Invasive species have substantial ecological and economic costs and removing them can require large investments by management agencies. Optimal spatial allocation of removal effort is critical for efficient and effective management of invasive species. Using a series of ecologically informed model simulations, we evaluated and compared different spatially explicit removal strategies for invasive rusty crayfish (Faxonius rusticus) in the John Day River, USA. We assessed strategies in terms of their performance on three likely management objectives: suppression (minimise overall population abundance), containment (minimise the spatial extent of invasion) and prevention (minimise spread into a specific area). We developed five spatial removal strategies to achieve those objectives, denoted as: Target Abundance (removal at locations with the highest population abundance), Target Growth (removal at locations with the highest population growth), Target Edges (removal at the most distant locations in the river), Target Downstream (removal at the most downstream invaded segments on the Mainstem), and Target Random (removal at randomly selected locations). Each strategy was assessed at various effort levels, referring to the number of spatial segments in the river in which removals were conducted, after seven years of management. We identified the alternative that best achieved each objective, based on decision criteria for risk-neutral and risk-averse decision-makers and further evaluated strategies based on Pareto efficiency, which identifies the set of alternatives for which an improvement on one objective cannot be had without a decline in performance on another. We found that Target Abundance and Target Growth strategies best achieved the suppression objective, for risk neutral and risk averse decision-makers, respectively and Target Downstream was always best in achieving the prevention objective across both types of decision-makers. No single strategy consistently performed best in terms of the containment objective. In terms of all three objectives, Target Downstream was consistently Pareto efficient across all levels of management effort and both decision criteria. The modelling framework we provided is adaptable to a variety of riverine invasive species to help assess and compare spatial management strategies.

Aquatic invasive species, crayfish, invasive species management, spatially explicit model

Invasive species are a primary threat to global biodiversity, economies and human health (Pyšek and Richardson 2010; Early et al. 2016; Diagne et al. 2021). Managers of invasive species often seek to reduce two of the main contributors to negative species impacts: population abundance and range extent (Parker et al. 1999; Kumschick et al. 2015). However, desired management outcomes can be challenging to achieve due to imperfect detection, the ineffectiveness of available management actions and invasive species whose rapid growth and spread can largely nullify the effect of management (Rendall et al. 2021; Cuthbert et al. 2022). In addition, with widespread invasions and constrained budgets, natural resource managers are frequently limited by when and where they can manage (Donlan et al. 2015; Wenger et al. 2018). Approaches for identifying effective spatiotemporal allocation of management effort remains a primary need of managers.

Predicting the effectiveness of alternative spatial allocations of management effort is challenging, yet choosing the most effective allocation is critical for successful population suppression or containment of abundant invaders (Travis and Park 2004; Eppinga et al. 2021). Various alternative spatial allocation rules of thumb have been posited for invasive species management to achieve objectives of suppressing and limiting the spread of invasive species. For example, to suppress population size, the “targeting the source” rule involves allocating management effort in locations where the invasive population is the most abundant (Baker 2017) and to limit invasive species spread, the “managing the edges’’ rule involves expending effort at the invasion front (Bradley 1988; Moody and Mack 1988; Bossard et al. 2000). Ultimately, however, in any given case, the optimal spatial allocation of effort will depend on management objectives, the ecology of the invader and the characteristics of the invaded system. For instance, if dispersal of the invasive species is small relative to population growth, removal at the edges of the invasion may be a more successful approach in reducing spread of an invader because efforts to remove at the core of the population may be overwhelmed by population growth (Baker 2017).

Quantitative population models are useful tools for evaluating invasive species management strategies in a virtual environment before management is implemented (García‐Díaz et al. 2019; Thompson et al. 2021; Hudina et al. 2022). Simulation models can be efficiently used to compare a variety of alternatives under varying ecological and management assumptions without the substantial time and expense of on-the-ground experiments. In particular, spatially explicit population models are powerful tools for modelling population growth and spread and evaluating alternative spatial allocations of management effort (Epanchin-Niell and Hastings 2010; Bertolino et al. 2020; Goodenberger et al. 2020). Spatially explicit population models are especially useful in largescale invasion contexts to identify crucial locations wherein management resources could be directed to reduce further expansion and growth of the invasive population (Pepin et al. 2019).

