Seasonal life-history models for the integrated management of the invasive weed nodding thistle Carduus nutans in Australia


Katriona Shea, The Pennsylvania State University, Department of Biology, 208 Mueller Laboratory, University Park, PA 16802, USA (fax +814 865 9131; e-mail


  • 1It is widely accepted that combining several control options into integrated pest management strategies is the most effective way to provide long-term suppression of pest populations. However, full factorial field trials of all single and integrated control options for a pest species would be prohibitively expensive and time consuming. Methods to allow triage of the huge array of management options would be of great value in streamlining the decision-making process.
  • 2We present a seasonally structured, individual-based model, specifically designed to compare and rank detailed management strategies for a noxious pasture weed. The model structure is determined in part by the demographic data available, and in part by the management options under consideration. The case study is for nodding thistle Carduus nutans in Australia. Eight years of demographic data, for more than 8000 mapped plants, were used to parameterize the model, which is age-, size- and density-dependent and incorporates individual variation. Management options for this plant include three biocontrol agents, as well as conventional herbicide and grazing management strategies, which can be used alone or in a variety of combinations. Data on management impacts were drawn from multiple studies.
  • 3The model predicts that the root-crown weevil Trichosirocalus mortadelo will more effectively suppress weed populations than either of the two flowerhead-feeding insect agents Urophora solstitialis and Rhinocyllus conicus. Crash grazing (up to four times the regular grazing pressure) in any single season, or when most effectively applied across spring and summer, is less effective than T. mortadelo, while combinations of crash grazing and biocontrol agents strongly decrease weed population persistence. However, lethal herbicide is the best single strategy, while spring spray–grazing (a combination of non-lethal herbicide and grazing) is the best integrated weed management strategy.
  • 4Synthesis and applications. The model is structured by, and serves to integrate, available information on demography and management from multiple sources. The subset of strategies that performed well forms the focus for fewer, more thorough, field trials. The decision-making approach illustrated here is also applicable to any species and any array of management options.


A major problem facing managers is to find the best management strategy for invasive species among the plethora of possibilities. Pests may be managed by a suite of biological, chemical and cultural methods that operate on different spatial and temporal scales. The effective integration of these options may be hard to evaluate in real-time field trials, where the benefits of a particular strategy might only be measurable at far longer time scales.

Modelling of invader dynamics and of possible management options can facilitate the search for the best management strategy (Godfray & Waage 1991; Rees & Paynter 1997; Shea & Kelly 1998; Shea et al. 1998; Buckley et al. 2001, 2004, 2005; Buckley, Briese & Rees 2003a,b; Rees & Hill 2001; Shea et al. 2005). Models help to summarize relevant biology and ecology, highlight uncertainties, and assess and prioritize potential control strategies through ‘computer experiments’ for field testing. Models also allow us to ask questions that are hard or even impossible to answer in the field. Thus a modelling component may save valuable time and resources.

Past models of invasive plants have taken many different forms, from models based on basic difference equations (Caughley & Lawton 1981), matrix models (Shea & Kelly 1998; Shea et al. 2005), spatial models (Rees & Paynter 1997) and individual-based models (Buckley et al. 2003b) to full-blown process-based simulation models with many parameters (Kriticos et al. 2003). The type of model is usually influenced by the extent of available data and the types of ecological or management question being asked. Rarely, however, have management options and the time frames over which these can be applied been the basis of model construction. Models that do not take such aspects into account may fail to provide the decision-support component required to help land managers. Furthermore, the integrated management of exotic invasive species increasingly requires the compatible use of biological control with more conventional weed control options and, to our knowledge, only twice previously has this been the aim of a simulation model (Rees & Hill 2001; Buckley et al. 2003b).

In this study we developed the approach of management-motivated modelling for integrated weed management with a case study of an important noxious weed. Nodding thistle Carduus nutans L. (Asteraceae) has been accidentally introduced into four continents outside its native range: North and South America, Australasia and southern Africa. It has become an extensive weed of perennial pasture systems in cold winter climates, given a tendency to form large dense infestations that can make up more than 60% of the available biomass (Popay & Medd 1995). In Australia alone it is estimated that 80 000 ha are heavily infested, 220 000 ha are infested at intermediate levels and 800 000 ha are lightly infested (total 1·1 million ha). The estimated cost to wool production of C. nutans is Australian $9·4 million per annum; including the loss of meat production generates economic cost estimates of Australian $18·8 million per annum (Popay & Medd 1995).

