Containment can be a viable strategy for managing invasive plants, but it is not always cheaper than eradication. In many cases, converting a failed eradication programme to a containment programme is not economically justified. Despite this, many contemporary invasive plant management strategies invoke containment as a fallback for failed eradication, often without detailing how containment would be implemented. We demonstrate a generalized analysis of the costs of eradication and containment, applicable to any plant invasion for which infestation size, dispersal distance, seed bank lifetime and the economic discount rate are specified. We estimate the costs of adapting eradication and containment in response to six types of breach and calculate under what conditions containment may provide a valid fallback to a breached eradication programme. We provide simple, general formulae and plots that can be applied to any invasion and show that containment will be cheaper than eradication only when the size of the occupied zone exceeds a multiple of the dispersal distance determined by seed bank longevity and the discount rate. Containment becomes proportionally cheaper than eradication for invaders with smaller dispersal distances, longer lived seed banks, or for larger discount rates. Both containment and eradication programmes are at risk of breach. Containment is less exposed to risk from reproduction in the ‘occupied zone’ and three types of breach that lead to a larger ‘occupied zone’, but more exposed to one type of breach that leads to a larger ‘buffer zone’. For a well-specified eradication programme, only the three types of breach leading to reproduction in or just outside the buffer zone can justify falling back to containment, and only if the expected costs of eradication and containment were comparable before the breach. Synthesis and applications. Weed management plans must apply a consistent definition of containment and provide sufficient implementation detail to assess its feasibility. If the infestation extent, dispersal capacity, seed bank longevity and economic discount rate are specified, the general results presented here can be used to assess whether containment can outperform eradication, and under what conditions it would provide a valid fallback to a breached eradication programme. Keywords: biological invasions, breach, containment, eradication, management strategy, net present value, weeds Introduction The invasion of unwanted plants and animals into natural and agricultural systems costs billions of dollars across the globe every year. For example, the total loss of environmental welfare to the Hawaiian state from the invasion ofMiconia calvescens D.C. has been estimated at several billion dollars over a one-hundred-year period (Kaiser 2006). Production losses to agriculture due to weeds were estimated at $2·2 billion in Australia in 2001–2002 (Sindenet al. 2004; Sinden & Griffith 2007), and at over $24 billion in the United States in 2000 (Pimentelet al. 2000; Pimentel, Zuniga & Morrison 2005). In response to these costs, farmers invested $1·5 billion managing weeds in Australia in 2001–2002 (Sindenet al. 2004), and over $8 billion in the United States in 2000 (Pimentelet al. 2000; Pimentel, Zuniga & Morrison 2005). Driven by these significant impacts and investments, programmes to manage invasive plants aim to prevent the introduction of problematic species (Hulme 2006), eradicate infestations before they become established (Simberloff 2003; Panetta 2007) or contain spread if eradication fails (Hulme 2006; Panetta 2009; Radosevichet al. 2009; Panetta & Cacho 2012). From a theoretical perspective, however, many infestations are likely to be no more amenable to containment than eradication because the ecological drivers that determine containment success are the same as those that limit successful eradication. Sharov & Liebhold (1998a) illustrated that the economically optimal strategy for managing the spread of gypsy mothLymantria dispar L. in the United States changed from ‘eradication’ to ‘slowing the spread’ via a barrier zone, and eventually to ‘doing nothing’ as the area occupied by the infestation increased. Cachoet al. (2008) extended this bioeconomic approach to identify ‘critical decision points’ at which eradication, containment or no management were the most economically rational strategy for isotropically spreading scotch broomCytisus scoparius L. in Australia. Carrascoet al. (2010) extended Sharov and Liebhold's formulation to show that in many cases, the optimal choice between applying an eradication strategy or a strategy designed to slow the rate of spread applied even when parameter estimates were uncertain. Panetta & Cacho (2012) found that because containment was susceptible to breaches by rare long-distance dispersal events, surveillance and fecundity control were likely to be important components of an effective management strategy. They recently extended this work and found that the use of barrier zones was unlikely to be successful for weeds exhibiting fat-tailed dispersal with high median dispersal distances (Panetta & Cacho 2014). However, despite well-founded theoretical recognition of the limitations of containment as a management strategy, practical on-ground management programmes have continued to view containment as a default fallback option for failed eradication programmes. In Australia, for instance, of the original national plans for twenty Weeds of National Significance released in 2000 (Thorp & Lynch 2000), the management plans of only two, Athel pineTamarix aphylla (ARMCANZ & ANZECCFM 2000a) and salviniaSalvinia molesta (ARMCANZ & ANZECCFM 2000b), did not employ the term ‘containment‘. Both of those species had a reference to containment added during review in 2012 (AWC 2012a,b). Clearly, many of the simple insights into containment from the modelling literature have not achieved common acceptance within management circles. Worse yet, many strategies that identify containment as an option give insufficient guidance as to how it might be achieved in practice. This prevents the management objective being linked to the biology of the invader, its environment or the capacity of managers on the ground. To begin addressing these concerns, Griceet al. (2012) proposed a simple definition of a containment unit consisting of an occupied zone inhabited by the invasive species and a buffer zone into which propagules are dispersed (Fig.(Fig.1).1). In Griceet al.'s formulation, the width of the buffer zone is related to the ‘maximum dispersal capacity’ of the invader but, because long-distance dispersal does not exhibit a hard maximum limit, the possibility of a containment breach must be recognized (Panetta & Cacho 2012). In an earlier publication, Griceet al. (2010) identified three types of breach that could affect a containment programme. Similar criteria can also be applied to an eradication programme (Fletcheret al. 2014), and here we extend and generalize Griceet al. (2010) types of breach to consider the relative impacts of a breach on eradication and containment programmes. Figure 1 A simple model of invasion, consisting of an ‘occupied zone’ (dark shading) of radius r around the current extent of reproductive individuals, and a ‘buffer zone’ (light shading) of width d related to the effective dispersal ... We frame Griceet al. (2012) proposal in a simplification of the form pioneered by Sharov & Liebhold (1998a) and Cachoet al. (2008) to derive rules to guide land managers in determining the circumstances under which a containment strategy is likely to be more effective or efficient than an eradication strategy, the effect of a breach of the management unit on each type of management and the situations in which containment would form a valid fallback strategy for a breach in an eradication programme. We focus our analysis on well-specified systems in which eradication and containment are expected to perform comparably, and ask under what conditions a single unexpected breach or change in system specification would change the choice of management strategy.