Currently used control methods comprise a variety of manual or mechanical methods, grazing and chemical control (Nielsen et al. 2005). The probability of eradication success increases if control measures are conducted exhaustively and repeatedly within seven to ten years (Holzmann et al. 2014, Nicholas et al. 2005). The prevalence of H. mantegazzianum populations along steep embankments, in deep ravines and other inaccessible places makes manual treatments difficult (Nielsen et al. 2005, Nicholas et al. 2005). The current preventive control options are:

• Avoidance of vegetation gaps, dense vegetation cover, respectively (Pergl et al. 2007) or presence of the same functional group as invader in the endangered plant community (Longo et al. 2013, Wang et al. 2013, Mwangi et al. 2007, Kahmen et al. 2005, Pokorny et al. 2005),

• General increase of diversity in endangered plant communities (Henry et al. 2009, Pfisterer et al. 2004, van Ruijven et al. 2003, Kennedy et al. 2002, Moore et al. 2001, Naeem et al. 2000),

• Low grade of human disturbance of the ‘natural’ ecosystem ‘degree of hemeroby’ (Mwangi et al. 2007, Machado 2004, Steinhardt et al. 1999, Jalas 1955).

Recent active control options according to the literature are:

• Manual or mechanical control such as pulling out the whole plant by hand (EPPO 2009), root cutting or umbel removement by hand (Pyšek et al. 2007a, Pyšek et al. 2007b, Nielsen et al. 2005), cutting the plant from above surface with scythe, mowing or milling machines (Westhus et al. 2006, Nielsen et al. 2005),

• Grazing by sheep whereas a time frame of at least 10 years was most effective (Westhus et al. 2006, Nielsen et al. 2005, Andersen and Calov 1996, Williamson and Forbes 1982) Grazing seems meaningful for control of large stands and areas inaccessible for machinery,

• Chemical control whereas glyphosate³ was the most successful herbicide (Nielsen et al. 2007, Nicholas et al. 2005, EPPO 2009). To reduce damage to surrounding vegetation, applications are recommended as spot spraying early in the growing season. However, in the final calculation we suggested chemical treatment with hand-held equipment due to the lowest cost of the alternatives for medium and unprotected areas and its suitability for areas difficult to access.

Revegetation programs after giant hogweed eradication are required to restore the dense vegetation layer and prevent further re-infestations successfully (Noxious Weed Control Program 2015).

Since there are only few data available for giant hogweed management in Germany, cost estimations are based on a nationwide survey of n = 287 German districts (Thiele and Otte 2008) and benefit estimations are based on a choice experiment survey of n = 282 German households. The data from the survey of Thiele and Otte (2008) contain also information on population density. In detail, the questionnaire included questions about the maximum spatial extent of single H. mantegazzianum stands in three proposed categories (up to 100 m², >100–1,000 m², >1,000 m²) for different habitat types (e.g. roadside or forest margin) and, about occurrences in nature reserves per district or city. Because no conclusion of the total frequency of single stands per district or city was possible, our calculations are based on the assumption of a minimum occurrence of the evaluated stands per district or city. This means, the available data indicate, if at least one small, medium or large area is infested and if at least one of these areas is protected. A range of possible control measures (manual, mechanical, chemical and grazing) is identified and shown in Table 1. The crosses (X`s) indicate meaningful applications of infestation control measures. Suggested measures are root destruction with shovel (small areas), mechanical cutting with a scythe (medium areas) or flail mower (large areas). Regarding chemical control, hand-held equipment is suitable for small and medium areas, tractors with spraying machines for large areas. Chemical treatment includes the cost of restoration such as seeds, sowing and working hours. For nature reserves, where chemical control is prohibited by law, we suggest root destruction with shovel (small areas) and mechanical cutting with scythe (medium and large areas).

Workload, frequency and effectiveness of treatments are shown in Table 2 (based on Nielsen et al. 2005). It must be considered that chemical control has several restrictions. Grazing is a ‘continuous treatment’ and includes the workload for fencing and maintenance. Grazing is supposed for medium and large areas, where suitable conditions for livestock farming are given with regard to soil and climatic conditions.

