• circular correlation;
  • glyphosate resistance;
  • invasion;
  • long-distance dispersal;
  • resistance management;
  • spread;
  • wind-dispersed seeds


  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  • 1
    Glyphosate-resistant Conyza canadensis populations now infest more than 44 000 ha of arable land in eastern USA, only 5 years after the first resistant population was reported. Seed dispersal, the expansive use of glyphosate and the lack of tillage are all factors contributing to this high invasion speed.
  • 2
    Seed collected from deliberately established C. canadensis source populations were found at the furthest seed traps in our empirical studies, providing one of the most complete dispersal kernels for studying long-distance dispersal. The results indicate that seed regularly disperses at least 500 m from source populations. While a relatively small number of seeds moves long distances, 99% of the seed was found within 100 m of the source.
  • 3
    Empirical and mechanistic models were fitted to the data to predict the dispersal in the prevailing wind direction. Both models underestimated seed deposition beyond 200 m but the mechanistic model provided a better fit to the data (lower Akaike information criterion). A two-dimensional analysis examined the correlation between angular directions of wind and seed movement. All trials were anisotropic but only the cumulative wind and seed direction were significantly correlated (P < 0·05).
  • 4
    The empirical model was used to explore the effect of increasing source strength, which would be expected as an infestation of glyphosate-resistant C. canadensis expands on a producer's farm. At infestation levels consistent with a heavy infestation in a 5-ha field, seed dispersed further than 1·5 km, easily affecting 10s to 100s of surrounding farms.
  • 5
    Synthesis and applications. Emigration of C. canadensis seed, from a source farm to adjacent farms, means that population dynamics and weed management are dependent on both intra- and interfield dispersal phenomena. Wind-dispersed plants challenge the common practice of single field management as a viable management option for herbicide-resistant weeds. Farms coupled by seed dispersal require proactive management practices by every producer to prevent and minimize the development of glyphosate-resistant infestations of undesirable and alien plants.


  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

The dispersal of herbicide-resistance genes via pollen or seed has the potential to connect farms once thought to be independent. The implications of such interconnections have taken on new importance as the appearance of herbicide-resistant biotypes increases together with reliance on herbicide use in genetically modified crops.

The adoption curve for genetically modified glyphosate-resistant soybeans Glycine max L. Merr., cotton Gossypium hirsutum L. and maize Zea mays L. is unprecedented (Carpenter et al. 2002). Glyphosate is a non-selective herbicide now applied to more than 25 million ha and approximately 85% of the total soybean area (USDA-NASS 2005). While its use has reduced overall weed abundance (Mortensen 2005), glyphosate represents a strong selection pressure for glyphosate-resistant survivors. Conyza canadensis L. Cronq. (formerly Erigeron canadensis L.; common names include horseweed, marestail and Canada fleabane) is an increasing problem in no-tillage agriculture (Buhler 1995) and is a cosmopolitan species distributed globally in roadsides, field edges and abandoned fields (Buhler 1992; Holm et al. 1997; Weaver 2001). Glyphosate-resistant C. canadensis was first reported in 1999 (VanGessel 2001) and resistant populations are now found in 44 000 ha in 12 states in the USA (Heap 2006). The rapid expansion in geographical range of glyphosate-resistant C. canadensis is largely the result of long-distance seed dispersal.

Wind dispersal, of seed or pollen, changes the scale at which resistance genes can move (Marvier & Van Acker 2005). Watrud et al. (2004) recorded pollen dispersal distances of 20 km. Regehr & Bazzaz (1979) recorded C. canadensis seeds being transported 100 m in a corn field, and Dauer, Mortensen & Humston (2006) showed that C. canadensis seed probably travels hundreds of metres in controlled environments. The invasion speed of glyphosate-resistant biotypes is further accelerated by propagule pressure. Effective management is essential because crop yield can be reduced by 90% at high densities (100–200 plants m−2) and even one plant can release thousands of wind-dispersed seeds (Bruce & Kells 1990; Weaver 2001). Smisek et al. (1998) reported 96% of the florets were self-pollinated because pollen was released before capitula were fully opened. A single plant produced between 100 000 seeds when densities reached 200 plants m−2 and 200 000 seeds when plant densities were low (10 plants m−2) (Bhowmik & Bekech 1993).

