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1. Eradication is often the preferred strategy in the management of new weed invasions, but recent research has shown that the circumstances under which eradication can be achieved are highly constrained. Containment is a component of an eradication strategy and also a management objective in its own right. Just as for eradication, containment of a weed invasion should be attempted only if it is considered feasible. However, very little guidance exists for the assessment of containment feasibility for weeds.
2. Numerous factors have been proposed as influencing feasibility of containment, but those that relate to the potential for management of dispersal pathways and timely detection of new foci of infestation appear to be critical. Theory suggests that the rate of spread is largely driven by long-distance dispersal (LDD). However, LDD is generally unpredictable and often occurs for species that do not appear to be adapted for it. Furthermore, many (if not most) LDD events fail to give rise to new infestations.
3. As the probability of colonisation is related to the numbers of propagules immigrating (‘propagule pressure’) at a point in the landscape, dispersal pathways that move relatively large numbers of propagules simultaneously and/or repeatedly should most enhance weed spread. It is these pathways whose potential for management has the greatest bearing upon containment feasibility. A key impediment to containment is undetected spread; this need not occur through LDD and is more likely to occur through dispersal to lesser distances.
4.Synthesis and applications. Feasibility of containment should be viewed in terms of the effort required to reduce weed spread rate, as well as the effectiveness of relevant management actions. Where dispersal vectors are not readily manageable and the probability of detection via structured and/or unstructured surveillance is low, a much greater reliance upon fecundity control will be needed to contain a weed. A combination of empirical and theoretical approaches should be used to develop and refine estimates of containment feasibility. Such estimates will aid decision-making with regard to whether to attempt to reduce weed spread and assist in prioritisation of different weeds for containment.
Hulme (2006) has stated that containment is most effective as a strategy when the targeted species naturally spreads slowly as a result of short-distance movements, or where effective barriers either exist or can be established. Containment can be either absolute (stopping spread) or partial (slowing spread); both can be economically viable propositions (Sharov & Liebhold 1998; Keller, Frang & Lodge 2008). It must be noted, however, that the concept of absolute containment has very limited applicability, because even a 99% reduction in spread rate constitutes partial containment.
A weed’s rate of spread is determined by both population growth and dispersal (Neubert & Caswell 2000). Reducing a weed’s local abundance and reducing its spatial spread are different management objectives and may require different control tactics (Shea 2004). Recent research has utilised detailed demographic data sets to quantify contributions of life-cycle transitions and other parameters (including those related to dispersal) to population growth and spread (Jongejans et al. 2008, 2011; Shea et al. 2010). While this approach holds considerable theoretical interest, its application is limited to species whose demographic behaviour has been studied intensively. Furthermore, the practicality of targeting particular life stages or life-cycle transitions within large infestations remains to be demonstrated for a range of weed growth forms and environmental contexts. Other theoretical work (e.g. Coutts et al. 2011) has supported the notion that weed spread is driven primarily by dispersal ability, with demographic features being of secondary importance.
Weed spread occurs primarily through the movement of propagules (mainly seeds but sometimes plant fragments and other vegetative structures). Obviously, if propagule production is either prevented or markedly reduced, the potential for spread will diminish. While reducing weed fecundity can be expected to be a component of most containment programmes, this paper will focus instead on processes occurring subsequent to reproduction – how these might vary between different weeds and the implications for slowing spread through management intervention. In particular, we concentrate on propagule dispersal and its effects upon both the establishment and detection of new foci of infestation (Fig. 1).
A rigorous assessment of the technical feasibility of containment would need to take many factors into account (Grice 2009; Grice et al. 2010). With this in mind, the aim of this review is to demonstrate how empirical and theoretical approaches might be combined to assess containment feasibility from a technical perspective. As for eradication feasibility (Panetta 2009), it is acknowledged that nontechnical factors (e.g. the need for prolonged institutional and community support) may be equally or more important.