Carduus nutans is a short-lived monocarpic plant that can live up to 3 years (Popay & Medd 1995; Woodburn & Sheppard 1996). Most germination is linked to rainfall and takes place in autumn from a persistent seed bank. This is followed by a period of vegetative growth of variable length as a rosette, before a single flowering event. Flowering is vernalization-, age- and size-dependent (Popay & Medd 1995). Seeds are produced in capitula in summer. Seeds are either dispersed by wind on a well-developed pappus an average of about 2·1 m (O. Skarpaas & K. Shea, unpublished data) or shed with the capitula as these drop to the ground below the parent plant (Smith & Kok 1984). Small amounts of seed can be dispersed locally by ants, heavy rainfall or within detached capitula that lodge in the fur of grazing livestock; however, most long-distance movement results from accidental contamination of seeds or hay of other pasture species moved for commercial purposes (Popay & Medd 1995).

A variety of approaches has been used to control C. nutans. Three insects have been widely distributed as biocontrol agents for C. nutans: the receptacle weevil Rhinocyllus conicus Frölich, receptacle gallfly Urophora solstitialis L. and root-crown weevil Trichosirocalus mortadelo (Alonso-Zarazaga & Sanchez-Ruiz 2002: formerly Trichosirocalus horridus (Panzer); Julien & Griffiths 1999). Carduus nutans is also controlled by conventional weed control tactics, involving herbicide and grazing strategies (Popay & Medd 1995). Here again there are many options involving chemical levels, and timing of application, that multiply further when combined strategies are considered. Successfully integrating chemical and grazing strategies, increasingly in the presence of biocontrol agents, intimately depends on the overall effect of such strategies on long-term thistle reproductive success.

In this study we synthesized an extensive ecological database for C. nutans in Australia, as well as data on impacts from the literature, into an individual-based model of the plant life history and dynamics, specifically designed to assess optimal management strategies and application timing in Australia. This general approach is applicable to any invasive pest species. We used the model to compare the potential effectiveness of single and integrated control options (including conventional management strategies and different biocontrol agents) at providing long-term suppression of the target weed.

Materials and methods

We developed an individual-based simulation model (IBM) for C. nutans based on field data from Australia. Most managers with a C. nutans problem make a decision to manage the weed based on season (e.g. whether to spray in autumn or spring), and the impacts of most of the biological control agents available for nodding thistle are also highly seasonal. For this reason, a seasonal time step was used in the data analysis and model (where seasons were chosen to coincide with the onset of the rains rather than with a fixed calendar date). The overall structure of the model, including seasonal transitions (from spring to summer to autumn to winter, etc.) between stages, is shown in Fig. 1.

Figure 1.

Carduus nutans life cycle: seasonal transitions between physiological stages, including individual variation. The four life-history stages are seed, seedling, rosette and flowering plant. Transitions between stages are indicated by arrows on the graph. Note that all plants that flower die (C. nutans is a monocarpic perennial).

The model was parameterized with data collected from a field site at Kybeyan near Canberra in southern New South Wales, Australia (grid reference 36°10′45″S, 149°27′45″E) between 1988 and 1996. At the site, 10 fixed quadrats (each 0·5 × 0·5 m) were placed at random within a 20 × 20 m study area in a grazed paddock infested with C. nutans. Censuses used in this study were taken approximately every 6 weeks (i.e. approximately two per season) for just over 8 years. Individuals in the quadrats were mapped and followed throughout their lives. Data were collected for 8489 plants in total.

Plants in the model are characterized by their stage (seed, seedling, rosette and flowering plant). Transitions between those stages depend on individual characteristics (age and size), population-level parameters (seedling and rosette density) and season as defined by the data. Statistical analyses assessed fate variables (including germination, survivorship and probability of flowering, growth and fecundity) as a function of individual- or population-state variables, in a nested or hierarchical structure (Shea 1994; see also Caswell 2001; Table 1). These analyses were used to parameterize the model.