Regehr & Bazzaz (1979) modelled the dispersal distance of C. canadensis seed using a negative exponential function. The negative exponential, and other empirical models, have been used to quantify the spread of forbs (Bullock & Clarke 2000) and trees (Clark et al. 1999; Greene & Calogeropoulos 2001). Such empirical models can provide information about the spread of a species but do so with little knowledge of underlying mechanisms. Mechanistic models have also been used to model the dispersal of forbs (Tackenberg, Poschlod & Kahmen 2003; Skarpaas et al. 2004; Soons et al. 2004) and trees (Greene & Johnson 1989; Nathan, Safriel & Noy-Meir 2001; Katul et al. 2005). These differ from empirical models because they rely on parameters that account for meteorological (horizontal and vertical wind speed) and biological (settlement velocity) dynamics known to be important in seed dispersal. Mechanistic models require precise meteorological measurement to represent accurately seed movement during the dispersal period. Many experiments have averaged wind speed over many months (McEvoy & Cox 1987; Greene & Johnson 1989; Bullock & Clarke 2000), making it impossible to resolve the importance of stochastic wind events that occur over short time intervals. Vertical instability, in the form of infrequent updrafts, may affect dispersal distance even more than wind speed alone, and can be included in mechanistic models by slowing the settlement velocity (Nathan, Safriel & Noy-Meir 2001; Tackenberg, Poschlod & Kahmen 2003; Skarpaas et al. 2004; Boehm & Aylor 2005).

Another important component in dispersal patterns is the variation in horizontal wind direction and speed. Prevailing wind direction is important to measure movement in one dimension, but sampling designs often cannot accurately assess two-dimensional seed dispersal patterns. The two-dimensional spatial distribution of weedy species has been studied frequently, but often for gravity-dispersed seed (R. Humston, unpublished data). Bullock & Clarke (2000) examined seed movement in four directions, analysing each direction independently. While this study revealed a dispersal kernel that was anisotropic, causal mechanisms underlying such distributions are poorly understood.

In this study, seed dispersal was measured in both the prevailing wind direction (PWD) to 500 m and in two-dimensions to 70 m. One-dimensional empirical models were fit to the data to determine which model provided the best fit. A mechanistic model was also evaluated to determine if the meteorological conditions measured could account for seed movement in PWD. The analysis was then expanded to incorporate wind and seed movement in two dimensions. Circular statistics were used to compare the two-dimensional spatial distributions as described by Batschelet (1981) and Jammalamadaka & SenGupta (2001). Wind speed and direction were correlated with seed direction and distance over short time intervals. By understanding the interplay between wind speed and direction of seed dispersal, we can better predict the movement of species that rely on wind as a vector to overcome dispersal constraints. One- and two-dimensional sampling and modelling can elucidate extra-field dispersal and also quantify intrafield spread patterns.

This research attempted to define the dispersal kernel of Conyza seed from a source population. If the spatial extent is sufficiently large, the dispersal kernel would connect individual fields, i.e. one farmer's problem may very well be another farmer's problem. The dispersal of resistance genes via pollen or seed connects farms once thought to be independent. The degree of interconnection was explored by coupling empirical data from several study sites and extending that data through the use of the empirical 2Dt model (Clark et al. 1999). Identification and parameterization of dispersal models will enable us to assess methods of managing the ever-growing problem of glyphosate-resistant weeds in managed landscapes.

Materials and methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

field experiments

The seed trapping method was assessed in 2002 by locating two transects 180 and 360 m in length radiating away from a naturally occurring Conyza source with seed traps spaced at 10-m intervals. This prototype experiment revealed that Conyza seeds were mostly collected near the source area, but small numbers of seed were trapped at the farthest distance. Based on those results, the method was expanded in a number of important ways.

In 2003, two experimental sites at the Russel E. Larson Agricultural Research Center, Rock Springs, Pennsylvania, USA (N 40·72237, W 77·92995), were chosen to represent typical soybean production fields and were sufficiently large to contain the anticipated dispersal pattern (Fig. 1). These fields measured 120 × 650 m and were surrounded by a C. canadensis-free buffer of at least 300 m. The two study sites, PA1 and PA2, were chosen to be approximately aligned with PWD during the dispersal window of C. canadensis (August–September). Both fields were treated with a pre-plant glyphosate application (0·84 kg active ingredient (a.i.) ha−1), planted with glyphosate-resistant soybeans in late May, and treated with a post-emergence glyphosate application (0·84 kg ha−1) 5 weeks after soybean planting.


Figure 1. Sampling design of Pennsylvania fields in 2003 and density of seed collected in a selection of trials. A Conyza canadensis source population was established at the centre of the radiating transects. One-dimensional dispersal analysis used the five transects in PWD (12° east-north-east) and all of the arcs. The two-dimensional analysis utilized data from the eight transects in the cardinal directions relative to PWD and truncated to the shortest transect. The density of seeds collected at each trap is represented by the colour gradation obtained using an inverse weighted density interpolation with a maximum distance of 50 m. The panels show PA1, trial 5 (left), trial 6 (middle) and cumulative distribution (right).