Weed propagule dispersal
The movement of propagules away from their source is characterised numerically by a frequency distribution of the distances travelled. This distribution generally assumes a shape that reflects the fact that most propagules come to rest relatively close to the parent plant as a result of short-distance dispersal (SDD) events and that very few are deposited remotely through long-distance dispersal (LDD) events. LDD may be difficult to define (Nathan 2006) and is scale dependent (Pergl et al. 2011), as it can be addressed over a spectrum ranging from intercontinental distances to those between patches of habitat (Pergl et al. 2011). However, LDD is generally defined in terms of either a proportional threshold based on some percentile at the tail of the dispersal frequency distribution (e.g. <1% of the total number of dispersal events) or an absolute threshold (e.g. 500 m from the parent plant). For practical purposes, the absolute threshold distance is more relevant for the assessment of containment feasibility because it can be used to inform surveillance strategies.
Dispersal frequency distributions can be expressed in terms of probabilities or seed numbers/densities, which behave differently (Cousens, Dytham & Law 2008). Total seed numbers (or densities) are more relevant to the focus of this review, because propagule pressure is a determining factor in colonisation success (Lockwood, Cassey & Blackburn 2005; Rejmánek, Richardson & Pyšek 2005), and fecundity will affect the numbers of propagules that travel a given distance, not the probability that dispersal to this distance will occur.
For any given species, dispersal vectors, acting either alone or in combination (hereafter referred to as ‘vector suites’), contribute to the dispersal kernels (Nathan & Mueller-Landau 2000) that are described by these density frequency distributions. Some mechanisms (e.g. dispersal by ants, explosion, splash or gravity) tend to generate considerably fewer LDD events than others (e.g. dispersal by vertebrates, water or wind) (Willson 1993; Vittoz & Engler 2007). However, LDD is by nature rare and unpredictable. Furthermore, it can be achieved by nonstandard mechanisms of dispersal and may involve seeds with no particular morphological specialisations (Higgins, Nathan & Cain 2003; Nathan 2006).
Effects of vector suites on the establishment of new foci of infestation
Weeds can be expected to vary in spread dynamics as a function of differences in their vector suites. A number of studies (e.g. Neubert & Caswell 2000; Caswell, Lensink & Neubert 2003) have shown that the rate of spread is highly influenced by the numbers of propagules that are dispersed furthest. It follows that if a number of dispersal vectors are involved, the vector that contributes most to LDD will most influence the potential rate of spread of a weed. However, there can be a vast difference between simple deposition of propagules and that which leads to colonisation and establishment (‘effective dispersal’). This has marked implications for the assessment of containment feasibility.
Even for well-adapted species, the creation of new populations is a very risky business (Crawley 1989; Minton & Mack 2010). At low numbers, populations are highly prone to extirpation through both environmental and demographic stochasticity (National Research Council 2002). Unless relatively large numbers of propagules are involved, the probability of establishment and persistence may be very low (Panetta & Randall 1994; Minton & Mack 2010). The risk of failure may be mitigated by directed dispersal (i.e. the disproportionate arrival of seeds at microsites with particularly favourable conditions for establishment; Wenny 2001). However, the contribution of directed dispersal to invasion success may be difficult to demonstrate, let alone quantify (but see references in Wenny 2001; Seiwa et al. 2008). Habitat suitability clearly plays a key role in the establishment phase, but there is a trade-off between habitat suitability and propagule pressure whereby high propagule pressure may increase the probability of establishment in less suitable habitats (Rejmánek, Richardson & Pyšek 2005). Pergl et al. (2011) found that the fraction of long-distance dispersed seeds that provided the best prediction of the spread of giant hogweed Heracleum mantegazzianum Sommier & Levier over a number of decades was significantly negatively correlated with the percentage of habitats within the landscape that were suitable.
The greatest threat to weed containment posed by LDD may exist where multiple propagules are deposited simultaneously and/or repeatedly. This is often likely to occur where humans and their agents are involved (Benvenuti 2007; Hogan & Phillips 2011). Unless large numbers of propagules are expected to be involved, the extreme part of the dispersal distance distribution is of less practical importance, because much higher numbers of propagules are deposited closer to the source, with potentially higher probabilities of establishment.
