A practical optimal surveillance policy for invasive weeds an application to hawkweed in australia

Dear author, Please note that changes made in the online proofing system will be added to the article before publication but are not reflected in this PDF We also ask that this file not be used for submitting corrections ARTICLE IN PRESS ECOLEC-05346; No of Pages 10 Ecological Economics xxx (2016) xxx–xxx 001 067 Contents lists available at ScienceDirect 002 068 003 069 004 070 Ecological Economics 005 071 006 072 007 journal homepage: www.elsevier.com/locate/ecolecon 008 074 009 010 075 Analysis 076 011 Q1 013 014 077 A practical optimal surveillance policy for invasive weeds: An application to Hawkweed in Australia F 012 017 018 019 PR OO 015 Q2 016 Tom Kompas* , a, b , Long Chu b , Hoa Thi Minh Nguyen b a b Centre of Excellence for Biosecurity Risk Analysis, University of Melbourne, Melbourne, VIC 3010, Australia Crawford School of Public Policy, Australian National University, Crawford Building (132), Lennox Crossing, ACT 2601, Australia 020 021 022 A R T I C L E I N F O A B S T R A C T 023 025 026 027 Article history: Received 19 July 2015 Received in revised form February 2016 Accepted 13 July 2016 Available online xxxx 028 031 032 033 034 TE 030 Keywords: Surveillance Containment Eradication Invasive weeds Hawkweed Stochastic programming EC 029 We propose a practical analytical framework which can help government agencies determine an optimal surveillance strategy for invasive weeds, including cases of slow-growing or ‘sleeper weeds’, and for all weeds at early stages of invasion where quantitative information is scant or rough The framework consists of three key components: (a) a simple rule that can determine weed surveillance zones or where early detection is desirable, (b) a function that maps surveillance effort to early detection probability, and (c) a schedule to determine an optimal surveillance budget A calibration to Hawkweed in Australia provides an example of the framework and shows that the optimal annual surveillance budget for this sleeper weed is substantial © 2016 Published by Elsevier B.V D 024 035 036 037 038 Introduction 042 043 044 045 046 047 048 049 050 051 052 053 054 055 056 057 The damage from ‘invasive alien species’ (IAS), including exotic weeds, pests and diseases, is widely acknowledged Costing not only billions of dollars every year in agricultural and environmental losses (European Commission, 2008; Pimentel et al., 2005; Sinden et al., 2005), damages to biodiversity are, in some cases, irreversible (Gurevitch and Padilla, 2004; Vitousek et al., 1996; Wilcove et al., 1998) These damages are often, in fact, underestimated due to the lack of a suitable demand function that accurately reflects the value of ecological services (Costanza et al., 1989; Hester et al., 2006) Progress in achieving a significant reduction in the rate of biodiversity loss due to IAS, to 2010, has clearly been disappointing (Butchart et al., 2010), despite the fact that targets have been incorporated into the United Nations Millennium Development Goals designed to arrest IAS-related biodiversity loss Preventing the introduction of IAS at the border, or pre-border, has been considered a first-line of defence against all bio-invasions (Finnoff et al., 2007; NISC, 2008; Olson and Roy, 2005) However, it is impossible to prevent all such pathways even when, as often is UN CO 041 RR 039 040 058 059 060 061 062 * Corresponding author at: Centre of Excellence for Biosecurity Risk Analysis, University of Melbourne, Melbourne, VIC3010, Australia E-mail addresses: tom.kompas@unimelb.edu.au (T Kompas), long.chu@anu.edu.au (L Chu), hoa.nguyen@anu.edu.au (H Nguyen) 079 080 081 082 083 084 085 086 087 088 089 090 091 092 093 094 095 096 097 098 099 100 102 103 the case, the chance of a successful invasion and establishment may be small (Williamson, 1996) For this reason, local or post-border surveillance for early detection and rapid response, a second line of defence, has recently attracted considerable attention as it increases the likelihood that localised invasive populations will be found, contained, and potentially eradicated before they become more widely established (NISC, 2008) As early detection generally requires substantial upfront investment, while delayed detection can cause otherwise considerable if not devastating damages, there exists a clear trade-off between surveillance expenditures for an invasive species and any potential damage and control costs This trade-off has been explored in the literature in a number of different ways Some authors have stressed the importance of detectability and biological relationships as factors influencing the optimal level of surveillance (e.g Bogich et al., 2008, Kompas and Che, 2009, Mehta et al., 2007) Others have highlighted the impact of spatial heterogeneity on budget allocation (Hauser and McCarthy, 2009; Homans and Horie, 2011), and the design of optimal long-term strategies with spatial heterogeneity, rather than one-off surveillance programs (Epanchin-Niell et al., 2012) All of these models vary in complexity, and also in terms of the spatial distribution of species and detection probability functions Immediate need and effective policy responses often shift the emphasis to more basic models that explore this early detection tradeoff in contexts where biosecurity measures and surveillance 