- Top of page
- Materials and methods
The within-field spread of weeds depends on the dispersal characteristics of seeds and the subsequent site-dependent success of emergence and growth. Within agricultural fields, weed spread and establishment result from the interaction between the innate dynamics of the weed, as determined by its spatial life-history characteristics and density-dependent survival/growth of seedlings, and the anthropogenic vectoring and facilitation/inhibition that result from management. Emergence and growth are dictated by underlying spatial heterogeneities in environmental characteristics (e.g. local nitrogen and potassium availability; Dieleman et al. 2000), imposed disturbance regimes (e.g. tillage; Rew & Cussans 1997), and herbicide application (Mortensen & Dieleman 1998). Seed dispersal is likewise a combined function of natural and management-related process (Cousens & Mortimer 1995). When seed set coincides with crop harvest, mechanical vectoring may dominate dispersal. The influence of cultivation and harvest on horizontal movement of the seed bank has been assessed in various agricultural settings using direct observation and simulation models (Ballaréet al. 1987a,b; Howard et al. 1991; Rew, Froud-Williams & Boatman 1996; Rew & Cussans 1997; Paice et al. 1998; Woolcock & Cousens 2000; Gonzáles-Andújar, Plant & Fernandez-Quintanilla 2001). Most studies conclude that redistribution of the seed bank following cultivation is generally of the order of ≤ 1 m (Rew & Cussans 1997). Dispersal of weed seed during mechanical harvest (combine harvester) has been found to be more significant, although the exact shape of the resultant ‘dispersal kernel’ varies (Woolcock & Cousens 2000). Few studies have quantified the influence of mechanical practices on rates of patch spread, although Woolcock & Cousens (2000) demonstrated through simulation that combine-aided seed dispersal can increase rate of spread by an order of magnitude.
Seed dispersal is an integral process in weed patch expansion, but realization of the dispersal kernel is the combination of dispersal and establishment. The transition from ‘seed kernel’ to ‘seedling kernel’ is therefore filtered by habitat suitability, density-dependent self-thinning during emergence and management intended for weed control. Patch expansion, then, is a function of dispersal and reproductive success.
We used common sunflower Helianthus annuus L. as our study species to quantify its dispersal kernel and the role anthropogenic vectoring plays in weed patch expansion. This species was chosen for several reasons. First, it is an important summer annual weed of crops. Secondly, a body of knowledge regarding life-history transitions and density-dependent mortality has developed over the past decade (Dieleman, Mortensen & Martin 1999; Burton et al. 2004; Humston, Mortensen & Wyse-Pester, in press). Finally, because this species drives management decisions in western maize production, its spread within and between fields is of great practical concern.
Our statistical analysis had two facets. First, we quantified the degree of anisotropy in seed dispersal relative to the direction of management. This provided a direct test for whether anthropogenic vectoring is a significant force in the weed patch expansion. Secondly, we studied the consequences of such vectoring on the rate of weed-patch expansion. In order to pursue these interrelated topics we used two complementary sets of statistical methods. We first used an anisotropic geostatistical analysis to test for anisotropy. Secondly, we developed a stochastic integro-difference model (Kot & Schaffer 1986; Kot, Lewis & van den Driessche 1996; Latore, Gould & Mortimer 1998), incorporating both innate and anthropogenic dispersal, to make predictions about rate of spread. We estimated the parameters in this model from successive snapshots of weed distribution and abundance using maximum likelihood.
- Top of page
- Materials and methods
Agricultural ecosystems are characterized by high levels of disturbance, relatively rich resource supply and, in fields where disturbance includes tillage, limited interspecific competition early in the life of annual plants. A limited seed supply coupled with high levels of seedling-targeted mortality result in weed populations that are often recruitment limited. Therefore, factors influencing the size of weed seed banks are likely to strongly influence the persistence and spread of weedy populations (Westerman et al. 2003). The temporal trajectory of seed bank density is regulated by seed bank persistence, fecundity, immigration and emigration.