Detection of new foci of infestation
From a management perspective, weed establishment should be viewed in relation to the detectability of new foci of infestation. For example, a satellite that arises within relatively close proximity of a known infestation is likely to be detected and controlled before it can contribute to further spread. In contrast, if a remote population establishes, its detection will probably lag and allow it to spawn further foci of infestation. For this reason, any establishment that occurs beyond the area that is searched for a weed will be problematic. If a weed is not readily detectable, small foci need not be far from known infestations for them to escape detection. In this case, many dispersal events that are less extreme (and therefore more frequent) may be of considerable importance to weed spread.
Two types of surveillance exist for the detection of new foci of infestation. ‘Structured’ surveillance leads to active detection of a targeted species. This type of surveillance is particularly suitable where infestations are not widely distributed (i.e. there are relatively low amounts of area to search) and/or where the occurrence of the species is relatively predictable (i.e. where the surveillance strategy can be informed by habitat suitability models; see Fox et al. 2009). ‘Unstructured’ surveillance gives rise to so-called ‘passive’ detection of a species and subsumes the multifarious ways in which a weed is detected by chance. It relies upon the general knowledge of land managers and often an informed public, and is an essential component of weed detection where weed occurrences are highly disjunct, where relatively high human population densities occur or where the weed is found within an amenable land use, such as in agriculture (Grice 2009). The role of passive detection is probably greater for highly detectable species.
There is very little published concerning the relative importance of different types of detection. The one study of which we are aware addressed the contribution of various types of surveillance to the detection of weeds targeted for eradication in tropical Queensland. It found that most (73%) detections resulted from passive surveillance, with 19% and 8% of detections made through tracing links from infestations and structured surveillance, respectively (Brooks & Galway 2008). A recent theoretical paper (Cacho et al. 2010) dealt with the importance of passive detection and its interaction with active detection in the management of invasions. In this work, a spatially explicit simulation model was used to estimate the minimum expenditure required to contain an invasion. It was found that even small increases in the probability of passive detection led to marked increases in the probability of containment, together with substantial cost savings (although the costs associated with public information campaigns were not incorporated in the analysis).
Grice et al. (2010) have highlighted the contribution of the directionality of dispersal to the feasibility of containment; it will be easier to detect a new focus at distance if dispersal is unidirectional (such as downstream for a water-dispersed aquatic weed), rather than multidirectional, as could be the case for plants that are dispersed by birds or by wind. The degree of directionality of dispersal may also have important effects upon optimal management rules for networks of invasive species (Chadès et al. 2011). However, the key aspect may be the degree to which the direction of dispersal can be predicted. For example, the deposition of water-dispersed propagules along a watercourse could deviate considerably from a ‘linear’ pattern during periods of flooding, when propagules may be transported over large floodplain areas, thus vastly increasing the area that might have to be searched for a weed. On the other hand, wind-dispersed propagules may be deposited over a relatively narrow arc if the period of seed release coincides with strong prevailing winds (Cousens, Dytham & Law 2008; Caplat, Coutts & Buckley 2010). Human-assisted dispersal can be highly multidirectional, but is predictable to a certain degree and can be traced potentially. Four basic scenarios are definable with regard to species detectability and the directionality of dispersal (Fig. 2). Differences between the extreme scenarios (1 and 4) with regard to feasibility of detection are straightforward. For scenario 2, the dispersal distance is high, but because its direction is relatively predictable, it should be possible to search in most areas where the weed is likely to occur. For scenario 3, although dispersal distance is less, the lack of predictability in dispersal direction means that the overall search area might need to be very large, because most suitable areas would have to be searched.