A number of spatially explicit population models have been developed to evaluate spatial allocation of management effort in terrestrial invasion contexts (e.g. Epanchin-Niell et al. (2012); Baker and Bode (2016); Pepin et al. (2020)); however, such models have rarely been developed for freshwater contexts (but see Albers et al. (2018) and Kallis et al. (2023)). Spatially explicit population models in rivers are particularly difficult to parameterise due to challenges imposed by dendritic networks, including understanding individual movements (Corrales et al. 2020; Caradima et al. 2021). For instance, it is rare to observe marked individuals in aquatic systems (Ogburn et al. 2017), limiting the utility of tools such as multi-state mark-recapture models (Arnason 1973) for understanding movement. In addition, software for mechanistic modelling of animal movement has primarily been developed for terrestrial systems and only recently has been advanced for modelling animal movements in rivers (Quaglietta and Porto 2019). However, as technology for studying movement continues to develop for aquatic species, spatially explicit population models may be increasingly valuable tools for informing management in river systems.

In this study, we used a spatially explicit population model to assess removal alternatives for the management of invasive rusty crayfish (Faxonius rusticus) in the John Day River (JDR) of Oregon, USA, a major tributary of the Columbia River. The JDR is one of the largest free-flowing rivers in the United States and holds high conservation importance as it supports a variety of salmon species of significant cultural and economic value, such as endangered spring Chinook salmon (Oncorhynchus tshawytscha) and the threatened steelhead (Oncorhynchus mykiss). The presence of rusty crayfish in the JDR remains a significant concern because they are spreading rapidly (18 km year^-1), reaching high local abundances (up to 50 m^-2) and have the potential to inflict severe ecological impacts due to polytrophic and generalist feeding habits (Olden et al. 2011; Twardochleb et al. 2013).

Using a spatially explicit population model for rusty crayfish, we assessed alternative management strategies involving different spatial allocations of removal effort over a multi-year management time horizon. We evaluated the alternatives, based on performance of three management objectives that capture commonly held values of natural resource managers concerned with invasive species: suppression (minimise the overall population abundance), containment (minimise the spatial extent of invasion) and prevention (minimise spread into a particular area). The results from this study broadly seek to provide a template for the evaluation of invasive species management strategies in dendritic riverine systems.

The Target Abundance strategy performed best on the suppression objective with respect to expected value, regardless of the number of segments receiving removal effort (Fig. 2A, Table 2). The final population distribution further revealed that this strategy led to overall population suppression in the JDR (Fig. 3; with 16 segments of removal effort; see Suppl. material 1: fig. S2 for other segments receiving removal effort). However, this strategy was not optimal under the risk-averse mini-max criterion for the suppression objective (Table 3). In addition, the Target Abundance performed poorly on the containment and prevention objectives across all levels of removal effort (Tables 2, 3).

Figure 2.

Boxplots displaying the performance of each crayfish removal alternative, except No Removals, across all parameter sets and simulations for each objective A suppression: final total crayfish abundance (millions) B containment: percent invaded and C prevention: total crayfish in the Columbia River (millions). The horizontal black dotted line represents the expected value outcome under No Removals. In each boxplot, the red line is the mean, the black line is the median and the red point is the maximum value. In subfigures A–C, the facet plots represent 1, 4, 8 and 16 segments receiving removal effort. We express strategies Target Abundance as Abundance, Target Growth as Growth, Target Edges as Edges, Target Downstream as Downstream and Target Random as Random.

The Target Growth strategy, across all levels of removal effort, performed best on the mini-max criterion for the suppression objective (Table 3), yet was the worst in terms of expected value (Table 2, Fig. 2A). Target Growth had the best expected value performance for the containment objective given one segment of removal effort and was the second-best strategy for this objective given 4, 8 or 16 segments of effort (Table 2). This strategy was never optimal with respect to the prevention objective given either the expected value or the mini-max criteria and any level of removal effort (Tables 2, 3).

The Target Edges strategy performed poorly on the suppression objective across all levels of removal effort (Tables 2, 3). However, with 16 segments of effort, this strategy did suppress crayfish population at the “edges” of invasion, as there were low final populations in all major tributaries of the JDR and in the most upstream and downstream segments of the Mainstem of the JDR (Fig. 3). Therefore, this strategy had the best expected value for the containment objective for 16 segments of effort (Table 2, Fig. 2B).

Figure 3.

Segment-level total crayfish abundance after 7 years of management, averaged across simulations and parameter sets for each strategy (No removal, Target Abundance, Target Growth, Target Edges, Target Downstream and Target Random) with 16 segments of removal effort. The colours show segment level abundance.

Target Downstream was the best strategy on the prevention objective regardless of the decision criterion and regardless of the number of segments of removal effort (Tables 2, 3, Figs 2C, 3). In addition, this strategy performed the best in terms of expected value for the containment objective for 4 or 8 segments of effort (Table 2). Overall, the Target Downstream strategy did not perform well on the suppression objective (Tables 2, 3).

