Model Description

The simulation model developed in this study is composed of three main modules: treatment development, spread simulation and treatment plan evaluation (Figure 1). Treatment plans are developed and evaluated in an interactive process between user and model. Spatial and non-spatial data are required to provide the current infestations across a landscape of interest, as well as user-defined treatment options (i.e., herbicides) and application methods (AM) (i.e. helicopter, backpack, etc.) for treatment development. Initially, the simulation model uses current infestation areas provided by the user to determine candidate treatment units (TU), which are defined as spatially contiguous areas (i.e., polygons) that are homogeneous in terms of land attributes, such as weed composition, upland or riparian (i.e., areas within a user-defined distance from water bodies), and proximity to roads and trails. The model presents these units to the user for prioritization. User-prioritized units are then entered into the model to determine herbicides and AMs for each TU based on application feasibility (e.g., riparian areas, vehicle accessibility, etc.). Treatment locations for the first planning period are used to simulate weed spread across the landscape for the following planning period. Simulated weed spread is then used by the model to select candidate TUs for the next planning period, which are presented to the user for prioritization. This iterative process continues until a 5-yr treatment plan is completed for the landscape. This treatment plan is then evaluated by the plan evaluation module in terms of total simulated infestation area and total treated area. All three modules are implemented as a series of functions in ArcMap®, a Geographic Information System (GIS) computer program widely used among land management agencies. Details on each module as well as the required user input data are presented below.

Figure 1.

Overview of the simulation model consisting of three main modules: treatment development, spread simulation, and plan evaluation.

Treatment Development

Selecting treatments requires TU with the attributes of homogeneity described above. We selected these attributes because they are important factors in deciding herbicides and AMs. For example, specific herbicides are often selected based on weed species and land class, while feasible AMs depend on the accessibility to TUs. The model begins with creating buffers around the stream network to designate riparian areas based on user-input distance from the stream, and then identifying accessible areas by each AM by creating buffers around trails and roads based on user-input distance limits.

We created a treatment development algorithm to build annual treatment plans for a landscape of interest, which is described in detail in Figure 2. The algorithm first develops candidate TUs from known infestation areas. These TUs are then prioritized by the user based on preferred treatment strategy (i.e., weed species, site priorities, or a combination of the two). The algorithm begins with the highest priority TU and selects an applicable herbicide and AM for the TU. This process repeats until the given annual budget is used up or no more unassigned TU is available. Herbicides are selected based on weeds and land type attributes of TUs. If more than one herbicide option is available, the algorithm chooses the least cost option per hectare. For AM, the algorithm first considers the least cost method on a hectare basis and examines its feasibility. Low cost AMs usually have a large minimum treatment size requirement in order to recover high fixed costs (e.g., aerial spraying). If the current TU is not large enough, it becomes a seed TU and the algorithm searches for neighbor TUs to form a cluster that can be treated with the same herbicide and AM (Figure 3).

Figure 2.

An algorithm developed to build an annual treatment plan based on TUs, user-defined priorities, herbicides, application methods, and available budget. The shaded box represents user inputs.

Figure 3.

Building a cluster of treatment units (TU) by the simulation model to meet the minimum treatment size requirement for a given application method (AM). TU1 and TU2 are high priority units serving as the center of search windows. AM 1 (e.g., helicopter) is the least cost method available and considered first for its feasibility. Case 1 shows that there are sufficient TUs near TU1 that collectively meet the minimum treatment size requirement for AM 1, whereas in case 2, AM 2 (e.g., truck) is selected for TU2 and its neighbor units because of insufficient area for AM 1.

This proximity-based clustering function of the algorithm uses a rectangular search window centered at the seed TU with a size approximately seven times larger than the minimum treatment size requirement of the AM being examined. If the cluster size exceeds the minimum treatment size requirement and budget is available for the treatment, the cluster becomes part of the treatment plan for the given year (Case 1 in Figure 3). Otherwise, the algorithm moves to the next least cost AM that requires a smaller minimum treatment size, and examines its feasibility (Case 2 in Figure 3).

Spread Simulation

Modeling dynamics of weed species spread is challenging because there exist many influencing factors, both biotic and abiotic components of the environment affecting their movement, as well as the effects of treatments that may change the spread dynamic over time and space. In this study, we considered the currently infested areas, vegetation susceptibility to infestation, and selected treatments (i.e., herbicides) as influencing factors to determine newly infested areas over time for the purpose of developing and evaluating short-term action plans.

