The population dynamics of Anisantha sterilis in winter wheat: comparative demography and the role of management


R.P. Freckleton (fax 01603 592250; e-mail


1. We report on a 3-year field study designed to monitor the detailed population dynamics of Anisantha sterilis in winter wheat, as well as to explore the consequences of changing broad-scale patterns of management, in the form of reduced fertilizer inputs.

2. In the absence of herbicides, population dynamics were dominated by density-dependent population growth. Unusually, this occurred mainly through density-dependent recruitment. This was estimated to reduce population growth rates by 50-fold, compared with the effects of density-dependent competition between plants for resources. Density-dependent recruitment also tended to buffer populations against year-to-year variations in emergence levels.

3. Little evidence for temporal variations in allometric seed production, the strength of competition between plants for resources or maximal mean plant performance was found in this study, or in comparison with previously published data.

4. No aspect of the life cycle was significantly affected by variation in the level of applied nitrogen fertilizer. In the case of competitive interactions we postulate that this lack of effect results from reduced intraspecific competitive effects as a consequence of decreased maximal plant size under low nitrogen conditions. The highly competitive nature of the environment in which A. sterilis occurs means that such changes tend to mask the effects of changing nitrogen levels.

5. Estimates of the effects of cultivation, on the other hand, indicated that seed germination, and hence population growth, was reduced by up to 90% when ploughing was employed rather than minimum tillage. While to some extent the effects of variation in the form of cultivation on population numbers may be buffered by density-dependent recruitment, this effect outweighs any effects of nutrients or spatial or temporal variability in population dynamics.

6. Using previously published models for the dynamics of Alopecurus myosuroides, Avena sterilis and Avena fatua, we show that the response of populations of Anisantha sterilis to cultivation is very different from that of other grass weeds. In addition we show how single species models for population dynamics may be used to predict the responses of weed assemblages to changes in forms of management.


Much of the recent work on the dynamics of weed populations and communities has been motivated by changes in farming practices (Firbank et al. 1984; Tunney 1992; Cussans 1995; Ramussen & Ascard 1995). In western Europe, for example, there has been an increase in the incidence of winter-sown cereals, an increase in minimum tillage, a decreased frequency of crop rotation, as well as an increased use of herbicides, pesticides and inorganic fertilizers (Potts 1991). In an experiment that attempted to explore the consequences of such changes for population and community dynamics in an assemblage of 12 species of arable weeds, McCloskey et al. (1996) found that the impacts of the cultivation regime outweighed those of the amount and form of fertilizer applied. In contrast, a number of studies have suggested that changed forms and amounts of fertilizer application may impact on both population dynamics and community composition (Carlson & Hill 1985; Baylis & Watkinson 1991; Wright & Wilson 1992; Jørnsgård et al. 1996). If we are to understand the consequences of changed forms of management, it is clearly necessary to elucidate those factors most important in determining the abundance and dynamics of weed species, and it is imperative that we understand the relative roles of temporal and spatial variability (Cousens & Mortimer 1995; Freckleton & Watkinson 1998a).

The recent changes in farming practice have led to the virtual extinction of some species, such as Agrostemma githago (Firbank & Watkinson 1986; Firbank 1988), whilst other species, such as Anisantha sterilis and Alopecurus myosuroides, have increased in abundance (Froud-Williams, Pollard & Richardson 1980; Peters, Froud-Williams & Orson 1993; Cussans et al. 1994). One of the key problems that faces weed biology is to be able to explain, and ultimately to predict, how groups of species respond to changes in the forms of management. As, however, there are few, if any, common characteristics of arable weeds that may be used as predictors of occurrence (Perrins, Williamson & Fitter 1993), such predictions have to rely on species by species evaluations of the impacts of management. Detailed models, generally based on empirical population growth functions, have now been developed to predict the dynamics of a range of species under specific management regimes (Cousens et al. 1986; Doyle, Cousens & Moss 1986; Firbank & Watkinson 1986; Gonzalez-Andujar & Fernandez-Quintanilla 1991). There have, however, been few attempts to apply such models to groups of species and to predict the broad-scale impacts of changing forms of management.

In this paper we report a detailed analysis and review of the population dynamics of Anisantha sterilis in winter wheat. In order to develop as broad an understanding as possible of the dynamics of this species, we combine the detailed analysis of a 3-year field experiment on the dynamics of this species with a comparison of other studies on the ecology and demography of A. sterilis. We also compare the responses to management of this species with those of other important grass weeds. Taken together these results present a robust quantitative description and analysis of the population ecology of A. sterilis, analysing the impact of varying conditions on weed abundance and dynamics.

Materials and methods

Field experiment

The field experiment was sited in a field with a sandy loam soil at the Institute of Arable Crops Research, Broom's Barn Experimental Station at Higham, Suffolk, UK (52°16′ N; 0°32′ E; altitude 75 m a.s.l.), a location with a mean annual rainfall of 570 mm, a mean January minimum temperature of 1 °C and a July maximum of 21 °C. It was run for 3 years, during which time the field was cropped to the same variety of winter wheat (cv. Hornet). The experimental treatments, at two levels of nitrogen fertilization, consisted of an additive design where Anisantha sterilis (L.) Neviski (syn. Bromus sterilis L.) was the sole introduced weed or was grown in combination with either or both of two other species (Papaver rhoeas L. and Galium aparine L.). Preliminary analysis of the data indicated that A. sterilis completely dominated the other two weed species, and that competitive effects of these on A. sterilis were undetectable (McCloskey et al. 1996). Consequently the analysis below ignores the presence of other weeds.

