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

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 effo

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Ecological Economics xxx (2016) xxx–xxx

ECOLEC-05346; No of Pages 10

Contents lists available atScienceDirect

Ecological Economics

j o u r n a l h o m e p a g e : w w w e l s e v i e r c o m / l o c a t e / e c o l e c o n

Analysis

A practical optimal surveillance policy for invasive weeds: An

application to Hawkweed in Australia

Q1

aCentre of Excellence for Biosecurity Risk Analysis, University of Melbourne, Melbourne, VIC 3010, Australia

bCrawford School of Public Policy, Australian National University, Crawford Building (132), Lennox Crossing, ACT 2601, Australia

Article history:

Received 19 July 2015

Received in revised form 2 February 2016

Accepted 13 July 2016

Available online xxxx

Keywords:

Surveillance

Containment

Eradication

Invasive weeds

Hawkweed

Stochastic programming

A B S T R A C T

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.

1 Introduction

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

environmen-tal 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

biodiver-sity 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

* 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).

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, con-tained, and potentially eradicated before they become more widely established (NISC, 2008) As early detection generally requires sub-stantial upfront investment, while delayed detection can cause oth-erwise 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 surveil-lance 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

http://dx.doi.org/10.1016/j.ecolecon.2016.07.003

0921-8009/© 2016 Published by Elsevier B.V.

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policies, in particular, are often implemented with imperfect

infor-mation 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

con-trol 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

infor-mation 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

pol-icy 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

inva-sion, 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 inSection 2with 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

contain-ment 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 3of 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

con-text, 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

expendi-ture and the pre-eradication loss caused by the weed InSection 5,

the model is calibrated to Hawkweed in Australia, as an example

of the approach Hawkweed is listed as one of 28 non-native

inva-sive 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

estab-lishment and spread of Hawkweed, since it is such a relatively

slow-growing weed This turns out not to be the case Section 6

concludes

2 Containment and Surveillance Zones

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

sup-ports eradication is when the spread rate of the weed is larger

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 erad-ication expenditure, so early eraderad-ication 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 exist-ing invasive weed in a land parcel If not eradicated, for a period of

time [0, T], the weed spreads at rate r>0 Let x0be 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

The presence of a weed in a parcel causes losses, including quan-tifiable 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 0

to T, discounted at annual rate q is thus

L(T)=

 T

0

[d × x(t)] e −qt dt = x0 d

r − q



Another cost incurred in a weed control strategy is, when needed,

an eradication expenditure Here, the literature over the relation-ship 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 indi-cate that eradication expenditures per unit of successfully eradiindi-cated 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, particu-larly 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 expendi-ture 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

expen-ditures spent on physical removal, monitoring and other follow-up activities The eradication expenditure discounted to the time of entry is

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 eco-nomic 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

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T Kompas, et al / Ecological Economics xxx (2016) xxx–xxx 3

total cost and differentiating with respect to T, we can derive a rule

that determines when immediate eradication is efficient as

Eq (4) provides an insight into the dynamic nature of the

trade-off between an immediate eradication and delay The left-hand side

is the benefit of an immediate action (against delay), or the avoided

losses (d) plus the avoided cost of eradicating a newly invaded area

(c × r) that would be incurred with delay On the other hand, the

right-hand side represents the cost of an immediate action, or the

interest payments that could be earned if the eradication

expendi-ture was not spent immediately (c × q) The equation not only covers

the case of a fast-spreading weed, but also highlights the fact that

when the spread rate is smaller (or even when it is zero), as is often

the case with a sleeper weed, immediate eradication is still efficient

if losses are large and/or the eradication expenditure is small enough

This point suggests that a weed, if present in an area with frequent

human activities (e.g., crop land or land with a large amenity value),

should usually be removed quickly, since the potential loss is large

while the eradication expenditure is relatively small (especially in

easy-to-access areas) It thus follows that large-scale weed and more

contentious surveillance programs normally focus on remote areas

where the loss caused by the weed invasion is mainly due to

substan-tial non-market environmental and ecological values Finally, Eq (4)

can be expressed with the cost components as a ratio of each other

as follows:

c(q − r)

