Biological Conservation 143 (2010) 1737–1750
Contents lists available at ScienceDirect
Biological Conservation
journal homepage: www.elsevier.com/locate/biocon
Development and application of a model for robust, cost-effective investment
in natural capital and ecosystem services
Brett A. Bryan *
CSIRO Sustainable Ecosystems, Waite Rd., Urrbrae, South Australia 5064, Australia
a r t i c l e
i n f o
Article history:
Received 19 August 2009
Received in revised form 30 March 2010
Accepted 12 April 2010
Available online 7 May 2010
Keywords:
Portfolio analysis
Planning
Preference programming
Compositional analysis
Prioritization
Conservation
a b s t r a c t
Identifying good investments in environmental management is complex as several prioritization strategies may be used and significant uncertainty often surrounds cost, benefits, and agency budgets. In this
paper I developed a model for robust portfolio selection based on preference programming to support
cost-effective environmental investment decisions under uncertainty and applied it to the South Australian Murray-Darling Basin. Benefits and costs of 46 investment alternatives (called targets) for managing
natural capital and ecosystem services were quantified and the associated uncertainty estimated. Thirtysix investment portfolios were selected using mathematical programming under four investment prioritization strategies (cost-effectiveness (E-max), cost-effectiveness including a suite of pre-committed (or
core) costs (E-max*), cost-only (C-rank), and benefit-only (B-rank)), three decision rules (pessimistic, most
likely, and optimistic), and three budget scenarios (minimum, most likely, maximum). Compared to the
optimally performing investment strategy E-max, the E-max* and C-rank strategies only slightly reduced
portfolio performance and altered portfolio composition. However, the B-rank strategy reduced performance by half and radically changed composition. Uncertainty in costs, benefits, and available budgets
also strongly influenced portfolio performance and composition. I conclude that in this case study the
consideration of uncertainty was at least as important as investment strategy in effective environmental
decision-making. Targets whose selection was less sensitive to uncertainty were identified as more
robust investments. The results have informed the allocation of AU$69 million in the study area and
the techniques are readily adaptable to similar conservation and environmental investment decisions
in other areas at a variety of scales.
Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction
A perennial problem facing environmental agencies is how to
allocate a limited budget across many worthy conservation, management, and restoration projects that enhance natural capital
and ecosystem services (Prato, 2007; Wilson et al., 2007;
Hajkowicz et al., 2009a). The need to consider the costs and multiple benefits of investment options and the uncertainty that surrounds these estimates makes systematic and efficient resource
allocation a complex problem (Messina and Bosetti, 2003; Ehrgott
et al., 2004; Lesiö et al., 2007, 2008; Phillips and Bana e Costa,
Abbreviations: E-max, Most cost-effective investment strategy; E-max*, Most
cost-effective investment strategy including core costs; C-rank, Cost-only investment strategy; B-rank, Benefit-only investment strategy; SAMDB, South Australian
Murray-Darling Basin; NRM, Natural Resources Management; SAMDB NRM Board,
South Australian Murray-Darling Basin Natural Resources Management Board;
MCA, Multiple Criteria Analysis; PDF, Probability density function; RCT, Resource
condition target; CC, Climate change.
* Tel.: +61 8 8303 8581; fax: +61 8 8303 8582.
E-mail address: [email protected]
0006-3207/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.biocon.2010.04.022
2007). Due in part to this complexity, environmental agencies have
rarely considered both costs and benefits when setting investment
priorities (Hughey et al., 2003; Ferraro, 2003; Polasky, 2008) and
instead, have directed investment towards projects with greatest
benefit, or lowest cost, or some other ad hoc objective (Ferraro,
2003; Newburn et al., 2005; Phillips and Bana e Costa, 2007). Overall, these investment strategies usually fail to achieve the most
effective outcomes from environmental funds (Babcock et al.,
1997; Wu et al., 2000; Crossman and Bryan, 2009). The need for
agencies to prioritize the investment of scarce resources, satisfy
due diligence requirements, and maximize the effectiveness of
conservation funds has been widely recognised (Wu and Boggess,
1999; Ferraro, 2003; Polasky, 2008; Hajkowicz, 2009a; Wilson
et al., 2009).
Similar capital budgeting investment problems routinely occur
in management economics and finance when finite resources need
to be allocated across a range of investment alternatives with the
goal of maximizing benefits (Steuer and Na, 2003; Bana e Costa
et al., 2006; Ho et al., 2007; Huang, 2008). Phillips and Bana e Costa
(2007) divided the investment prioritisation and selection problem
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B.A. Bryan / Biological Conservation 143 (2010) 1737–1750
into the two elements of option appraisal and portfolio selection.
Option appraisal involves calculating the costs and benefits, and
ranking options. Costs and benefits are often measured in monetary terms and cost–benefit analysis used to evaluate the net gains
in social welfare of an investment (Hanley and Barbier, 2009).
However, conservation and environmental management investments in particular, typically accrue a complex and diverse suite
of benefits. Many of these benefits (e.g. bequest and intrinsic values; Raymond et al., 2009) are not expressed in markets and are
therefore not readily amenable to economic valuation (Hughey
et al., 2003). For these reasons, the benefits of environmental
investments are often evaluated in terms of multiple attribute utility (Keeney and Raiffa, 1976; Steuer et al., 2007; Hajkowicz et al.,
2008). Multiple attribute estimates of benefits might not tell us
anything about the net gains in social welfare of an investment,
but they do enable effective comparison among competing alternatives (Hughey et al., 2003). Portfolio selection then involves allocating resources to those alternatives that offer the highest
return on investment subject to budgetary and other constraints
(Ferraro, 2003; Steuer and Na, 2003; Murdoch et al., 2007; Phillips
and Bana e Costa, 2007).
Portfolio selection integrating both costs and benefits has been
used to identify cost-effective spatial priorities for investment in
biodiversity conservation (Ando et al., 1998; Balmford et al.,
2000; Naidoo et al., 2006; Wilson et al., 2006, 2009; Bottrill
et al., 2008; Polasky et al., 2008; Underwood et al., 2009), restoration (Macmillan et al., 1998; Crossman and Bryan, 2006; Bryan and
Crossman, 2008), and the enhancement of natural capital and ecosystem services (Crossman and Bryan, 2009; Nelson et al., 2009).
Portfolio selection has also been widely used to identify cost-effective management priorities in conservation (Wu and Boggess, 1999;
Wilson et al., 2007), water quality management (Alam et al., 2008;
Hajkowicz et al., 2008; Bryan and Kandulu, 2009), natural resource
management (Hajkowicz, 2007, 2009b; Crossman and Bryan, 2009;
Marinoni et al., 2009), and enhancing ecosystem services (Prato,
2007). The studies cited above have shown that investment strategies which consider both costs and benefits may lead to substantially greater environmental benefits from limited budgets.
However, few studies have considered the influence of uncertainty
in such decision parameters as cost, benefit, and budget on the efficiency and composition of conservation investments or have provided a means for environmental agencies to select investment
portfolios that are robust to this uncertainty.
Techniques proposed for portfolio selection and resource allocation under uncertainty include fuzzy simulation (Huang, 2008),
info-gap theory (McDonald-Madden et al., 2008), Bayesian inference (Prato, 2007), contingent portfolio programming (Gustafsson
and Salo, 2005), multiple criteria analysis (MCA), and preference
programming (Kleinmuntz, 2007). Preference programming has
been used to inform robust investment in research and development projects (see Lesiö et al., 2008), and offers significant potential for guiding investment in natural capital and ecosystem
services under alternative investment strategies. Preference programming (Salo and Hämäläinen, 1992) has enabled the robust
selection of portfolios despite incomplete information about the
costs and benefits of investments (Lesiö et al., 2007, 2008). The
dominance concepts and decision rules in preference programming
provide a transparent basis for making investment decisions under
uncertainty (Salo and Hämäläinen, 2004) that decision-makers are
more likely to adopt (Kleinmuntz, 2007).