This experiment to study the population dynamics of A. sterilis under conditions of interspecific competition was part of a larger design that consisted of 48 3 × 3-m plots marked out in an area of field (36 × 48 m) that had been ploughed and rolled prior to the start of the experiment. The field was drilled with wheat at a depth of 4 cm at a density of 370 seeds m–2 (192 kg ha–2) on 23 October 1990 following ‘roterra’ cultivation to 6 cm depth. The plots were separated by a 3-m discard area. Three replicates of each of eight weed treatments (all three species, all pairwise combinations, each species alone and weed free) at each of two nitrogen levels were allocated at random to the experimental plots. Seeds of A. sterilis were supplied by Herbiseed (The Nurseries, Billingbear Park, Wokingham, UK). Each weed species was sown at a density of 50 seeds m–2, and the nitrogen levels chosen were 240 kg ha–2, the standard application on the farm, and 123 kg ha–2, approximately half the normal amount. The fertilizer was applied in three split applications (40/23 kg ha–2 in March; 100/50 kg ha–2 in April and May). Apart from the specific requirements of the experiment, crop husbandry and cultural practices were performed in keeping with current practices, except that no herbicides were applied to the experimental plots. Full details of the crop management during the experimental period are provided by Lintell Smith (1995).

Throughout the growing season undesired weeds were removed from the experimental plots by hand, while pre-cultivation applications of herbicides were used to control weeds in the discard areas between the experimental plots. During August of each year of the experiment, weeds were harvested individually from the central square metre of each plot, dried at 70 °C, partitioned into vegetative matter and seeds, and then weighed. During the summer the weeds in the remaining plot area were allowed to shed seed naturally, but when the wheat was harvested by combine harvester in August, the straw (plus remaining weeds) was collected to prevent contamination between plots. The plots were surveyed in September to assess the number of A. sterilis seedlings germinating prior to cultivation. Populations were then monitored subsequent to cultivation, during November, to measure post-cultivation emergence.

The experimental procedure was repeated in subsequent years. In 1990, 1991 and 1992 the wheat was sown on 2 October, 19 October and 15 October, respectively, following minimum tillage as described above.

Seed bank analysis

The numbers of seeds in the soil seed bank were monitored through the extraction of soil cores. Soil samples for seed bank analysis were extracted from the experimental plots in the autumn after the plots had been cultivated and the seeds incorporated into the soil, and in the early summer before the new seeds had been dispersed, during the second and third years of the experiment. On 11 and 12 October 1990 an auger of diameter 4·75 cm was used to extract six samples of soil to a depth of 15 cm from each plot. Pairs of samples were taken from adjacent soil and bulked together to make three samples per plot. The samples were subdivided into three depths: 0–5 cm, 5–10 cm and 10–15 cm, and stored at 2 °C until processed. For the analysis, the numbers of seeds per square metre was calculated from the average of the three samples in each plot, in order to minimize the effect of spatial variation in the seed bank. On 12 June 1991, soil samples were taken in the same manner from eight of the 48 experimental plots; the remainder of the plots were sampled on 17 June with an auger of diameter 7·3 cm, and just three cores per plot were extracted and divided into three depths. The larger augur was used to make extraction of the soil cores easier, and to halve the number of cores required for a similar volume of soil. These samples were also stored at 2 °C until processed. Soil samples were extracted in the same manner from the plots using the larger augur on 22–23 October 1991 and 9–10 June 1992 and then dried at 70 °C and stored dry prior to processing.

The soil samples were processed individually. The soil was first mixed in a 500-ml solution of Calgon (Benckiser Ltd, Schiphol Airport, the Netherlands) to disperse the soil particles. The solution was then washed through a sequence of metal sieves of apertures 4, 2 and 1 mm to remove all seeds of A. sterilis. These were then counted.

Seed germination tests

The seeds of A. sterilis were tested for germinability each year. Samples of seeds supplied for the field experiment were tested at the start of the experiment; eight replicates of 25 seeds were placed on Whatman no. 1 filter paper (Whatman, UK) moistened with de-ionized water in Petri dishes in natural light at ambient temperature. The dishes were kept moist and monitored daily and any germinated seeds recorded and removed. In subsequent years, seeds collected from the field in late summer were tested for germinability by monitoring the germination of 20 replicates of 25 seeds, as previously.

The effect of seed burial on seedling emergence

Five replicates of 50 seeds were sown at each of seven soil depths: surface, 2·5, 5·0, 7·5, 10·0, 12·5 and 15 cm. The seeds were sown in 18-cm diameter pots in Levington compost (Fisons, UK) on 26 May 1992. The seeds planted on the surface were lightly covered with a thin layer of compost. The experiment was conducted in an unheated, unlit glasshouse and the pots watered as necessary. Pots were re-randomized weekly when seedling emergence was monitored and recorded. The experiment was completed on 6 June 1992.

Analytical methods

The proportion of seed produced in one season germinating over the course of the next season was found to be best modelled by a density-dependent function of the form:

gt + 1gm(1 + cSt)–1(eqn 1)

where gt + 1 is the proportion of the seeds produced at time t, St, germinating at time t + 1. In equation 1, gm is the maximal seed germination in the absence of density-dependent effects, and c is a constant describing the intensity of the reduction in mean germination with increasing seed density.

The data on seed production and biomass were used to estimate general allometric relationships of the form:

s = fwk(eqn 2)

where s is the number of seeds produced per plant, w is the weight (in g) of the shoot, and f and k are population parameters. Equations obtained from linear regression of the log10 transformed data were compared between nitrogen levels and between years following standard procedures (Zar 1996).