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 064 066 078 101 063 065 073 130 http://dx.doi.org/10.1016/j.ecolecon.2016.07.003 0921-8009/© 2016 Published by Elsevier B.V Please cite this article as: T Kompas, et al., A practical optimal surveillance policy for invasive weeds: An application to Hawkweed in Australia , Ecological Economics (2016), http://dx.doi.org/10.1016/j.ecolecon.2016.07.003 131 132 ARTICLE IN PRESS 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 F 139 PR OO 138 x (T ) = x0 erT Containment and Surveillance Zones 193 195 196 197 198 201 202 203 204 205 206 207 208 209 210 211 212 214 216 217 218 219 220 221 222 223 224 T d e(r−q)T − [d × x (t)] e−qt dt = x0 r−q L (T ) = (2) 225 226 227 Another cost incurred in a weed control strategy is, when needed, an eradication expenditure Here, the literature over the relationship between total eradication expenditures and infestation size is mixed Some authors claim that it may be impossible to eradicate a weed if its infestation is large (Adamson et al., 2000; Harris et al., 2001; Hester et al., 2006), while others show estimates that indicate that eradication expenditures per unit of successfully eradicated land size become smaller as land size increases (Cunningham et al., 2003; Rejmánek and Pitcairn, 2002; Woldendorp and Bomford, 2004) These latter estimates are often biased, however, by the fact that they ignore some basic eradication-feasibility issues, particularly where the possibility of an unsuccessful eradication and the geographical characteristics of an eradication site are not adequately considered or controlled Some weed specialists also emphasise that the eradication of a large area can often be successful if adequate resources are devoted to it (Panetta and Timmins, 2004; Rejmánek and Pitcairn, 2002; Simberloff, 2003), though the needed expenditure can be very high indeed as seeds can remain hidden in the soil for a long time (Cacho et al., 2006; McArdle, 1990) With this in mind, we denote the total present value of all costs associated with the eradication of weeds on a land parcel as a finite number c This may not be a ‘one-off’ item, but can be a flow of expenditures spent on physical removal, monitoring and other follow-up activities The eradication expenditure discounted to the time of entry is 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 R (T ) = e−qT cx (T ) = cx0 e(r−q)T (3) 255 256 191 194 200 215 190 192 199 213 (1) The presence of a weed in a parcel causes losses, including quantifiable losses in agriculture and losses measured by non-market values such as environmental and socio-economic amenities and externalities We denote d as this annual multi-criteria impact for losses in monetary terms (Cook and Proctor, 2007) caused by the invasion of the land parcel The present value of the loss from time to T, discounted at annual rate q is thus D 137 than the discount rate (Clark, 1976; Fraser et al., 2006; Harris et al., 2001; Olson and Roy, 2002) This is a sufficient condition because it guarantees that the loss will grow at a faster rate than the eradication expenditure, so early eradication is cost-effective In this section, we will illustrate a broader condition that determines the cost-effectiveness of early eradication even when the spread rate is smaller than the discount rate; a rule that can also help determine the benefit of early detection Suppose that we are considering whether to eradicate an existing invasive weed in a land parcel If not eradicated, for a period of time [0, T], the weed spreads at rate r > Let x0 be the initial entry size Using a simple exponential formula, typically applied to model the dynamics of an invasive species in the early stages of a biological invasion, the invaded area at time T will be TE 136 EC 135 policies, in particular, are often implemented with imperfect information about the target species, or the many underlying and hard-to-quantify parameters needed for complex modelling Indeed, difficulties in specifying key parameters, especially those in terms of measures of uncertainty and the variability of model components, are often the main obstacle to obtaining an objective measure of control programs and needed expenditures (Hulme, 2012) For instance, if a model requires detailed habitat suitability maps or a detection probability function that is specified in a particular context, it is likely not relevant for policy makers, simply because the required information is not yet available or too context-specific to apply to new situations in a timely manner We propose a simple but practical framework which can help government agencies and other decision-makers to determine a surveillance strategy for invasive weeds Our model requires only a few, albeit indispensable, parameters which can be collected by policy makers or adopted from other studies where relevant This is important because quantitative information about a slow-growing weed (also referred to as ‘sleeper weeds’), at its early stage of invasion, is often scant or rough, even though the weed may have drawn the attention of both policy makers and the scientific community We start our analytical framework in Section with an analysis of the economics of weed eradication from a single entry The key result of this section is a rule that characterises the difference between containment and surveillance zones The rule can be applied in any spatially-heterogeneous context, as is