In this paper, I present a model for supporting cost-effective
investment decisions for managing natural capital and ecosystem
services under uncertainty, and describe its application in informing
resource allocation by the South Australian Murray-Darling Basin
(SAMDB) Natural Resource Management (NRM) Board (the Board).
A natural capital and ecosystem services framework was used to
provide a flexible basis for quantifying the diverse suite of benefits
associated with achieving environmental targets. I quantified the
benefit of 46 potential investment alternatives (or targets, Appendix
A) for natural capital and ecosystem services in MCA workshops and
simulated uncertainty using Monte Carlo simulation. Costs of
achieving targets were quantified in dollar terms and the uncertainty estimated. Investment in targets was prioritized using four
strategies: cost-effectiveness (E-max), cost-effectiveness including
a suite of pre-committed (or core) costs (E-max*), cost-only (C-rank),
and benefit-only (B-rank). From preference programming, three
decision rules (pessimistic, most likely, optimistic) and three budget
scenarios (minimum, most likely, maximum) were used to assess
the impact of uncertainty in the cost and benefit of targets, and in
available budgets, respectively. I used mathematical programming
to select 36 portfolios under each combination of investment strategy, decision rule, and budget scenario. The more robust investments were those selected for investment in more portfolios given
the uncertainty in the investment problem. The Board’s use of the results to guide the investment of AU$69 million in environmental
funds, and the adaption of the techniques to other jurisdictions at
a variety of scales, is discussed.
2. Theoretical framework
2.1. Investment strategies
The principle of prioritizing investment based on value-formoney is ‘‘deceptively simple, uncontroversial, yet seldom used
in organizations” (Phillips and Bana e Costa, 2007). Value-formoney, or cost-effectiveness, can be calculated using a benefit-cost
ratio Bk/Ck where Bk is the benefit and Ck is the cost of target k.
Maximally efficient E-max (Ferraro, 2003) portfolios may be selected simply by ranking investments in descending order and allocating resources until the budget is exhausted (Sinden, 2003).
Often, the E-max portfolio selection strategy is formulated as
a mathematical programming problem to enable the inclusion of
more complex constraints on investment. The model developed
below employs a variant on the maximal covering formulation
(Church and ReVelle, 1974) which considers the level of investment in each target as a continuous variable rk. Hence, partial
investment in a target is possible and the level of benefit
achieved is linearly related to the level of investment in the target. To select an efficient E-max portfolio based on both costs
and benefits we:
K
X
rk
Bk ;
C
k
k¼1
maximize :
ð1Þ
subject to :
0 6 rk 6 C k
K
X
r k ¼ RT ;
for k ¼ 1; 2; . . . ; K; and;
ð2Þ
ð3Þ
k¼1
where Ck is the cost of achieving target k and RT is the total budget
available.
The benefit of achieving targets for multiple natural capital assets and ecosystem services can be combined into a single measure
of utility using a multi-attribute utility function (Keeney and Raiffa, 1976). The benefit bk for natural capital and ecosystem services
of achieving target k can be calculated as the product of the impact
Qik of achieving the target on asset/service i and the management
priority Mi of the asset/service, summed over all assets/services
D0 such that:
bk ¼
D0
X
i¼1
Q ik Mi
ð4Þ
B.A. Bryan / Biological Conservation 143 (2010) 1737–1750
Another consideration in the environmental investment problem is that targets and their associated benefits may be partially
or wholly achieved without any agency investment. For example,
consider a target that involves the restoration of 1000 ha of native
habitat. Some of this may be achieved, say 200 ha, through the actions of external agents such as private landholders or community
groups even if the environmental agency allocates no funds. In this
model, a factor Tk (0 6 Tk 6 1) is introduced representing the background level of target achievement to calculate the real benefit
achieved through agency investment Bk such that Bk ¼ ð1 T k Þbk .
However, in practice, environmental agencies more commonly
prioritize investment using strategies other than E-max such as
benefit-only (B-rank) or cost-only (C-rank; Wu et al., 2000; Ferraro,
2003; Sinden, 2003). The B-rank strategy involves ranking alternatives from highest to lowest benefit and allocating resources until
the budget is exhausted (Newburn et al., 2005). To select a B-rank
P
portfolio we maximize Kk¼1 rk Bk subject to Eqs. (2) and (3). Similarly, the C-rank strategy involves ranking investments from lowest to highest cost and allocating resources until the budget is
exhausted (Ferraro, 2003; Sinden, 2003). To select a C-rank portfoP
lio we maximize Kk¼1 r k =C k subject to Eqs. (2) and (3).
In addition, constraints on resource allocation often characterize the environmental investment problem (Lesiö et al., 2008).
One common constraint is the obligation and prior commitment
of parts of the budget to achieving specific targets. I call these core
costs. To analyse the effect of the prior commitment of core costs
on portfolio performance and composition we can include them
in a constrained E-max (E-max*) investment strategy using Eq.
(1) subject to Eq. (3) and C k 6 rk 6 C k for k ¼ 1; 2; . . . ; K where C k
is the core cost committed to target k. Under E-max*, the agency
commits the core costs to specific targets first and invests the
remaining budget in the most cost-effective manner.
1739
Targets can then be classified as core, borderline, and external
investments based on the core index (Lesiö et al., 2007, 2008). Core
targets are those where CIk = 100. They can be recommended with
certainty as they are always selected for full investment in nondominated portfolios under all combinations of cost, benefit, and
budget. External targets are those where CIk = 0. They can be rejected with certainty as they are never selected in any non-dominated portfolio. Borderline targets are those where 0 < CIk < 100.
The higher the core index for borderline targets the more robust
the investment given the inherent uncertainty.
3. Methods
3.1. Study area
The SAMDB is an area of approximately 56,000 km2 (Fig. 1).
Apart from the hilly eastern Mt. Lofty Ranges, the topography is
2.2. Robust portfolio selection under uncertainty
Uncertainty plagues environmental investment decisions.
Uncertainty, or incomplete information (Lesiö et al., 2007), occurs
in key parameters including the costs Ck and benefits (comprised
of the benefit of achieving targets bk and the background level of
target achievement Tk), and the available budget RT. Incomplete
information is represented here by the most likely (denoted ml),
minimum (denoted min), and maximum (denoted max) values. Using
preference programming techniques (Salo and Hämäläinen, 2004),
incomplete information on costs, benefits, and background target
achievement can be incorporated into portfolio selection using
three decision rules – optimistic, most likely, and pessimistic. Decision rules enable the selection of portfolios based on optimistic
max
ml
ml
ml
, and T min
(C min
k ), most likely (C k , bk , T k ), and pessimistic
k , bk
min
max
,
b
,
and
T
)
parameter
estimates
under
the four invest(C max
k
k
k
ment strategies (E-max, E-max*, C-rank, B-rank).
Non-dominated portfolios are those that perform as well as or
better than all others. A Pareto front of non-dominated portfolios
can be identified under the three decision rules and four investment strategies. By setting cut-offs at the minimum (Rmin
T ), most
max
) budget estimates, a set P of 36
likely (Rml
T ), and maximum (RT
non-dominated portfolios p (4 investment strategies 3 decision
rules 3 budgets) can be selected.
Robust portfolio modeling helps quantify the robustness of
investment in individual targets through a core index (Lesiö
et al., 2007, 2008). A core index can be calculated for each target
as the mean level of investment allocated in non-dominated portfolios within each investment strategy s, for all s in S{E-max, EP
r
max*, C-rank, B-rank} such that CIs;k ¼ ð100 p2Ps Cs;k Þ=jPs j, where
k
rs,k is the investment in target k identified in the |Ps| non-dominated portfolios selected under investment strategy s (note that
|Ps| = 9, from three decision rules three budgets).