Table 1.  Results of statistical analysis of seasonal data; these equations and the measured variation provide the functions and parameters used in the IBM. In all tables: a, age; s, maximum size, R, rosette density; J, juvenile (i.e. seedling) density; f, seed set (fecundity); σ2, overall variance in the dependent variable; %, percentage deviance explained (where appropriate). All variables were retained if significant at P < 0·05. NA, Not applicable
ProcessPotential explanatory variablesSeasonal formulae from minimal adequate modelnσ2%
GerminationSeason, seed bank, R, f    
Spring ln(J + 1) = 1·149 802·497 
Summer ln(J + 1) = 1·418 802·935 
Autumn ln(J + 1) = 2·409 803·489 
Winter ln(J + 1) = 1·252 902·629 
Seedling survivalSeason, J, R, aln(p/(1 – p)) = −0·8011736  
Seedling size increaseSeason, J, R, a    
Spring ln(p/(1 – p)) = 0·9831 + 1·843a − 0·6837ln(J + 1) 78 15·1
Summer ln(p/(1 – p)) = 4·344–1·698a − 0·7962ln(J + 1)110 17·2
Autumn ln(p/(1 – p)) = 2·342 + 0·687ln(R + 1) − 1·02ln(J + 1)164 18·8
Winter ln(p/(1 – p)) =−4·303 + 1·928ln(R + 1) 94 39·8
Seedling growthSeason, J, R, a    
Spring ln(new size) = 2·554 482·480 
Summer ln(new size) = 5·215 − 0·4812ln(J + 1) 971·85322·3
Autumn ln(new size) = −1·05 + 0·881a + 0·619ln(J + 1)1061·32425·1
Winter ln(new size) = 2·071–0·784a 431·17511·7
Rosette survivalSeason, R, a, s    
Spring ln(p/(1 – p)) = −0·7935 + 0·5707ln(s)219 12·9
Summer ln(p/(1 – p)) = −1·048 + 0·4176ln(s)227  8·0
Autumn ln(p/(1 – p)) = −0·5599 − 0·607a + 0·404ln(s)318 10·8
Winter ln(p/(1 – p)) = −2·352 + 0·5446ln(s) + 0·6856ln(R + 1)256 17·8
FloweringSeason, R, a, s    
Spring ln(p/(1 – p)) = −11·35 + 1·928ln(s)196 63·4
Summer ln(p/(1 – p)) = −8·428 + 0·6339a + 1·054ln(s)179 37·8
Autumn ln(p/(1 – p)) = 0  0 NA
Winter ln(p/(1 – p)) = 0  0 NA
FecundityR, a, sln(f + 1) = 3·364 + 0·512ln(s) 751·132 
Rosette growthSeason, R, a, s    
Spring ln(new s) = 1·591 + 0·9184ln(s) – 0·1981ln(R + 1)1701·40854·1
Summer ln(new s) = 4·922 + 0·4941ln(s) − 0·6766ln(R + 1)1672·37027·9
Autumn ln(new s) = −0·4481 + 0·6872ln(s) + 0·2745ln(R + 1)2301·87551·1
Winter ln(new s) = 0·6342 + 0·8103ln(s)1971·01771·4

Individual-state variables assessed for predicting fate in the next season included age in seasons (providing more detail than age in years) and size. Size was estimated from width and breadth measurements of each rosette's diameter. A mean radius was calculated and then converted into a circular area measure. Maximum size (log-transformed to normalize data) in a season was used as the size measure in all the statistical analyses.

Population state variables assessed included number of rosettes per quadrat and number of seedlings per quadrat. Estimates of density provided a reasonable measure of actual competitive pressure within the pasture at high C. nutans densities, being less accurate at lower densities, when interspecific competition (not measured) is likely to have been increasingly important. Seedlings were investigated for their impact on seedlings. Asymmetric competition was evident between rosettes and seedlings (including the number of seedlings did not explain any more of the variation than the number of rosettes alone), so the number of rosettes only was considered in analyses of rosette fate. Density-dependence of rosettes was assessed initially using the number of individuals within a 5-, 10- or 20-cm radius of a target individual. Additionally, the overall quadrat density (number of rosettes in the quadrat) was compared with these measures. Overall quadrat density had more explanatory power than the number of individuals within any given radius. The effect of (rosette and seedling) density on seedling survivorship, stasis and growth could only be assessed at the level of a quadrat, as in many cases seedlings were so numerous that they were counted but not mapped within a quadrat. For all these reasons the simulation model did not require an explicit spatial component.