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To create a seed source, glyphosate-susceptible C. canadensis plants were germinated from seed in mid-March in a greenhouse maintained between 15 °C and 25 °C, and from those germinants approximately 500 seedlings were transplanted in late April, when rosettes were approximately 5 cm in diameter. The source populations were sheltered from the herbicide spray by covering each patch with a plastic sheet for approximately 30 min while glyphosate was applied. Each 28 m2 patch was located 150 m from the windward edge of the field. Concerns about successful establishment of the original transplants in PA2 led to augmentation of this population with additional transplants. The resulting C. canadensis densities in the source populations were 17·2 (PA1) and 45·1 (PA2) plants m−2, below the density-dependent fecundity constraints reported by Bhowmik & Bekech (1993).

The sampling design for both fields focused on two areas: the first 100 m from the source, to elucidate two-dimensional dynamics, and greater than 200 m from the source in PWD, to examine one-dimensional dynamics (Fig. 1). Ten transects radiated from the source, at angles relative to PWD (12° east-north-east) of 0°, 22·5°, 45°, 90°, 135°, 180°, 225°, 270°, 315° and 337·5°. Beyond 200 m in PWD, arcs were utilized in place of transects to maintain a linear increase in area with distance. Arcs covered 25° every 50 m from 200 m to 500 m. Seed traps were spaced at 10 m along the 10 transects and seven arcs. Seed traps were 454-cm2 metal frames (Collier Metal Specialties Inc., Austell, Georgia, USA), adjusted to canopy level at the beginning of each trial, with cardboard sheets placed in the metal frames and coated with a sticky substance commonly used for insect capture (Tangle-Trap, exterior formulation; TangleFoot Company, Michigan, USA).

Traps were replaced every 8–10 days as weather permitted, comprising six dispersal ‘windows’ between late August (onset of seed release) and early October (approximate cessation of seed release) for a total of 37 days. Dispersal windows were offset between fields because of resource constraints, so traps were replaced in alternating sites every fourth day. After removal from the field, traps were covered with plastic film and all C. canadensis seeds were counted in the laboratory. Meteorological measures (wind speed, wind direction, humidity, temperature, atmospheric pressure and weather condition, e.g. rain, haze, clear) were recorded at 1-min intervals at the Pennsylvania State University meteorological station located 300 m upwind of the source populations.

Seed production in the source was estimated by determining the number of plants in the source and multiplying by individual plant fecundity. Fecundity was determined by counting all capitula on 18 randomly selected source plants and multiplying by mean seed number per capitula as determined by counting 10 capitula prior to seed shed.

one-dimensional model fitting

Only seed collected downwind of the source (± 45° from PWD) were included in the one-dimensional analysis. The corresponding wind measurements consisted of all wind events except highly variable (wind shifted greater than 60° during a 2-min recording period) and non-seed dispersing (zero wind speed) wind events. Additionally, only wind data in PWD (± 45°) were included as explanatory of seed movement. Lastly, wind events occurring at night (16:00–08:00) were eliminated because previous work has shown organisms often maximize dispersal by utilizing updrafts, which occur during the day (Isard & Gage 2001).

Data were fit using the empirical 2Dt (Clark et al. 1999) and mechanistic (Green & Johnson 1989) models (Table 1). Both models are based on the simple equation that seed count (c) can be estimated as:

Table 1.  Empirical and mechanistic models used for one-dimensional analysis of Conyza canadensis dispersal. The dispersal kernel (S, seeds m−2) provides the dispersal portion of the estimate of seed deposition at radial distance r (m) from the source. The GJ mechanistic model is modified from Greene & Johnson (1989) and is similar but not identical to revisions from Skarpaas et al. (2004). Further model explanations can be found in the references. Parameter definitions and estimates are recorded in Table 2.
TypeNameDispersal kernel, SPublication
Empirical2Dtinline imageClark et al. (1999)
MechanisticGJinline imageGreene & Johnson (1989)
  • c = Q × T × S(r)

where Q is the source strength, T the trap area (m2) and S the dispersal kernel (seeds m−2) as a function of radial distance, r (Skarpaas et al. 2004). The 2Dt was selected because it is a probability density function and therefore can be used to explore the importance of source strength (infestation level) on invasion speed, an important practical application of this work. Parameter values for the 2Dt model were estimated by numerically optimizing the joint likelihood of the data using the ‘optim’ routine of the open-source software package (R Development Core Team 2005). To compare the fit of the models, the Akaike information criterion (AIC) was computed to determine the best fit model (Burnham & Anderson 2002; Johnson & Omland 2004).