The advantage of this expression is that the rule becomes

unit-free

An appealing feature of Eqs (4) and (5) is that they can be applied

in a region with spatial heterogeneity In practice, land parcels

are heterogeneous in terms of their values (both market and

non-market), and their accessibility for eradication, as well as suitability

for a weed’s spread, all of which have to be considered in any decision

regarding a bio-invasion (Wilen, 2007) For example, the invasion

of one remote parcel may generate less impact than that of slight

damages to grassland or small losses in economic grazing values

However, if the weed’s dense mat threatens (say) the health of a

river, or generates significant agricultural or amenity damages, the

losses can be large, in terms of both market values (such as the

effects on fish habitat and migration) and non-market values (such as

losses in environmental services) Similarly, the eradication

expen-diture (both the cost of physically removing the weed and the cost of

follow-up activities), depends significantly on the accessibility of the

site, and varies from parcel to parcel In addition, the spread rate of a

weed in each parcel depends on various characteristics such as slope,

wind direction, landscape, and so on (Kot et al., 1996; Meentemeyer

et al., 2012; Shigesada and Kawasaki, 1997) If we can estimate a set

of parameters (d, r and c) for each specific parcel of land, in a

spa-tial map, we will be able to identify where any delay in eradication is

cost-effective, and where it is not

3 Surveillance Effort and Detectability

The effectiveness of surveillance critically depends on how much

surveillance can improve detectability This effectiveness is

mea-sured via a detection probability function, mapping surveillance

effort to detection probability, which is normally not easy to

esti-mate Many authors specify their detection probability functions as

Fig 1 Surveillance grid and paths.

an exponential decay function, where parameters are either esti-mated using particular experiments or simply specified by experts (Bogich et al., 2008; Cacho et al., 2007, 2004; Hauser and McCarthy, 2009; Moore et al., 2011; Sharov and Liebhold, 1998) Others have estimated the relationship using a generalised linear mixed model (Chen et al., 2009), or through the use of a CPUE (i.e., catch per unit effort) concept in fisheries, with Cobb-Douglas harvest func-tions (Kotani et al., 2009) While the available empirical parameters contribute insights into the detection probability function, questions remain over their use outside of the context where they are esti-mated The reason is simple Apart from the inherent difficulties in estimating the parameter of a probability distribution with limited data, many other non-quantified factors such as morphology, the skills of observers (Garrard et al., 2008; Moore et al., 2011), geo-graphical characteristics, as well as the surveillance pattern itself, must be taken into account

We use an alternative and practical approach to estimate the detection probability function, specifically applied to invasive weeds The idea is to simulate the function under the assumption that observers follow a specific search pattern for weeds and that they can detect with certainty when they see a weed For example, if surveil-lance takes place in parallel paths which create a grid of cells, as illustrated inFig 1, the larger is the surveillance effort, the smaller the cell and the more likely an infestation at a given size will be detected by an observer walking along a path Furthermore, the detection probability also depends on the shape of an infestation For example, for a given area, an oblong infestation would more likely be detected than a circular one In summary, if we know the surveillance pattern, we could build an empirical function that largely maps the size of an infestation and the amount of surveillance effort in place

to the probability that the weed is detected

Our empirical detection function is thus calibrated as follows:

∀x, y : p(x, y)=

N j=1 p j (x, y)

where x is infestation size; y is the ‘fineness’ of the surveillance grid

or the size of a surveillance cell; N is the number of simulated shapes; and p j (x, y) is the detection probability for an infestation of a given size (x) with shape j ∈ {1 .N} and for a given surveillance intensity

(y).

The empirical detection probability function is illustrated inFig 2

Here, we randomly select N = 1, 000, 000 infestation areas, different

in shape and size, and calculate p j (x, y) analytically as follows:

p j (x, y) = a

b

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Fig 2 Empirical detection probability function.

where a and b are longest distances from the northern to the

south-ern side and from the eastsouth-ern to the westsouth-ern 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

cal-ibrated with the grid cell being square (i.e., surveillance carried out

in square-cell-grid pattern, and A × B = y) at three levels of

surveil-lance 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

surveil-lance effort that is involved, the higher chance an infestation will be

detected This particular feature of our empirical detection

probabil-ity 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 do not

4 Surveillance Budgeting

In this section, we determine how much should be spent on

surveillance in the case of sequential entries We denote the entry

times (with unknown locations) of an invasive species as a

random-walk process in the form

t i = t i−1 +b+e i for i = 1, ., ∞; t0≡0 and e i∼iid(0, s2)