Costs and benefits arise because invasive species interfere with the functioning of natural or human-modified ecosystems which yields flows of economically valuable goods and (ecosystem) services (Emerton and Howard 2008). Cost-benefit analysis (CBA) aims to quantify the value of all positive and negative consequences of a project or measure to all members of society in monetary terms. Usually, benefits and costs accrue over extended periods (years). From today’s point of view all resources available in the future are less valuable than those available today. Therefore, in CBA future benefits (costs) are discounted relative to present benefits (costs) to obtain their present values. A benefit (cost) that occurs in year t is converted to its present value by dividing it by (1+d)^t where d is the social discount rate.

So if a project has a duration of n years with yearly benefits (B_t) and costs (C_t), the present value of the benefits (PV (B)) is

\[PV(B) = \sum_{i=0}^{n} B_{t}/(1+d)^{t}\]

and the present value of the costs (PV (C)) is

\[PV(C) = \sum_{i=0}^{n} C_{t}/(1+d)^{t}\]

If the present value of the benefits exceeds the present value of the costs, the project is valued positively because it leads to a more efficient allocation of society’s resources (Boardman et al. 2011). The purpose of this CBA application is to compare different control measures in order to select the most efficient eradication strategy. As they can crucially influence CBA outcome, we also vary social discount rates between 1% and 3% (Florio and Sirtori 2013, Drupp et al. 2015).Within sensitivity analysis, we consider potential overestimation of empirically investigated benefits (scenario 1). In the second part of sensitivity analysis, we assume a worst case scenario (scenario 2), in which every German district is infested. Benefits of control measures are based on results of a choice experiment (n = 282 respondents) investigated as WTP per person and year (for further details see chapter Calculation of benefits). WTP can be regarded as indicator showing if responents are in favor or disfavor for a change from the status quo situation when comparing different alternatives (see Suppl. material 2). WTP results are particularly important where no market proxies or prices are available, as this is usually the case for public goods. In order to meet potential criticism on WTP results in terms of possible overassessment, we suggest several approaches to calibrate our WTP results. In the sensitivity analysis, we recalculate WTP results based on Arrow et al. (1993) proposing a calibration factor of 0.5. It seems impossible to develop a unique calibration factor but we can at least compare our WTP results with other empirical studies which is done in the discussion part of this paper.

Bräuer and Suhr (2005) evaluated 43 empirical studies comparing hypothetical and real WTP for various environmental conservation programs. The term ‘hypothetical WTP’ describes the fact that WTP is ‘just’ stated as answer in a survey situation, whereas the term ‘real WTP’ means the truly payment of the amount stated by respondents. The authors suggest calculating ‘switching values’ which equal WTP necessary for benefit-cost relations >1. WTP divided by ‘switching values’ identify the maximum allowed overestimation (Bräuer 2002:264). The maximum allowed overestimation in the study of Bräuer results in a factor of 9.38 and the switching value is 0.08 € (recreation tax as average one-time payment), meaning that if respondents where only willing to pay 8 cent per day during their vacation or stated WTP was overestimated by a factor of 9, the benefits of the described program would still exceed the costs.

For some public goods, such as recreation in uninfested landscapes, there are simply no market proxies for preferences. Many analysts have concluded that in this case, there is no alternative to asking a sample of people directly about their preferences (Boardman et al. 2011, Bateman et al. 2002, Hanemann 1994). Questionnaires to elicit such preferences have to be prepared carefully, e.g. the formulation of valuation scenario, including sampling, and data analysis. In some countries, economically relevant benefits from eradication of invasives on direct production may arise (e.g. benefits from commercial crops and livestock), as well as secondary effects on other sectors and times in terms of markets and nutrition (Emerton and Howard 2008). This seems not to be the case for Germany in an economically relevant dimension (Bundesamt für Naturschutz 2015). In our calculations, we focus only on one benefit of eradication control: the recreational value in terms of WTP for an environment being free of giant hogweed and its risks for humans (for further benefits see Pergl et al. 2007, Nielsen et al. 2005, Pfisterer et al. 2004, Williamson and Forbes 1982). The calculation of benefits is based upon an empirical face-to-face survey using results of a choice experiment (stated preference method see e.g. Adamowicz et al. 1998, Bateman et al. 2002). The main survey was preceded by qualitative preliminary studies (face-to-face; n = 16), pre-test interviews (as mail survey and face-to-face; n = 57) and pilot study (face-to-face; n = 106). Our qualitative pre-study showed that respondents were aware of non-native plants, particularly the giant hogweed was mentioned in several independent interviews (open question format). Thus, we decided to use H. mantegazzianum as an indicator for invasive plants. To prepare respondents to the choice experiment task, there was a section in the questionnaire, were some details of the attributes and levels were explained. In the explanation we focused on the risks of giant hogweed to humans in order to justify different types of potential eradication measures. The proposed eradication measures of the attribute ‘Invasive plants’ are shown in Table 4.

