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# GRA Prospectus: Optimizing Protected Areas for Conservation, September 2001 

By David Halsing and Richard Bernknopf

**Open-File Report 02-67**

**2002**

**U.S. Department of the Interior**

**U.S. Geological Survey**

# Introduction[^1]

This Open-File Report is being submitted in accordance with Geographic
Research and Applications (GRA) Prospectus guidelines. It is intended to
be a report on the research activities and progress made in the third
and fourth quarters of fiscal year (FY) 2001, an extension of the
literature review in the March 2001 Open-File Report, and an outline of
the next steps that will be taken in the project. This report is
organized in eight sections. Section 1 gives a general update and
describes the progress made by our collaborators and research partners.
Section 2 reviews important literature found since the last report and
explains how we intend to use it. Sections 3 through 6 describe major
project stages and the research products that are being developed for
each of them. In each section, we first report achievements and then
outline the next steps for each project stage. Section 7 elaborates on
the framework for the Land Use Portfolio Model that was developed for
the previous Open-File Report. Section 8 contains the references for
this paper and other selected references.

# Section 1: Update and Collaborator Progress

The strategy for this project was for the U.S. Geological Survey (USGS)
researchers to use information---including ecological, geographic, and
socioeconomic data---from protected areas created by Conservation
International (CI) as case studies to develop a suite of analytical
tools and methods to improve the site selection and management of
tropical protected areas. The research products would be usable by
managers of those areas, but they would also be adaptable and
transferable to other protected areas that exist or will be created in
the future. Therefore, much of our research depends on the activities of
our research partners. Here, we report on their recent accomplishments.

In June 2001, the Field Museum of Natural History (FM) and Hardner and
Gullison Associates (HGA)---working in conjunction with a Peruvian
conservation group called the Asociación Peruana par la Conservación
Naturaleza (APECO)---completed the establishment of Parque Nacional
Cordillera Azul (PNCA) in the Biabo region of Perú. Unlike the
"conservation concession" approach that was described in the original
proposal and that will be characteristic of efforts by another
collaborator, CI, this protected area was established as a true national
park. Scientific research and some tourism will be permitted there, but
resource extraction will not. PNCA continues to be Peruvian public lands
but, unlike most national parks, was established and will be managed
with private funds (J. Hardner, oral communication, 2001). The park is
over 1.1 million hectares in size and is located in a transition zone
between the Amazon Plain to the east and the foothills of the Andes to
the west. The FM completed a Rapid Biological Inventory (RBI) of the
area, published a detailed report of the geology, geography, ecology,
and biology of the park, and outlined the land use and threats arising
from human activities around the PNCA (Alverson and others, 2001).

The FM also completed and published an RBI of the Pando region of
Bolivia (Alverson and others, 2000), where CI is currently negotiating
the terms of another protected area. For their part, CI and HGA have
also neared completion of a concession-based protected area in Guyana.
Data from that site should begin arriving in early 2002.

The Ecosystem Science and Technology Branch of the National Aeronautics
and Space Administration (NASA) Ames Research Center has also signed on
as a collaborator. Dr. Liane Guild, tropical systems ecologist and
remote sensing scientist, has agreed to provide assistance and technical
expertise in procuring and analyzing remote sensing imagery of these
protected areas. To satisfy NASA's full-cost accounting procedures, this
project's budget request for FY 2002 included funding for Dr. Guild's
participation. Her cooperation will be vital to the remote sensing
aspects of the research products that are described in Sections 3
through 6.

# Section 2: Additional Literature Review

Since the March 2001 Open-File Report was submitted, we have continued
to review the literature on creating and managing protected areas,
measuring and ranking biodiversity, prioritizing conservation efforts,
analyzing and managing risk, determining the economics of conservation,
and exploring remote sensing technologies as used in detecting land
use/land cover change in tropical forests. Here, we summarize three
papers that provide strong conceptual guidance for our project, so that
we can refer to them in Sections 3 through 6 of this report. Section 8
lists other background research that provides data or support but is not
so integral that it needs to be described here.

## Annotated References

Cassel-Gintz, M., and Petschel-Held, G., 2000, GIS-based assessment of
the threat to world forests by patterns of nonsustainable
civilization--nature interaction: Journal of Environmental Management,
v. 59, p. 279-298.