A mechanistic approach was also evaluated using a model developed by Greene & Johnson (1989), hereafter referred to as GJ, and revised by Skarpaas et al. (2004). This model required information about mean wind velocity, source strength and settlement velocity (Table 2). Source strength and settlement velocity were determined independently as described above. Settlement velocity experiments followed Andersen (1993) and the settlement velocity for C. canadensis was 0·323 (SD = 0·069) m s−1 (Dauer, Mortensen & Humston 2006). The mean wind velocity was determined based on the subset of the total weather record as described above, and assumed that the air was mixed uniformly during seed dispersal and that variance in wind speed at 10 m was equivalent to that found at mean seed height. Because wind speed increases with height, Lowry & Lowry (1989) suggested a wind speed adjustment for the difference between the height at which wind speed is measured (zm) and the mean seed release height (H):

Table 2.  Definition and estimates of parameter values (SE) used in one-dimensional model fitting for Conyza canadensis. Where applicable, units are provided in parentheses. Parameters are from PA1. Source strength, mean plant height, wind speed and the estimated parameters were somewhat different in PA2.
Parameter symbolModelDefinition (units)Measured parametersEstimated parameters
rAllRadial distance from source (m)  
SAllDispersal kernel (m−2)  
TAllTrap area (m2) 0·0454 per trap 
QAllSource strength (seeds) 1·0 E7 
p2DtShape parameter 0·2667
u2DtShape parameter (m2) 6·0 E-3
HGJMean seed release height (m) 1·12 (2·2E-2)1·38
zmGJMeasurement height for wind speed (m)10·0 
FwGJSettlement velocity discounted by vertical wind speed (m s−1) 0·220·28
w*GJVertical wind speed (m s−1) 0·1 
σuGJStandard deviation of the mean wind speed (m s−1) 0·212·03
UHGJMean wind speed at mean seed release height (m s−1) 0·58 (3·0E-5)0·88
FGJSettlement velocity (m s−1) 0·32 (6·0E-7) 
UmGJMean wind speed at measured height (m s−1) 3·02 (1·4E-2) 
z0GJRoughness length (m) 0·2 
DGJDisplacement length (m) 0·7 
  • image

where Um is the measured wind speed, z0 the height at which turbulence transfer equals zero (10% crop height) and D the displacement height (66% crop height; Oke 1992). Mean seed height was treated as a point source because its variation was small compared with dispersal distance (Greene & Johnson 1989). The adjusted settlement velocity (Fw) is the measured settlement velocity minus the vertical wind speed (w; Skarpaas et al. 2004). The vertical wind speed was not measured during these experiments but assumed to equal 0·1 m s−1, as reported by Nathan, Safriel & Noy-Meir (2001) and used in Skarpaas et al. (2004). The integration of vertical wind over a day at a single point is commonly zero (what goes up must come down) but further integration over many days (as reported by Nathan, Safriel & Noy-Meir 2001) includes significant variation in this value and the mean value can be larger than zero. For the reported vertical wind speed value, the standard deviation (0·35 m s−1) includes the zero value and does not invalidate the possibility that there was an average updraft over the recorded time period. Future work to examine the importance of updrafts will need to use smaller time scales (less than hours) to connect updrafts with dispersal potential.

An alternative approach with the mechanistic model involved parameter estimation using the method described for the 2Dt model. Instead of fixing the parameters, maximum likelihood estimation (MLE) was used to determine the value of the parameters. With the estimated parameters, seed dispersal distance was calculated similar to the 2Dt model.

While these experiments were carried out within a single field, the data can provide useful information about larger infestations. An extrapolation of the 2Dt model was conducted to examine the effects of source strength on distance that seed will travel. Source strength varied from a single patch to a large infestation in a 5-ha field and the dispersal kernel was described using 2Dt model parameters determined previously (Table 2). Seed quantity (seeds m−2) was calculated at 250-m intervals from 500 m to 3 km away from the source.