The potential for managing dispersal
As was noted earlier, reducing weed fecundity can be expected to be a component of most, if not all, containment strategies. However, the potential for managing the dispersal of propagules that are produced will depend upon the vectors involved. For species that are primarily dispersed by wind, it has been suggested that establishing vegetative barriers to wind movement may be useful (Davies & Sheley 2007a). This could be more relevant to low growing species, as Caplat, Coutts & Buckley (2010) have provided evidence that barriers for tree weeds may be breached by seed uplift several metres above the canopy. Dispersal by water may be reduced by maintaining barrier zones by watercourses to reduce the number of propagules that gain access to water (Davies & Sheley 2007b), but this management tactic would probably be rendered ineffective during periods of flooding (see above). It has also been suggested that dispersal by birds may be manipulated by the engineering of ‘seed sinks’, for example, the construction of perches (McDonnell & Stiles 1983; McClanahan & Wolfe 1987). The effectiveness of this tactic would clearly depend upon the behaviour of the vector (see Cousens et al. 2010), as well as the cost of implementation over large areas. It is reasonable to assume that the potential for managing dispersal will decrease as follows: dispersal primarily mediated by humans, including their agents (domesticated animals) > dispersal via a mixture of human- and non-human-mediated vectors > dispersal primarily abiotic or biotic (non-human-mediated). We note that Nathan (2006, p. 788) has stated, ‘Human-mediated LDD is almost certainly now the single most important mechanism of LDD of plants and animals’, a view that has been supported by later plant-related studies (e.g. Vittoz & Engler 2007; Wichmann et al. 2009; Bläßet al. 2010).
The important contribution of human-mediated dispersal to weed spread is reflected to some extent in legislation relating to weeds. For example, qualitative analysis of the dispersal syndromes of 233 Australian non-native noxious weeds showed that humans contributed to the dispersal of nearly 90%, including 21% that were dispersed by humans alone (Panetta & Scanlan 1995). Assuming a high degree of compliance with regulations associated with a containment programme, species spread primarily by humans and their agents should be most readily containable. The most useful approximation of the potential for managing dispersal will therefore be an estimate of the degree of human involvement.
Clearly, the ability to manage dispersal will be less important if it is possible to prevent/manage weed establishment (Davies & Johnson 2011) (Fig. 1), but this option may not be available commonly for either extensively managed production systems or natural ecosystems.
We now consider three Australian case studies, in order of decreasing feasibility of containment (see Table 1).
Table 1. Examples demonstrating different degrees of containment feasibility
Relative feasibility of containment
Potential determinants of containment feasibility
Minimum time to maturity (weeks)
Propagule type and dimensions (mm)
Detectable via unstructured surveillance?
The vector apparently moving the most propagules is marked with an asterisk. See text for additional information on each species.
aBetween emergence and seed production.
Humans* Domesticated vertebrates Wind Water
Achene (2–3·5 × 2)
Humans* Water Wind
Multiseeded fruit (6–7)
Wild vertebrates* Water
Orobanche ramosa L. (branched broomrape)
This annual parasitic species produces tiny, dust-like seeds. The pathway of introduction to Australia is unknown, but it is suspected that two separate incursions have occurred in South Australia. The first (detected in 1910) appears to have gone extinct. The second (detected in 1992) has been the subject of a national cost-shared eradication programme since 2000 (Panetta & Lawes 2007). SDD (up to several metres) is achieved via wind and is strongly influenced by the amount of ground cover (Ginman 2009). Because seeds have the potential for aerodynamic lift, they could conceivably gain LDD via strong winds and whirlwinds, but this has not been confirmed. Seeds are also dispersed (both externally and internally) by sheep (Ginman 2009). However, machinery seems to be the most important dispersal vector (Secomb 2006). Any machinery that comes in contact with soil (e.g. tillage equipment, seeders, harvesters, tractors and transport vehicles) can carry seeds. Strict management protocols, including wash-down procedures required before machinery can be moved within or beyond the quarantine area (Fig. 3), have undoubtedly contributed to the containment of this weed.
The sustained eradication effort targeting this weed (Panetta & Lawes 2007) has included an extensive structured surveillance programme. The area searched annually between 1999 and 2010 was 274 000 ± 88 300 ha (mean ± SD) (F.D. Panetta, unpublished data). The annual search effort is primarily concentrated within a quarantine area (QA) of approximately 210 000 ha (Fig. 3), with a substantial allocation to the area adjacent to, but within 7 km of, the QA. For instance, 150 000 ha outside the QA were surveyed during 2010 (P. Warren, personal communication). In addition, approximately 10% of all South Australian properties with links to those with known branched broomrape infestations and up to 5000 ha of interstate properties with links to those with known infestations are surveyed on an annual basis. No detections have been made through unstructured surveillance, but this might be an artefact of the very heavy reliance upon structured surveillance.