The effect of the seedling density, N, of A. sterilis on w, the mean biomass per plant, was described by the model (Watkinson 1980):

wwm(1 + aN)–1(eqn 3)

where wm estimates the shoot biomass of an isolated plant in the absence of competition, while a is a parameter that characterizes the strength of competition, scaling the reduction in mean performance with increasing density. The parameter a may also be assumed to incorporate the effects of competition from the crop (Watkinson 1985). There was no indication in the data that the exponent of equation 3 deviated from unity. Inclusion of an exponent in the density-dependent portion of equation 3 tended to over-parameterize the model with regard to model fitting, with the result that the parameter variance/covariance matrix became singular and standard errors could not be estimated.

Equations 1 and 3 were fitted using a maximum likelihood model that assumed an error distribution drawn from a continuous member of the exponential family, for example a gamma or exponential distribution (Pacala & Silander 1990; Rees, Grubb & Kelly 1996). A Rosenbrock pattern search (Rosenbrock 1960) was used to obtain numerically the maximum likelihood parameter estimates. The statistical significance of parameters was assessed using log-likelihood ratio tests (Dobson 1990).

Using the models fitted to the data it is possible to construct a general model predicting the total number of seedlings emerging at time t + 1, Nt + 1, as a function of the number of seedlings emerging post-cultivation at time t, Nt. Comparison of the fitted values of the population growth rate with the observed values should indicate, therefore, whether the process of model construction has tended to introduce a bias into the fitted overall model. The model was constructed by calculating (i) the numbers of seeds germinating prior to cultivation; (ii) subtracting this from the previous years’ seed production to calculate the numbers of seeds emerging post-cultivation; and (iii) using this figure, combined with an estimate of plant mortality (if, for example, plants are killed by control), to estimate the number of adult plants. Using equations 1, 2 and 3, after some algebra, this yields:

image(eqn 4)

The function φ (Nt) = (1 + aNt)–1 – (1 +[a + c1sm]Nt)–1 arises because of the inclusion of three phases of density-dependence in the life cycle. In equation 4, c2 is the density-dependent parameter for post-cultivation emergence (equation 1); sm is the maximal mean seed production of an isolated individual, given by applying equation 2 to wm, the maximal weight of an isolated plant (i.e. s = 


); gm is the pre-cultivation maximal seed emergence; it is assumed that, in the absence of density-dependent effects all seeds emerge post-cultivation; there is no carry-over of seeds between years; p is the proportion of seedlings that survive to flowering and a is the parameter from the yield-density response, equation 3.

Comparison with previous studies

In order to assess the degree to which the parameters of the life cycle estimated above are likely to vary across different sites, the results obtained from analysis of the experiment were compared with data published in previous studies on the population dynamics of A. sterilis. Data on seed germination were obtained from Froud-Williams (1983), Froud-Williams, Chancellor & Drennan (1984), Budd (1981), Mortimer, Putwain & Howard (1993) and Peters, Froud-Williams & Orson (1993), while data on the vertical distribution of seeds in the soil was obtained from Cousens & Moss (1990). The allometric relationships between seed production and plant biomass were compared with the results of Firbank et al. (1984) and Cousens, Pollard & Denner (1985), while the yield–density relationships were compared with those produced by Firbank et al. (1984). Firbank et al. (1984) also produced a model of the population dynamics of A. sterilis against which the models fitted to the population growth rate data may be compared. In addition to the results of these studies, which could be directly compared with the results from the field experiment, a number of other studies have explored the biology of A. sterilis, and in particular its seed ecology. These studies, which are particularly useful in assessing the impact of control practices on the dynamics of seed populations, were reviewed and their results are summarized.

Results and comparison with previous studies

Soil seed bank and seed biology

Surveys of the discard areas during the first autumn and spring showed that A. sterilis was not naturally occurring in the field prior to the start of the experiment. The germination tests indicated that viability of seeds was high [1989: 92(± 0·05)%; 1990: 99(± 0·02)%; 1991: 99(± 0·02)%]. Apart from the first year when the weeds were sown with the crop, roughly equal numbers of seedlings emerged before and after cultivation. Because cultivation kills many emerging seedlings, this represents an important loss of seeds. A consequence of the high level of germination was that only relatively low numbers of seeds persisted in the soil until the spring after they were shed (Fig. 1a). Although the methodology for obtaining the soil samples changed slightly between the years, the change in plant and seed densities was massive (Fig. 1a) and would have masked small biases that may have resulted from the change in methodology. The rates of seed loss due to mortality and germination in the field from seed shed to the time of flowering were estimated from the data in Fig. 1a as 98·2% (1990–91) and 99·6% (1991–92).

Figure 1.

Seed bank dynamics in Anisantha sterilis. (a) The dynamics of seeds and seedlings during the course of the field experiment. The figure shows the input of seed each year (the density at which seedlings were sown in 1989 or the numbers of seeds produced in 1991 and 1992) together with the numbers of seeds germinating before or after cultivation of the field. The error bars indicate ± 1 SD. (b) The vertical distribution of seeds in the soil measured in soil cores in 1990 (open) and 1991 (filled), compared with the pattern of vertical distribution of seeds measured under rigid tine cultivation (●) or ploughing (○) by Cousens & Moss (1990). (c) The effect of depth of burial on the emergence rates of seeds in a glasshouse experiment (see text for details).

Figure 1b shows the vertical distribution of seeds in the soil observed in the autumn cores following seed shed. In both years the distribution was uneven, with most seeds remaining within 10 cm of the soil surface. In 1991–92 this uneven distribution was more marked than in 1990–91. In Fig. 1b these vertical distributions are compared with the patterns of vertical distribution observed by Cousens & Moss (1990), who examined the distributions of plastic beads in the soil following cultivation. The vertical distributions of beads (initially scattered across the soil surface) they observed for rigid tine cultivation corresponded quite well to the patterns of seed distribution observed in this experiment. The distribution of seeds that they observed following ploughing was, however, quite different, with most seeds in this case being deposited at a depth greater than 10 cm.