two-dimensional model fitting

While a one-dimensional analysis can provide insight into seed dispersal in a single direction, a two-dimensional approach describes the density distribution of the dispersal kernel. Correspondence between wind events and seed dispersal are best elucidated when studies are conducted with relatively short time intervals. Wind events presumed to be unrelated to seed dispersal were eliminated as described for the one-dimensional model. Each dispersal window was analysed separately and consisted of data from midday of the beginning of a dispersal window through to midday of the end day. A balanced design was created by eliminating data from transects at 22·5° and 337·5° and all arcs and using data up to the length of the shortest transect (70 m in PA1 and 80 m in PA2). This resulted in eight transects of equal length and spacing. Wind and trap data were tested for uniform direction using the Rayleigh test (Jammalamadaka & SenGupta 2001). Failure of the Rayleigh test implied wind and seed direction were not isotropic but were concentrated near a mean direction. The mean angle (µ) was then defined as having cosine and sine coordinates of:

  • image

where θi is the angle of wind movement, with cosine and sine representing the x and y components, and si the weight associated with the corresponding wind speed (modified from Jammalamadaka & SenGupta 2001) for the ith value within the jth trial. A similar analysis was conducted for seed movement with distance from source as the weighting factor. Weighted mean direction and angular deviation (κ, similar to standard deviation in linear distribution) for seed movement and wind for each dispersal window were estimated using maximum likelihood methods assuming a circular normal (Von Mises) distribution (modified for weights; R Development Core Team 2005). Smaller angular deviations represent a greater concentration of values (wind or seed angles) near the mean angle. Mean wind and seed angles were compared using Rao's test for equality of polar vectors (Jammalamadaka & SenGupta 2001), which compares groups of directions based on the spacing of angles about a mean.


  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

The methodological approach had a number of key features not present in most dispersal sampling experiments, including a defined point source, increased sampling intensity, increased maximum distance of seed collection and inclusion of sampling in two dimensions. The seed source in PA1 contained 492 plants, while the PA2 source contained 1263 plants, at a mean density of 17·2 and 45·1 plants m−2, respectively. The average plant height was 1·34 m (n = 10, SD = 0·221) and 1·44 m (n = 15, SD = 0·125) in PA1 and PA2, respectively, approximately 50 cm taller than the surrounding soybeans at onset of seed release and consistent with naturally occurring C. canadensis populations in soybean fields (M. VanGessel, personal observation). As seeds are approximately normally distributed in the upper third of the plant, the mean seed release height is always less than the plant height. Therefore, the mean seed release height was calculated to be 1·12 m and 1·20 m in PA1 and PA2, respectively.

On average, plants produced 2541 capitula (n = 18, SD = 1541·3), which yielded 54 seeds capitula−1 (n = 10, SD = 3·4). The source strength was calculated to be approximately 70 million seeds in PA1 and approximately 180 million seeds in PA2. In PA1, 32 012 seeds were collected (0·05% of those released), while 71 155 seeds (0·04% of those released) were collected in PA2. The majority (93% in both fields) were collected on traps located in the source, but 2255 and 4689 seeds were trapped outside the source (PA1 and PA2, respectively), providing sufficient data to interpolate seed densities throughout the fields (Fig. 1). An inverse distance weighted interpolation of the seed count data estimated 18 million (PA1) and 43 million (PA2) seeds were deposited in each field, a considerably smaller number than the estimated fecundity of the source populations. The estimated source strength, total seed collected and seed collected outside of the source in PA1 were approximately double those values in PA2. Because of the similar deposition pattern, the model fitting was performed using data from PA1. While seeds collected during experiments were similar in size and filled, seed viability was not evaluated directly and is an area requiring further study.

one-dimensional analysis

Seeds were deposited continuously out to the end of the 500-m transects, with a classically distributed dispersal kernel with a very high density centre and very fat tails (Table 3). All three models, 2Dt, GJ with fixed parameters and GJ with estimated parameters, underestimated seed deposition at long distances. The GJ model with estimated parameters had the lowest AIC value and therefore provided the best fit of the three models. The parameters for the GJ model were similar whether these values were fixed or estimated (Table 2). For example, the geometric mean wind velocity in the downwind direction at mean plant height was 1·27 m s−1 (n = 6937 min, SD = 0·46, θ= 38° east-north-east) when measured independently, while MLE resulted in 0·88 m s−1 (Table 2). In addition, the settlement velocity estimated by the model was greater than the empirically derived value of 0·323 m s−1 (Dauer, Mortensen & Humston 2006). The one exception was the value for the variance of the horizontal wind speed, σu. This value may be high as a result of incorporating variation in both horizontal and vertical wind into a single value. While subtracting the vertical wind from the settlement velocity, Fw, and including the vertical wind variance into the horizontal wind variance simplifies the equation, the importance of occasional vertical wind gusts is masked. These stochastic events can affect the timing of seed abscission. Research has shown that abscission of seeds is proportional to wind speed (Greene & Johnson 1996; Skarpaas, Auhl & Shea 2006) but was not examined in this research. Nonetheless, the GJ estimated model had similar parameter estimates to the GJ fixed model, and the fit was improved considerably (lower AIC) by using this technique.