(8)

where t i is the time of the ith entry, b>0 is the expected entry

inter-val, or the interval between two consecutive entries, and where noise

e allows variability in entry times including the possibility of

mul-tiple patches of invaders at one time Conditional on entry at time

t i, the weed spreads following Eq (1) and causes losses as specified

in Eq (2) until detected and eradicated at size x i, as probabilistically

dependent on the fineness of the surveillance grid y and infestation

size x i The discounted value of the expected losses and eradication

expenditures of all entries will be

C(s)=∞

i=1 E t i e −qt i E x i L(T(x i))+ R(T(x i))|(ti , y(s))

i=1 E t i

e −qt i

 ∞

x0

[L(T(x))+ R(T(x))]∂p(x, y(s))

where q is the discount rate; E t i and E x i are expectation operators

over t i and x i ; 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

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 con-cern 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 follow-ing 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 sub-stantial 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) environ-mental 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 bud-get will be the one that minimises the expected sum of these three cost components, or

min

The minimisation problem in Eq (10) does not have an analyt-ical solution due to its non-linearity Therefore, we have to rely on

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T Kompas, et al / Ecological Economics xxx (2016) xxx–xxx 5 numerical techniques For each possible value of the annual

surveil-lance 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

distri-bution 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

Admit-tedly, 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

infesta-tion spreading from site to site However, in practice, this situainfesta-tion

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

5 Application to Hawkweed in Australia

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

world-wide weeds, causing serious problems in New Zealand, the United

States, Canada, and Japan For example, a Hawkweed infestation

cov-ers 500,000 ha in New Zealand’s South Island (Hunter et al., 1992) In

the United States, the Hawkweed infestation is estimated at 480,000

ha (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 ha

of agricultural land are in a high risk area for a Hawkweed

inva-sion with a production value of $AU1.25 billion.Cunningham et al

(2003)estimate the area at risk is 1.2 million ha with production

value of $AU1.77 billion and yearly agricultural profits of $AU0.3

bil-lion Climatic changes may contract Hawkweed’s habitat, but much

of the Australian Alps, which contain large contiguous tracts of reserves and many native species, will continue to remain climat-ically 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 1 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 erad-icating 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 eradica-tion 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 equiv-alent to an eradication expenditure of $AU20,000/ha if the wage is

$AU25/h, not including the chemicals and other necessary equip-ment needed to do 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

Table 1

Parameter set for Hawkweed invasion.

Q3

Scale factor of the variance in the noise of entry interval e ∼ N(0, lb)e 0.1 0.1–0.1 Nil

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)

PR

OOF

661

662

663

664

665

666

667

668

669

670

671

672

673

674

675

676

677

678

679

680

681

682

683

684

685

686

687

688

689

690

691

692

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701

702

703

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715

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719

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721

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723

724

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726

727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792

Fig 3 The economics of surveillance for each 10,000ha at risk with baseline parameters.

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 1 km, whileMorgan (2000)recognises that some

popu-lations have established more than 1 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

usu-ally 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 byStoneham 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 ha (10 km×10 km) area at risk in a

square-cell-grid 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 ha We believe this is a modest estimate, given

the potentially wide distribution of this weed in Victoria and

Tasma-nia, where Hawkweed has even appeared and been sold in nurseries

in these states, as well as appearing in New South Wales and

Queens-land, 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

−qb(1−ql

2)

1 − e −qb(1−ql

2)

 ∞

x0

[L(T(x))+ R(T(x))]

∂px, ysl

w

if 1 −ql

2



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)>0 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 1 month and 3 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 prob-lems, 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 inTable 1, Fig 3 illus-trates 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 bud-get 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 ha (Cunningham et al., 2003), the total surveil-lance 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 surveil-lance 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

Table 2

Sensitivity of the spread rate and discount rate.

Annual spread rate

Note: Optimal surveillance budget ($AU) for each 100 km 2 at risk.

PR

OOF

793

794

795

796

797

798

799

800

801

802

803

804

805

806

807

808

809

810

811

812

813

814

815

816

817

818

819

820

821

822

823

824

825

826

827

828

829

830

831

832

833

834

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839

840

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844

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848

849

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859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924

T Kompas, et al / Ecological Economics xxx (2016) xxx–xxx 7

Table 3

Sensitivity to the loss rate and eradication expenditure.