Fig. 1. Location and broad land use in the South Australian Murray-Darling Basin
study area.
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B.A. Bryan / Biological Conservation 143 (2010) 1737–1750
mostly flat. The climate ranges from Mediterranean to semi-arid
climate. The SAMDB’s high value ecological assets include the River
Murray and its floodplain and lower lakes, Lake Alexandrina and
Lake Albert, the Coorong estuary, and some 30,748 km2 of remnant
native woodland and shrubland habitat. Both dryland and irrigated
agriculture are common land uses in the region. Land clearance
and agriculture has increased soil erosion, dryland salinity, and river salinity, and has degraded native ecosystems. Reduced environmental flows over the past decade have further degraded riparian
ecosystems.
The SAMDB NRM Board is the community-based regional
agency responsible for public investment in environmental management in the region. Four geographically-based groups (Rangelands, Ranges to River, Mallee and Coorong, Riverlands) advise
the Board. Board and group members come from such backgrounds
as primary production, soil conservation, local government, pest
animal and plant control, salinity management, indigenous issues,
ecology, and water resource management (SAMDB NRM Board,
2009a).
3.2. Regional priorities for managing natural capital and ecosystem
services
The concept of natural capital and ecosystem services provided
a structure for quantifying regional environmental management
priorities in this study. Natural capital assets included Land, Water,
Biota, Atmosphere, and People. The Millennium Ecosystem Assessment framework (MEA, 2005), tailored to the study area through
extensive community consultation (Cast et al., 2008; Raymond
et al., 2009; Bryan et al., 2010), provided the ecosystem services
typology for this study (Table 1).
To quantify the management priority of capital assets and ecosystem services, I facilitated five MCA workshops, one with the
Board and one with each of the four regional advisory groups.
The Analytical Hierarchy Process (Saaty, 1980) and the Simple Multi-Attribute Rating Technique (von Winterfeldt and Edwards, 1986)
enabled the quantification of the management priorities of capital
assets and ecosystem services. Of the 43 decision-makers who attended the workshops, 40 valid individual responses were returned. Bryan et al. (2010) described the results of this process in
detail.
3.3. Identifying investment alternatives and quantifying impacts
Specialist asset-based program groups within the Board specified 46 management action targets (or simply targets) under the
natural capital assets of Atmosphere, Biota, Land, Water and People, to be achieved by 2014 (Appendix A). To quantify the relative
impact of targets on natural capital and ecosystem services, I facilitated another five MCA workshops with the asset-based program
groups. Forty-nine participants attended these workshops. At each
workshop, participants arrived at a consensus score for the impact
of achieving each target on the nine capital assets and 23 ecosystem services (Table 1) using a variant of the Simple Multi-Attribute
Rating Technique (von Winterfeldt and Edwards, 1986). Participants scored impact on a scale of 10 to +10, where 10 represented the strongest negative impact, 0 represented no impact,
and +10 was the strongest positive impact (Appendix B). They also
estimated the uncertainty surrounding the impact scores.
Table 1
Capital assets and ecosystem services assessed in this study.
Capital assets
Natural capital
(NC1) Water
(NC2) Land
(NC3) Biota
(NC4) Atmosphere
Built capital
(BC1) Built environs and infrastructure
(BC2) Zoning and planning
(BC3) Economic viability and employment
Social capital
(SC1) Family
(SC2) Community
Ecosystem services
Provisioning services
(P1) Food and fiber
(P2) Biochemical resources
(P3) Fresh water
(P4) Geological resources
(P5) Energy
Regulating services
(R1) Air quality
(R2) Climate
(R3) Water quantity
(R4) Erosion
(R5) Water quality
(R6) Disease, pests, and natural hazards
(R7) Pollination
Cultural services
(C1) Cultural diversity and heritage
(C2) Spiritual, sense of place, and lifestyle
(C3) Knowledge and education
(C4) Aesthetics and inspiration
(C5) Social relations
(C6) Recreation and tourism
(C7) Bequest, intrinsic, and existence
Supporting services
(S1) Soil formation
(S2) Photosynthesis and plant primary production
(S3) Nutrient cycling
(S4) Water cycling
ment priority Mi of the asset/service (Eq. (4)). To capture their
uncertainty, both impact Qik and management priority Mi are specified as random variables sampled from probability density functions (PDFs). I specified triangular PDFs to quantify the impact of
each action on each asset/service Qik based on results of the
MCA-derived impact scores (Section 3.3) and Gaussian PDFs to
quantify the management priority of each asset/service Mi based
on a centred log transform of MCA-derived weights (Appendix C).
The benefit bk of achieving each target k was then calculated as a
random variable with a PDF obtained through 10,000 Monte Carlo
iterations of Eq. (4), with each iteration using values drawn from
the impact Qik and management priority Mi PDFs. The minimum
min
ml
max
bk , most likely bk , and maximum bk benefit values were the
5th percentile, mean, and 95th percentile taken from the normally
distributed benefit PDF simulated for each target k. Appendix C details the derivation of benefit values.
3.4. Simulating benefit distributions
3.5. Quantifying costs and budgets
In the robust portfolio selection model described in Section 2,
the benefit bk of achieving each target k is the sum over all natural
capital assets and ecosystem services D’ of the product of the impact Qik of achieving the target on each asset/service i and manage-
The relevant asset-based program leaders estimated the miniml
max
costs, and the minmum C min
k , most likely C k , and maximum C k
ml
max
,
most
likely
T
,
and
maximum
T
level of background
imum T min
k
k
k
target achievement, for each target k (Appendix D). The Board’s
B.A. Bryan / Biological Conservation 143 (2010) 1737–1750
1741
finance manager estimated the core costs Rk committed to each
target k (Appendix D) and defined three budget scenarios to reflect
= $37.5 M), most likely (Rml
the minimum (Rmin
T
T = $62.5 M), and
max
maximum (RT = $87.5 M) budgets based on forward estimates
over the 5 years to 2014.
3.6. Robust portfolio selection
With cost, benefit, and budgets estimated, I applied the preference programming model described in Section 2 to inform more
efficient and robust investment decisions by the Board. First, I calculated the cost-effectiveness of each target in enhancing natural
capital and ecosystem services given uncertainty in benefits and
costs. Next, I calculated and graphed Pareto optimal frontiers of
non-dominated portfolios for each decision rule under each investment strategy. Using mathematical programming to implement
the robust portfolio selection models in Section 2, I then selected
36 non-dominated investment portfolios and quantified the performance and composition of each. Finally, I calculated the core index and assessed the robustness of targets under each investment
strategy.
4. Results
4.1. Cost-effectiveness
Appendix D details the costs and benefits of targets. Cost-effectiveness varied significantly between targets (Fig. 2) as evidenced
by high standard deviations relative to the mean. The mean costeffectiveness of targets was 1.04 (r = 1.25) under the pessimistic
decision rule, 2.45 (r = 2.98) under the most likely, and 6.56
(r = 8.68) under the optimistic decision rule. Cost-effectiveness
also varied significantly within individual targets (Fig. 2) as evidenced by the mean difference in cost-effectiveness between the
pessimistic and optimistic decision rules (5.53) being more than
twice the mean cost-effectiveness of targets under the most likely
decision rule (2.45).
4.2. Robust portfolio selection under uncertainty
Initial exploration revealed different Pareto front shapes under
the four investment scenarios and three decision rules (Fig. 3). Pareto-optimal portfolios selected under the E-max strategy represent
the maximum total benefit for natural capital and ecosystem services (i.e. maximum performance) for a given budget. The convex
shape of the E-max Pareto front also suggests that much of the
benefits can be achieved at low cost with diminishing marginal returns accruing from additional expenditure. With the E-max* strategy the inclusion of core costs caused a small dip at the beginning
of the Pareto front. The C-rank Pareto front also returned slightly
less benefit than E-max. The B-rank Pareto front, however, is
significantly different in shape than the E-max front reflecting
the B-rank strategy’s poorer performance. There is also substantial
difference in the benefits achieved by portfolios selected under the
three decision rules within each investment strategy (Fig. 3).