Table 3.  Actual and predicted Conyza canadensis seed collections at a subset of distances using the empirical 2Dt, mechanistic GJ with fixed parameters and GJ with estimated parameters. Actual and predicted values represent PA1 but results were proportional in PA2. Because the GJ with fixed parameters has zero estimated parameters, the calculated AIC is −2 times the log-likelihood.
Distance (m)ActualPredicted
Seed collected2DtGJ (fixed)GJ (estimated)
101061 785·7732·41045·4
20 195 127·4 17·7 205·3
30  80  43·9  2·0  79·2
40  37  20·7  0·4  40·3
50  19  11·5  0·1  23·9
100   4   1·5  0·0   3·8
200   1   0·3  0·0   0·9
300   0   0·2  0·0   0·6
400   3   0·1  0·0   0·5
500   2   0·1  0·0   0·3
AIC 3132409 120 

The source strength extrapolation found seeds travelling kilometres from the larger source (Fig. 2). As the source strength increased, the number of seeds reaching a field 1 km from the source increased from less than 1 seed m−2 when the infestation was small, to nearly 10 seeds m−2 when the infestation was large.


Figure 2. Seed deposition (predicted, seeds m−2) as source strength (Q, seeds) increases using the empirical 2Dt model. Contours represent the upper bound of seed deposition. Source strength represents a range from a small patch (outbreak) to a field-scale infestation.

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two-dimensional analysis

The two-dimensional spatial analysis used a temporal division of the dispersal period into six intervals, where wind and the corresponding pattern of seed deposition were compared. The mean wind direction was variable throughout the season (Table 4). Mean seed direction was also variable during the season, but the angular deviation (κ) around the mean angle was higher than for the wind. The pattern of seed deposition was orientated with wind direction. In 10 of 12 dispersal intervals (two sites and six dispersal intervals) the difference in the mean angles for wind and seeds was less than 90°. While visual assessment found that the angles for the wind and seeds were close, Rao's test for equality of polar vectors found the angles were significantly different in nearly all dispersal intervals (P < 0·05; Table 4). Despite the variability throughout the season, the cumulative mean direction of wind and seed data were not significantly different.

Table 4.  Mean angle (degrees) and angular deviation for seeds and wind for individual time periods in PA1. Mean angle and angular deviation were weighted by distance (seeds) and speed (wind) and were relative to PWD. H is the test statistic for Rao's test of equality of polar vectors with the corresponding P-value, where P-values less than 0·05 represent significantly different distributions.
 Seed dataWind dataHP
Mean angleAngular deviationMean angleAngular deviation
Trial 1344·2 62·38108·7 49·33 40·93<0·01
Trial 2352·3154·11 77·5 43·80 74·08<0·01
Trial 3 21·0100·63 63·1 34·62211·45<0·01
Trial 4163·3 52·80242·5 68·75223·93<0·01
Trial 5113·8 67·41298·7 30·03  1·17 0·28
Trial 6 29·6 80·07 54·8109·16 74·07<0·01
Cumulative 42·4 39·04 38·2 23·49  1·61 0·20


  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Long-distance dispersal is inherently difficult to quantify because seed detection decreases with distance and inferring the dispersal distance of seed becomes a study of theoretical approaches. This study examined an empirical method that effectively quantified and accounted for the spatial pattern of seed deposition at distances much greater than previously reported for C. canadensis (Regehr & Bazzaz 1979). While small numbers of seeds were found at the ends of the sample transects, it is almost certain that seeds were dispersing beyond 500 m. The method provided meaningful insights into the distance and direction of C. canadensis seed movement, resulting in a uniquely rich seed-dispersal data set.