The spread of weeds was considered to be affected by vegetation susceptibility in the surrounding area of current infestation and existence of treatments. Vegetation susceptibility is assumed to be in one of three categories which vary with weed species and vegetation cover types: (1) closed to invasion; vegetation is not susceptible to the particular weed species, (2) disturbance allows invasion; in normal condition the vegetation is not susceptible, but becomes susceptible if disturbed, and (3) susceptible; vegetation is susceptible to weed species. The modeled spread of weeds is linear in all directions at a user-provided spread rate.

The simulation model also takes into account multiple weeds and the effects of treatments that might vary on different species. If the selected treatment is known to work on a particular weed, the model assumes that such treatments stop weed spread for a given number of years (i.e., user-defined duration of treatment effect). After this duration of treatment effects expires, weeds reestablish in the TU and start spreading at a given spread rate. If there exist multiple weeds in the same TU, only the ones that are affected by the treatment stop spreading. Figure 4 illustrates our assumptions on weed spread with treatment effects in three different cases with multiple species. Figure 4a shows weed spread with no treatment, where weeds spread along the perimeters of existing infestation at a given linear spread rate per year. Figures 4b and 4c present the two cases where only one weed (Weed B) is treated, while there is an overlap area with other weeds. Weed A spreads into the overlap area (Figure 4b) unless herbicide used for Weed B also affects Weed A (Figure 4c). Figure 4d shows the last case scenario where both Weeds A and B are treated, and therefore both weeds stop spreading.

Figure 4.

Weed spread logic with treatment effects on multiple weed species. Assuming surrounding vegetation is susceptible to invasion of Weeds A and B: a) no treatment, both Weeds A and B spread, b) Weed B is treated, and the herbicide affects only Weed B, c) Weed B is treated, and the herbicide affects both Weeds A and B, and d) Both Weeds A and B are treated.

Plan Evaluation

After a 5-yr treatment plan is built for a landscape of interest, the plan is evaluated in terms of total infestation areas, the amount of selected areas to be treated, and cost-effectiveness of treatments. The total infestation areas represent future infestation potential, while the total selected areas for treatment account for the amount of containment efforts on an area basis. For cost-effectiveness of treatments, we calculate a cost-effectiveness ratio (CE) using Equation 1. The denominator of the ratio represents the effects of weed treatments in terms of areas (ha) to be maintained weed-free because of treatments. These areas can be obtained from a comparison between the simulation results of a treatment plan and those of no action plan. The lower CE value indicates the more cost-effective the treatment plan would be. This ratio can be also interpreted as the annual cost of maintaining 1 ha free of weeds from the area that would have been infested without treatments. However, any of these measures do not represent qualitative aspects of treatments that might be necessary to assess for the overall goodness of treatment plans. Diverse evaluation criteria should be explored to assess plans and conduct trade-off analysis based on given management goals. Since our simulation model generates a spatial database for selected treatments on a yearly basis and the estimates of infestation over time, individual treatments and their effects can be further analyzed per species, herbicides, and AMs.

Model Application

We applied our simulation model to a study landscape of 24,867 ha (61,447 ac) located in the Salmon River watershed in the southwestern portion of the Nez Perce National Forest in North-Central Idaho (Figure 5). In 1994, the Idaho State Department of Agriculture created the Salmon River Weed Management Area (SRWMA) to coordinate weed management efforts among federal, county and private land managers (Idaho State Department of Agriculture 2009). Because weed treatments have been applied actively in the drainage and geospatial databases required for our model have been well established, it was deemed as an appropriate application landscape for our model.

Figure 5.

The 24,867 ha study landscape located in the Nez Perce National Forest.

User Input

Treatment Plan Options

The total selected areas for treatment in hectares were mainly constrained by annual budgets (Figure 6). Compared to the lowest budget level at $25,000, the highest annual budget at $150,000 allowed additional treatments of more than 8,000 ha. However, the treatment locations were highly affected by the prioritization scheme employed in selection of TUs (Figure 6). For example, in the $25,000 budget level scenario, the 23-ha area located in the north-west corner of the study landscape was selected for treatments under the sites priority scheme, whereas it was not selected under the species priority scheme. In the $150,000 budget level scenario, large differences in areas selected for treatment between the two prioritization schemes were observed in the south-central region of the study landscape owing to the different priorities assigned to those areas under each prioritization scheme (Supplemental Appendix 6a and 6b;  http://dx.doi.org/10.1614/IPSM-D-13-00043.SA (10.1614_IPSM-D-13-00043.SA.docx)).

Figure 6.