often the case with biosecurity measures (Albers et al., 2010; Williamson, 2010), to specify containment zones where eradication is not cost-effective, and hence where there is no need for early detection Outside the containment zone, termed for our purposes as a ‘surveillance zone’, where any delays in eradication are costly, and the location of a weed is not known, one may want to allocate more resources to find or detect the weed early Section of the paper builds a detection-effort relationship (i.e., a detection probability function) which maps surveillance effort and infestation size to detection probability While many authors specify a particular function, or an estimated function from a specific context, our approach draws on a simulation based on how surveillance activities are usually implemented The advantage of the simulation approach is its wider applicability since information on surveillance patterns is often available to policy makers, while the applicability of a specified parametric function is much more limited outside of the specific context where it is estimated In Section 4, we analyse the economics of surveillance in the case of sequential entries where a weed can re-enter multiple times A stochastic programming algorithm is used to determine the optimal surveillance budget which minimises the total cost of the surveillance expenditure itself, the expected eradication expenditure and the pre-eradication loss caused by the weed In Section 5, the model is calibrated to Hawkweed in Australia, as an example of the approach Hawkweed is listed as one of 28 non-native invasive weeds that threaten biodiversity and cause other environmental damages in Australia Many might typically assume that only limited (or no) surveillance is required in the early stages of the establishment and spread of Hawkweed, since it is such a relatively slow-growing weed This turns out not to be the case Section concludes RR 134 UN CO 133 T Kompas, et al / Ecological Economics xxx (2016) xxx–xxx When it comes to controlling a weed at a particular location and point in time there are two basic options, namely eradication and doing nothing The costs and benefits of eradication versus doing nothing depend on various factors One of the conditions that supports eradication is when the spread rate of the weed is larger The total cost of controlling a known invasion is the sum of the cumulative loss in Eq (2) and the eradication expenditure in Eq (3), where both depend on the chosen eradication time T The effect of the eradication time on the total cost will determine the economic viability of an immediate eradication If a delay in eradication increases the total cost, it is cost-effective to eradicate the weed immediately Otherwise, one will choose not to eradicate the weed, at least for a period of time Summing up the two components for the Please cite this article as: T Kompas, et al., A practical optimal surveillance policy for invasive weeds: An application to Hawkweed in Australia , Ecological Economics (2016), http://dx.doi.org/10.1016/j.ecolecon.2016.07.003 257 258 259 260 261 262 263 264 ARTICLE IN PRESS T Kompas, et al / Ecological Economics xxx (2016) xxx–xxx 265 266 total cost and differentiating with respect to T, we can derive a rule that determines when immediate eradication is efficient as 331 332 267 333 268 269 334 d + cr > cq (4) 335 270 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 c (q − r) is the expected entry interval, or the interval between two consecutive entries, and where noise e allows variability in entry times including the possibility of multiple patches of invaders at one time Conditional on entry at time ti , the weed spreads following Eq (1) and causes losses as specified in Eq (2) until detected and eradicated at size xi , as probabilistically dependent on the fineness of the surveillance grid y and infestation size xi The discounted value of the expected losses and eradication expenditures of all entries will be C (s) = = ∞ i=1 ∞ i=1 Eti e−qti Exi L (T (xi )) + R (T (xi )) |(ti , y(s)) ∞ Eti e−qti x0 ∂ p (x, y(s)) dx [L (T (x)) + R (T (x))] ∂x 461 462 480 481 482 483 484 fineness y is determined by the surveillance expenditure s Here, we assume that surveillance is carried out at the best time of the year for detection, following previous literature (Hauser and McCarthy, 2009) Furthermore, detection is assumed to occur instantaneously There are two reasons to argue for this instantaneous detection in the model First, our model is relevant to relatively static invasive species/plants, such as invasive weeds, that are detected largely by visual inspection Second, confirmation with experts, if needed, should (hopefully) be relatively quick Thus, not taking into full account a possible delay due to waiting for expert confirmation would unlikely alter the model results given the slow growth rate of weeds, especially sleeper weeds, and the low discount rate applied to environmental problems As mentioned, we also assume perfect detectability once the weed is encountered Despite some risks of oversimplification, there are two reasons why we feel this assumption is not a major concern First, adjusting the labour cost per unit of surveillance and/or the length of surveillance path an observer can walk/bike per day, can lead to very high detectability and thus an effective outcome regardless Second, if not first detected at a certain period