As with most long-distance dispersal studies, seeds were collected more frequently near the source but the dispersal tail was considerably longer than related results for this and other wind-dispersed species (Regehr & Bazzaz 1979; McEvoy & Cox 1987; Greene & Johnson 1989; Portnoy & Willson 1993; Bullock & Clarke 2000; Skarpaas et al. 2004). The focus of many of these studies has been to compare dispersal models and determine the model that best fits the data. In addition to those reported on in this study, a number of models were considered for the analysis, including empirical (Bullock & Clarke 2000; Greene & Johnson 2000; Ribbens et al. 1994) and mechanistic models (Soons et al. 2004; Katul et al. 2005). Some were not probability density functions and lacked realistic biological assumptions, while others contained parameters that were not measured in this research. The models selected have been used successfully to model dispersal of lightweight seeds (Clark et al. 1999; Skarpaas et al. 2004), are simple enough that non-mathematicians studying plant dispersal can utilize them, and predict dispersal that is close to observed values. Other empirical models [negative exponential, inverse power, mixed (Bullock & Clarke 2000) and Ribbens (Greene & Calogeropoulos 2002)] fit the data poorly (AIC > 500). Either the 2Dt model (Clark et al. 1999) or log-normal model (Greene & Johnson 2000) could have been used (AIC values were lower for log-normal in PA1 but higher in PA2), but the fewer parameters in the 2Dt model (two compared to four) made it simpler to manipulate. Likewise, the Greene & Johnson (1989) mechanistic model did not rely on variation of the vertical wind speed, σw, which was critical for other models (Nathan et al. 2002; Katul et al. 2005). Both the mechanistic and empirical models have utility in studying long-distance dispersal. A mechanistic approach is useful for evaluating the importance of meteorological and biological factors, while the empirical approach does not depend on specific mechanisms and, with the assumption that the dispersal kernel is representative of a wide range of conditions, can be extended to explore applied questions associated with species spread.

One area of exploration with mechanistic models is the importance of vertical instability affecting dispersal distance. The mechanistic model overestimated seed deposition near the source but vertical wind stochasticity may have led to a conservative estimation of dispersal distances. Longer dispersal distances are possible and, given the low settlement velocity and vertical wind instability expected in a field, updrafts could extend the expected dispersal distances (Nathan et al. 2002; Tackenberg, Poschlod & Kahmen 2003). The empirical data contain some discontinuities, where gaps in seed deposition between 200 and 400 m may reflect a second mode of seed deposition with additional seed deposited at 400 or 500 m (Table 3). Quantifying whether a second mode exists will require either sampling at greater dispersal distances or measuring the vertical seed concentration as distance from the seed source increases.

The mechanistic approach provides the additional benefit that parameters can be collected independently. Where little data are available on dispersal distance of a species, it is possible to measure settlement velocity, monitor wind speed during the dispersal season using a basic meteorology station and estimate seed production to develop a dispersal kernel relevant to the species. The predicted dispersal distances are likely to be underestimates of true distances but will reduce the error in field sampling.

Unfortunately, wind dispersal is never solely in PWD. Sampling in two-dimensions offers insights into seed densities but adds a layer of complexity. Wind speed and direction varied within and among the six dispersal windows and integrating across this variation resulted in a season-long seed distribution that was isotropic (Rayleigh test, P > 0·05; Table 4 and Fig. 1). Comparison of the wind direction and seed deposition during each dispersal interval showed that the two were similar but statistical analysis found most were significantly different. It is likely that a stronger correspondence between wind direction and seed deposition would be found if wind events and resulting seed dispersal were isolated over shorter time periods (Nathan et al. 2002). Tackenberg (2003) found that updrafts are often associated with low wind, cloud-free days, when vertical mixing is greatest, and downdrafts are associated with stormy weather. Wind data could be filtered on other meteorological classifications to test Tackenberg's (2003) findings. For example, high humidity or cloudy days, when updrafts were minimal, could all be removed from the subset to determine if a stronger correspondence occurs. An attempt with this truncated data set revealed a stronger correlation between wind direction and seed deposition in some trials and a weaker correlation in others. Furthermore, removal of wind data to test this correspondence was subjective, based on an estimate of optimal conditions that were not tested during these experiments. Determining optimal flight conditions, with vertical and horizontal wind movement over shorter time intervals, and the corresponding seed distribution will be the subject of ongoing work to increase our ability to predict the spread of this species (Dauer et al. 2006; Shields et al., in press).

Additional benefits of the sampling method include maximizing seed collection and coupling temporal and spatial dynamics. While many studies have elected to use collection plates at ground level (Regehr & Bazzaz 1979; Bullock & Clarke 2000; Skarpaas et al. 2004), elevating the traps provided excellent data and they were easy to locate and replace during the experiments. We assumed that seed collected at the surface of the soybean canopy would have dropped to the soil surface and that secondary dispersal (post-settlement) was limited.