Assessment of the 36 non-dominated portfolios further quantifies the impact of investment strategy, decision rule, and budget
scenario on portfolio performance (Table 2). The investment strategies, particularly B-rank, strongly influenced portfolio performance (Table 2, Fig. 3). To illustrate, under the most likely
decision rule and the most likely budget, benefits achieved under
both E-max* (128.96 (94.12%)) and C-rank (131.16 (95.72%)) were
slightly less than achieved under E-max (137.02). The B-rank strategy, however, returned fewer than half of the benefits of E-max
(67.71 (49.42%)) (Table 2).
Fig. 2. Cost-effectiveness of targets for enhancing natural capital and ecosystem
services under uncertainty. The colored bar represents cost-effectiveness calculated
under the most likely decision rule while the error bars represent cost-effectiveness
calculated under the pessimistic (low bar) and optimistic (high bar) decision rules.
The letter in the target ID (right axis) and bar colour refers to the relevant natural
capital asset the target addresses (A = Atmosphere, B = Biota, L = Land, W = Water,
and P = People).
Uncertainty in cost and benefit parameters very strongly influenced portfolio performance (Table 2). To illustrate, under the
most likely budget scenario ($62.5 M), the benefit of portfolios selected under the optimistic decision rule ranged between 165.39%
(E-max) and 180.96% (B-rank) of the benefit achieved under the
most likely decision rule whilst under the pessimistic decision rule
benefit ranged between 53.91% (C-rank) and 64.38% (B-rank) of
that achieved under the most likely decision rule.
Uncertainty in available budget also strongly influenced portfolio performance (Table 2). To illustrate, under the most likely decision rule, the total benefit of portfolios selected under the
maximum budget scenario ranged between 112.79% (E-max) and
142.64% (B-rank) of the benefit achieved under the most likely
budget scenario whilst under the minimum budget scenario,
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B.A. Bryan / Biological Conservation 143 (2010) 1737–1750
Fig. 3. Pareto fronts of non-dominated portfolios of targets under optimistic (top green line), most likely (middle orange line), and pessimistic (bottom red line) decision rules
for each of the four investment strategies. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 2
Performance of the four investment strategies under three decision rules and three
budget scenarios measured in terms of benefit for natural capital and ecosystem
services.
Budget scenario
Decision rule
Investment strategy
E-max
E-max*
C-rank
B-rank
Minimum ($37.5 M)
Optimistic
Most likely
Pessimistic
185.24
102.41
57.66
157.41
81.98
45.79
181.51
89.55
46.86
84.26
42.88
27.2
Most Likely ($62.5 M)
Optimistic
Most likely
Pessimistic
226.62
137.02
77.78
219.59
128.96
71.86
220.85
131.16
70.71
122.53
67.71
43.59
Maximum ($87.5 M)
Optimistic
Most likely
Pessimistic
252.52
154.55
91.98
250.75
152.39
88.58
250.2
151.68
80.12
183.9
96.58
58.41
L1.3, W1.2, W1.3, W2.2, W2.3, P1.1, P1.3, P2.2, P2.3, and P3.2. These
tended to be of low cost, low background level of target achievement, high benefit, and had low levels of uncertainty in these
parameters (Appendix D). Conversely, external investments (i.e.
where core index = 0) under E-max included targets B1.2, L1.4,
and W2.1. These tended to have high cost and background levels
of target achievement, low benefit, and high levels of uncertainty
in these parameters (Appendix D). Core investments under B-rank
included targets L1.3, W1.3, and W1.4. Whilst these targets had
very high benefit scores their costs were not excessive resulting
in a high core index under the E-max and E-max* investment strategies also (Table 3; Appendix D).
5. Discussion
5.1. Supporting environmental investment decision-making
benefit ranged between 63.33% (B-rank) and 74.74% (E-max) of
that achieved under the most likely budget scenario.
Table 3 illustrates the composition of portfolios selected under
each investment strategy, decision rule, and budget scenario.
Increasing the budget simply added more targets to the portfolio.
Uncertainty in costs and benefits had a moderate effect of portfolio
composition as evidenced by differences in targets selected under
the three decision rules within each investment strategy. There
was also some difference in portfolio composition between the Emax, E-max*, and C-rank investment strategies. However, the
adoption of the B-rank investment strategy radically changed portfolio composition (Table 3).
Targets with a high core index under the E-max investment
strategy also tended to have a high core index under E-max* and
C-rank (Table 3). Core investments (i.e. where core index = 100)
under E-max included targets A1.1, A1.2, A1.4, A2.1, B1.1, B2.2,
In this study, the value-for-money principle was implemented
by prioritising investment based on cost-effectiveness using the
E-max strategy. Inclusion of core costs in the constrained Emax* strategy selected some different targets for investment
and achieved only slightly lower performance than E-max as core
costs comprised only a small proportion of the total budget. Larger reductions in portfolio performance and changes in composition may be expected when environmental agencies commit
larger proportions of their budgets to investments of low costeffectiveness.
The cost-only (C-rank) strategy caused a minor reduction in
portfolio performance while the benefit-only (B-rank) strategy
reduced performance to roughly half that of E-max and radically
altered portfolio composition. These results suggest that
decision-makers in the study area may ignore the benefits of
B.A. Bryan / Biological Conservation 143 (2010) 1737–1750
1743
Table 3
Portfolios selected under the four investment strategies, three decision rules, and three budgets. Green represents full investment, orange, partial investment, and red, no
investment. Included is the core index (%) and investment classification (core (C), borderline (B), and external (E)).
1744
B.A. Bryan / Biological Conservation 143 (2010) 1737–1750
investment alternatives without a major impact on portfolio performance but should ignore costs at their peril. The strong influence of considering benefits-only on portfolio performance is
likely to be a product of the greater relative variability in the costs
of targets compared to benefits (Babcock et al., 1997; Ferraro,
2003; Appendix D). Bode et al. (2008) recently found that greater
variation in costs rather than benefits is likely to hold for many
environmental management and conservation investment problems. However, it is far more common for studies such as this
one to focus on assembling information on the benefits of conservation and environmental management alternatives rather than
the costs. This imbalance needs to be addressed and calls for more
effort in the assembly of cost data have been made (Polasky, 2008).
Uncertainty in both costs and benefits was the major influence
on portfolio performance and composition. The cost-effectiveness
of individual targets in this study varied substantially due to uncertainty in parameter values. For decision-makers, this makes the
systematic consideration of costs and benefits extremely complex
and forms a barrier to efficient investment decision-making for
environmental management. To illustrate this point, portfolio performance under the optimistic decision rule was, on average, 211%
higher than under the pessimistic rule. Budget uncertainty also
influenced portfolio performance but not as strongly. This is illustrated by the 77% higher portfolio performance under the maximum budget than the minimum budget scenario. These results
suggest that considering uncertainty in selecting efficient portfolios is at least as important in environmental investment decisions
as is the prioritization of investments through a cost-effective
investment strategy.
Robust portfolio selection using preference programming provides a practical way of evaluating investments, given the pervasive influence of uncertainty. The calculation of a core index
based on the concepts of dominance provides a simple and transparent metric for evaluating more robust investment alternatives.