The importance of considering the vertical distribution of seeds is demonstrated by the glasshouse experiment dealing with the effects of burial depth on emergence rates. As shown in Fig. 1c, germination was highest (nearly 100%) at depths less than 5 cm. At depths greater than 5 cm there was a rapid decline in emergence, with only very low (< 5%) emergence from depths greater than 10 cm. This corresponds well with the effect of depth on emergence of A. sterilis reported by Mortimer, Putwain & Howard (1993). They found that emergence was 100% within the top 5 cm of the soil, around 50% at depth of 5–10 cm, and 5% at depths of 10–15 cm.

The relationship between seed emergence (the probability of a seed germinating to give a seedling either pre- or post-cultivation) and density indicated strong density-dependent effects (Fig. 2). The proportion of seeds germinating prior to cultivation was calculated simply as the number of seedlings emerging divided by the number of seeds produced at the end of the previous cropping season. For the seeds emerging following cultivation, the proportion emerging was estimated as the number of seedlings that emerged after cultivation divided by the number of seeds remaining after pre-cultivation germination (i.e. the number of seeds produced in the summer minus the number that germinated prior to cultivation). As indicated in Fig. 2a, b, density-dependence was observed in the levels of emergence both before and after cultivation, although there was an indication in these plots that density-dependence was stronger post-cultivation than pre-cultivation.

Figure 2.

Density-dependent emergence rates in Anisantha sterilis. (a) The effect of increasing density of seeds produced on the proportion of seeds emerging prior to cultivation. (b) The effect of increasing the density of seeds remaining after cultivation on emergence rates. (c) The effect of increasing the density at which seeds are produced on the total proportion of seeds emerging.

This pattern was confirmed by fits of equation 1 to the data, with the model fits being very much better for post-cultivation emergence than for pre-cultivation emergence (Table 1). In particular, it was possible to fit models to the emergence data from each year at both nitrogen levels for post-cultivation emergence (Table 1c), whereas equation 1 could only be fitted to the data combined over the 3 years for pre-cultivation emergence (Table 1b). The value of gm was much lower pre-cultivation than post-cultivation, ranging from 0·17 to 0·23 for pre-cultivation emergence. In contrast, the log-likelihood ratio tests indicated that the value of gm did not differ significantly from unity post-cultivation, confirming the pattern that would be expected given the results of the germination tests (above). While, in practice, the maximum level of emergence is likely to be less than unity, this would not be detectable using non-linear modelling as the germination tests indicated that levels of germination were likely to range between 92% and 99% (above). The values of c ranged from 2·1 × 10–5 to 3·7 × 10–5 for pre-cultivation emergence, but from 5·7 × 10–4 to 1·9 × 10–3 for post-cultivation emergence, indicating that the strength of density-dependence is higher post-cultivation than pre-cultivation.

Table 1.  Density-dependent emergence rates. Equation 1 was fitted to the data in Fig. 2, using the methodology outlined in the text. Equation 1 was fitted to (a) the overall proportion of seeds emerging; (b) the proportion of seeds emerging pre-cultivation; and (c) the proportion of seeds emerging post-cultivation. The r2 value records the proportion of variance in the log-transformed data explained by the fitted model. Where the value of gm = 1, inclusion of a non-unity value of gm was determined to not significantly improve the fit of the model according to a log-likelihood ratio test (see text for details)
 Treatmentgm± SEc± SEr2
(a) Overall emergence response
Combined N19901– 4·5 × 10–44·0 × 10–50·55
 19911– 1·8 × 10–41·0 × 10–50·64
 19921– 1·5 × 10–48·4 × 10–60·69
 Overall1– 1·9 × 10–41·1 × 10–50·54
High N19901– 4·4 × 10–45·0 × 10–50·55
 19911– 1·9 × 10–42·0 × 10–50·68
 19921– 1·5 × 10–41·2 × 10–50·71
Low N19901– 4·7 × 10–46·7 × 10–50·53
 19911– 1·8 × 10–41·2 × 10–50·58
 19921– 1·6 × 10–41·1 × 10–50·44
(b) Pre-cultivation emergence rates
Combined N 0·1960·0232·8 × 10–58·0 × 10–60·34
High N 0·1710·0262·1 × 10–58·0 × 10–60·34
Low N 0·2280·0433·7 × 10–51·4 × 10–50·33
(c) Post-cultivation emergence rates
Combined N19901– 9·0 × 10–46·0 × 10–50·66
 19911– 5·8 × 10–43·0 × 10–50·70
 19921– 1·3 × 10–31·8 × 10–40·69
 Overall1– 8·9 × 10–46·0 × 10–50·91
High N19901– 9·6 × 10–49·0 × 10–50·52
 19911– 5·8 × 10–45·0 × 10–50·58
 19921– 1·9 × 10–33·8 × 10–40·71
Low N19901– 8·4 × 10–48·0 × 10–50·68
 19911– 5·7 × 10–43·0 × 10–50·75
 19921– 9·9 × 10–49·0 × 10–50·57

Table 2 summarizes a number of factors that have been shown to affect the germination and survival of seeds of A. sterilis. These studies indicate that germination levels tend to be enhanced by periods of drying following seed shed (Okereke, Blair & Caseley 1981; Hilton 1987) and that germination rates are depressed by increasing moisture (Mortimer, Putwain & Howard 1993). In reality, therefore, germination will tend to be enhanced by hot and dry weather during the late summer after the crop is harvested, and depressed by wet weather during this period and the autumn. Germination levels are depressed by light (Ellis, Hong & Roberts 1986; Hilton 1984) and are highest following burial (Froud-Williams 1983), particularly in the presence of stubble (Howard et al. 1991; Mortimer, Putwain & Howard 1993), although burial below 7·5 cm depressed germination (Fig. 1c; Froud-Williams, Chancellor & Drennan 1984; Mortimer, Putwain & Howard 1993). In general, Table 2 confirms the patterns seen in our data and we would expect to observe high (> 90%) levels of seedling emergence in the autumn following minimum tillage. Table 2 indicates that a number of factors may reduce this considerably. The impact of the presence of crop stubble and the effects of stubble burning in particular may lead to losses of seed in the range of 91–99·9% (Froud-Williams 1983; Howard et al. 1991).