The effects of potential explanatory variables (Table 1) on life-history transitions (Fig. 1) were analysed using a variety of methods (Sokal & Rohlf 1995) using GLIM (Crawley 1993). Seedling survival, seedling size increase, rosette survival and flowering were estimated as probabilities using binomial models with logit link functions (logistic regressions) tested against the χ2 statistic (Crawley 1993). Growth and fecundity transitions were estimated using multiple linear regressions. In each case, where appropriate, the effect of individual age (in seasons) and size, and density (rosette, seedling or both) and season (spring, summer autumn or winter), were assessed. Data were log-transformed as necessary to ensure normality. The starting point was the most complex possible model given the measured variables. We then performed backwards elimination with a criterion of P < 0·05, using likelihood ratio tests for the logistic regressions, and F-statistics in the case of the multiple regressions, to arrive at the final model, which we call the minimum adequate model. If a significant effect of season was detected, linear models were generated for each season separately, except in the case of fecundity where a regression analysis was carried out using all individuals that successfully produced flowers. Other potential explanatory variables tested for germination density were the amount of seed set and the seed bank size (Table 1). In analyses of quadrat data where density was a potential explanatory variable, up to five plants were randomly sampled from each quadrat in each season to reduce the bias with respect to density (i.e. to reduce the difference in error variance between quadrats). Seed incorporation and seed survival in the soil were estimated from seed bank measurements. The seed bank was measured 14 times during the 8-year study, either in spring or autumn or both in any given year. One hundred 32-mm diameter circular soil cores were taken for the first seven samples (after which the number was 50) at random across the study area, providing seed bank estimates at the level of the site. Cores were taken at the end of either spring (after the bulk of spring germinations had happened) or autumn (after seed fall). Soil cores were stored at 5 °C until they were wet sorted to extract the seeds. Extracted seeds were placed on moistened filter paper in Petri dishes and the number that germinated was recorded. After 2 weeks, seeds were moistened with a giberellic acid solution to break dormancy. Survival of seeds in the soil was estimated from annual losses from the seed bank.

The use of an IBM allows the inclusion of measured variation in individual plant life histories, even if plants are the same size and age and grow at the same density. Previous stage-structured matrix models for C. nutans have averaged over potentially important individual variation (Shea & Kelly 1998). The IBM parameters for transitions involving germination, growth and fecundity incorporate variation, as both the measured means and variances are considered when the new size of an individual is calculated. For example, two plants of the same size and age will have the same expected new size (based on the mean) but will differ in their realized new size because of different random draws from the standard deviations. Thus, we attribute all of the variability as a result of both observational uncertainty and individual variation to individual variation only (Rees et al. 1999). Other transitions are probabilistic (e.g. probabilities of survivorship or flowering).

Model simulations were carried out at the level of a quadrat. The code for the model was written in Pascal and run on a Linux platform. In all scenarios, 1000 populations were simulated, as this is a stochastic model. The maximum number of individuals (rosettes and seedlings) in the quadrat was capped at 800 (more than the maximum number ever observed in a real quadrat). The model was initialized with field data from a quadrat: a distribution of seeds, seedlings and rosettes. The model is stochastic, with an upper reflecting boundary (the cap) and with a lower absorbing boundary (once all individuals, including seeds in the soil, are dead the population is extinct); thus model populations will eventually go extinct just by chance.

There are several possible measures of relative population persistence. Differences in mean time to population extinction tend to be clouded by extremely wide confidence intervals. Probability of extinction by a given time, for example 100 years, can be useful for very specific questions but does not allow an overview of differences between entire extinction trajectories. Time to 100% extinction includes no measure of variation, and again only provides information about outcome not the entire trajectory. Expected minimum population size is useful for endangered species (McCarthy & Thompson 2001); in this case it would have to be assessed over a specified time frame (or all results would be zero). Time to outbreak is appropriate for models without density dependence (Buckley, Briese & Rees 2003a,b). Cumulative probability of extinction curves allow a visual inspection of the entire extinction trajectory of a population of populations; one can examine the distribution of extinctions through time from the set of stochastic simulations for a particular scenario. Statistically significant differences can be assessed with Kolmogorov–Smirnov tests (which focus on the maximum separation of the curves, Siegel 1956; Zar 1999). For this reason we use this last method to assess the sensitivity of results to different parameters, as well as the relative levels of success of management strategies.