Parthenium hysterophorus (L.) King and Robinson (parthenium)
The propagule for this species is a cypsela with two appended sterile florets, which act as air sacs and increase both mobility in the air and flotation (Navie et al. 1998). Dispersal occurs locally by wind, but whirlwinds can carry seeds for considerable distances (Haseler 1976). Dispersal by water is also important, as indicated by spread along waterways in central Queensland (Auld, Hosking & McFadyen 1983). In addition, LDD occurs via movement of propagules on motor vehicles or machinery, on livestock, with crop and pasture seed, or in fodder (Navie et al. 1998).
Two studies have documented the capacity for containment of parthenium. In the first, Auld, Hosking & McFadyen (1983) showed a decrease in the rate of spread over time in a region of central Queensland where the weed had been subjected to a coordinated control programme. Blackmore & Johnson (2010) have demonstrated the contribution of early detection and control of small infestations of parthenium in New South Wales to the containment of the invasion of this weed to Queensland in the north. Of the infestations detected between 1982 and 2009 (see Fig. 4a for locations of detections between 1982 and 2011), 73·6% were detected in roadside corridors or wash-down areas and 24·2% were found on private properties. Almost 94% of the probable pathways leading to outbreaks detected on private property between 1982 and 2004 were human related (Table 2). Over 80% of the detections comprised 10 or fewer plants (Fig. 4b).
Table 2. Probable pathways for parthenium weed infestations detected on private properties in New South Wales during 1982–2004. Modified from the study by Blackmore & Johnson (2010)
Vehicles and other machinery
Oilseed by-product transport
Because parthenium has a distinctive appearance when flowering and occurs in pastures, crops and disturbed sites in readily accessible areas, there is considerable scope for the detection of this weed through both structured and unstructured surveillance. However, detection of the largest infestations on private property (Blackmore & Johnson 2010) indicates the need for ongoing investment in public awareness programmes to support timely detection through unstructured surveillance. Overall, the containment feasibility of parthenium is considered to be moderate, primarily owing to the (as yet unquantified) potential for spread through flood events.
Miconia calvescens DC. (miconia)
The earliest record of this plant in Australia is an ornamental specimen planted at the Townsville Botanical Gardens in 1963. Nurseries are believed to have propagated and sold the plant during the 1970s. Consequently, its initial distribution was determined by its use in public and private gardens. However, its invasiveness in the wet tropics of Australia was quickly recognised (Fig. 5) and its use in the nursery trade ceased. Since 1997 miconia has been the target of a coordinated, nationally funded eradication programme. Humans no longer constitute a vector for the spread of miconia, which occurs almost exclusively from naturalised populations via frugivores. Owing to their small size, fruits are accessible to almost all frugivorous birds inhabiting tropical rain forests (Murphy et al. 2008). The maximum distance measured from a source individual in an isolated infestation of miconia was 1191 m (Murphy et al. 2008), suggesting that effective dispersal occurs to substantial distances via this pathway.
While its large leaves (up to 70 cm long) with distinctive venation and strikingly purple undersides make this plant distinctive, detection is made difficult by the dense vegetation that it invades, along with rugged terrain over which invaded communities are distributed. Detection by structured surveillance therefore requires considerable effort and the probability of detection by unstructured surveillance is low, suggesting that the feasibility of containment of miconia is equally so.
Our ranking of these weeds is based upon a limited number of attributes, for example vector suites (in particular the prominence of human-mediated dispersal) and likelihood of detection through different types of surveillance. For two of the examples (branched broomrape and parthenium), there is evidence supporting the effectiveness of containment efforts. No doubt, additional attributes should be taken into account in an empirical approach to the problem; this is addressed later. Next we develop a theoretical basis for the assessment of containment feasibility.