Table 2.  Review of previous studies on the germination behaviour of seeds of Anisantha sterilis. These studies provide information on seed biology and are compared in the text with the results of the field experiment. The table indicates the source of information, the effect studied, a brief summary of the results of the study, and the type of study performed (germination cabinet experiment, glasshouse experiment or field experiment)
1Seed moisture content, time to burial and temperature on germination over 3 weeks96% germination of dried seed; 61% germination of fresh seed; 98% germination of seed buried immediately following shed, declining to 29% 24 weeks after shed; 90% emergence of seeds at 26/16 °C, 16/10 °C and 14/10 °C; 68% emergence at 10/6 °CGermination cabinet and glasshouse
Effects of method of straw disposal and cultivation regime on germination and mortality of seeds97% mortality of seeds; 94% mortality of seedlings due to stubble burning; shallow cultivation increased seedling emergence due to burial of seedField experiment
3Seasonal patterns of emergence, depth of burial and timing of cultivation (spring vs. summer)All germination observed between October and January; 93–98% emergence of seeds in top 7·5 cm of soil; no influence of timing of cultivation on numbers emergingField experiment
4Storage temperature and light on germination in two populationsGermination delayed by white and red light; no difference between populationsGermination cabinet
5Light on germinationGermination delayed by high levels of white lightGermination cabinet
6Effect of seed drying on germinationDried seeds (< 10% moisture content) germinate (at 15 °C) within 4 days; fresh seeds (52–54% moisture) germinate within 3–4 weeksGermination cabinet
7Dissemination of seeds by harvesting and cultivation; effect of cultivation and soil surface type on emergenceSeeds naturally disperse less than 1 m; combine harvester may increase this distance to up to 20 m; cultivation increases this distance to 2 m; 0·09% of seeds establish in uncultivated soil within stubble; 65% in soil cultivated to 5 cm over 2 weeks Field experiment
8Effect of cultivation and water supply on germination ratesIncreasing water supply (1 ml day–1 to 5 ml day–1) decreases germination from 100% to 65%; 90% germination of seed over 55 days in soil cultivated to 5 cm; 60% germination in uncultivated stubbleGlasshouse and field experiment
9Dormancy of seed on soil surface during set-aside; variations in germination rates between populations‘High’ and ‘low’ dormancy populations identified; 40% dormancy of ‘High’ dormancy populations on soil surface, 80% when buried; 100% germination of ‘low’ dormancy population under both conditions.Field experiment
10Predation of seeds in field margins27·7% of seeds removed by granivores in uncut margins; 5·8% of seeds removed by granivores in cut marginsField experiment

Seed production

Allometric models (equation 2) gave very good descriptions of the relationship between seed production and biomass, explaining between 75% and 96% of the variance in the log-transformed data (Table 3). In each year there were no differences between the slopes (c) or intercepts (b) between nitrogen levels, and visual inspection of the values in Table 3 yields no consistent differences between these parameters under the two nitrogen levels. Consequently these data were combined to generate allometric models for each year's data. This analysis revealed significant differences between intercepts calculated for 1990 and 1991 and significant differences between the slopes (b90 = b91b92). As illustrated in Fig. 3a, the scale of the impact of these differences on seed production was relatively slight, particularly in the range 0·1–1·0 g, which is approximately the range of mean weights per plant observed during the course of the experiment (Fig. 4). The allometric relationships given by the parameter values in Table 3 are compared in Fig. 3b with those fitted in other studies (Firbank et al. 1984; Cousens et al. 1988; note that the dry weights recorded by Firbank et al. and Cousens et al. include the biomass of seeds as well as vegetative biomass, while our dry weights include only the vegetative parts) and indicate that the slope of allometric relationship in their populations is very close to that reported here.

Table 3.  The effect of season and nitrogen (N) fertilizer on the allometric relationship between seed production and shoot biomass as quantified by equation 2. Equation 2 was fitted to the log-transformed data on seed production and plant weight
YearN level (kg ha–1)nc (log c ± SE)br2
199012021131·8 (2·12 ± 0·01)0·878 (± 0·041)0·96
 24023114·8 (2·06 ± 0·02)0·961 (± 0·084)0·86
 Combined44123·0 (2·09 ± 0·01)0·916 (± 0·047)0·90
199112024123·0 (2·09 ± 0·03)0·946 (± 0·058)0·92
 24024104·7 (2·02 ± 0·03)0·814 (± 0·081)0·81
 Combined48112·2 (2·05 ± 0·02)0·948 (± 0·046)0·89
199212024131·8 (2·12 ± 0·02)1·210 (± 0·071)0·87
 24024135·0 (2·13 ± 0·04)1·240 (± 0·105)0·75
 Combined48131·8 (2·12 ± 0·02)1·200 (± 0·061)0·80
 Combined140112·2 (2·05 ± 0·01)0·988 (± 0·024)0·90
Figure 3.