Selected treatment locations shown with the number of retreatments under different prioritization schemes and annual budget levels.

The results on the areas selected for treatment also show that many low priority units were selected for treatment especially under the site priority scheme. This is because of the clustering function of the simulation model. Nearby low priority TUs are included in a cluster which is developed to treat a high priority TU at relatively low costs. This essentially mimics the common practice of treatments where larger infestation areas are often treated together with the target area when the AM has a sufficient spraying capacity (e.g., aerial spraying).

Because the duration of treatment effects considered in this analysis last not more than 3 yr (Supplemental Appendix 4;  http://dx.doi.org/10.1614/IPSM-D-13-00043.SA (10.1614_IPSM-D-13-00043.SA.docx)), some areas were selected for retreatment during the 5-yr planning horizon. It appears that the prioritization schemes also affect the selection of TU for retreatment (Figure 6). For example, a 23 ha area in the north-west corner of the study area was not treated in the weeds priority plan at the $25,000 budget level, and treated only once in the other budget levels. However, the same area was treated at least three times in all budget levels in the sites priority plans because of its high site priority for treatment. Another difference between the two prioritization schemes in terms of TU selected for retreatment was found in the south-central region of the study area. The areas were retreated more times in the weeds priority plans than the sites priority plans across all the budget levels because of high priority weeds in the area.

From the AMs considered in this study, helicopter was the most popular method in all scenarios ranging from 1,752.4 ha to 10,271.7 ha (Table 1), leaving only small and spread out areas for other more expensive AMs. Backpack, the second most selected AM, but far below helicopter, was assigned to satellite treatments where there were not enough continuous areas for helicopter or where other AMs could not reach because of inaccessibility.

Table 1.

Total areas selected for treatment (ha) by application method in each of the 5-yr treatment plan options.

The number of weeds targeted for treatment was different between the two priority schemes with the exception of the $50,000 annual budget (Table 2). In general, the weed species priority plans targeted fewer weeds for treatment than the sites priority plans. This is because the weed species priority plans aimed to treat the highest priority weeds first as much as budget permits, whereas the sites priority plan selected treatment locations based on sites resulting in a wider weed species mix.

Table 2.

Total areas selected for treatment (ha) by weed species in each of the 5-yr treatment plan options.

It is noteworthy that the wider species mix targeted in the sites priority treatment plans also resulted in higher total treatment costs per hectare (i.e., herbicide plus AM) mainly because more expensive herbicides were selected in order to contain multiple weeds (Table 3).

Table 3.

Total costs per unit area ($ ha⁻¹) of herbicides and application methods in each of the treatment plan options.

Weed Spread Simulation

Total simulated infestation areas by weed species at the end of the 5-yr planning horizon show differences between the base case scenario and each of the treatment plan options (Table 4). The base case, which does not consider weed treatments, represents the worst case scenario resulting in the total infested area of 5,626 ha after 5 yr. The results indicate that the total infestation areas are reduced by 1.6% from the base case scenario when an annual budget is $25,000, but the reduction in infestation area would go up to 25.9% when an annual budget level is increased to $150,000 (Table 4).

Table 4.

Simulated total infestation areas (ha) per weed at the end of 5-yr planning horizon in each of the treatment plan options.

Results also show that the site prioritization scheme was more effective in reducing the total infestation areas across all the budget levels despite the fact that a smaller area was to be treated under this prioritization scheme (Table 2). This is mainly because a larger number of weeds are treated under the site priority plans. The results show that more infestation areas of rush skeletonweed, a high priority weed, were simulated under the site prioritization scheme, but other weeds such as spotted knapweed and scotch thistle seem to be more effectively contained by the site prioritization scheme (Table 4).

It appears that infestation areas of certain weeds such as diffuse knapweed, common crupina and puncturevine are not projected to increase from their initial infestation in both prioritization schemes (Table 4). This is mainly because most areas in the study landscape are not susceptible to invasion by those species unless disturbed, and the current infestations are not near the existing disturbance areas.

Locations of infestation areas for all scenarios show differences across budget levels and prioritization schemes (Figure 7). The higher budget results in fewer infestation areas because more areas can be treated. Differences between the two prioritization schemes at the same budget level, however, are caused mainly by treatment locations and timing. This indicates that it would be important to analyze trade-offs among different priority schemes and refine treatment plans in order to obtain the maximum benefits of treatments.

Figure 7.

Simulated infestation areas at the end of 5-yr planning horizon resulting from each of the treatment plan options.