Sensitivity of the model to uncertainty was explored by systematically testing modifications of model parameters, initial conditions and constraints against unmodified model versions for significant differences in outcomes. Sensitivity analyses (strictly, proportional sensitivities) were carried out for all parameters in the model (germination, seedling survival and growth, rosette survival, flowering, fecundity, growth, background grazing rates, seed incorporation and seed survival in the soil). Note that above-ground stages are easily monitored but that seeds in the soil are difficult to observe. Imperfect detection can bias estimates of seed survival and hence estimates of time to extinction (Kéry 2004; Kéry, Gregg & Schaub 2005) but are unlikely to affect ranking of scenarios. Additionally, all constraints and initial conditions were assessed. Probabilities were only decreased (to avoid the possibility of probabilities greater than one) while other parameters were both increased and decreased.

single and integrated weed management strategies

We collated information on the large number of possible management strategies that have been used for this species, including observational and experimental estimates of impact, and used these estimates in the model by modifying the appropriate life-history parameters. Specifically, we examined the effects of three biological control agents and the range of possible pasture management options recommended for C. nutans control (Moore, Doyle & Rahman 1989; Popay & Medd 1995); the estimates from these sources are summarized below.

The receptacle weevil R. conicus reduces seed production by 30% of measured field values (Sheppard, Cullen & Aeschlimann 1994; Kelly & McCallum 1995; Woodburn 1996b). The receptacle gallfly U. solstitialis reduces seed production by 70% of measured field values (Sheppard, Cullen & Aeschlimann 1994; Woodburn 1996a,b). The root-crown weevil T. mortadelo reduces plant growth by 86·6% (Woodburn 2000) and hence survivorship and fecundity are indirectly affected (Cartwright & Kok 1985; Woodburn 1997).

Lethal application of a recommended herbicide in autumn, winter or spring reduces the probability of rosette and seedling survival to the next season to 5% or 3% (depending on differences in application success and independent of plant size) in that season (Popay, Butler & Meeklah 1989; Dellow 1996; Harrington 1996). Crash grazing (which consists of three to four times the regular grazing pressure for one season in either spring or autumn) leads to a 20% reduction in the probability of survivorship for rosettes and seedlings in that season (Popay & Medd 1995; Huwer et al. 2005; R. Huwer, unpublished data).

Spray–grazing (Pearce 1969) integrates the previous two techniques and involves an application of a sublethal dose of herbicide (usually half to one-tenth the recommended rate) in autumn or winter followed by very high stocking rates of sheep or cattle [seven or more dry sheep equivalents (DSE) per hectare] enclosed on the infested paddock about 1 week after herbicide application. This treatment reduces rosette and seedling survivorship to 1% in the appropriate season (R. Huwer, unpublished data).

Management strategy effectiveness is assessed in this model by the rate at which simulated populations go extinct when the management is applied, relative to the baseline scenario of no management. This is similar in concept to studies that investigated management relative to population growth rates or population stability (Murdoch & Briggs 1996; Shea & Kelly 1998; Buckley, Briese & Rees 2003a,b).

Initially we assessed the effect of single management strategies on the cumulative probability of extinction of 1000 populations. We then examined the projected effect of a number of integrated management strategies, such as spray–grazing. We also examined combinations of these strategies with biocontrol agent use. In all cases we made the parsimonious assumption of no interaction between treatments or agents; relatively little work on interactions exists for C. nutans (but see Milbrath & Nechols 2004a,b). More than 40 different single and integrated management strategies were examined using a stratified testing design (e.g., once the best crash-grazing strategy was identified, integration with other strategies focused only on that particular crash-grazing option).