Allometric models for seed production by Anisantha sterilis (equation 1). (a) Models fitted to the data obtained in this study, split by year (see Table 3 for parameter values). (b) Models fitted by Firbank et al. (1984) and by Cousens et al. (1988). Note that while the vegetative weights recorded in this study do not include the mass of seeds, those of Firbank et al. and Cousens et al. do.

Figure 4.

Intra-specific yield–density relationships in Anisantha sterilis. (a) The effect of increasing density of seedlings on the mean weight per individual, with the yield–density response (equation 4) fitted to the overall data (Table 4). Inset: the same data plotted on a double logarithmic scale. (b) The yield–density models fitted to the data from each nitrogen level, and compared with the models fitted by Firbank et al. (1984). As the models derived by Firbank et al. predict vegetative weight including the weight of seeds, whereas the models fitted to the data from this study predict vegetative weight excluding the mass of seeds, the models of Firbank et al. have been corrected to remove seed biomass. It was assumed that seeds constitute 70% of the above-ground biomass (Lintell Smith 1995).

Yield–density relationships

The fits of equation 3 to the data on yield–density relationships indicated that plant performance declined with density and that there were minimal impacts of the level of applied nitrogen fertilizer on the model parameters (Table 4). This is clearly demonstrated in Fig. 4a, where there is little apparent difference between the yield–density relationships observed in plants grown at the two nitrogen levels. The models fitted to the data derived from this experiment were in good accord with previously published yield–density relationships. As shown in Fig. 4b, the yield–density relationships for the two nitrogen levels were very similar to the one fitted by Firbank et al. (1984). As also shown in Fig. 4b, there was a considerable effect of the crop on the performance of A. sterilis. As discussed below, this may provide an explanation of why the effects of varying the nitrogen level on performance were observed to be so low.

Table 4.  Intra-specific yield–density relationships in Anisantha sterilis. The data were combined across the 3 years of the study and the model (equation 3) was fitted to data from each nitrogen level separately, and for the data from both nitrogen levels combined. All coefficients are significantly different from zero
Treatmentwm± SEa± SEr2
High N1·130± 0·1480·0024± 0·00050·63
Low N0·901± 0·0820·0014± 0·00030·66
Combined1·073± 0·2070·0018± 0·00060·62

Patterns of population growth and modelled dynamics

The mean parameter values are summarized in Table 5. There was generally a good correspondence between the fitted and observed population growth rates, with little evidence of systematic deviation with changing density (Fig. 5a). The combination of the fitted models therefore provided a good overall description of population growth.

Table 5.  Summary of parameters required to model the population dynamics of Anisantha sterilis (see equation 4) under the conditions of the field experiment, i.e. minimum tillage and no herbicide applied
gm1Maximal rate of pre-cultivation emergence10·20
c1Pre-cultivation density-dependent parameter12·8 × 10–5
gm2Maximal rate of post-cultivation emergence11·00
c2Post-cultivation density-dependent parameter18·9 × 10–4
fAllometric constant2112·2
kAllometric exponent21·00
wmMaximal mean plant biomass31·07
aDensity-dependent parameter for yield-density relationship30·002
pProportion of seedlings surviving to flowering60–1
Figure 5.

Analysis of the observed and fitted population growth rates of Anisantha sterilis. (a) The relationship between the observed and fitted (by combining the models fitted in Tables 1, 3 and 4 for each year) population growth rates. The dashed line is y = x. (b) The impact of density-dependent germination rates on population growth rates, calculated by the ratio of the growth rate predicted by combining the models fitted in Tables 1, 3 and 4 to that predicted by setting the parameter c in equation 3 to zero. (c) The patterns of population growth predicted by combining equations 1, 2 and 3 fitted to the data of each of the 3 years of this study with the population growth rates observed by Firbank et al. (1984).

The variations in population growth rates in Fig. 5a are largely determined by density-dependence; hence this played a significant role in determining population growth rates and population numbers. Density dependence was found, however, to affect both individual mean biomass and the emergence of seedlings. Typically it has been envisaged that annual plant populations are regulated through density-dependent reductions in mean fecundity (Watkinson 1985), but density-dependent emergence played a major role in determining population growth rates here. Figure 5b records the ratio of the predicted population growth rate in the absence of density-dependent emergence to that observed with density-dependent emergence (i.e. how many times larger the population growth rate would be without density-dependent emergence) across the range of densities for each year. This analysis indicated that populations would grow between approximately two and nine times faster in the absence of density-dependent emergence and if solely regulated by density-dependent fecundity.

Figure 5c compares the population growth rates predicted by the models fitted to the data from the experiment with those recorded by Firbank et al. (1984) in populations subject to comparable management (i.e. cropped with wheat; minimally tilled or rotavated; no herbicide applied) in the periods 1983–84 and 1984–85. The pattern of population growth recorded in these populations corresponded well with the models fitted in this study, with the rates fitted in 1991 and 1992 being very similar to the patterns of population growth recorded by Firbank et al.

As noted above, the complexity of equation 4 arises because of the inclusion of three sources of density-dependence: (i) in pre-cultivation emergence; (ii) in post-cultivation emergence; and (iii) in plant performance. One important consequence of this is that population sizes tend to be buffered against year-to-year variations in emergence levels prior to cultivation (Fig. 6). Clearly the impacts of varying the level of pre-cultivation emergence, gm, on population size are minimal. This means that despite the potential for significant variance in levels of pre-cultivation emergence (Table 2), the impacts of such variations on population dynamics will be slight.

Figure 6.