An examplary choice set used in the main survey is shown in Suppl. material 2. Choice cards included a picture of the H. mantegazzianum. Within the choice experiment, the following two options were offered to respondents:

• Option 1: removal of invasive plants in particular cases for which negative effects are known, or

• Option 2: large-scale removal of invasive plants even when unclear if they have negative effects or not.

Respondents were asked to state their choice regarding the preferred option. Including the ‘price’ (mandatory tax payment) of the hypothetical measure each choice option indicates benefits of respondents obtained by the choices. The ‘price’ for implementation of the proposed measures ranged from 0 to 80 Euro per programmed year. For the Status Quo situation, the cost was always zero. Statistically significant attribute coefficients allow for the calculation of WTP for attribute level changes. In the econometric analysis, WTP can not only be identified for a program or scenario but also for single attributes (details in Suppl. material 2). Average WTP of respondents for control measures is calculated as follows. For attributes linear in parameters, the marginal WTP equals the negative ratio of the respective attribute coefficient c_z and the coefficient of the monetary attribute c_y:

\[\text{WTP} = -\dfrac{c_{z}}{c_{y}}\]

WTP values refer to one-level change in the attributes. For respondents protesting the choice experiment, ‘0’ WTP is assumed in order to avoid a bias in favor of higher WTP than stated in the sample. Benefits are opposed as single payment to the costs of a ten year eradication program limiting stands of H. mantegazzianum. In the following analysis WTP results for the single attribute ‘Invasive plants’ are multiplied with the number of households per infested district accounting for nationwide control measures.

For the cost side, we calculate two different invasion scenarios for each area size, type and measure: (i) no re-infestation after successfully conducted control measures (optimistic) and (ii) re-infestation twice after conducting control measures within ten years (pessimistic). Both scenarios include the suggested number of treatments per yer (up to three treatments) and measure such as displayed in Table 2. For the cost-benefit analysis, we chose the measures with lowest costs for each area type (protected or not) and size. We calculate with yearly discount rates of 1%, 2% and 3% (Florio and Sirtori 2013, Drupp et al. 2015) and a yearly inflation rate of 1% (e.g. national bonds with expiry date of 2026, corresponding to a 10 year program starting this year, comprising a value of 0,96%, Deutsche Bundesbank 2016). Additionally, 1% increase in labor costs per year is assumed. Both scenarios include 50% additional costs for after-treatment and 30% additional costs for monitoring (30% of labor costs) for each year.