of time, an infestation will continue to grow and be detected in the following period(s) Given the low growth rate of weeds, a low discount rate, and the fact that the size of an infestation is fully considered in costing the damage and eradication expenses, a violation of this assumption would not likely change the model outcome in a substantial way On the other hand, the assumption makes our model simple and practical, which is the objective of this paper Interested readers can refer to existing literature (e.g Baxter et al., 2007, Moore et al., 2010, Regan et al., 2006) for the case of imperfect detectability and possible escape in eradication The total cost consists of three components, namely the expected eradication expenditure and the expected losses in (say) environmental values summed over all entries, as well as the surveillance expenditure itself The trade-off in this situation is that the more is spent on surveillance, the earlier is detection, and the smaller the losses and eradication expenditures The optimal surveillance budget will be the one that minimises the expected sum of these three cost components, or TC (s) = s + qC(s) (10) s≥0 where q is the discount rate; Eti and Exi are expectation operators over ti and xi ; T(x) is the inverse function of Eq (1); p(x, y(s)) is the detection probability function of the invasion size x, and surveillance 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 (9) 459 460 479 D 422 478 TE 421 where a and b are longest distances from the northern to the southern side and from the eastern to the western side of an invasion of any shape, respectively; A and B are the corresponding distances of the grid cell created by a surveillance path Here, the function is calibrated with the grid cell being square (i.e., surveillance carried out in square-cell-grid pattern, and A × B = y) at three levels of surveillance fineness: y = 50 m×50 m; 100 m×100 m; and 200 m×200 m As can be seen, the smaller the surveillance cell or the more surveillance effort that is involved, the higher chance an infestation will be detected This particular feature of our empirical detection probability function is similar to the ones in existing literature on search (e.g Hauser and McCarthy, 2009, Koopman, 1956) However, our function differs in the way that it takes into account the size of the infestation (and hence the time since infestation) explicitly, while others not EC 420 477 Fig Empirical detection probability function 416 419 476 PR OO 411 524 525 526 The minimisation problem in Eq (10) does not have an analytical solution due to its non-linearity Therefore, we have to rely on Please cite this article as: T Kompas, et al., A practical optimal surveillance policy for invasive weeds: An application to Hawkweed in Australia , Ecological Economics (2016), http://dx.doi.org/10.1016/j.ecolecon.2016.07.003 527 528 ARTICLE IN PRESS T Kompas, et al / Ecological Economics xxx (2016) xxx–xxx 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 Application to Hawkweed in Australia 553 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 TE 557 EC 556 RR 555 Invasive Hawkweeds are a group of invasive weeds originating from Europe The biological characteristics of these weeds allow them to survive and grow in various types of habitats and, more importantly, create ecological threats to biodiversity and substantial amenity and productivity losses Hawkweeds have become worldwide weeds, causing serious problems in New Zealand, the United States, Canada, and Japan For example, a Hawkweed infestation covers 500,000 in New Zealand’s South Island (Hunter et al., 1992) In the United States, the Hawkweed infestation is estimated at 480,000 (Duncan et al., 2004), growing by 16% per year (Wilson and Callihan, 1999) with $US58 million in control costs (Duncan and Clark, 2005) In Australia, Hawkweed is in its early stage of development and limited to New South Wales, Tasmania and Victoria (DPI, 2012) However, this weed can potentially cause very large damages For instance, Brinkley and Bomford (2002) estimate that 14.3 million of agricultural land are in a high risk area for a Hawkweed invasion with a production value of $AU1.25 billion Cunningham et al (2003) estimate the area at risk is 1.2 million with production value of $AU1.77 billion and yearly agricultural profits of $AU0.3 billion Climatic changes may contract Hawkweed’s habitat, but much 575 576 577 Q3 578 Q4 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 UN CO 554 of the Australian Alps, which contain large contiguous tracts of reserves and many native species, will continue to remain climatically suitable for Hawkweed through to 2070 (Beaumont et al., 2009) Strategies against weeds in general and Hawkweed in particular are largely driven by biological considerations That is, they often lack sound economic justification For example, while the prevention of further incursions is one of the main objectives, perhaps rightly so, resources are typically allocated to areas of high risk such as those near existing infestations, implicitly assuming a higher arrival rate (DPI, 2012; NRMMC, 2007) While the arrival rate is one important parameter, an optimal outcome is achieved when a combination of both economic and biological parameters is considered To find the optimal surveillance level for Hawkweed in Australia, we apply Eq (10) All parameter values used for this application are specified in