The Target Random strategy, in terms of the mini-max criterion, was the worst strategy for both suppression and prevention objectives and performed equally as bad as all other strategies on the containment objective, across all numbers of segments receiving removal effort (Table 3). Compared to other strategies, Target Random was neither the optimal nor the worst strategy in terms of the expected value criterion across all objectives. Overall, the Target Random strategy had variable outcomes on all objectives, as shown by the various outlier values (Fig. 2). However, Target Random did perform better than No removals. Overall, the No removals strategy performed the worst across every objective and criterion (Tables 2, 3).

The Pareto efficient strategies, in terms of expected value, included Target Abundance, Target Downstream and Target Random across all levels of removal effort (Table 2). For 4 and 8 segments of effort, the dominated strategies (Target Growth and Target Edges) were dominated by the Target Downstream strategy and, for 16 segments of effort, the dominated strategy (Target Growth) was dominated by Target Edges (Table 2). In terms of the mini-max criterion, Target Growth and Target Downstream were Pareto efficient regardless of the level of removal effort (Table 3). For 4, 8 and 16 segments of effort, the Target Random strategy was dominated by every other strategy (Table 3).

Since all the objectives were based on either final population abundance (suppression), final distribution (containment) or cumulative abundance (prevention), we did not focus on changes in the population over time. However, under all alternatives, the abundance of crayfish slightly increased over time (Suppl. material 1: figs S3, S4).

We used a spatially explicit population model to simulate rusty crayfish population growth, movement and removal in the JDR and evaluated different management strategies across various effort levels (i.e. number of locations receiving management). We evaluated the performance of all alternatives in meeting objectives of suppression (i.e. minimise the overall population size or total abundance of rusty crayfish), containment (i.e. minimise the range size or spatial extent of rusty crayfish in the JDR) and prevention (i.e. minimise the number of crayfish entering the Columbia River). Our results point to three major outcomes with respect to comparing spatially explicit management alternatives for an invasive species.

First, all strategies involving removal of invasive crayfish performed better than No Removals on every objective in terms of both decision criteria, yet the optimal strategy often varied by objective, decision criteria or the level of removal effort. For example, if the prevention objective was the priority, the Target Abundance strategy would be preferred for a risk-neutral decision-maker (expected value decision criterion), but for a risk-averse decision-maker (mini-max criterion), the Target Growth strategy would be preferred (Tables 2, 3, Fig. 2). The optimal strategy for the containment objective in terms of the expected value criterion varied across the number of segments that received management (Table 2). However, Target Downstream was consistently the best strategy for the prevention objective across all numbers of segments receiving management and across the two decision criteria, yet this strategy performed poorly on the suppression objective (Tables 2, 3, Fig. 2). In addition, for this objective, removing at one segment under the Target Downstream strategy performed better than any other strategy with four segments of removal effort (Table 2). The Target Downstream strategy is similar to other efforts in freshwater invasive species management to reduce spread rates into an uninvaded area (Rytwinski et al. 2019). For example, to minimise stone moroko (Pseudorasbora parva) spread in England and Wales, resource managers targeted management at lakes that were located on the floodplain (Britton et al. 2011). In addition, a study of invasive signal crayfish (Pacifastacus leniusculus) in Europe revealed that removing crayfish at the leading front of the invasion may delay colonisation to new areas (Moorhouse and Macdonald 2011).

Second, because no single management strategy performed the best across every objective and decision criterion, trade-offs amongst objectives are unavoidable. We found that the Target Downstream strategy was the only strategy that was Pareto efficient (i.e. not dominated by another strategy) regardless of the number of segments receiving removal effort and regardless of the decision criterion (Tables 2, 3, Fig. 2). This is because the Target Downstream strategy was always the best strategy for the prevention objective. This result differs from findings in terrestrial invasive species contexts that suggest targeting the core of invasion (e.g. Baker (2017); Lustig et al. (2019)), equivalent to the Target Abundance strategy here, is most effective. However, our result is similar to findings for invasive weed management, in which targeting outlier invasions can be effective (Bossard et al. 2000). In many invasive species management contexts, preventing spread into a new area is an important objective, especially when eradication is not feasible (Green and Grosholz 2021). For example, a primary objective of bigheaded carp (Hypophthalmichthys spp.) management in the mid-western United States is to minimise spread into the Great Lakes (MacNamara et al. 2016). In addition, the U.S. Forest Service developed a campaign for invasive spongy moth (Lymantria dispar) called “Slow the Spread” to minimise new invasions (Grayson and Johnson 2018). Hence, for a widespread invasion, management strategies that best prevent spread into new areas may be preferred. However, when managers make decisions regarding spatial management, it is important to acknowledge that some strategies may not be mutually exclusive and management locations may overlap (e.g. target growth and target edges strategies may involve removal at the same locations).