Annual loss rate ($/ha/year)

Note: Optimal surveillance budget ($AU) for each 100 km 2 at risk.

require the area of interest to be divided into homogenous cells and

allow for variation in parameters across sites, i.e., spatial

heterogene-ity For the latter,Hauser and McCarthy (2009)determine a one-off

search budget while our model provides yearly surveillance

expendi-ture Furthermore, the future cost of a failed detection inHauser 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

surveil-lance 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 inHauser 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 km2is estimated based on the Fig 2(f)

inHauser and McCarthy (2009)) Therefore, the one-off surveillance

budget inHauser 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 3is based on the fact that eradication is implemented optimally

in accordance with the rule in Eq (4) This helps avoid the

mislead-ing 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 inFig 3 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 ha

(instead of 0.01 ha 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 ha containment zone, which is well above

the minimum cost as illustrated inFig 3

Finally, we carry out a sensitivity analysis around the baseline

parameter set and report the results in Tables 2– The optimal

surveillance budget is very sensitive to the spread rate of the weed

(r) and the discount rate (q) as reported inTable 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 sensitiv-ity 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 3shows 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 com-ponent 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 opti-mal 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 4reports 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 5shows the sensitivity

of the arrival rate (b) and entry size (x0) As expected, the more fre-quent and/or the larger the entry, the larger the surveillance measure should be

6 Closing Remarks

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

Table 4

Sensitivity of the wage rate and length of the surveillance path.

Wage rate of weed detector ($/day)

Note: Optimal surveillance budget ($AU) for each 100 km 2 at risk.

PR

OOF

925

926

927

928

929

930

931

932

933

934

935

936

937

938

939

940

941

942

943

944

945

946

947

948

949

950

951

952

953

954

955

956

957

958

959

960

961

962

963

964

965

966

967

968

969

970

971

972

973

974

975

976

977

978

979

980

981

982

983

984

985

986

987

988

989

990

991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056

Table 5

Sensitivity of the arrival rate and entry size.

Expected entry interval (year)

Note: Optimal surveillance budget ($AU) for each 100 km 2 at risk.

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

surveil-lance budget for Hawkweed should be roughly $AU3000 for every

10,000 ha 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

pur-poses, 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

impor-tant, as usual, to do 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

param-eter values In our application, it turns out that all but the biological

parameters are either relatively insensitive or relatively easy to know

or estimate For example, the loss rate d is not sensitive at all while

the annual discount rate q can be obtained from the vast

litera-ture on what rate would best suit environmental problems, relative

to existing historical data on interest rates for government bonds and

treasury notes Parameters on the surveillance cost including the

wage rate w and the length of surveillance path covered per surveil-lance day l are also readily available Consequently, the challenge

for policy makers in our application amounts to getting good esti-mates 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 abil-ity to ‘move and adapt’ as insects naturally do Second, the model may not respond adequately to epidemic parasites because the low-probability/high-damage events, typical in epidemics (Perrings et al., 2010), will normally require a more stringent surveillance pro-gram 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 knowl-edge about the weeds Surveillance, apart from detecting weeds, can provide information on where weeds are likely to invade, and a bet-ter 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

Appendix A Appendix

The discounted value of the expected losses and eradication expenditures of all entries will be

C(s)=∞

i=1 E t i e −qt i A

where A =

∞

x0

[L(T(x))+ R(T(x))]∂p(x, y(s))

i=1 E t i e −qt i

where t i = t0+ i × b +i

z=1 e z = i × b +i

z=1 e z

i=1 E t ie −qib.e −qi

i=1 e −qib E t ie −qi

z=1 e z where e ∼ N(0, bl)

i=1 e −qib E t i



ei z=1 −qe z= A∞

i=1 e −qib.e q2bli/ where i

z=1 qe z∼N(0, q2bli)

i=1 e −qib(1−ql/ )= A e

−qb(1−ql

2)

1 − e −qb(1−ql

2) if (1 − ql/2) >0

Since q is the annual discount rate, typically 3% 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)>0 is normally satisfied

PR

OOF

1057

1058

1059

1060

1061

1062

1063

1064

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1066

1067

1068

1069

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1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188

T Kompas, et al / Ecological Economics xxx (2016) xxx–xxx 9

References

Adamson, D., Bilston, L., Lynch, K., 2000 The Potential Economic Benefits of the Siam

Weed (Chromolaena odorata) Eradication Campaign RDE Connections, The

Uni-versity of Queensland Available at [Access: 2 July 2015] https://adamsondavid.

files.wordpress.com/2011/05/siam-weed-evaluation.pdf

Akter, S., Kompas, T., Ward, M., 2015 Application of portfolio theory to asset-based

biosecurity decision analysis Ecol Econ 117, 73–85.