Table In particular, we consider the cost of an Hawkweed eradication c in the range of $AU20,000–40,000/ha, with a baseline parameter value of $AU30,000/ha This parameter value comes from the fact that the most cost-effective method of eradicating Hawkweed is with the use of herbicides applied by spot spraying or wick-wiping to reduce the risk of off-target damage (Stone, 2010) As a result, the eradication of Hawkweed is very labour-intensive Rejmánek and Pitcairn (2002) estimate the eradication effort per hectare is approximately 800 work hours in the United States, although the specific number depends on the geographical characteristics of the infestation site This eradication effort is equivalent to an eradication expenditure of $AU20,000/ha if the wage is $AU25/h, not including the chemicals and other necessary equipment needed to the job Overall, this cost is largely consistent with more recent estimates in Australia (Cunningham and Brown, 2006; Cunningham et al., 2003) As for the annual spread rate r, a specific measurement in Australia remains unknown We take the annual spread rate as given in the range of 4%–16% with the baseline value of 8% for three reasons First, in New Zealand, the area covered by mouse-ear Hawkweed increased by 50% during the period from 1982 to 1992 (Johnstone et al., 1999), roughly indicating an annual spread rate of 4.2% This forms the lower bound for our parameter value Second, in the United States, the spread of Hawkweeds is estimated to be up to 16% per year (Wilson and Callihan, 1999), which forms the upper bound of our parameter value Finally, in Australia, Hawkweed is still (largely) a sleeper weed, which has a relatively low initial spread rate, but it can be fast-spreading once its ‘naturalisation’ is completed Some authors have modelled the spread of Hawkweed in Australia by spatial simulation techniques (e.g Beaumont et al., 2009, Williams et al., 2008), although consensus on its annual spread rate is F 531 numerical techniques For each possible value of the annual surveillance budget, we calculate the value of the expected total cost and find the minimum The specific result will depend on (a) the set of four parameters (r, d, c, q), capturing the benefit of early detection; (b) the detection probability function p(x, y(s)); and (c) the distribution of entry times, b and D, which characterises how often an invasion will occur Finally, our model can be applied, or further calibrated, when more information on spatially differentiated parameters becomes available In this case, we can divide a research area into small homogenous sites and apply Eq (10) to each site independently to find an optimal level of surveillance relevant to that site Admittedly, our model does not allow for explicit interactions between sites in the sense that infestations in neighbouring sites can alter the expected entry interval due to the increased threat or infestation spreading from site to site However, in practice, this situation can be addressed by changing the parameter set in different sites In any case, the total annual surveillance budget for all sites is the sum of individual budgets Since our problem here is an unconstrained problem which asks how much one should spend on surveillance given the surveillance zone(s) identified using the rule of thumb, the sum of individual budgets is also globally minimised PR OO 530 D 529 a Eradication expenditure (c) Annual spread rateb (r) Annual lossc (d) Annual interest rated (q) Entry intervale (b) Scale factor of the variance in the noise of entry interval e ∼ N(0, lb)e Daily wage of detectorsf (w) Length of daily surveillance pathe (l) Entry sizeg (x0 ) 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 Table Parameter set for Hawkweed invasion Parameters 595 644 Baseline value Value range Unit 30 70 10 0.1 300 20 0.01 20–40 4–16 50–90 2–4 5–15 0.1–0.1 200–400 10–30 0.01 $AU1000/ha %/year $AU/ha/year %/year years Nil $AU/day km/day All values are in Australian Dollars 2011 a Based on Rejmánek and Pitcairn (2002), Cunningham et al (2003), Cunningham and Brown (2006), and Stone (2010) b Based on Wilson and Callihan (1999), Johnstone et al (1999), Morgan (2000), and Cunningham and Brown (2006) c Based on Stoneham et al (2003) and Akter et al (2015) d Based on Reserve Bank of Australia (2015) and Pearce et al (2006) e Authors’ assumption f Based on PayScale (2015) with 25% seasonal work loading g Based on Cunningham and Brown (2006) Please cite this article as: T Kompas, et al., A practical optimal surveillance policy for invasive weeds: An application to Hawkweed in Australia , Ecological Economics (2016), http://dx.doi.org/10.1016/j.ecolecon.2016.07.003 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 ARTICLE IN PRESS T Kompas, et al / Ecological Economics xxx (2016) xxx–xxx 727 662 728 663 729 664 730 665 731 666 732 667 733 668 734 669 735 670 736 671 737 672 738 673 739 F 661 674 676 677 678 679 681 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 743 744 745 746 747 where the detection probability function p(x, y) can be calibrated following the procedure in Eq (6) Since q is the annual discount rate, typically assumed to be low for environmental problems, and (l) is a scale factor in the variance of the noise (e) in the expected entry interval (b), the condition (1 − ql /2) > is normally satisfied Derivation of Eq (11) is provided in the Appendix Finally, we assume an annual