Impacts of varying the rate of pre-cultivation emergence on the equilibrium density of plants of Anisantha sterilis as predicted by equation 4. gm, the maximum rate of emergence, was varied at a range of values of p, the proportion of plants surviving control, as indicated. Other parameters were held at their mean values. The vertical dashed line indicates the mean value of gm fitted to the data from the experiment (see Tables 1 and 5).


The general picture of the population dynamics of A. sterilis that emerges from the analysis presented above is one of constancy from year to year and across sites, and of minimal impacts of varying nutrient levels. In the absence of herbicide application, management in the form of the timing and type of cultivation plays the dominant role in determining population persistence as well as population size. Under minimum tillage densities of plants rapidly become very high. Density-dependence plays an important role in determining population numbers, and acts primarily through effects on emergence. Importantly, the dynamics of A. sterilis appear, in the absence of herbicide application, to be largely invariant from site to site or across years.

The main sources of variability identified in the system result from year-to-year variability in germination rates, induced by variations in the timing of cultivation, as well as a range of other factors (Table 2). The impacts of such variations on population dynamics are, however, minimal (Fig. 6).

Dynamics and density dependence

The relative constancy of the population dynamics of A. sterilis from year to year is evidenced by the relatively low degree of variability in the maximal mean per capita finite rate of increase. Using the information on seed production and germination, and setting the density-dependent parameters in equation 4 equal to zero, we estimate the finite rate of increase of A. sterilis as 131 (1989–90), 120 (1990–91) and 143 (1991–92), which compares with a value of 129 recorded by Firbank et al. (1984). For these estimates, this yields a coefficient of variation of the finite rate of increase of only 7·2%, or of only 1·5% if the data are logarithmically transformed. While we are confident that dynamics are relatively invariant across the five growing seasons, the degree to which this estimate of the degree of variance in population dynamics is typical in the longer term depends on whether dynamics are likely to be influenced by rare extreme conditions and how this influences geometric mean population growth (Freckleton & Watkinson 1998a). The data reviewed in Table 2 indicate that, apart from variations resulting from cultivation, the germination of seeds is most likely to be influenced by rates of seed drying and temperatures. While we have not observed that such factors do significantly impact on population dynamics, conditions such as very wet late summers and autumns could tend to increase the level of variability in population dynamics. At moderate to high population densities, however, the impacts of such variability would be buffered by the multiple density-dependence in the life cycle.

The source of density-dependence in the levels of emergence is not clear. The seed germination tests did not show that maximal levels of germination of seeds varied widely between years. This implies that seed germination was unaffected by the increasing densities at which the parent plants grew during the course of the experiment. Density-dependence could arise in the level of seed germination (King 1975; Gorski, Gorska & Nowicki 1977; Rees & Brown 1991), the level of seed mortality (Watkinson, Lonsdale & Andrew 1989) or in the level of mortality between seed germination and seedling emergence. As indicated in Table 2, germination tends to be reduced by the presence of cover in the form of stubble (Mortimer, Putwain & Howard 1993), as well as high levels of red light (Hilton 1984, 1987) as would occur under a developing canopy. Whatever the mechanisms of this density-dependence, the importance of this response is that it sets a maximum limit to the numbers of seedlings that emerge, and tends to buffer populations against temporal variability (Fig. 5b and Fig. 6).

Impacts of nitrogen on population dynamics

The impact of varying nitrogen level on any aspect of the life cycle of A. sterilis was minimal. This is in contrast, for example, to the significant effects of changing nitrogen level on the yield of the crop (Lintell Smith, Watkinson & Firbank 1991). The explanation we suggest for this lack of response to changing nitrogen levels is that changes in performance owing to changed nutrient levels will be accompanied by compensatory changes in the per capita effects of competition. The rationale for this is that, while reducing nitrogen levels may reduce maximal plant sizes, there will be a corresponding reduction in the strength of intraspecific competition. This is because as plants become smaller, the effects of competition at a given density will become weaker. In a highly competitive environment (the mean weight of an isolated individual was reduced from 42·6 g to 4·8 g through the effects of competition from the crop in the study of Firbank et al. 1984) such compensatory changes may mask the effects of changing nutrient levels (Morris & Myerscough 1984; Freckleton & Watkinson 1997).

The low impact of varying nitrogen levels reported here and in other experiments (McCloskey et al. 1996, 1997) would appear to be in contrast with the results of long-term studies that have demonstrated major effects of nutrient levels on community and population dynamics (Crawley & Rees 1996; Jørnsgård et al. 1996). The range of variation in nitrogen level employed here was intended to encompass an agriculturally realistic range. Had we, for example, contrasted the conditions of normal levels of nitrogen fertilizer with conditions of no fertilizer input, then the results may have been different.

Responses to management

From the point of view of predicting the abundance of A. sterilis the most important results to emerge are that key population parameters are relatively invariant between sites and from year to year, and that at moderate to high densities the buffering effect of density-dependent emergence serves to negate most other sources of variability. This means that the model developed here has general applicability and is not restricted to a particular set of conditions. The effects of varying nitrogen levels also show that, under agriculturally realistic levels, there is little scope for managing the abundance of the weed through manipulating fertilizer applications. Instead it is the form of cultivation as well as the application of herbicides that are likely to have the major impacts on weed numbers (McCloskey et al. 1996).

In terms of understanding the consequences of recent agricultural changes, or predicting future trends in weed abundance, it is important to consider how the life cycle characteristics of A. sterilis impinge upon its dynamics and how its response to management compares with other arable weeds.