The statistical analyses provided the minimum adequate models for each process, in each season where relevant, and are presented in Table 1. The mean number of germinations was not statistically related to any measured variable (it was a season-specific constant) and as such acted as a strong source of density dependence; per capita recruitment is greatly reduced at high compared with low seed densities. In the model, however, germination is zero if the seed bank contains no seeds; the seed bank acts as a cap. Seedling survival was also independent of any measured variable and of season. Seedling density significantly affected the probability and amount of seedling growth. Rosette density also significantly affected seedling parameters, as well as rosette survival (winter only) and rosette growth. Age affected most processes in some seasons, except rosette growth and fecundity, while maximum size was the dominant factor affecting rosettes: rosette survival, growth, flowering probability and fecundity.

The annual seed bank incorporation rate, estimated from 3 years of seed bank data, was 0·43 (± 0·18). Annual seed bank mortality, estimated from both annual losses from the autumn to autumn sampling dates and annual losses from the spring to spring sampling dates, was 0·557 (± 0·136). Seed mortality in the seed bank is considered to be predominantly because of failed germination (Shea et al. 2005), so within-year seasonal seed bank mortality was calculated by apportioning the annual seed bank mortality across the four seasons in relation to the proportion of the total annual germination that was observed in each season.

The functions and parameters estimated from the data were used to parameterize the IBM. All management strategies examined significantly reduced population persistence of C. nutans: any management will help to diminish the impact of this exotic weed to some extent. Rather than present every result we focus on the best single management strategies in certain subsets (e.g. of all the possible crash-graze combinations) and then examine only the better options in combined strategies. The results for key management strategies are presented in Fig. 2: relative rankings for these 10 management options (based on the full cumulative probability of extinction curves) compared with the worst strategy of no control are given in parentheses in the figure legends.

Figure 2.

Cumulative probability of extinction (%) for model populations of C. nutans under different management regimes over 25 years: (a) single biological control agents, (b) combined seed and rosette weevils, (c) biocontrol compared with single chemical and grazing management strategies, (d) crash grazing in one or two seasons, (e) spray–grazing in spring or summer, (f) the optimal single and integrated management strategies. In all figures the ‘no control’ scenario is included for comparison. The rank of each management option is noted in parentheses in the legend for this subset of key management scenarios.

All three biological control agents were projected to provide significant levels of control, with the rosette weevil T. mortadelo having significantly more impact (P < 0·001) than the two seed receptacle insects (Fig. 2a). A combination of the rosette weevil and a receptacle feeder generated further improvement (Fig. 2b).

Use of lethal herbicide rates reduces C. nutans population persistence significantly more than any of the biocontrol agents alone or combined (Fig. 2c). Crash grazing is significantly less effective than lethal herbicide, T. mortadelo or U. solstitialis but more effective than R. conicus (Fig. 2c). The season in which the crash grazing is applied (i.e. in spring, summer, autumn or winter) makes no difference. If crash grazing is applied in two seasons rather than one, however, significant improvements are obtained, with a spring and summer coupling having the biggest impact (Fig. 2d). This crash grazing combination matches the effect of U. solstitialis, although spring–summer crash grazing is still less effective than the effect of T. mortadelo. Combining the effects of crash grazing in spring with one or more biocontrol agents leads to significant improvements with each additional biocontrol agent.

Spray–grazing in spring is far better than spray–grazing at any other time of the year (Fig. 2e). Spray–grazing in the other three seasons decreases in effectiveness the later in the year it is applied, but the effect is less marked. Spray–grazing in spring is projected to be far more effective than any of the biocontrol agents. Combining spray–grazing with the biological control agents is not projected to have any more significant impact on persistence of C. nutans than spray–grazing alone.

Lethal herbicide is the best single strategy (Fig. 2f). Crash grazing and biocontrol agents combined perform comparably to lethal herbicide alone, although still not as well as spray–grazing, which is the best integrated management strategy according to these projections (Fig. 2f).

Significant parameter sensitivity results are tabulated in Table 2 along with the direction of the effect. No alterations to model constraints (not even > 50% changes in the maximum number of plants possible within a quadrat) are significant. As increasingly extreme alterations to initial conditions are made, cumulative extinction curves do alter significantly; however, less major changes do not lead to significant differences in projected outcome. For the basic parameter sensitivity analyses, in all cases where both increases and decreases in a parameter are simulated, decreases lead to larger effects and often a change in significance level of the differences. Perturbations of the probability of flowering, seed production, incorporation rates and germination rates were not significant, or barely so, although seed bank survival was important. Changes in survival of seedlings and rosettes ‘and rosette growth’ all had significant effects on population persistence. These sensitivity results suggest that management strategies affecting reproductive output are less likely to reduce population persistence significantly than management affecting growth and survivorship, especially of rosettes.