Structured surveillance and the probability of escape
The contributions of different dispersal vectors in a weed’s vector suite will affect both the probability of establishment of new foci of infestation at distance from the source and the probability of their detection. These factors are related, in that relatively high propagule densities are likely – with some exceptions – to occur close to current infestations, where there is also a higher likelihood of detection of plants through structured surveillance. Establishment at larger distances will boost spread rates unless new foci can be detected and controlled in a timely manner. Key considerations in a quantitative assessment of containment feasibility include the area that must be searched, the effort required to detect a weed within this area and the potential for colonisation and establishment in sites where foci are unlikely to be detected. These aspects may be modelled as follows.
Consider the weed control problem in the context of a single reproductive plant that is to become the epicentre of a new invasion. The plant, located at distance x =0 from the epicentre, releases a number of propagules that disperse according to a kernel function:
where f(x|θ) is the probability that a propagule originating in the epicentre (at x =0) and moving in direction θ will land at distance x, and β is the median dispersal distance. For illustrative purposes, we have assumed a fat-tailed distribution, but other distributions may be more appropriate, depending upon the species. Equation 1 is a Cauchy dispersal kernel, commonly used to account for the presence of longer-distance dispersal events (Kot, Lewis & van den Driessche 1996). The cumulative distribution function for this is:
This is the probability that a propagule travelling in direction θ will land within a given distance xi of the epicentre. F(.) also represents the proportion of propagules expected to land within distance xi of the epicentre. It is noted that F =0·5 when xi = β.
The search radius required to attain a target probability PT of capturing a propagule is found by setting F(.) = PT and solving for xi to obtain:
Where xT is the search radius required to capture a proportion PT of propagules originating in the epicentre. The area that must be searched to attain PT is:
Once the target area aT is known, the intensity of surveillance must be decided upon; this will in turn determine the amount of search effort required. The intensity of surveillance can be set based on the target probability of detection zT. The probability of detecting a target is given by (Cacho et al. 2006):
where λ is the detectability of the target (in metres), s is search speed (metres per second) and w is the intensity of search (seconds per m2). The search effort required to achieve a given detection probability is obtained by solving for w in eqn 5, multiplying by search area (eqn 4) and converting seconds to hours:
Where E is the total amount of search effort (in hours) required to achieve the given target detection probability zT and target coverage PT. Equation 6 can now be solved for any given combination of parameter values (β, λ, s) and target probabilities of capture and detection (PT and zT). Estimates of E(PT, zT) can be used to assess resource requirements for containment, but they do not indicate the risk of escape beyond the search area.
Long-distance dispersal will result in escape of the invasion outside of the search area aT. In order to escape, a propagule must land outside the search area and it must become established. Therefore, the probability of escape depends on habitat suitability and number of propagules that escape:
where Pe is the probability that a plant will become established outside the search area; h is habitat suitability, defined as the probability that a single propagule landing on the site will become established (Leung, Cacho & Spring 2010), np is the number of propagules originating at the epicentre and (1-PT) is the proportion of propagules expected to land outside the search area.
The search area (aT) increases exponentially as the target capture probability (PT) increases, and this effect becomes more marked as the length of the dispersal kernel (given by β) increases (Table 3). The increase in search area is balanced by a reduction in the probability of escape as PT increases.
Table 3. Probability of escape (Pe) and search area (aT) required to achieve a target capture probability (PT). Two values of median dispersal distance (β) are considered. Probability of escape was estimated with eqn 7 and area invaded with eqn 4. Other parameters were set at λ = 5, s =1, np = 10,000 and h =0·001
Target capture probability (PT)
Probability of escape (Pe)
Search area (ha)
β = 5
β = 10
Our definition of probability of escape in eqn 7 is conservative, as it considers the establishment of a single plant. But this plant would need to survive and reproduce to start a new infestation, which would influence the true probability of escape. Fig. 6 shows that the effort required is more sensitive to increases in PT than in zT.
Strictly speaking there are two types of escape: (1) individuals that are not detected within the search area (1-zT) and (2) those that become established beyond the search area, given by Pe in eqn 7. The first type of escape can be negligible if treated sites are revisited prior to reproduction because the proportion missed = (1-Pd)n decreases quickly with the number of searches (n) (results not shown).