The objective of the sampling design was to quantify accurately the seed dispersal pattern, particularly at long distances (> 200 m). While the 2003 sampling design was large (366 traps, 2196 samples), the percentage of the field sampled was small (less than 0·02% in both fields). Nonetheless, thousands of seeds were trapped, representing an effective methodology for capturing wind-dispersed seed when studying highly fecund species. While a clearly defined dispersal kernel emerged from this work at both source populations, our interpolated kernel indicated that we recovered only one-third to one-quarter of the estimated seed produced by each patch. The disparity in seed recovery could have resulted from overestimating the number of seed produced in the source populations. Overestimation may have been caused by lack of replication of traps within the source or the result of extreme seed deposition coating the source trap and reducing the trapping efficiency. It is also possible that seed movement beyond the sample region may have occurred during extreme storms. Gaining greater resolution on seed movement beyond the currently defined dispersal kernel is the focus of continuing research.

Unfortunately, as with all long-distance dispersal studies, determining the dispersal distance of seeds that travel beyond the sampling design remains elusive. This study was conducted at the field level, but it is likely that seeds travelled well beyond the edges of the field. The utility of the empirical model can now assist in applied questions about source strength. Source populations used in this study were established as small patches, typical of fields that have been recently infested (1–2 years old) by glyphosate-resistant C. canadensis. As the invasion of the glyphosate-resistant population occurs, whole fields quickly become infested. A farmer with a neighbour that fails to control such resistant populations may receive hundreds of thousands of seeds in a single season. We extended this finding by using the fitted model to determine how source strength influences dispersal distance (Fig. 2). The range of source strengths is representative of those commonly observed in the field. As the source strength increases from a patch to a whole field, the maximum dispersal distance increases from less than 0·5 km for a patch to greater than 1·5 km for the whole field. This projection is profound and agrees with results by Rieger et al. (2002), who reported that canola pollen dispersal distances were an order of magnitude greater when originating from whole fields compared with individual plant and small plot sources.

Seeds that can travel beyond 500 m change common agricultural practices that focus on field-level suppression or eradication. Seed dispersal distances may stretch kilometres, effectively decoupling a farmer's management decision from the resulting weed control. A neighbour's field that contains a wind-dispersed weed will continue to act as a source for invasion into adjacent fields irrespective of the intrafield management practices to maximize control in the adjacent fields. In the case of glyphosate-resistant weeds, this work demonstrates that the invasion speed of herbicide-resistant biotypes is far greater than previously thought. Significantly expanding the spatial extent of resistant C. canadensis will increase the cost of managing such populations and compromise weed control, thus limiting the value of glyphosate-resistant crops. One solution is co-operation among farmers in an area-wide approach, to slow the spread of this and other wind-dispersed species.

Co-operation could be used in conjunction with active adaptive management (AAM). This process of making choices about management includes a feedback loop to adjust the management strategy as information about the success or failure is gathered (Shea et al. 2002). One problem noted by the authors is lack of replication in time and space to allow producers to learn from others’ management decisions. With the glyphosate-resistant horseweed biotype now widespread throughout eastern and central USA (Heap 2006), and no definitive management protocol, experiments to determine effective management practices are occurring simultaneously on a large scale. Already farmers who have faced glyphosate-resistant populations have developed useful techniques for slowing the spread out of their fields, often re-incorporating tillage or herbicide mixtures in their management plans (M. VanGessel, personal observation). Unfortunately, lack of co-ordinated or deliberate sharing of results limits the ability of the producers to learn about management decisions that reduce the potential of invasion into their fields. AAM, along with co-operation and information sharing, has the potential to offer farmers applicable solutions that will impact the surrounding network of farms. Providing farmers with options requires understanding the probability that C. canadensis seeds will arrive and establish in their fields. One-dimensional spatial analyses can yield predictions about the distances seeds may disperse, which can be combined with survivorship data to provide a level of risk to surrounding farms. A two-dimensional approach examines more closely the relationship of wind velocity and corresponding spatial seed distribution to yield in-field management decisions at a landscape scale. Collectively, these spatial analyses quantify the dispersal ability for this common agricultural weed and provide a framework for study of other wind-dispersed species.


  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Financial support was provided by The Pennsylvania State University Department of Crop and Soil Sciences, Intercollege Graduate Degree Program in Ecology, and The Pennsylvania State University Biotechnology USDA-NRI weedy and invasive plants grant 2004-02158 Seed Grant. Helpful suggestions were provided by O. Bjornstad, K. Shea, W. Curran, M. Ferrari, O. Skarpaas, E. Luschei and the dispersal discussion group. Invaluable field assistance was provided by past and present members of the University of Delaware and The Pennsylvania State University Weed Ecology Laboratories.


  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
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