This study set out to assess the importance of initial seed bank pool size on the persistence and spread of populations over a period of 4 years. The study species, H. annuus, is a summer annual weed with a persistent seed bank. Previous work in this study system revealed an interesting density-dependent dynamic influencing the survivorship probabilities in seed to seedling transitions. High densities of seedlings shortly following emergence resulted in reduced mortality when herbicides were applied for control (C. Neeser, J.A. Dille & D.A. Mortensen, unpublished data). With such controls as the overwhelming source of mortality in annual cropping systems, it is clear that one important way in which initial seed bank pool size influences the fate of populations is through seedling mortality. This study expands on previous work by following populations through time. With small initial seed banks, the likelihood of patch extinction was high and the rate of patch spread greatly constrained. Because of its large seed, innate dispersal of H. annuus seed is limited to several metres in distance (Teo-Sherrel 1996), with the largest proportion of seed falling within 1–2 m of the parent. This study used the spatial extent of seedling patches arising from seed banks established in 1994 to quantify the relative roles of natural and management-aided dispersal on weed patch expansion.
In the experiment we intentionally carried out all management-related traffic in a unidirectional fashion. This uniquely allowed us to characterize and separate the two dispersal processes. Directionality in spread is the signature of anthropogenic vectoring, while radial symmetry reflects natural dispersal. The significant anisotropy in our geostatistical analysis (Figs 2–4) testifies to considerable management-related dispersal. Management-influenced weed-patch expansion was highest in maize (Table 2 and Fig. 4). The crop type, thus, significantly influenced the proportion of weed seeds dispersed during harvest relative to those dispersed by natural means (i.e. P). Harvest of all fields occurred on the same day; therefore this may be attributable to differential weed–crop competition dynamics effected by tall maize plants vs. low-lying soybean plants.
Helianthus annuus recruitment is seed limited (Neeser, Dille & Mortensen, unpublished), where small seed banks are less likely to yield reproductive adult plants. While evidence suggests that seeds of the common sunflower are naturally long-lived in the seed bank with a small proportion germinating each year (Burnside et al. 1981, 1996), the seeds are favoured by many granivores (Pilson 2000; Alexander et al. 2001; Cummings & Alexander 2002) and experience high rates of post-dispersal mortality from seed predators (Teo-Sherrel 1996). Seed bank persistence (beyond 1 year) appeared to play a minor role in patch dynamics in our experiment. In this study, as in others, we found that H. annuus patches with small initial seed banks and high herbicide treatments declined to extinction.
The empirically parameterized integro-difference model allowed us to (i) measure the spatial scales of the two modes of dispersal (natural and management-aided), (ii) estimate their relative importance and (iii) calculate how the within-field rate of weed patch expansion is enhanced by manage-aided dispersal. Based on these calculations, we found that weed patch expansion may increase by as much as a factor of 3–4 with heavy management traffic (compare the length of the tails in Fig. 5). However, the actual traffic in our experiment resulted in somewhat less extreme effects. Woolcock & Cousens (2000) suggested a potential 16-fold increase in weed grass (Bromus sp.) patch expansion rate from seed dispersal by combine harvester. Their more extreme effect results from the assumption that anthropogenic dispersal distances were orders of magnitude greater than natural dispersal. This may be unrealistically great for large-seeded weeds such as H. annuus. Nevertheless, our experiment and analysis lend qualitative credibility to Woolcock & Cousens’ (2000) theoretical results, in that we confirm that management-related traffic results in considerable vectoring of seeds and affects patch expansion of an annual weed. In practice, such anisotropic dispersal may significantly influence field-scale population dynamics of H. annuus. Moderate and high density patches would serve as source populations from which local infestations would spread. In time, patches would coalesce, minimizing the effectiveness of site-specific management.
Figure 5. Effect of varying the contribution of natural vs. harvest dispersal (P) on patch expansion in one dimension parallel to direction of harvest. Density curves show results of 10 years of simulations projecting the integro-difference model using mean maximum likelihood parameter values. All populations were initiated at 0 m, with direction of combine harvest orientated from left to right. All densities are scaled relative to weed density at origin when P= 1·0 (i.e. no seed dispersal by harvest).