In the following, the procedure of cost calculation is briefly described (see Table 5): As hourly rate of labor costs, 33 € are calculated for all measures. For root destruction measures of H. mantegazzianum, additional job training of 5 hours for instruction are considered. One worker is suggested for every small area (up to 100 m²; average 50 m²), ten workers for every medium area (>100–1,000 m²; average 550 m²), and five workers for every large area using machines (>1,000 m²; average 5,500 m²). We considered establishment costs for protective clothing, shovel, scythe and flail mower. Running costs include monitoring (30% of labor costs) and two additional treatments, plus repair costs for machines (e.g. flail mower). Costs for chemical control include two treatments per area, protective clothing (safety glasses, (mouth-) mask, cap, coat and trousers, shoes and gloves), herbicide sprayer for small and medium areas and tractor with spraying machine for large areas, diesel and machine oil, technical inspection and machine check, glyphosate concentrate, restoration (seed mixture, e.g. 70% grass, 30% herbs, 4,000 seeds or 20 g per m²; planting costs, two cuttings per year), plough and seeder. Besides working hours for the described measures, we add five hours for job training for each area. Establishment costs for chemical control include protective clothing, shovel, scythe, machines (tractor with spraying machine, plough and seeder), herbicide sprayer, glyphosate and seeds for restoration. Running costs for chemical control are for diesel and machine oil, technical inspection and machine check. For calculations of technical agricultural cost (e.g. agricultural machines), we used KTBL software (2015). Grazing is suggested for medium (>100–1,000 m²) and large (>1,000 m²) infested areas. Considering sheep having to get used to H. mantegazzianum, we included an additional 5% of total costs for initiation of the measure. We consider establishment costs as those associated with the purchase of animals, fencing in a lifespan of 10 years and shelter. Running costs include maintenance of fencing, periodic inspection, and moving of animals between fenced areas as well as supplementary cutting of H. mantegazzianum outside the fenced area, in total, 1,000 hours (33 € per hour) workload per year. Additionally, we calculate 15 hours in administrative costs per area and year for planning, organisation and coordination of the grazing measures. Furthermore, additional fodder for the winter time as well as veterinary inspection with treatment in the case of diseases and water supply are considered. Thirty percent of total costs are suggested for yearly monitoring. Costs of labor are calculated with three people for medium areas (average 550 m²; by maximum 1,000 m²) and 5 people for large areas (average 5,500 m²; by maximum 10,000 m²). Assuming that the costs are financed by the public authority, we include an excess burden of taxation at the rate of 15% (see Boardman et al. 2011). The excess burden or efficiency cost of taxation recognizes that transfers between consumers, producers and the government are not costless to implement (Boardman et al. 2011). Finally, cost-effectiveness of eradication strategies depend on the length of the period over which they are implemented and observed.

The choice experiment was conducted as a household survey using face-to-face interviews in central Germany. Of the successfully contacted 302 households, 282 respondents completed the choice task (6.6% protest answers). An average interview took 35 minutes. Respondents preferred on average the first control option offered in the choice experiment, the ‘removal of invasive plants in particular cases for which negative effects are known’. Interviewees were willing to pay 9 € (p < 0.05) as annual contribution when compared to the more abrasive eradication program. For the 20 respondents (6.6% of interview respondents) protesting the choice experiment, ‘0’ WTP was assumed. Accepting a minimum advantage of invasion control for the German population living in infested districts, in terms of recreation in an environment free of giant hogweed plants, benefits amount to 238,063,641 € per year, average 829,490 € per district. To avoid overestimation, we calculated direct use values as only one single payment per household, despite WTP was investiagted as annual payment per person. The control of H. mantegazzianum, offered in two options, was identified as significant predictor of choice within the econometric model (p < 0.05; Chi² < 0.001; R² - values 0.19–0.22⁴). For more details on the conducted choice experiment and further results see Rajmis et al. (2009).

Table 6 shows the costs in terms of net present values for a ten year eradication program with varying discount rates (1%, 2% and 3%) for each proposed measure. Costs of control measures result in a total of 3.3 milion € for the optimistic invasion scenario and 5.8 million € for the pessimistic invasion scenario⁵ at a discount rate of 3%. Calculating a discount rate of 2% costs result in a total of 3.4 milion € for the optimistic invasion scenario and 6 million € for the pessimistic invasion scenario. The 1% discount rate leads to a total cost of 3.5 million € for the optimistic invasion scenario and 6.3 million € for the pessimistic invasion scenario. The costs for the single area types are as follows: for an optimistic scenario in non-protected areas, the lowest cost identified for small areas are root destruction with shovel and result in min. 810 € (max. 855 €), for medium areas the lowest cost resulted in chemical treatment with hand-held equipment including; which amount to min. 5,180 € (max. 5,385 €) and for large areas mechanical cutting with flail mower resulting in min. 44,631 € (max. 45,406 €). For a pessimistic scenario in non-protected and small areas lowest costs were also identified for root destruction with shovel resulting in min. 1,511 € (max. 1,628 €), for medium areas chemical treatment with hand-held equipment including restoration at a min. price of 11,028 € (max. 11,832 €), for large areas the lowest cost were reached by grazing with a min. of 49,251 € (max. 52,850 €). For an optimistic scenario in small protected areas, lowest costs are also reached by root destruction with shovel and amount to min. 810 € (max. 855 €), for medium areas the lowest cost result for mechanical cutting with scythe amounting to min. 7,424 € (max. 7,727 €). For large areas mechanical cutting with scythe is suggested which amounts to min. cost of 22,707 € (max. 24,071 €). For the pessimistic scenario in protected and small areas the lowest cost result in root destruction with shovel and amount to min. costs of 1,511 € (max. 1,628 €) for medium areas mechanical cutting with scythe resulting in min. cost of 15,658 € (max. 16,834 €), and for large areas (mechanical cutting with scythe as well) in min. cost of 40,157 € (max. 43,310 €). Some details of scenario calculations are shown in the supplementary material (Suppl. material 1).