The life cycle of A. sterilis is, in some senses, an extreme one. The lack of a seed bank, combined with the inability of seeds to germinate from depth, is restrictive. While many arable weeds in the UK are unable to germinate from much below 5 cm, relatively few lack a seed bank. In the case of systems subject to minimum tillage, the germination characteristics of A. sterilis mean that most seeds are in a position to germinate and establish following shedding. When ploughing occurs, however, most seeds fail to produce seedlings. Other species, on the other hand, would respond differently to such changes. This is demonstrated in Fig. 7a, which shows the effects of cultivation (as predicted by published population models; see figure legend for details) on population numbers of three other species of grass weeds, Alopecurus myosuroides, Avena fatua and Avena sterilis. These species differ from Anisantha sterilis in that their seeds tend to persist longer in the soil and in that they tend to produce fewer seeds. It is clear that while the effects of ploughing on the population density of Anisantha sterilis are severe, the effects on densities of other species are much less pronounced. This difference results from the presence of a seed bank in the other species: a proportion of the seeds buried by ploughing will produce seedlings in future years.

Figure 7.

Effects of cultivation on (a) densities and (b) the level of mortality required to control Anisantha sterilis (as measured by p, see Table 5) compared with the effects on three other species of annual grass weed. The densities of Anisantha sterilis were predicted by assuming that all seeds could germinate in the absence of density-dependence under minimum tillage, but that only 5% of seeds could germinate post-cultivation when ploughed (i.e. gm2 = 0·05). The densities predicted for Alopecurus myosuroides and Avena fatua under UK conditions were taken from Doyle, Cousens & Moss (1986) and Cousens et al. (1986), respectively. The densities of Avena fatua under Australian conditions and Avena sterilis were predicted using the models of Gonzalez-Andujar & Fernandez-Quintanilla (1991) and Medd & Pandey (1993), respectively. Densities for populations subject to ploughing were not available from the latter two studies. We therefore substituted the germination parameters from Cousens et al. (1986) for these models.

It is clear that the maximum densities of Anisantha sterilis under minimum tillage tend to be much higher than for the other species. There are two reasons for this. First, Anisantha sterilis has a very high maximum seed production compared with the other species, and secondly, as all of its seeds potentially germinate almost immediately following shedding, its seeds do not suffer mortality while dormant in the soil. Consequently Anisantha sterilis has a higher finite rate of population increase than the other species, which translates into a higher abundance. One consequence of this is that the level of herbicide efficiency (as measured by the proportion of plants that are removed by chemical treatments) that is capable of eradicating the other weed species, would be insufficient to control Anisantha sterilis under conditions of minimum tillage (Fig. 7b). While it has been noted previously that herbicides may be ineffective in controlling Anisantha sterilis under conditions of minimum tillage (Peters, Froud-Williams & Orson 1993), the lack of detailed demographic data means that it is unclear whether this is a consequence of the comparatively high finite rate of increase of Anisantha sterilis or a lower susceptibility to herbicides; the results presented above would appear to suggest the former.

That the form of cultivation plays the dominant role in determining the presence and persistence of Anisantha sterilis is demonstrated in Fig. 8, where the predicted effects of stubble burning on densities of Anisantha sterilis and Alopecurus myosuroides have been contrasted. While burning affects the density of Anisantha sterilis, predicted densities are reduced to a level only slightly lower than that of Alopecurus. Ploughing, on the other hand, reduces densities by a further order of magnitude. In contrast, the abundance of Alopecurus decreases only slightly with ploughing and under such conditions stubble burning then increases abundance.

Figure 8.

Effects of stubble burning and cultivation on densities of Anisantha sterilis compared with effects on populations of Alopecurus myosuroides. The effects of cultivation on populations of Anisantha sterilis were modelled as in Fig. 7. The effects of stubble burning were modelled by assuming that 97% of seeds and 94% of seedlings are removed prior to cultivation (see Table 2). Densities of Alopecurus myosuroides were predicted using the model of Cousens et al. (1986).

What the results presented in Figs 7 and 8 make clear is the difficulty of a priori predictions of the effects of management on weed assemblages. Superficially, the four species analysed are ecologically very similar. In the absence of detailed demographic data it would therefore be impossible to predict the domination by Anisantha sterilis under conditions of minimum tillage. Based on these results, we could generalize and predict that minimum tillage will favour winter annual grasses that lack a seed bank. In the UK, however, there is a range of such species that do not become weeds, while in other countries, such as Australia, where minimum tillage is widespread, Anisantha sterilis is not reported to be a problem but other annual grasses are, such as Avena fatua, Lolium rigidum and Vulpia spp. (Medd et al. 1996).

In general there are a number of problems associated with modelling the dynamics of multi-species mixtures. These include measuring and modelling differential responses of species to the same sets of environmental conditions and interactions between species. As weed populations within fields are generally maintained at low densities through control, we would expect interactions between species to play a minor role in determining dynamics (McCloskey et al. 1997). Hence analyses, such as the one presented here, that concentrate on the differential responses of a suite of weed species to the same management regimes will make a useful first step in analysing the dynamics of multi-species weed assemblages.

In terms of explaining the occurrence of weeds and in predicting the impacts of future changes in farming practice on weed assemblages, our data and approach have shown how we can generate predictions of dynamics within a system that are robust to the impacts of spatial and temporal variability (Freckleton & Watkinson 1998b). In evaluating the effects of management on weed population dynamics and assemblages we have shown how simple population models can be used to explain patterns of occurrence. In the future such approaches and models may be capable of generating predictions of where and under what circumstance particular species will be weeds.


We should like to thank Jenny Smith for assistance with the field work and Tudor Thomas and IACR Broom's Barn for help with setting up and managing the experiment. Financial support was received from the NERC through the Joint Agriculture and Environment Programme and GR9/02619 to A. R. Watkinson.

Received 25 July 1998; revision received 27 January 1999