Albers, H.J., Fischer, C., Sanchirico, J.N., 2010 Invasive species management in a

spa-tially heterogeneous world: effects of uniform policies Resour Energy Econ 32

(4), 483–499.

Baxter, P., Wilcox, C., McCarthy, M., Possingham, P., 2007 Optimal management of an

annual weed: a stochastic dynamic programming approach MODSIM 2007

Inter-national Congress on Modeling and Simulation Modeling and Simulation Society

of Australia and New Zealand pp 2223–2229.

Beaumont, L.J., Gallagher, R.V., Downey, P.O., Thuiller, W., Leishman, M.R., Hughes, L.,

2009 Modelling the impact of Hieracium spp on protected areas in Australia

under future climates Ecography 32 (5), 757–764.

Bogich, T.L., Liebhold, A.M., Shea, K., 2008 To sample or eradicate? A cost

minimiza-tion model for monitoring and managing an invasive species J Appl Ecol 45 (4),

1134–1142.

Brinkley, T.R., Bomford, M., 2002 Agricultural Sleeper Weeds in Australia: What is the

Potential Threat? Bureau of Rural Sciences, Canberra, Australia

Butchart, S.H., Walpole, M., Collen, B., van Strien, A., Scharlemann, J.P., Almond, R.E.,

Baillie, J.E., Bomhard, B., Brown, C., Bruno, J., et al 2010 Global biodiversity:

indicators of recent declines Science 328 (5982), 1164–1168.

Cacho, O., Hester, S., Spring, D., 2007 Applying search theory to determine the

feasibil-ity of eradicating an invasive population in natural environments Aust J Agric.

Resour Econ 51 (4), 425–443.

Cacho, O., Spring, D., Pheloung, P., Hester, S., 2004 Weed search and control: theory

and application Working Paper No 2004-11 in Agricultural and Resource

Eco-nomics, University of New England Available at [Accessed: 3 July 2015] http://

ageconsearch.umn.edu/bitstream/12919/1/wp040011.pdf

Cacho, O., Spring, D., Pheloung, P., Hester, S., 2006 Evaluating the feasibility of

eradicating an invasion Biol Invasions 8 (4), 903–917.

Chen, G., Kery, M., Zhang, J., Ma, K., 2009 Factors affecting detection probability in

plant distribution studies J Ecol 97 (6), 1383–1389.

Clark, C.W., 1976 Mathematical Bioeconomics, the Optimal Control of Renewable

Resources John Wiley and sons, New York.

Cook, D., Proctor, W., 2007 Assessing the threat of exotic plant pests Ecol Econ 63

(2), 594–604.

Costanza, R., Farber, S.C., Maxwell, J., 1989 Valuation and management of wetland

ecosystems Ecol Econ 1 (4), 335–361.

Cunningham, D., Brown, L., 2006 Some Priority Agricultural Sleeper Weeds for

Eradi-cation Bureau of Rural Sciences, Canberra, Australia.

Cunningham, D., Woldendorp, G., Burgess, M.B., Barry, S.C., 2003 Prioritising Sleeper

Weeds for Eradication Bureau of Rural Sciences, Canberra.

DPI, 2012 New South Wales orange Hawkweed strategy, 2011–2017 New South

Wales Government, Department of Primary Industries Available at [Access: 4 July

2015]

http://www.dpi.nsw.gov.au/ data/assets/pdf_file/0009/416763/orange-hawkweed-strategy12-web.pdf

Duncan, C., Jachetta, J., Brown, M., Carrithers, V., Clark, J., DiTomaso, J., Lym, R.,

McDaniel, K., Renz, M., Rice, P., 2004 Assessing the economic, environmental, and

societal losses from invasive plants on rangeland and wildlands Weed Technol.

18 (sp1), 1411–1416.

Duncan, C.A., Clark, J.K., 2005 Invasive Plants of Range and Wildlands and Their

Environmental, Economic and Societal Impacts Weed Science Society of America.

Epanchin-Niell, R.S., Haight, R.G., Berec, L., Kean, J.M., Liebhold, A.M., 2012 Optimal

surveillance and eradication of invasive species in heterogeneous landscapes.

Ecol Lett 15 (8), 803–812.