Changes in infestation areas modeled over the 5-yr planning horizon show that a large area is newly infested during the first yr and then the increase in infestation areas slows down (Figure 8). This large influx of newly infested areas in the first yr is due mainly to the effects of the disturbed area of 6,658 ha (Supplemental Appendix 3;  http://dx.doi.org/10.1614/IPSM-D-13-00043.SA (10.1614_IPSM-D-13-00043.SA.docx)) that was considered susceptible to invasion during the first yr of simulation. This result suggests that managers might need to prioritize disturbance areas for treatment if such areas are indeed more prone to invasion.

Figure 8.

Simulated infestation areas in each time period resulted from each of the treatment plan options. WPP and SPP indicate the weed species priority plans and the site priority plans, respectively.

Cost-effectiveness of Treatment Plans

To assess cost-effectiveness we calculated a CE value for each treatment plan. In our application, the treatment plans developed under the site prioritization scheme are more cost-effective than the weed species priority plans across all the budget levels (Figure 9). It is noteworthy that large differences in CE values between the two prioritization schemes occur at the low budget levels. These results suggest that more careful planning for treatment locations and timing should take place when a budget is tighter because of the large number of options that are available for treatment selection, and the cost-effectiveness of individual treatments may vary widely.

Figure 9.

Cost-effectiveness ratio values calculated from the treatment plan options. WPP and SPP indicate the weed species priority plans and the site priority plans, respectively.

In our simulations, the site priority plan with the annual budget of $25,000 appears to be the most cost-effective option. However, if the management objective is to minimize total infestation areas, higher budget levels would be required (Table 4).

Model Limitations and Strengths

Our simulation model provides a semi-automated method to develop treatment plan options based on the user's management strategies. This process of plan development requires extensive guidance from the model user, especially in prioritizing TUs. Although this interaction between the user and the simulation model would be still beneficial, a mathematical optimization modeling method, when combined with this simulation model, would provide additional benefits by automatically identifying the optimal treatment plan for a given management objective. Our simulation model capable of generating and evaluating plans can certainly provide an essential component for a future optimization tool for weed treatment planning.

Our simulation model considers that weeds spread consistently along the weed patch perimeter without explicit consideration of existence of other weeds or density. Regarding treatment effects, it is assumed that an application of herbicides would stop weeds from spreading for a given duration, but no shrinkage or eradication of current infestations is modeled. We also assumed that the treatment effects and costs do no vary with the density of weeds, and that vegetation susceptibility to invasion is deterministic and known. It is important to understand these assumptions for the proper use of the model and interpretation of the results.

Evaluating treatment plans using our simulation model would allow weed managers to analyze trade-offs and identify the plan that best meets the management goal. Evaluation criteria used in the model include infestation areas over time and areas selected for treatment with spatial, temporal, and operational attributes. However, our model does not consider any measures of economic losses or impacts caused by the presence of weeds (e.g., market and non-market costs and benefits). Since the economic, ecological, and social impacts of one hectare of invasion can vary substantially by location, weed species, plant community, and land use, more inclusive evaluation metrics and criteria could be developed and incorporated in the model in the future.

Targeting single weed species often becomes the norm in weed management perhaps because of the lack of analytical tools to evaluate spatial and temporal effects of treatment decisions on multiple weeds. Our modeling method can provide a means to develop, simulate and evaluate weed treatment plan options for multiple weed species considering their spread dynamics across a landscape over time. Despite the model limitations aforementioned, we hope our model can be used as an analytical approach that helps weed managers better allocate limited resources to efficiently and effectively accomplish their management goals.

Potential Practical Application Issues

Like any other complex simulation models, our model relies on the availability and quality of required input data, as well as a workforce who can properly operate the model. Spatial data required for the model (i.e., current infestation areas, vegetation cover, streams, roads, trails, etc.) become more available and accessible as more land management agencies and other interested parties participate in invasive species monitoring programs and provide geospatial databases (Hunt et al. 2005; USFS 2013). However, obtaining certain data, such as weed spread rates and treatment efficacy, can be still challenging. When such data do not exist, model users will have to initially rely on their best estimates based on their past experiences, and refine them as more knowledge and supporting data become available. Although the model is designed to produce and evaluate 5 yr treatment plans, it should be rerun frequently with newly updated data to improve the practicality of the model results. In order to address the potential issue of workforce development, we have been incorporating our simulation modeling approach into an easy-to-use decision support tool that will be able to fully optimize weed treatment planning. Since the tool will be developed as an embedded program within a widely-used GIS system, we envision that any existing GIS users can easily operate the tool with little or no training.