Table 2.  Results of parameter sensitivity analyses. Significance levels marked are the results of Kolmogorov–Smirnov tests of differences between the cumulative extinction curves (data not shown) with and without the alteration. Significance level is tested against a two-tailed distribution as direction is not specified, with ‘not significant’ indicated by NS, P < 0·05 indicated by * and P < 0·001 indicated by **. The direction of the effect is indicated by +/–, where – indicates a significantly quicker decline to extinction and + indicates a slower decline to extinction
Sensitivity alteration relative to the baselineOutcome
Increased by 10%NS
Decreased by 10%*
Probability of seedling survival decreased by 10%**
Probability that seedlings grow to be rosettes decreased by 10%**
Seedling growth
Increased by 10%NS
Decreased by 10%NS
Adult survival probability decreased by 10%**
Probability of flowering decreased by 10%*
Incorporation rate of seeds
Increased by 10%NS
Decreased by 10%*
Flowering graze rate
Increased by 10%NS
Decreased by 10%NS
Seed production
Increased by 10%NS
Decreased by 10%*
Adult growth
Increased by 10%+**
Decreased by 10%**
Seed bank survival rates decreased by 10%**


Carduus nutans population persistence was significantly reduced by all management strategies examined. Spring spray–grazing was the best strategy overall. This result agrees with a recent field trial (Huwer et al. 2005); rosette-forming broadleaf weeds are generally vulnerable to spray–grazing because it is applied at times of active growth and maximum competition from pasture grasses. Crash grazing in combination with attack by biocontrol agents also performed strongly, and this integrated strategy had an impact comparable to the best single strategy of lethal herbicide application. Crash grazing alone performed relatively poorly; even two seasons of crash grazing (in spring and summer) was less effective than the best biocontrol agent. This also agreed with a recent field trial that found crash grazing of only limited effectiveness against C. nutans (Huwer et al. 2005). The results from this study clearly support field observations that, of the three biological control agents released, T. mortadelo is likely to be the most effective and R. conicus the least effective biological control agent in Australia (Swirepik & Smyth 2002). This reflects the fact that T. mortadelo attacks a life stage critical to the thistle's invasive success in Australia while the seed feeders do not (Shea et al. 2005). While R. conicus is still present in the field in Australia, redistribution of this insect has recently been discontinued.

Using our IBM, which is based on the best data available, we have been able to rank potential management strategies. However, there are also practical considerations. Our model was developed to assess which management strategies provide the most effective control in terms of the sole objective of local extinction of the thistle. In practice, management costs will also be of importance; all the possible management strategies can be ranked in terms of their costs. It would also be possible to rank management strategies in terms of both ecological and economic performance indicators (i.e. local extinction and cost). This could be done subjectively, by weighting the two performance indicators according to the manager's overall aim (Milner-Gulland et al. 2001), or even objectively if costs for failing to control the weed in terms of lost revenue can be computed. For example, our model suggests that repeated annual lethal herbicide applications will provide most effective control, however, this practice is unlikely to be economic and will probably lead to the evolution of herbicide resistance (Harrington 1996). From this practical standpoint, we suggest C. nutans might be most effectively controlled by spray–grazing when at high density and by a combination of spring crash grazing and biological control agents where the densities of the thistles do not make spray–grazing economic (Fig. 2). From an economic perspective, the low cost of the biological control agents may mean that in many rough grazing pastures biological control alone may be sufficient, and it certainly increases its appeal for many farmers, especially in marginal areas.