discount rate of 3% The average interest rate for treasury notes in Australia, with terms of month and months, is 3.90% and 3.86%, respectively, over the last decade (Reserve Bank of Australia, 2015) However, since it is more typical to assume a low discount rate when applied to environment problems, typically 3% or lower (Pearce et al., 2006), we choose 3% as our baseline value and vary it in the range [2%, 4%] In our application, all values are in Australian Dollars in 2011 unless otherwise specified Using the baseline parameters specified in Table 1, Fig illustrates the trade-off between ‘strict’ and ‘loose’ surveillance strategies (i.e., more or less expenditures) The expected annualised total cost of controlling Hawkweed and its three components are plotted against the annual surveillance budget For each 10 km×10 km at risk, the surveillance budget that minimises total cost is $AU3100 associated with a total cost of $AU4160 a year This optimal surveillance budget is equivalent to approximately 10 days of surveillance effort or a 200 km surveillance path If we take into account the total area at risk is 1.2 million (Cunningham et al., 2003), the total surveillance budget would be approximately $AU372,000 a year Note that the u-shaped measure for total cost exhibits the relevant tradeoff: large surveillance expenditures give early detection, but the cost of the program itself is also very expensive, while at low levels of surveillance expenditures, detection is delayed and all other costs are larger We also compare our model result with that of an existing surveillance model against Hawkweed in Australia (Hauser and McCarthy, 2009) Before doing so, it is important to specify key similarities and differences between the two models For the former, both models ED 687 742 CT 686 RE 685 CO R 684 yet to be reached For example, Cunningham and Brown (2006) find that the wind-dispersed seed has a normal annual dispersal distance of less than km, while Morgan (2000) recognises that some populations have established more than km from the presumed source In summary, our proposed range of values for this parameter broadly take into account the evidence overseas as well as rough estimates in Australia With regard to the annual loss d caused by Hawkweed, it will depend very much on the type of land it invades Cropland is usually more valuable than idle or grazing area However, if Hawkweed invades high-value agricultural land where human activities are frequent, it may be detected and eradicated early without active surveillance Thus, we focus on idle or grazing land which has an estimated environmental value in Australia ranging from $AU50– 90/year/ha, as provided by Stoneham et al (2003) and Akter et al (2015) For the surveillance pattern, we assume that surveillance for Hawkweed is implemented by weed detectors who walk or bike over each 10,000 (10 km×10 km) area at risk in a square-cellgrid pattern In the baseline scenario, the length that each detector can walk/bike a day (l) is 20 km and their daily wage (w) is $AU300 The salary is estimated based on the median salary level for an environmental scientist, who does not have more than 10 years of experience (PayScale, 2015), plus a 25% seasonal pay-loading We assume that an entry size of 0.01 ha, occurring once every 10 years for each 10,000 We believe this is a modest estimate, given the potentially wide distribution of this weed in Victoria and Tasmania, where Hawkweed has even appeared and been sold in nurseries in these states, as well as appearing in New South Wales and Queensland, a good distance away (Cunningham and Brown, 2006) The noise in entry time is assumed to follow a normal distribution with the variance proportional to the length of the expected entry interval e ∼ N(0, lb), where l is a positive scale factor In particular, the larger l is, the more variable the arrival time will be In our application, we assume a l of 0.1 We vary these parameters in our sensitivity analysis Given the normality assumption in the noise of entry time, Eq (9) can be simplified to UN 683 741 Fig The economics of surveillance for each 10,000ha at risk with baseline parameters 680 682 740 PR OO 675 725 726 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 784 785 786 Annual spread rate 787 722 724 749 783 Table Sensitivity of the spread rate and discount rate 721 723 748 C(s) = ql ( e−qb 1− ) ql 1− − e−qb( ql if − >0 ∞ ) [L (T (x)) + R (T (x))] x0 ∂ p x, y ∂x sl w dx (11) Annual discount rate 2% 3% 4% 4% 6% 8% 12% 16% 2450 1300 550 3400 2400 1550 3950 3100 2350 4550 3900 3300 4850 4350 3850 Note: Optimal surveillance budget ($AU) for each 100 km at risk Please cite this article as: T Kompas, et al., A practical optimal surveillance policy for invasive weeds: An application to Hawkweed in Australia , Ecological Economics (2016), http://dx.doi.org/10.1016/j.ecolecon.2016.07.003 788 789 790 791 792 ARTICLE IN PRESS T Kompas, et al / Ecological Economics xxx (2016) xxx–xxx 793 794 Table Sensitivity to the loss rate and eradication expenditure 796 797 798 800 Eradication cost ($/ha) 801 802 803 860 Annual loss rate ($/ha/year) 795 799 859 20,000 25,000 30,000 35,000 40,000 861 50 60 70 80 90 2800 2950 3100 3200 3350 2800 2950 3100 3250 3350 2800 2950 3100 3250 3350 2800 3000 3100 3250 3350 2800 3000 3100 3250 3350 862 863 864 865 866 867 868 Note: Optimal surveillance budget ($AU) for each 100 km at risk 869 870 805 871 