Download figure to PowerPoint
To gain insights into scales of dispersal, and the relative importance of anthropogenic vs. natural dispersal, we made several assumptions. First, we assumed negligible density-dependence in emergence and survival of weeds. It is realistic that density-dependence effects are negligible in this early post-invasion time frame (Buckley, Briese & Rees 2003). Secondly, we made assumptions about the shape of the dispersal kernels. For instance, we assumed that the kernel of natural dispersal is predominantly shaped by diffusive movement of seeds, predicting the dispersal distance distribution to be proportional to exp(–d2): a Gaussian kernel. Although previous studies have considered the plausibility of alternative kernel forms (Kot, Lewis & van den Driessche 1996; Latore, Gould & Mortimer 1998), we made this assumption by appealing to first principles. In considering patch expansion in a single agricultural field immediately following weed invasion, recruitment is probably dominant in near-source ‘shoulders’ of the dispersal kernel (where seed rain is highest). Using leptokurtic or ‘heavy-tailed’ kernels would probably increase the predicted expansion rate. However, we suggest such dispersion is probably of lesser relevance at these scales. Interestingly, our geostatistical analysis renders critical evidence on the validity of this assumption: Bjørnstad & Bolker (2000) show that the spatial correlation function (e.g. Fig. 1) inherits its shape from the dispersal kernel, and Bjørnstad & Falck (2001) show that the spline correlogram is a non-parametric estimate (in the sense of not assuming any specific functional form) of this correlation function. A visual inspection of the non-directional spline correlograms from Tr1 (Fig. 1a), reveals distinct Gaussian features: there is a ‘Gaussian shoulder’ near the origin and a seemingly exponentially decaying tail. Furthermore, we can use the result in Bjørnstad & Bolker (2000) to validate our likelihood estimates of the scale of the natural dispersal kernel; specifically the distance at which the scaled spline correlograms drops to 1/e (≈ 0·37), the so-called Le-correlation length is equivalent to the scale D of the Gaussian kernel (equation 4) or the scale h of the exponential kernel (equation 5). Across the treatments, the average correlation length is 1·80 m (SE = 0·51). This compares well with the averaged likelihood estimate of D in Tr1 (2·04 m, SE = 0·68).
Ribbens, Silander & Pacala (1994) pioneered the use of likelihood methods to parameterize integro-difference equations from sequential spatial mappings of plant distributions. We extended their approach for applicability in the agro-ecological setting, and to parameterize mixtures of dispersal kernels (natural and anthropogenic) from differences in the anisotropy of the signatures of the two. Admixed modes of dispersal are likely to be common. Invasions, for instance, are often argued to result from rare (e.g. long-distance) dispersal events. One may speculate that this is the admixed signature of the kernel of a rarer, more distant, dispersal mode. We believe that our protocol of combining geostatistical analysis of sequential mappings with parameterization of spatial population models facilitates characterization and separation of distinct modes of dispersal. Independence of the two methods provides a system for cross-validating model assumptions and estimated parameters.
Our focus is on how localized seed limitation and local dispersal are the keys to weed control. We found that a critical minimum seed bank density was needed for patch persistence and spread. Once that minimum density was met, patches became a seed source to move propagules rapidly about the field. The relatively rapid anisotropic spread of populations observed in the study provides compelling evidence that once a critical minimum density in a local population is exceeded, increased management is needed to contain the spread of this weed. Study of these local dynamics is a different perspective from the many important past studies on how rare long-distance events determine long-term colonization and range expansion (Clark et al. 1999; Clark, Lewis & Horvath 2001; Nathan & Muller-Landau 2000). However, for precision agriculture and ecological recommendations that are relevant to individual farms, rare long-distance processes are of lesser concern. For precision agriculture, finer spatiotemporal scales and the methodology presented here may be more relevant.