We chose the measures with lowest costs for each area type (protected or not) and size (small, medium and large) for the final calculation. The lowest cost measures are root destruction with shovel in small areas (optimistic and pessimistic scenario), chemical treatment with hand-held equipment in medium areas (optimistic and pessimistic scenario), mechanical cutting with flail mower in large areas (optimistic scenario), and grazing for large areas in the pessimistic scenario. Root destruction with shovel and mechanical cutting with scythe are due to legal constraints the only options for protected areas. The benefit-cost relation of German districts for control measures of H. mantegazzianum lies between 69:1 (discount rate of 1%) and 72:1 (discount rate of 3%) for optimistic scenario and 38:1 (discount rate of 1%) and 41:1 (discount rate of 3%) for pessimistic scenario calculations for each area size. Results indicate that every euro of calculated costs can be opposed to averagely 55 € of benefits (discount rates between 1% and 3%). To give consideration to the earlier mentioned concerns of potential overestimations, we calculate the maximum allowed overestimation (Bräuer 2002, Bräuer and Suhr 2005).

Switching values range between 0,02 and 0,03 € (average 2,5 cent) in Scenario 1 and between 0,24 and 0,30 € (average 26 cent) in Scenario 2. This is the amount necessary to result in a benefit-cost relation >1. Calculating the net-benefit of measure implementation (WTP/switching value), a factor of 448 results for optimistic and 299 for pessimistic scenario calculations. This means, if our empirically investigated results would be overestimated by factors between 299 (pessimistic scenario) and 448 (optimistic scenario), ‘necessary’ real WTP would be still the amount of the switching values (0.03 € and 0.02 €), hence high enough to keep the benefit-cost relation positive.

Since the utilized source of data (Thiele and Otte 2008) may not represent the current state of invasion status in Germany, we also provide a sensitivity analysis in terms of infestation assumptions (Scenario 2). We assume that every German district is infested with at least one small, one medium and one large area and calculate the pessimistic infestation scenario without chemical treatment (due to possible infested nature reserves or other sensitive landscape areas), control cost amount to 57 and 61 million euro for ten years of treatment. As this is a worst case scenario, we assume the most expensive cost for each measure and area size here. This cost estimate is well within the range of similar calculations for other countries (Reinhardt et al. 2003, Sampson 1994, van Wilgen et al. 2004). The cost estimates of Gren et al. (2009) are somewhat higher than our results (see below). Opposed to the benefits of our survey with one single payment per German household in the infested districts, this results in a benefit cost-relation of 4:1. The maximum allowed overestimation ranges between 30 and 37 and is thus lower as in scenario 1 (between 38 and 72). This result seems reasoned due to average benefit-cost relation in scenario 2 is ten times lower (e.g. 4 versus 40 using DR of 2%) comparing pessimistic scenario calculations. Switching values range between 0,24 and 0,30 €, meaning that even if WTP would have been be overestimated 37 times, we would still have a benefit-cost relation >1. As mentioned earlier, the NOAA Panel suggests calibrating empirical WTP results by a factor of 0.5 (Arrow et al. 1993). If we recalculate scenario 1 with halved WTP, the allowed overestimation is 50% reduced and results in a factor of 150 considering pessimistic assumptions and a factor of 225 for optimistic assumptions. For scenario 2, the allowed overestimation with halved WTP has still a factor of 17, meaning that even if WTP would have been stated 17 times higher then conceived by respondents, we would still have a benefit-cost relation >1.