Third, as expected, it is better to conduct management at a higher intensity. For example, the expected value outcome of the suppression objective under the Target Abundance strategy showed a 3% improvement comparing No removals to one segment receiving management, an 8% improvement comparing 1–4 segments managed, an 11% improvement comparing 4–8 segments managed and a 29% improvement when comparing 8–16 segments receiving management. In general, the outcomes of the best alternative under all objectives and decision criteria improved with increasing management intensity (Tables 2, 3). A variety of invasive crayfish management studies have also recognised that higher intensity removals achieve better management results (Hansen et al. 2013; Perales et al. 2021; Reisinger et al. 2024). For example, a whole lake invasive rusty crayfish removal study in Wisconsin, USA, showed that intensive trap efforts could suppress rusty crayfish populations (Hein et al. 2007). However, although intensive crayfish removal may effectively suppress populations, especially in closed systems, these intensive efforts often come at a significant economic cost and are increasingly challenging to conduct in open systems like rivers (Fausch and García-Berthou 2013).

Cost is often a major consideration in management (Epanchin-Niell 2017). To account for this, we considered alternatives with varying intensities (i.e. number of segments with removal effort) as a proxy for cost. Implementing a “proxy” for cost is a simple and effective way to help identify the degree to which management outcomes may improve if budget is increased. Here, we showed that increasing the number of segments that received management greatly improved outcomes in suppressing the population, yet there were only marginal benefits in improving outcomes for the prevention objective (Fig. 2).

We relied on simulations of a population model to conduct this study and, with all such studies, there are some limitations to acknowledge. In terms of the ecology of rusty crayfish, in our model, temperature was the only covariate included, but other environmental factors may be important. For example, river flow results in variability in dispersal rates of crayfish (Ehrlén and Morris 2015), though it would be challenging to simulate at the scale of our study. In addition, we assumed that every location was available for removal, which may not be the case in reality due to restrictions in access and this assumption may impact management outcomes. For instance, Bertolino et al. (2021) showed that restricting access of natural resource managers to private property can cause delays and lead to more costly management. In addition, our model assumed a high level of trap coverage in each segment and various levels of trap coverage could be evaluated in future studies. Finally, the only management technique we considered involved removal of adult crayfish (i.e. older than 1 year old) via physical trapping. Removal techniques involving juvenile crayfish are rare and difficult to implement. Invasive crayfish management programmes will benefit from studies that identify novel, effective techniques (e.g. biocides, Manfrin et al. (2019)).

We selected segments for management, based on perfect knowledge of the system, which will not be the case in real applications. If we do not have perfect knowledge of the state of the system, we would need to rely on monitoring data to identify removal segments, allowing for the implementation of dynamic or adaptive management (Lyons et al. 2008; Williams and Brown 2014). We attempted to create this case study in an adaptive management context, which relied on creating a Bayesian estimation model for abundance. However, we were unable to produce reasonably accurate estimates, likely because we were collecting data from only a subset of segments in only four months of the year. If management were to occur more frequently or additional data streams were integrated (e.g. detection-non/detection or radio telemetry data), an adaptive management framework may be appropriate, as abundance and other parameters could be better estimated. However, our results provide insight into the management strategies that may be most effective, as well as their overall effectiveness in the best-case scenario, when knowledge about the system is perfect.

The JDR represents a particularly challenging system, in terms of the extent of the basin and of the crayfish invasion, making it difficult to accurately manage or monitor the entire basin. While managers are not currently removing crayfish in the JDR, we provide context on the potential effects of management which could be used by future decision-makers. Although we showed that removing crayfish resulted in better management outcomes than No Removals, on average, no strategies resulted in eradication, successful containment or prevention of crayfish moving downstream into the Columbia River. Therefore, rusty crayfish invasion in the JDR can serve as a precautionary tale, as management outcomes would have likely improved if management had begun earlier in the invasion process (Messager and Olden 2018). Therefore, we emphasise the value of early detection and rapid response for minimising the impacts of invasive species before the invasion becomes too large for management to be effective (Reaser et al. 2020).

In conclusion, we provided an approach to simulate an aquatic invasive species in a complex riverine environment. In general, there are very few applications of population models that evaluate spatially explicit management in riverine contexts (Corrales et al. 2020). We described a flexible modelling framework that integrated different spatial management strategies and is broadly applicable to different species and regions of interest. Spatially explicit population models can offer natural resource managers a cost effective tool to examine management alternatives.

We thank two anonymous reviewers whose comments greatly improved the article. We would like to thank Theresa Thom and Paul Heimowitz for guidance in developing this study. Any use of trade, firm or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.