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 PR OO 811 D 810 TE 809 EC 808 surveillance budget is very sensitive to the spread rate of the weed (r) and the discount rate (q) as reported in Table 2, since these are the two key parameters that determine the benefit of early detection Larger spread rates or smaller discount rates increase the incentive for surveillance to find and eradicate the weed early The sensitivity analysis also shows that the surveillance budget is approximately zero when the discount rate and the spread rate are equal Since Eq (4) holds, early detection is still desirable in this case, but simply too expensive given other parameters in the model Table shows the sensitivity of the loss rate (d) and eradication expenditure (c) In general, higher eradication expenditures and/or loss rates are associated with more ambitious surveillance programs which help reduce the cost of a Hawkweed incursion However, the surveillance budget is not responsive to losses, at least in the range of parameters under consideration here This is because the loss component in the total cost is relatively small, compared to the value of surveillance and eradication expenditures This point further relaxes the challenge in specifying parameters when determining the optimal budget for a parcel of land, in practice, since the loss rate, which is often hard to estimate, does not need to be as accurate as the spread rate of the weed Table reports the sensitivity of wages for weed surveillance (w) and surveillance length (l) An increase in the salary paid to weed detectors will increase the surveillance budget, but not by the same proportion, so the length of the surveillance path is actually reduced On the other hand, the more distance a weed-detector can cover in a day, the smaller the budget allocation, and the larger the length of the surveillance path It is worth noting that these two parameters are relatively easy to estimate Finally, Table shows the sensitivity of the arrival rate (b) and entry size (x0 ) As expected, the more frequent and/or the larger the entry, the larger the surveillance measure should be require the area of interest to be divided into homogenous cells and allow for variation in parameters across sites, i.e., spatial heterogeneity For the latter, Hauser and McCarthy (2009) determine a one-off search budget while our model provides yearly surveillance expenditure Furthermore, the future cost of a failed detection in Hauser and McCarthy (2009) is kept constant, while in our model it varies with a number of factors such as the spread rate of the weed, the damage rate caused by the weed, the eradication cost and the possibility of failed detection in the future Finally, in our model, the eradication cost and detection probability depends on the size of an infestation, and (multiple) invasions can occur at the current and/or at any future time In terms of calibration, our model predicts that the annual surveillance budget for each 100 km2 is roughly $AU3000 using baseline parameters Therefore, at the discount rate of 3%, the present value of the total budget stream is about $AU80,000 for 50 years and $AU98,000 for 100 years The one-off budget identified in Hauser and McCarthy (2009) is 1125 search hours or about $AU48,000 using a wage rate of $300 per 7-hour search-day over approximately 100 km2 (the search area of 100 km2 is estimated based on the Fig 2(f) in Hauser and McCarthy (2009)) Therefore, the one-off surveillance budget in Hauser and McCarthy (2009) is between the annual and the total (lifetime) budget calibrated in our model It is important to note that the calculation of the total cost in Fig is based on the fact that eradication is implemented optimally in accordance with the rule in Eq (4) This helps avoid the misleading perception that it may be optimal to ignore the weed (i.e., no surveillance, no eradication) until it starts invading higher-value land because of the initially small loss component It is the optimal (i.e., immediate) eradication that helps maintain the expected loss at a relatively small level as presented in Fig If eradication was not implemented optimally (e.g., it was delayed), the total cost would be significantly larger because of the exponentially growing losses To be specific, suppose the weed was to allowed to invade 100 (instead of 0.01 in our model) before being contained, then the loss per year would be around $AU7000 plus the cost of eradicating the area outside this 100 containment zone, which is well above the minimum cost as illustrated in Fig Finally, we carry out a sensitivity analysis around the baseline parameter set and report the results in Tables 2–5 The optimal RR 807 UN CO 806 F 804 856 857 858 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 We propose a modelling framework to determine an optimal and practical surveillance budget for invasive weeds In essence, the optimal surveillance expenditure is the one that minimises the expected value of three types of costs incurred in controlling a weed: eradication costs and all environmental or other direct damages, and 907 908 909 910 911 912 913 914 915 916 Wage rate of weed detector ($/day) 852 855 875 906 Table Sensitivity of the wage rate and length of the surveillance path 851 854 874 905 850 853 873 904 Closing Remarks 848 849 872 Length of surveillance path covered in one-day surveillance (km) 10 15 20 25 30 917 200 250 300 350 400 