Models are not perfect real-world representations but rather heuristic tools for improving our understanding. As with any model, there remain uncertainties. Agent populations and attack rates will clearly fluctuate much more widely in the real world where agent density is coupled to C. nutans dynamics and seasonal weather patterns. Combinations of strategies were simulated assuming no interaction; clearly this will not always be the case, and additional data would be very useful. Information was not collected on seed dispersal or interspecific competition, and no measure of background vegetation was taken during the course of this study; thus these aspects were not included in the model. Understanding and managing the competitiveness of the background vegetation as part of an integrated strategy against nodding thistle is important (Huwer et al. 2005), as many of the management strategies (e.g. herbicides and crash grazing) probably have unquantified indirect effects on the pasture. As the available data only allowed our model to focus on the population dynamics of this target, some predictions (e.g. that two seasons of crash grazing are better than one) may not hold out in the field if there are such unmeasured indirect effects. Extensive crash grazing may even be detrimental, potentially reducing the perennial competitive capacity of the pasture and opening the ground up to improved recruitment by the thistle. Seedling recruitment will always be the critical transition for such pasture weeds (Rees & Hill 2001) and so maintaining pasture cover prior to autumn, the most suitable season for germination (Table 1), will be a key management requirement. Acquiring information to improve the model and reduce uncertainties will be an additional focus of field trials.

While we have developed a model specific to C. nutans in Australia, the modelling approach is generally applicable to other weed species. Such models can also focus on which data are most cost effective to collect for developing reliable predictions. Working under the assumption that full information is the most ‘realistic’ we can assess which state variables (age, size or density) contribute most to our understanding of population dynamics and management for this species; effectively a structural sensitivity analysis. For C. nutans plant density was the least significant predictor of plant fate; removing density information from the analyses, as if it had never been collected, caused very little loss of explanatory power (analyses not shown). Previous work on monocarpic perennials has suggested that size is more important than age in such models (Shea 1994; Rees et al. 1999; Rose, Rees & Grubb 2002); however, such studies have usually addressed the age of a plant in years. In our study, both age and size were important to our predictions: the increased relevance of age may be because age is measured in seasons and thus more effectively reflects the variation in plant life histories. Therefore future field studies may be streamlined by omitting thistle density measurements if only a subset of target plants are to be monitored, but seasonal-scale age information should prove useful.

The model presented here is an integrated weed management (IWM)-focused model, based on the temporal scale at which landowners manage weed problems. It provides a test bed for the myriad of different management options available, to assess which are most likely to ameliorate the impacts of C. nutans in Australia. The next stage in improving management recommendations for this species is to test the predicted optimal strategies (our ‘best bets’) in the field in Australia (Huwer et al. 2005). Such field trials will also allow us to reduce uncertainties and will provide important feedback to validate and improve the model, for example by inclusion of the unquantified processes, indirect effects and interactions highlighted here. Ideally, subsequent wider implementation of optimal strategies should be within an active adaptive management framework (AAM; Walters 1986; Parma et al. 1998; Shea & Possingham 2000; Shea et al. 2002). AAM is management with a deliberate plan for learning about the managed system, so that management can continue to be improved in the face of uncertainty. Use of an AAM approach is important as recent research comparing Australian and New Zealand populations has shown that the underlying reasons for the invasion success, and hence optimal management strategies, for this species may differ markedly (Shea et al. 2005). Differences arise because invasion success is determined not only by characteristics of the invader but also by properties of the invaded community (Sheppard 2000; Shea & Chesson 2002). This insight moves us even further away from generalized and widely applicable single management recommendations towards context-dependent solutions; the results presented here for Australia would not necessarily apply elsewhere in the invaded range. However, the approach used here, of developing comprehensive models targeted to the time scale relevant to management and the range of available options, is generally applicable and could be easily linked into economic optimization models (Jones, Cacho & Sinden 2004). In conjunction with AAM, such models will target the most appropriate management strategies for a region far more effectively than a static approach.


The Australian CRC for Weed Management Systems and CSIRO Entomology provided support for K. Shea. We thank Cyelee Kulkarni, Mick Neave, Madeleine Say and Andrew White for technical assistance. We are grateful to the community ecology discussion group in RSBS at ANU and the Mangel lab group at UCSC, as well as Suzanne Alonzo, Ottar Bjørnstad, Peter Chesson, Kendi Davies, Dan Doak, Eelke Jongejans, Dave Kelly, Mark Lonsdale, Marc Mangel, Brett Melbourne, Joslin Moore, Mark Rees, Stephen Roxburgh, Mike Runge and Chris Wilcox for valuable discussions. We thank Australia Wool Innovation Limited for funding the field work. Part of this work was supported by USDA-CSREES (Biology of Weedy and Invasive Plants) NRI grant number 2002-35320-12289 to K. Shea.