This study assessed 36 portfolios covering a diverse set of investment strategies, decision rules, and budget scenarios. To reduce
complexity in making investment decisions, a more pragmatic approach for an environmental agency is to adopt a single investment
strategy, ideally E-max (or E-max* if there are core costs committed), and to refine the selection of a robust portfolio based on this
strategy. To illustrate this using Table 3, several core investments –
targets selected in portfolios under all combinations of decision
rule and budget scenario under the E-max strategy, can be identified. External investments – targets that are not selected in any
portfolio, can also be identified. All other targets are borderline
investments and may be prioritized using the core index (Table 3).
I undertook this study in collaboration with the SAMDB NRM
Board in parallel with the development of the Board’s regional natural resource management plan (SAMDB NRM Board, 2009b). The
results of this study have begun to informed the strategic investment of AU$69 million in achieving environmental targets (Appendix A) over 3 years to 2012 (SAMDB NRM Board, 2009c). The
techniques are directly transferable to other environmental investment problems for which uncertainty in costs and benefits are the
norm rather than the exception and transparency is important in
decision-making. The methods can be applied at a variety of scales
including national (e.g. Caring for Our Country program in Australia, Conservation Reserve Program in the US), regional (e.g.
Somanathan et al., 2009, this study), and local (Hajkowicz et al.,
2008; Connor et al., 2008).
5.2. Advantages, limitations, and further research
Although several techniques exist for selecting efficient portfolios under uncertainty, this study’s robust portfolio selection model
provides a transparent picture of how investment strategies and
decision parameter uncertainty affect both the performance and
composition of investment portfolios. I found three advantages of
this approach in practice. First, once decision-makers obtain costs
and benefit information, they can implement robust portfolio
selection in a spreadsheet. Importantly, this means that environmental agencies can undertake robust portfolio selection in-house
without the burdensome overhead of implementing complex algorithms (Kleinmuntz, 2007). Next, the simplicity and transparency
of the techniques is important in building trust in the modeling
process and increasing stakeholder acceptance (Hajkowicz et al.,
2009) and use (Kleinmuntz, 2007) of the results. Finally, embracing
uncertainty and analysing its effects may also help to build confidence and trust in the model among decision-makers by not forcing them to arrive at a single complete parameter specification
when they know these values are inherently uncertain
(Kleinmuntz, 2007).
However, whilst the simplicity and transparency of the preference programming-based robust portfolio selection techniques
used in this study were one of the major advantages, this is also
a major limitation. Portfolios were selected for 36 combinations
of investment strategies, decision rules, and budget scenarios to
capture the range of possible outcomes. Whilst analysing only
36 portfolios enabled a clearer understanding of the technical details by decision-makers and more effective communication of the
results (e.g. Table 3), the treatment of uncertainty distributions
was simplistic. In calculating a core index, I assumed equal probability of portfolios selected at the extrema (i.e. optimistic and
pessimistic decision rules, low and high budget estimates) as
for those selected using the most likely estimates. In reality,
uncertainty in costs, benefits, and budgets is continuous and better characterised as probability distributions. Monte Carlo simulation has potential for better incorporating uncertainty as
probability distributions in the selection of robust investment
portfolios.
Similarly, using just three decision rules restricts the assessment to these points and does not cater for the continuous scale
of preferences decision-makers typically have. Decision-makers’
preferences usually occur somewhere between absolute pessimism and absolute optimism. One way to address this limitation
would be to add an interactive stage to portfolio selection that allows decision-makers to use the Hurwicz principle to tailor the
decision rule to suit their individual levels of pessimism or optimism (Lang and Merino, 1993). The Hurwicz principle enables
users to select efficient portfolios based on user-specified preferences which may further increase the acceptance and use of decision model recommendations.
Future work should consider the covariance in costs and/or benefits of investments in environmental management and the riskreturn profile of portfolios. It is likely that variation in costs and/
or benefits between individual investments is correlated which increases the risk of under-performance. For example, the cost of targets involving fencing such as ecological restoration and water
quality management may all increase together following price increases for fencing materials. Similarly, the benefits of investments
addressing the same natural capital asset, say wetland restoration,
may decrease together under prolonged drought. In these cases,
the cost-effectiveness of the portfolio is reduced. Modern portfolio
theory (Markowitz, 1952) enables the selection of portfolios that
maximize returns under variable risk profiles where risk also considers covariance in costs and/or benefits between investments.
Extending the model to consider correlated variance in costs and
benefits of investments can increase the cost-effectiveness of portfolios through diversification (or not putting all of our eggs in one
basket).
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B.A. Bryan / Biological Conservation 143 (2010) 1737–1750
6. Conclusion
Appendix A (continued)
Environmental investment decisions are plagued by a lack of a
clearly articulated investment strategy, and by significant uncertainty in investment decision parameters such as the costs and
benefits of investment alternatives and available budgets. This
study quantified the impact of investment strategies and uncertainty on the performance and composition of portfolios for
enhancing natural capital and ecosystem services. I conclude that
it is at least as important to consider uncertainty in investment
decision parameters as it is to adopt the value-for-money principle as an efficient investment strategy in environmental investment. Robust portfolio selection based on preference
programming concepts provides a transparent means for guiding
investment towards those targets that are selected more often in
efficient portfolios. These investments will be good ones no matter what the true values of highly uncertain cost, benefit, and
budget parameters turn out to be. The techniques presented here
provide a pragmatic and transparent approach to supporting
investment decisions for enhancing natural capital and ecosystem
services. As such, decision-makers and stakeholders are more
likely to trust, accept, and adopt the resulting decision recommendations. This study’s findings have already informed the strategic investment of more than AU$69 million over three years in
the SAMDB and the techniques are directly transferable for supporting environmental investment decisions in other areas at a
range of scales.
Acknowledgements
Target
ID
Short description
A1.3
Energy use
efficiency
A1.4
Promote carbon
offsets and NRM
A2
RCT: 100% of natural resource managers incorporating
climate change adaptation into planning by 2030
NRM managers
25% of natural resource managers
respond to CC
incorporating climate change
adaptation into planning
RCT: native ecosystem extent increased to 60% of the
region and native vegetation condition improved by 10%
by 2030
Protect remnant
Protect and manage an additional
vegetation
10,000 ha of priority remnant
native ecosystems
Increase native
The extent of native vegetation
vegetation
ecosystem is increased by
15,000 ha
Manage native
A 10% improvement in the
vegetation
condition of 25% of the native
vegetation in the region
Community
Increase community appreciation
ecological
of native ecosystems and species
appreciation
by 30%
A2.1
B1
B1.1
B1.2
B1.3
B1.4
I am grateful to the SAMDB NRM Board, and CSIRO’s Sustainable
Regional Development theme, Sustainable Agriculture Flagship,
and Water for a Healthy Country Flagship for supporting and funding the research. I am also grateful for the support of the planning
team at the SAMDB NRM Board and Darran King from CSIRO, and
for the participation of the decision-makers and community of
the SAMDB.
B2
B2.1
Appendix A. Full description of the targets specified by the
SAMDB NRM Board
B2.2
In the recent round of regional planning the Board set aspirational goals of sustaining Atmosphere, Biota, Land, Water and People assets in the region typically by the year 2030. To give effect to
these aspirational goals, specialist asset-based program groups
specified 13 Resource Condition Targets (RCTs), also mostly to be
achieved by 2030. To provide a more pragmatic basis for planning,
the Board specified 46 management action targets to be achieved
over 5 years to 2014. The table below lists targets in detail. The letter in the ID field refers to the asset addressed (A = Atmosphere,
B = Biota, L = Land, W = Water, and P = People).