-   This paper details a way of using spatial information in a
    geographic information system (GIS) format to systematically assess
    and rank the risks of forests for anthropogenic degradation or
    destruction. Their study is conducted at a global scale and with
    less detail than we will need to manage risks that face a specific
    area, but their method seems readily adaptable to our purposes. In
    short, the method consists of developing a list of narrowly defined
    threats (that is, land clearing for agriculture, clear cutting for
    timber sales, poaching of wildlife) and using a GIS to demonstrate
    and quantify aspects of the dynamics that are involved in each. The
    goal is to create a relative-risk ranking of each area based on a
    combination of its vulnerability and the value of its resources of
    land uses other than protected forest. Logging for timber sales, for
    example, is most likely in areas that have high vulnerability (good
    roads and/or near a river, little slope) and high desirability for
    loggers (many board-feet per acre, high market price per
    board-foot). Even a readily accessible area will not face this
    threat if it is grassland or scrub, but it might face overgrazing or
    urban development threats. The vulnerability and the desirability of
    each area combine to demonstrate the relative risk of each area and
    can point out areas where conservation efforts, resources, and
    dollars should be directed. We are developing a list of threats and
    measures of both vulnerability and desirability for the case study
    areas and will soon begin setting up the GIS to support this type of
    analysis.

Ramirez-Sanz, L., Alcaide, T., Cuevas, J.A., Guillen, D.F., and Sastre,
P., 2000, A methodology for environmental planning in protected natural
areas: Journal of Environmental Planning and Management, v. 43, no. 6,
p. 785-798.

-   The authors develop a GIS-based method for prioritizing areas for
    protection. A protected area was divided into a matrix of grid
    cells, each of which was evaluated in terms of four
    components/resources: vegetation, fauna, soil, and landscape. Each
    cell was ranked in terms of its "natural value" and "state of
    conservation." The rankings for these components were scored on the
    basis of information extracted from GIS layers---things like slope,
    soil maturity, number of bird species, and forest seral stage, for
    example. This method allows a quantitative assessment of areas for
    protection. Cells with high value and low protection would be first,
    while areas with low value that were not at risk would not be
    aggressively defended. We are currently investigating ways to apply
    this system to tropical forests. We will have to develop a similar
    system to assess both the ecological value and the level of threat
    that various parts of the protected areas face.

Balmford, A., Gaston, K.J., and Rodrigues, A.S.L., 2000, Integrating
costs of conservation into international priority setting: Conservation
Biology, v. 14, no. 3, p. 597-605.

-   The authors investigate different methods of including costs of
    conservation in the allocation of conservation efforts among
    countries. Using numbers of mammal species and estimates of costs to
    adequately protect reserves in 111 countries, the authors compared
    different methods of measuring "protection per dollar spent." They
    compared priority ranking on the basis of absolute species richness,
    richness for endemics, ratio of total species richness to cost, and
    ratio of species endemism to cost. They also ran a linear program to
    maximize species coverage at a range of cost levels. Since
    cost-effectiveness of conservation is the central goal of this
    project, this approach is potentially very useful for us. We would
    have to adapt it from using countries as the unit of analysis to
    using grid cells, watersheds, or some other unit. We would also want
    to substitute some other measure of biological/ecological value
    instead of simply numbers of mammal species.

# Section 3: Remote Sensing and Geographic Information System Database

One of the first steps in this project is the creation of a database in
which to manage and analyze all the GIS information and remote sensing
imagery that have been and will be developed as work progresses on the
PNCA. This database is not simply a storage site for the information.
Rather, it will serve a range of purposes to our research partners and
the agencies responsible for managing the protected areas that have been
or will be established.

First, the principal investigators at the USGS will use this GIS and
remote sensing (RS) data in various statistical and optimization models.
This database currently holds baseline GIS/RS information on the PNCA
and its surroundings. As the literature review above describes, most of
the prioritization and cost-effectiveness analyses we are using as
conceptual frameworks for our research take place in a GIS/spatial
analytical context, so working with our partners to collect and organize
this information was an important first step.

The database currently includes Landsat thematic mapper (TM) imagery
from 1999, 1996, and 1989 (four contiguous scenes per year) that we are
using to conduct a land use/land cover change analysis of the area
surrounding the park for that time period. We have created mosaics of
the scenes and are currently experimenting with vegetation
classification algorithms.

The next steps are to quantify the rate of change and locate the areas
in which land use/cover change has occurred. We have also ordered
several higher resolution SPOT scenes that we will use to assess what
gains this more detailed information can bring. This analysis is a
product in itself and will be submitted for publication, but the
information in the imagery will also be a key component of other project
stages, as described in Section 4.

Our research collaborators will also be making use of the GIS/RS
database in several important ways. The protected-area managers will be
acquiring annual remote sensing imagery to verify that the protected
areas have been maintained as such. As was described in the original
project proposal, the "conservation concession" approach includes annual
payments to the host countries and communities pending such
verification. The imagery that they acquire for this purpose can also be
used to direct management, enforcement, or mitigation efforts to areas
in and around the park where degradation is occurring. While we will be
building tools to improve the efficiency of these efforts, the park
managers will also be using the database to develop and implement
baseline management strategies. We will also be using this annual
imagery to conduct ongoing land use/land cover analyses, measuring
changes in the patterns and dynamics of land use around the park in the
years after its establishment. This will result in another publication.