European Commission, 2008 Towards an EU Strategy on Invasive Species .

[COM(2008) 789, EC, Brussels 2008] Available from [Accessed: 6 December

2013] http://ec.europa.eu/environment/nature/invasivealien/docs/1_EN_ACT_

part1_v6.pdf

Finnoff, D., Shogren, J.F., Leung, B., Lodge, D., 2007 Take a risk: preferring prevention

over control of biological invaders Ecol Econ 62 (2), 216–222.

Fraser, R.W., Cook, D.C., Mumford, J.D., Wilby, A., Waage, J.K., 2006 Managing

out-breaks of invasive species: eradication versus suppression Int J Pest Manag 52

(4), 261–268.

Garrard, G.E., Bekessy, S.A., McCarthy, M.A., Wintle, B.A., 2008 When have we looked

hard enough? A novel method for setting minimum survey effort protocols for

flora surveys Austral Ecol 33 (8), 986–998.

Gurevitch, J., Padilla, D.K., 2004 Are invasive species a major cause of extinctions?

Trends Ecol Evol 19 (9), 470–474.

Harris, S., Brown, J.A., Timmins, S.M., 2001 Weed surveillance-how often to search?

New Zealand’s Department of Conservation: Wellington.

Hauser, C.E., McCarthy, M.A., 2009 Streamlining search and destroy: cost-effective

surveillance for invasive species management Ecol Lett 12 (7), 683–692.

Hester, S.M., Sinden, J.A., Cacho, O., 2006 Weed invasions in natural environments:

towards a framework for estimating the cost of changes in the output of

ecosys-tem services Working Paper Series in Agricultural and Resource Economics.

University of New England.,

Homans, F., Horie, T., 2011 Optimal detection strategies for an established invasive

pest Ecol Econ 70 (6), 1129–1138.

Hulme, P.E., 2012 Weed risk assessment: a way forward or a waste of time? J Appl.

Ecol 49 (1), 10–19.

Hunter, G., et al 1992 The distribution of Hawkweeds (Hieracium spp.) in the South Island, indicating problem status Rev J N Z Mt Land Inst 48, 21–31.

Johnstone, P., Wilson, J., Bremner, A., 1999 Change in Hieracium populations in Eastern Otago over the period 1982–1992 N Z J Ecol 31–38.

Kompas, T., Che, T., 2009 A practical optimal surveillance measure: the case of papaya fruit fly in Australia Australian Centre for Biosecurity and Environmental Economics, Crawford School of Economics and Government, Australian National University, Canberra, ACT Available from [Accessed: 15 January 2014] http:// www.acbee.anu.edu.au/pdf/publications/Papaya_Fruit_Fly.pdf

Koopman, B., 1956 The theory of search II Target detection Oper Res 4 (5), 503–531 Kot, M., Lewis, M.A., van den Driessche, P., 1996 Dispersal data and the spread of invading organisms Ecology 77 (7), 2027–2042.

Kotani, K., Kakinaka, M., Matsuda, H., 2009 Dynamic economic analysis on invasive species management: some policy implications of catchability Math Biosci 220 (1), 1–14.

McArdle, B.H., 1990 When are rare species not there? Oikos 57 (2), 276–277.

Meentemeyer, R.K., Haas, S.E., Václavík, T., 2012 Landscape epidemiology of emerg-ing infectious diseases in natural and human-altered ecosystems Annu Rev Phytopathol 50, 379–402.

Mehta, S.V., Haight, R.G., Homans, F.R., Polasky, S., Venette, R.C., 2007 Optimal detec-tion and control strategies for invasive species management Ecol Econ 61 (2), 237–245.

Moore, J.L., Hauser, C.E., Bear, J.L., Williams, N.S., McCarthy, M.A., 2011 Estimating detection-effort curves for plants using search experiments Ecol Appl 21 (2), 601–607.

Moore, J.L., Rout, T.M., Hauser, C.E., Moro, D., Jones, M., Wilcox, C., Possingham, H.P., 2010 Protecting islands from pest invasion: optimal allocation of biose-curity resources between quarantine and surveillance Biol Conserv 143 (5), 1068–1078.

Morgan, J., 2000 Orange Hawkweed Hieracium aurantiacum: a new naturalised species

in Alpine, Australia Vic Nat 117, 329–348.