B2.3
B2.4
B3
B3.1
B3.2
Target
ID
Short description
A1
RCT: reduce net greenhouse gas emissions in the SA MDB
by 60% by 2050
Renewable
Voluntary renewable energy use
energy uptake
at 20% and support for local
generation
Industry response Natural resource affecting
to CC
industries adopting climate
A1.1
A1.2
Targets
L1
L1.1
L1.2
Targets
change sector agreements
Increase carbon efficiencies of
vehicle fleet and buildings by 20%
and 10% respectively
Revegetation for future carbon
(CO2-E) sequestration of
126,000 t
RCT: by 2030, water dependent ecosystems in priority
areas maintain ecological function, resilience and
biodiversity
Protect
75% of priority floodplains and
floodplains/
wetlands actively managed as
wetlands
per management plans
Protect
Adoption of sustainable grazing
watercourses
practices, erosion prevention and
rehabilitation
Terrestrial/
A 20% increase in connectivity
aquatic
between / within aquatic and
connectivity
terrestrial ecosystems
Pest management Reduce the extent of priority pest
coast & lakes
species in the coast and lower
lake areas by 10%
RCT: no species moves to a higher risk category and 50%
of species move to a lower category by 2030
Manage threats
Reduce the impact of critical
to species
threats on priority threatened
species
Manage threats
Reduce the impact of critical
to ecosystems
threats on listed threatened
ecosystems
RCT: a 10% improvement in soil and land condition from
2008/2009 levels by 2030
Dryland water
Dryland water use efficiency is
use efficiency
maintained at 80%
Manage pastures 90% of landholders are managing
pastures sustainably
(continued on next page)
1746
B.A. Bryan / Biological Conservation 143 (2010) 1737–1750
Appendix A (continued)
Appendix A (continued)
Target
ID
Short description
Targets
Target
ID
Short description
L1.3
New pest
incursions
W3
L1.4
Manage pests
50% increase in participation in
early warning system
(communication network)
Species specific control targets
for 80% of priority species are
met or ‘on track’ to be met
RCT: improve water quality to achieve the regionallyendorsed environmental values by 2030
Manage
All appropriate houseboat, vessel,
recreational
and marina policies adopted and
impacts
implemented
Increase re-use of 70% of effluent generated in
effluent
region to be reused
Influence
Influence investment in crossupstream water
state water quality (non-salinity)
quality
improvements
Manage water
50% of land in the agricultural
quality
zone to have neutral or beneficial
effects on water assets
Reduce
At least one major settlement
settlement
(>2000 people) with neutral or
impact
beneficial effects on water assets
Fit-for-purpose
70% of total water used in region
water use
shall be taken from sources that
are fit-for-purpose
L2
L2.1
L2.2
L2.3
L2.4
W1
W1.1
W1.2
W1.3
W1.4
W2
W2.1
W2.2
W2.3
W2.5
RCT: the area of land affected by land degradation
processes is reduced by 2030
Reduce erosion
Achieve a 6% improvement in
wind erosion protection for
agricultural cropping land
Increase soil
A 3% increase in the area of
cover
grazing land with soil surface
cover (based on 2009 levels)
Reduce recharge
7500 ha of appropriate perennial
vegetation established in priority
areas
Manage soil
Net balance alkaline inputs are
acidification
equal to acidification levels
(approx 194,000 ha at risk)
RCT: maintain or improve soil condition and water
tables under irrigated land at 2007/08 levels
Reduce Murray
Maintain position on salinity
salinity
register in balance
Minimize saline
Minimize impacts of irrigation
impacts
induced saline groundwater
flows to water or ecosystem
assets
Reduce irrigation 60% of irrigated land in at least
impacts
four priority districts
implemented
Irrigation water
90% of the irrigated area
use efficiency
achieving water use efficiency
RCT: all water resources managed within sustainable
limits by 2030
Increase
100% of water resources have a
knowledge of
risk assessment
risks
Protect water
Process for water management
resources
policy commenced for priority
water resources
Implement water 6 Water Allocation Plans
protection
implemented
Increase
50% of water dependant
environmental
ecosystems are delivered their
water
environmental water
requirement
W3.1
W3.2
W3.3
W3.4
W3.5
W3.6
P1
P1.1
P1.2
P1.3
P2
P2.1
P2.2
P2.3
P3
P3.1
P3.2
P3.3
Targets
RCT: 80% increase in the number of people managing
natural resources sustainably by 2030
50% of regions’ community is
Increase
awareness of
aware of NRM
NRM
Increase
25% of the NRM community have
participation in
the knowledge and skills for
NRM
sustainable NRM
Increase NRM
Increase the level of NRM
volunteers
volunteering in the SAMDB NRM
Region above 1200 members
RCT: increase protection and preservation of aboriginal
culture by 80% by 2030
Awareness of
50% increased awareness of
aboriginal culture aboriginal culture
Engage aboriginal 50% increased participation of
people in NRM
aboriginal people in NRM
Protect cultural
Management of cultural sites and
sites
assets improved
RCT: all landscape development and management have
a neutral or beneficial impact on natural resources by
2030
Communication
Effective institutional
NRM
arrangements in place for all
stakeholders
major stakeholders
Institutional
All state and local government,
alignment with
and Industry development plans
NRM
align with regional plan
Support
All local government
development
development decisions are
decisions
consistent with NRM goals
B.A. Bryan / Biological Conservation 143 (2010) 1737–1750
1747
Appendix B. Impact of targets on capital assets and ecosystem services scored during five MCA workshops with the Atmosphere,
Biota, Land, Water, and People groups using the modified Simple Multi-Attribute Rating Technique
1748
B.A. Bryan / Biological Conservation 143 (2010) 1737–1750
Appendix C. Simulating benefit probability distributions for
targets and extracting maximum, most likely, and minimum
values for inclusion in robust portfolio selection
The benefit bk of achieving each target k equals the sum over all
natural capital assets and ecosystem services D0 of the product of
the impact Qik of achieving the target on each asset/service i and
management priority Mi of the asset/service (Eq. 4). Both impact
Qik and management priority Mi are random variables sampled
from distributions defined by probability density functions (PDFs)
f(z) such that f(z) = P(Z = z) and P(Z = z) is the probability that the
random variable Z = z at any given random draw. Benefit bk was
also a random variable with a PDF obtained through Monte Carlo
simulation of Eq. (4).
To describe the uncertainty surrounding the group consensus
score for the impact Qik of each target k on each asset/service i, I used
a triangular PDF. Three parameters are required to describe the triangular distribution, the mode (most likely value), minimum, and
maximum. The modeik was equal to the group consensus impact
score. The minimum (minik = modeik 1, 10 6 minik 6 10) and
maximum (maxik = modeik +1, 10 6 maxik 6 10) values of the distribution were specified to reasonably reflect the level of uncertainty. The following function defined the triangular impact PDFs:
PðQ ik ¼ qik Þ ¼
8
2ðqik minÞ
>
ik
>
< ðmodeik minÞðmax minÞ
9
>
for min 6 qik 6 modeik >
=
ik
2ðmax qik Þ
>
>
: ðmax modeik Þðmax minÞ
>
;
for modeik 6 qik 6 max >
ik
ik
ik
ik
ik
ik
ik
ik
ðC5Þ
I then derived PDFs describing the variation in management priority Mi for each asset/service i from the variation in weights over
the 40 decision-makers. However, simulating raw MCA-derived
weights is not straightforward. As the weights for capital assets
and for ecosystem services sum to one (a unit-sum constraint) for
each participant, the data is compositional. The sample space of
compositional data is the simplex S rather than unconstrained real
space R (Aitchison, 1986). In simulation, random sampling from
probability distributions fit to compositional data does not maintain the unit-sum constraint.
