995). An alternative approach is the development of transition matrices of seed movement in the soil profile (Mead, Grundy & Burston 1998). Seedling emergence is dependent on depth of burial; recent work (Grundy, Mead & Burston 1999) combines models of vertical and horizontal seed displacement.

The use of p.d.f.s has been discussed by Brain & Marshall (1996; in press), who showed that if the effect of superimposed cultivations are independent (the assumption used in this analysis), then the Fourier deconvolution approach can be used to predict future behaviour of weed patches. They simulated the behaviour of a patch under the assumption that the cultivation p.d.f. was exponentially distributed. A more realistic description of the cultivation p.d.f. is the Gamma distribution, used here, and in Fig. 6 we present the effect of harrowing a patch of seeds of constant density using this distribution. Nevertheless, within typical arable production regimes cultivations are not always in the same direction; some smearing of high density distributions is likely, but patch integrity could be retained over time. Further modelling of cultivation effects is needed, which would be best combined with data on the population dynamics of selected weeds and with information on other dispersal processes, particularly seed rain patterns and movement by harvesting machinery, and movement in the soil profile. The approach used here will contribute to the development of those detailed spatial models of weed populations, which in turn will contribute to precision weed control and more sustainable management of arable land.

Acknowledgements

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

We thank Yvonne Jones, Doug James, Linda Dugdale, Jonathan Entwhistle and the LARS experimental husbandry staff for their practical help with this work. Useful discussions were held with S.R. Moss, IACR–Rothamsted, and Mike Shaw, University of Reading, made a valuable suggestion for the analyses. The work was conducted under a commission from the UK Ministry of Agriculture, Fisheries and Food. IACR–Long Ashton Research Station receives grant-in-aid from the UK Biotechnology and Biological Sciences Research Council.

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
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Received 26 May 1998; revision received 11 March 1999