NISC, 2008 2008–2012 National Invasive Species Management Plan Available at [Accessed: 20 April 2015] www.invasivespecies.gov

NRMMC, 2007 The Australian weeds strategy A national strategy for weed manage-ment in Australia Natural Resource Managemanage-ment Ministerial Council Available

at [Access: 4 July 2015] http://www.weeds.org.au/aws.htm Olson, L.J., Roy, S., 2002 The economics of controlling a stochastic biological invasion.

Am J Agric Econ 84 (5), 1311–1316.

Olson, L.J., Roy, S., 2005 On prevention and control of an uncertain biological invasion Appl Econ Perspect Policy 27 (3), 491–497.

Panetta, F., Timmins, S., 2004 Evaluating the feasibility of eradication for terrestrial weed incursions Plant Protection Q 19 (1), 5–11.

PayScale, 2015 Compensation software [Accessed: 8 July 2015] http://www payscale.com/research/AU/Job=Environmental_Scientist/Salary

Pearce, D., Atkinson, G., Mourato, S., 2006 Cost–benefit Analysis and the Environment: Recent Developments OECD: Paris.

Perrings, C., Mooney, H., Williamson, M., 2010 The problem of biological invasions In: Perrings, C., Mooney, H., Williamson, M (Eds.), Bioinvasions & Globalisation: Ecology, Economics, Management, and Policy Oxford University Press., pp 1–16 Pimentel, D., Zuniga, R., Morrison, D., 2005 Update on the environmental and eco-nomic costs associated with alien-invasive species in the United States Ecol Econ 52 (3), 273–288.

Regan, T.J., McCarthy, M.A., Baxter, P.W., Dane Panetta, F., Possingham, H.P., 2006 Optimal eradication: when to stop looking for an invasive plant Ecol Lett 9 (7), 759–766.

Rejmánek, M., Pitcairn, M., 2002 When is eradication of exotic pest plants a realistic goal In: Veitch, C., Clout, M (Eds.), Turning the Tide: The Eradication of Invasive Species IUCN: Cambridge., pp 249–253.

Reserve Bank of Australia, 2015 Interest rates and yields money market daily

-1976 to 17 May 2013 Reserve Bank of Australia, Historical Data [Accessed: 8 July 2015] http://www.rba.gov.au/statistics/historical-data.html

Sharov, A.A., Liebhold, A.M., 1998 Bioeconomics of managing the spread of exotic pest species with barrier zones Ecol Appl 8 (3), 833–845.

Shigesada, N., Kawasaki, K., 1997 Biological Invasions: Theory and Practice Oxford University Press.

Simberloff, D., 2003 Eradication - preventing invasions at the outset Weed Science 51 (2), 247–253.

Sinden, J., Jones, R., Hester, S., Odom, D., Kalisch, C., James, R., Cacho, O., Griffith, G., 2005 The economic impact of weeds in Australia Plant Protect Q 20 (1), 25.

Stone, K., 2010 Hieracium aurantiacum Fire Effects Information System, [Online].

U.S Department of Agriculture, Forest Service, Rocky Mountain Research Station, Fire Sciences Laboratory (Producer) Available at [2015, July 6] http:// www.fs.fed.us/database/feis/

Stoneham, G., Chaudhri, V., Ha, A., Strappazon, L., et al 2003 Auctions for conservation contracts: an empirical examination of Victoria’s BushTender trial Aust J Agric Resour Econ 47, 477–500.

Vitousek, P.M., D’Antonio, C.M., Loope, L.L., Westbrooks, R., et al 1996 Biological invasions as global environmental change Am Sci 84 (5), 468–478.

Wilcove, D.S., Rothstein, D., Dubow, J., Phillips, A., Losos, E., 1998 Quantifying threats to imperiled species in the United States BioScience 48 (8), 607–615 Wilen, J.E., 2007 Economics of spatial-dynamic processes Am J Agric Econ 89 (5), 1134–1144.

Williams, N.S., Hahs, A.K., Morgan, J.W., 2008 A dispersal-constrained habitat suitability model for predicting invasion of alpine vegetation Ecol Appl 18 (2), 347–359.

NRMMC, 2007 The Australian weeds strategy A national strategy for weed manage-ment in Australia Natural Resource Managemanage-ment Ministerial Council Available... Australia Australian Centre for Biosecurity and Environmental Economics, Crawford School of Economics and Government, Australian National University, Canberra, ACT Available from [Accessed: 15 January... 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 inTable