To overcome this effect, I used a centred log ratio (clr) transformation to open and normalize the raw MCA-derived weights for capital
assets and ecosystem services. Let X ¼ fxj ¼ ½x1j ; x2j ; :::; xDj 2 SD : j ¼
1; 2; . . . ; ng define the two matrices of compositional raw weights
(capital assets weights and ecosystem services weights) each consisting of 40 rows x1, x2, . . . , x40, with one row per decision-maker
(i.e. n = 40), and D columns X1, X2, . . . , XD (D = 9 for capital assets
and D = 23 for ecosystem services). Each row xj represents manage-
ment priority weights xij for each capital asset/ecosystem service i
for i = 1, 2, . . . , D of each decision-maker j. Weights for both the capital assets and ecosystem services were subject to clr transformation
calculated for each decision-maker (row) j as the natural log of the
raw weights over the geometric mean of the raw weights gD(xj):
xj ¼ clrðxj Þ ¼ ln
xj
g D ðxj Þ
x1j
x2j
xDj
¼ ln
; ln
; . . . ; ln
;
g D ðxj Þ
g D ðxj Þ
g D ðxj Þ
j ¼ 1; 2; . . . ; n
ðC6Þ
and
g D ðxj Þ ¼
D
Y
i¼1
!1=D
xij
!
D
1X
¼ exp
ln xij ;
D i¼1
j ¼ 1; 2; . . . ; n
ðC7Þ
Kolmogorov–Smirnov tests confirmed that clr-transformed
weights for each asset/service over all 40 participants did not differ
significantly from a normal distribution (P < 0.05). I then used a
maximum likelihood estimator to fit Gaussian PDFs P(M = m) to
the column vector of clr-transformed management priority
weights X i of each asset/service i such that:
2 !
1
1 mi li
PðM i ¼ mi Þ ¼ pffiffiffiffiffiffiffi exp 2
ri
2pri
ðC8Þ
where li and ri are the mean and standard deviation of the column
vector of clr-transformed weights X i of each asset/service.
Each iteration in the simulation returned two vectors of simulated clr weights m ¼ ½M 1 ; M 2 ; . . . ; M D 2 RD1 where D = 9 for capital assets and D = 23 for ecosystem services. At each iteration, an
inverse clr transformation was used to return the simulated random management priority variable vector m to the raw simplex
sample space for capital assets and ecosystem services:
1
m ¼ clr ðm Þ
"
#
exp M 1
exp M2
exp M D
; PD
; . . . ; PD
¼ PD
i¼1 exp M i
i¼1 exp M i
i¼1 exp M i
ðC9Þ
Thus, for each simulation iteration m ¼ ½M1 ; M 2 ; . . . ; M D 2 SD
P
and Di¼1 M i ¼ 1 for both capital assets and ecosystem services.
Benefit PDFs were established using 10,000 Monte Carlo simulations of Eq. (4) with each simulation using values for the random
variables of impact Qik and management priority Mi derived from
min
ml
max
the PDFs. The minimum bk , most likely bk , and maximum bk
benefit values were the 5th percentile, mean, and 95th percentile
from the normally distributed benefit PDF simulated for each target k.
B.A. Bryan / Biological Conservation 143 (2010) 1737–1750
Appendix D. Cost, benefit, and background target achievement of management action targets.
1749
1750
B.A. Bryan / Biological Conservation 143 (2010) 1737–1750
References
Aitchison, J., 1986. The Statistical Analysis of Compositional Data, Monographs on
Statistics and Applied Probability. Chapman & Hall Ltd., London, UK.
Alam, K., Rolfe, J., Donaghy, P., 2008. Assessing the cost-effectiveness of water quality
interventions in South-East Queensland. Aust. J. Environ. Manage. 15, 30–40.
Ando, A., Camm, J., Polasky, S., Solow, A., 1998. Species distributions, land values,
and efficient conservation. Science 279, 2126–2128.
Babcock, B.A., Lakshminarayan, P.G., Wu, J.J., Zilberman, D., 1997. Targeting tools for
the purchase of environmental amenities. Land Econ. 73, 325–339.
Balmford, A., Gaston, K.J., Rodrigues, A.S.L., James, A., 2000. Integrating costs of
conservation into international priority setting. Conserv. Biol. 14, 597–605.
Bana e Costa, C.A., Fernandes, T.G., Correia, P.V.D., 2006. Prioritisation of public
investments in social infrastructures using multicriteria value analysis and
decision conferencing: a case study. Int. Trans. Oper. Res. 13, 279–297.
Bode, M., Wilson, K.A., Brooks, T.M., Turner, W.R., Mittermeier, R.A., McBride, M.F.,
Underwood, E.C., Possingham, H.P., 2008. Cost-effective global conservation
spending is robust to taxonomic group. Proc. Natl. Acad. Sci. USA 105, 6498–
6501.
Bottrill, M.C., Joseph, L.N., Carwardine, J., Bode, M., Cook, C., Game, E.T., Grantham,
H., Kark, S., Linke, S., McDonald-Madden, E., Pressey, R.L., Walker, S., Wilson,
K.A., Possingham, H.P., 2008. Is conservation triage just smart decision making?
Trends Ecol. Evol. 23, 649–654.
Bryan, B.A., Kandulu, J.M., 2009. Cost-effective alternatives for mitigating
Cryptosporidium risk in drinking water and enhancing ecosystem services.
Water Resour. Res. 45, W08437.
Bryan, B.A., Crossman, N.D., 2008. Systematic regional planning for multiple
objective natural resource management. J. Environ. Manage. 88, 1175–1189.
Bryan, B.A., Grandgirard, A., Ward, J.R., 2010. Quantifying and exploring strategic
regional priorities for managing natural capital and ecosystem services given
multiple stakeholder perspectives. Ecosystems, accepted for publication.
Cast, A., Hatton MacDonald, D., Grandgirard, A., Kalivas, T., Strathearn, S., Sanderson,
M., Bryan, B.A., Frahm, D., 2008. South Australian Murray Darling Basin
Environmental Values Report. Water for a Healthy Country National Research
Flagship Report, CSIRO.
Church, R., ReVelle, C., 1974. The maximal covering location problem. Pap. Reg. Sci.
Assoc. 32, 101–118.
Connor, J.D., Ward, J.R., Bryan, B., 2008. Exploring the cost effectiveness of land
conservation auctions and payment policies. Aust. J. Agric. Resour. Econ. 52,
303–319.
Crossman, N.D., Bryan, B.A., 2006. Systematic landscape restoration using integer
programming. Biol. Conserv. 128, 369–383.
Crossman, N.D., Bryan, B.A., 2009. Identifying cost-effective hotspots for restoring
natural capital and enhancing landscape multifunctionality. Ecol. Econ. 68,
654–668.
Ehrgott, M., Klamroth, K., Schwehm, C., 2004. An MCDM approach to portfolio
optimization. Eur. J. Oper. Res. 155, 752–770.
Ferraro, P.J., 2003. Assigning priority to environmental policy interventions in a
heterogeneous world. J. Policy Anal. Manag. 22, 27–43.
Gustafsson, J., Salo, A., 2005. Contingent portfolio programming for the
management of risky projects. Oper. Res. 53, 946–956.
Hajkowicz, S., 2007. Allocating scarce financial resources across regions for
environmental management in Queensland. Aust. Ecol. Econ. 61, 208–216.
Hajkowicz, S., 2009a. The evolution of Australia’s natural resource management
programs: towards improved targeting and evaluation of investments. Land Use
Policy 26, 471–478.
Hajkowicz, S., 2009b. Cutting the cake: supporting environmental fund allocation
decisions. J. Environ. Manage. 90, 2737–2745.
Hajkowicz, S., Spencer, R., Higgins, A., Marinoni, O., 2008. Evaluating water quality
investments using cost utility analysis. J. Environ. Manage. 88, 1601–1610.
Hajkowicz, S., Higgins, A., Miller, C., Marinoni, O., 2009. Is getting a conservation
model used more important than getting it accurate? Biol. Conserv. 142, 699–700.
Hanley, N., Barbier, E.B., 2009. Pricing Nature: Cost–Benefit Analysis and
Environmental Policy. Edward Elgar, Cheltenham, UK.