3850 2850 2300 1950 1700 4550 3350 2700 2300 2000 5200 3850 3100 2650 2300 5800 4300 3500 2950 2600 6400 4750 3850 3250 2850 Note: Optimal surveillance budget ($AU) for each 100 km at risk Please cite this article as: T Kompas, et al., A practical optimal surveillance policy for invasive weeds: An application to Hawkweed in Australia , Ecological Economics (2016), http://dx.doi.org/10.1016/j.ecolecon.2016.07.003 918 919 920 921 922 923 924 ARTICLE IN PRESS T Kompas, et al / Ecological Economics xxx (2016) xxx–xxx Table Sensitivity of the arrival rate and entry size 925 926 991 992 Expected entry interval (year) 927 928 929 0.005 0.008 0.010 0.012 0.015 930 Entry size (ha) 931 932 933 934 993 10 13 15 3550 3700 3800 3850 3950 3100 3250 3300 3400 3450 2900 3050 3100 3150 3250 2750 2900 2950 3000 3050 2550 2700 2750 2800 2850 995 996 997 998 999 1000 Note: Optimal surveillance budget ($AU) for each 100 km at risk 935 994 1001 1002 937 1003 F 936 938 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 968 969 970 Appendix A Appendix 972 973 974 976 977 C (s ) = i=1 Eti e−qti A 979 980 =A 981 982 983 984 =A =A 985 986 987 =A ∞ i=1 ∞ ∞ i=1 e−qib(1−ql /2) = A =A =A 1− ( 990 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1040 1041 1042 [L (T (x)) + R (T (x))] i z=1 ) ql e−qb 1− 1043 ∂ p (x, y(s)) dx ∂x where 1045 i ez = i × b + i z=1 ez 1044 z=1 1046 ez 1047 where e ∼ N(0, bl) i z=1 1048 qez ∼ N(0, q bli) 1049 1050 1051 ) if (1 − ql /2) > 988 989 1011 1039 e−qib Eti e−q i=1 ∞ e−qib eq bli/2 i=1 ql 1010 1038 ( 1009 1037 ∞ e−qb 1− 1008 1036 where ti = t0 + i × b + Et e−qib e−q i=1 i ∞ i e−qib Eti e z=1 −qez i=1 1007 1034 x0 i z=1 ez 1006 1035 where A = Eti e−qti 1005 1033 ∞ ∞ 1004 1032 The discounted value of the expected losses and eradication expenditures of all entries will be 975 978 UN CO 967 971 PR OO 943 D 942 treasury notes Parameters on the surveillance cost including the wage rate w and the length of surveillance path covered per surveillance day l are also readily available Consequently, the challenge for policy makers in our application amounts to getting good estimates for biological parameters including the arrival rate, entry size and especially the spread rate What values to use will be based on whatever literature is available, any up-to-date information and how risk-averse a policy maker desires to be A number of cautions apply when our model is used to guide practical surveillance policies First, our model is more suitable for invasive plants than (say) insects (e.g Epanchin-Niell et al., 2012) This is because the simulation approach we use to calibrate the detection probability function may not be able to control for the ability to ‘move and adapt’ as insects naturally Second, the model may not respond adequately to epidemic parasites because the lowprobability/high-damage events, typical in epidemics (Perrings et al., 2010), will normally require a more stringent surveillance program Third, our model does not allow for uncertainty in detection and possible escape in eradication (e.g Baxter et al., 2007, Moore et al., 2010, Regan et al., 2006) Finally, our model does not take into account another benefit of surveillance, i.e., the build-up of knowledge about the weeds Surveillance, apart from detecting weeds, can provide information on where weeds are likely to invade, and a better estimate for the average spread rate of those weeds This new information needs to be incorporated into the measure of optimal surveillance when it becomes available TE 941 the cost of the surveillance program itself The larger the surveillance expenditure the earlier the weed can be detected and eradication can take place, so that total losses and eradication expenditures can be kept at a low level On the other hand, a small expenditure on a surveillance program can generate late detection and thus larger eradication expenditures and total losses Our model is calibrated to Hawkweed in Australia The result shows that for a basic range of parameter values, the annual surveillance budget for Hawkweed should be roughly $AU3000 for every 10,000 at risk Specific surveillance expenditures depend on a number of parameters, including the spread rate, the discount rate, and the damage caused by the weed, as well as eradication expenditures Our model is intentionally tailored to be relevant for policy purposes, with a minimum set of critical parameter values Nonetheless, we understand that having good estimates of parameters is still a challenge for policy makers To handle this challenge, it is important, as usual, to sensitivity analysis to determine how sensitive the parameters are to model outcomes, and how large is the range of the model outcomes given changes in the most sensitive parameter values In our application, it turns 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Note: Optimal surveillance budget ($AU) for each 100 km at risk Please cite this article as: T Kompas, et al., A practical optimal surveillance policy for invasive weeds: An application to Hawkweed. .. schedule to determine an optimal surveillance budget A calibration to Hawkweed in Australia provides an example of the framework and shows that the optimal annual surveillance budget for this... Eradication Invasive weeds Hawkweed Stochastic programming EC 029 We propose a practical analytical framework which can help government agencies determine an optimal surveillance strategy for invasive weeds,