To understand the role of habitat suitability (h), we set a range of values for h and PT and solve eqns 3, 4 and 7. We then plot the resulting values of Pe and aT against each other (Fig. 7). Consider a target to achieve a Pe = 0·1; this would require a search area of 29 ha in the base case (h =1·0 × 10−3), decreasing to 7 ha or increasing to 65 ha when h decreases or increases by 0·5 × 10−3, respectively, as indicated by dotted lines.
When fecundity control is paramount
The appropriate management strategy will depend upon the dispersal characteristics of the targeted species. For example, Minor & Gardner (2011) have concluded that the spread of species with a high probability of random LDD is best reduced by targeting the largest weed infestations or source populations (i.e. fecundity control), whereas weeds with a lower probability of random LDD are best managed by considering landscape configuration and the connectivity of patches of suitable habitat. Levels of LDD should be potentially reducible for weeds that are observed to achieve considerable amounts of carriage by human-mediated pathways. If significant LDD occurs via other pathways, it may not be possible to contain a weed without substantial reductions in fecundity. Equally, if it is not possible to reduce spread by manipulating habitat suitability or through timely detection and control, reducing fecundity in source populations will be essential. Pergl et al. (2011) have recently argued that the management impact of fecundity reduction stems from the reduction in the absolute numbers of seeds that achieve LDD. This would represent a reduction in the value of np in eqn 7.
Application and future research
Full application of our quantitative model would require parameters to be estimated from field data. The parameters of interest include the median dispersal distance (β), habitat suitability (h), search speed (s) and detectability of the target (λ). While s and λ could be estimated fairly readily (see Moore et al. 2011), direct estimation of β and h will be problematic. Generalised dispersal distances (Vittoz & Engler 2007) can be used to inform estimates of β if vectors are known. Use of these three parameters allows estimation of search effort (eqn 6). It is noted, however, that our model assumes that the entire habitat within the search radius is suitable. To overcome this limitation, the estimate of search area could be refined by using a species distribution model based upon species presence data (e.g. Giljohann et al. 2011). Similarly, a species distribution model could be used to assess the risk posed by potential spread beyond any defined search area, because the estimation of the probability of escape (eqn 7) depends upon habitat suitability. The acquisition of data relating to h as it is defined in the model (i.e. the proportion of seeds that gives rise to plants) could be expected to be technically demanding owing to the effects of temporal and spatial variability.
Examination of a range of containment and eradication programmes should assist in the refinement of the empirical approach to the assessment of containment feasibility. In addition to the factors that we have employed, and among those identified by others (Grice 2009; Grice et al. 2010) as being influential, we believe that generation time and possible interactions between factors warrant particular consideration. For example, while we considered the weed with the longest generation time to be the least readily containable (Table 1), this attribute clearly interacted with poor accessibility and detectability. With sufficient case studies, it should be possible to employ statistical methods to model effort (cost) as a function of multiple factors.
Use of our general framework (Fig. 1) should assist in identifying where efficient allocations of effort could be made to slow spread. A bioeconomic extension of our analysis would consider the damages caused by escape as well as the costs of different types of control to identify optimal strategies.
An assessment of the feasibility of any potential management strategy must take into account the amount of available resources, because optimal strategies are determined by budget constraints (Taylor & Hastings 2004; Cacho et al. 2008). As the limitations for eradication as an invasion management strategy for weeds are becoming increasingly clear (Rejmánek & Pitcairn 2002; Panetta 2009; Gardener, Atkinson & Rentería 2010), it is essential that the scope for partial containment be better defined. In this paper, we have outlined an approach that can assist in the estimation of the amount of investment required to reduce weed spread. Our framework also could be used to rank different weeds with regard to containment feasibility. Whether measures taken to reduce spread are actually (cost) effective is a matter that requires further research.
We thank Phil Warren and Simon Brooks for providing the maps for branched broomrape and miconia, respectively. Locations of infestations for parthenium weed in New South Wales (NSW) were provided by the NSW Department of Primary Industries and NSW local governments. Raghu Sathyamurthy and three reviewers provided valuable comments on the manuscript. O.C. acknowledges funding from the Australian Centre for Risk Analysis.