Ho, W., Higson, H.E., Dey, P.K., 2007. An integrated multiple criteria decision making
approach for resource allocation in higher education. Int. J. Innov. Learn. 4, 471–486.
Huang, X.X., 2008. Mean–variance model for fuzzy capital budgeting. Comput. Ind.
Eng. 55, 34–47.
Hughey, K.F.D., Cullen, R., Moran, E., 2003. Integrating economics into priority
setting and evaluation in conservation management. Conserv. Biol. 17, 93–103.
Keeney, R.L., Raiffa, H., 1976. Decisions with Multiple Objectives: Preferences and
Value Tradeoffs. John Wiley & Sons, New York.
Kleinmuntz, D.N., 2007. Resource allocation decisions. In: Edwards, W., Miles, R.F.,
Jr., von Winterfeldt, D. (Eds.), Advances in Decision Analysis: From Foundations
to Applications. Cambridge University Press, NY, USA, pp. 400–418.
Lang, H.J., Merino, D.N., 1993. The Selection Process for Capital Projects. John Wiley,
New York.
Liesiö, J., Mild, P., Salo, A., 2007. Preference programming for robust portfolio
modeling and project selection. Eur. J. Oper. Res. 181, 1488–1505.
Liesiö, J., Mild, P., Salo, A., 2008. Robust portfolio modeling with incomplete cost
information and project interdependencies. Eur. J. Oper. Res. 190, 679–695.
Macmillan, D.C., Harley, D., Morrison, R., 1998. Cost-effectiveness analysis of
woodland ecosystem restoration. Ecol. Econ. 27, 313–324.
Marinoni, O., Higgins, A., Hajkowicz, S., Collins, K., 2009. The multiple criteria
analysis tool (MCAT): a new software tool to support environmental investment
decision making. Environ. Model. Softw. 24, 153–164.
Markowitz, H.M., 1952. Portfolio selection. J. Finance 7, 77–91.
McDonald-Madden, E., Baxter, P.W.J., Possingham, H.P., 2008. Making robust
decisions for conservation with restricted money and knowledge. J. Appl.
Ecol. 45, 1630–1638.
MEA, 2005. Ecosystems and Human Well-being: Synthesis. Millennium Ecosystem
Assessment. Island Press, Washington, DC.
Messina, V., Bosetti, V., 2003. Uncertainty and option value in land allocation
problems. Ann. Oper. Res. 124, 165–181.
Murdoch, W., Polasky, S., Wilson, K.A., Possingham, H.P., Kareiva, P., Shaw, R., 2007.
Maximizing return on investment in conservation. Biol. Conserv. 139, 375–388.
Naidoo, R., Balmford, A., Ferraro, P.J., Polasky, S., Ricketts, T.H., Rouget, M., 2006.
Integrating economic costs into conservation planning. Trends Ecol. Evol. 21,
681–687.
Nelson, E., Mendoza, G., Regetz, J., Polasky, S., Tallis, H., Cameron, D.R., Chan, K.M.A.,
Daily, G.C., Goldstein, J., Kareiva, P.M., Lonsdorf, E., Naidoo, R., Ricketts, T.H.,
Shaw, M.R., 2009. Modeling multiple ecosystem services, biodiversity
conservation, commodity production, and tradeoffs at landscape scales. Front.
Ecol. Environ. 7, 4–11.
Newburn, D., Reed, S., Berck, P., Merenlender, A., 2005. Economics and land-use
change in prioritizing private land conservation. Conserv. Biol. 19, 1411–1420.
Phillips, L.D., Bana e Costa, C.A., 2007. Transparent prioritisation, budgeting and
resource allocation with multi-criteria decision analysis and decision
conferencing. Ann. Oper. Res. 154, 51–68.
Polasky, S., 2008. Why conservation planning needs socioeconomic data. Proc. Natl.
Acad. Sci. USA 105, 6505–6506.
Polasky, S., Nelson, E., Camm, J., Csuti, B., Fackler, P., Lonsdorf, E., Montgomery, C.,
White, D., Arthur, J., Garber-Yonts, B., Haight, R., Kagan, J., Starfield, A., Tobalske,
C., 2008. Where to put things? Spatial land management to sustain biodiversity
and economic returns. Biol. Conserv. 141, 1505–1524.
Prato, T., 2007. Selection and evaluation of projects to conserve ecosystem services.
Ecol. Model. 203, 290–296.
Raymond, C.M., Bryan, B.A., Hatton MacDonald, D., Cast, A., Strathearn, S.,
Grandgirard, A., Kalivas, T., 2009. Mapping community values and risks
towards natural capital and ecosystem services for environmental
management. Ecol. Econ. 68, 1301–1315.
Saaty, T., 1980. The Analytical Hierarchy Process. McGraw-Hill, USA.
Salo, A.A., Hämäläinen, R.P., 1992. Preference assessment by imprecise ratio
statements. Oper. Res. 40, 1053–1061.
Salo, A.A., Hämäläinen, R.P., 2004. Preference programming. Systems Analysis
Laboratory, Helsinki University of Technology. <http://www.sal.hut.fi/
Publications/pdf-files/msal03b.pdf>.
SAMDB NRM Board 2009a. SAMDB Website. <http://www.samdbnrm.sa.gov.au>
(accessed 11.05.09).
SAMDB NRM Board, 2009b. Regional NRM Plan, vol. 1. Strategic Plan 2009–2019.
SAMDB NRM Board, 2009c. Regional NRM Plan. vol. 4. Business Plan 2009–2012.
Sinden, J., 2003. Decision rules, government rules, and the costs of vegetation
protection in New South Wales. J. For. Econ. 9, 1–4.
Somanathan, E., Prabhakar, R., Mehta, B.S., Singh, B., 2009. Decentralization for costeffective conservation. Proc. Natl. Acad. Sci. USA 106, 4143–4147.
Steuer, R.E., Na, P., 2003. Multiple criteria decision making combined with finance: a
categorized bibliographic study. Eur. J. Oper. Res. 150, 496–515.
Steuer, R.E., Qi, Y., Hirschberger, M., 2007. Suitable-portfolio investors,
nondominated frontier sensitivity, and the effect of multiple objectives on
standard portfolio selection. Ann. Oper. Res. 152, 297–317.
Underwood, E.C., Klausmeyer, K.R., Morrison, S.A., Bode, M., Shaw, M.R., 2009.
Evaluating conservation spending for species return: a retrospective analysis in
California. Conserv. Lett. 2, 130–137.
von Winterfeldt, D., Edwards, W., 1986. Decision Analysis and Behavioral Research.
Cambridge University Press.
Wilson, K.A., Carwardine, J., Possingham, H.P., 2009. Setting conservation priorities.
Year Ecol. Conserv. Biol. 1162, 237–264.
Wilson, K.A., McBride, M.F., Bode, M., Possingham, H.P., 2006. Prioritizing global
conservation efforts. Nature 440, 337–340.
Wilson, K.A., Underwood, E.C., Morrison, S.A., Klausmeyer, K.R., Murdoch, W.W.,
Reyers, B., Wardell-Johnson, G., Marquet, P.A., Rundel, P.W., McBride, M.F.,
Pressey, R.L., Bode, M., Hoekstra, J.M., Andelman, S., Looker, M., Rondinini, C.,
Kareiva, P., Shaw, M.R., Possingham, H.P., 2007. Conserving biodiversity
efficiently: what to do, where, and when. Plos Biol. 5, 1850–1861.
Wu, J.J., Adams, R.D., Zilberman, D., Babcock, B.A., 2000. Targeting resource
conservation expenditures. Choices, 33–38 (2nd Quarter).
Wu, J.J., Boggess, W.G., 1999. The optimal allocation of conservation funds. J.
Environ. Econ. Manag. 38, 302–321.