After its initial establishment, the database will be updated with
information collected regularly by park rangers and/or scientists
working in the protected areas. They will submit these updates to the
principal investigators, who will update the database and use the
information to conduct repeated, more detailed analyses. Our
collaborators and park managers are currently developing the procedures
for the field surveys that will be used to provide these database
updates.

Another long-term goal of the GIS/RS database subproject will be to link
it to the World Wide Web using ESRI's ArcIMS software. This program
allows simple GIS functions and applications to be performed on the Web
without requiring the end user to purchase GIS software or have special
training. The park managers will be able to access the
database---updated with annual remote sensing and periodic field-level
inputs---and adapt their management strategies quickly and wisely.
Putting the GIS/RS information on the Web also makes it accessible to
the general public. Increasing public awareness of conservation efforts,
biodiversity protection, and USGS cooperation with nonprofit
organizations is a positive side benefit of this project.

# Section 4: Cost-Effectiveness of Remote Sensing 

The GIS/RS database that we have created will also form the foundation
for a study of the cost-effectiveness of remote sensing data. Since
financial resources for conservation management are scarce, making the
most efficient use of those resources is crucial. One area where
potential gains in efficiency can be made is in the remote sensing
imagery that is acquired for verification and management purposes. Thus,
we have begun a cost-effectiveness analysis of the various RS
technologies.

The default imagery for the conservation of large areas has been Landsat
TM, and it appears to work reasonably well for this purpose. But we are
investigating whether the informational gains from augmenting or
replacing it with other types of imagery (or changing the frequency of
acquisition) would justify the increased costs of doing so.

Our methodology for this analysis is fairly simple. We are investigating
the spatial, spectral, and temporal resolutions of different RS
technologies to assess the threat-specific ability to detect, recognize,
and analyze susceptibility to different threats. By combining these
abilities with the likelihood of the various threats, we can develop an
index of the utility of each technology in monitoring the protected
area. This yields a measure of "effectiveness," which can be compared
with the known costs of acquiring the data.

Several types of remote sensing technology (SPOT, for example) will be
investigated singly and in combination with others, particularly Landsat
TM, to see if any cost-effectiveness gains can result from this
combination. We wish to determine at which point increased-resolution
data do not lead to substantial new discrimination of features of
interest on the ground. We are also investigating whether targeted or
random higher resolution imagery might bring further efficiency gains.

To date, we have begun acquiring imagery and compiling the costs and
specifications of each. We are developing the list of threats and the
spatial scale at which each takes place and are beginning to work on the
utility index.

# Section 5: Analyses and Methods for Improving Management

Bruner and others (2001) found that parks could be effective at
preventing human impacts, provided that adequate management practices
(this is, patrols, education) could be employed. This project stage
involves conducting a set of analyses for improving the efficiency and
cost-effectiveness of those management procedures in protected areas. We
will do this by developing risk assessment methods and by prioritizing
areas for increased enforcement or mitigation activities.

In the literature review section, we discussed a risk assessment
strategy developed by Cassel-Gintz and Petschel-Held (2000) and
mentioned briefly our plans to adapt it from a global- to a
landscape-level scale, and to include more detail specific to the area
in question. This paper provides a conceptual framework for how to
measure threat-specific risks to an area (for example, threats from land
clearing for cash-crop agriculture vs. for grazing vs. for timber). We
also summarized a paper by Ramirez-Sanz and others (2000) that contains
a method for using information typically available in a GIS to rank the
ecological values of an area on the basis of a suite of characteristics.
Finally, we discussed work by Balmford and others (2000) that sought to
integrate the costs of conservation into the areas that were selected
for protection.

The goal of this project stage is to apply and integrate these three
approaches. We are currently developing a list of threats specific to
the first case study area, the PNCA. We are also beginning to use the
GIS information and the remote sensing imagery we have acquired for
previous project stages to create baseline measurements of the
biophysical factors that can measure those risks. Some of these factors
include presence and quality of roads, extent of navigable rivers,
suitability of the land for grazing or crop agriculture, distance from
population centers, degree of slope, and so on. Each of these factors
can be assessed, quantified and tracked in a GIS format, and used to
develop a measure of vulnerability.

We are also beginning to develop a system for ranking the
ecological/biological values of different regions of the park and its
surroundings. This system will be similar in design to the one presented
by Ramirez-Sanz, but with variables and scores that are adapted to the
local area. Factors here include species richness and rarity, continuity
of habitat, proximity to park borders, and others.

When we have these systems for measuring both the risk factors and the
ecological/biological values of each subregion within the
protected-area, we can begin prioritizing them for enhanced monitoring,
enforcement, and, if necessary, mitigation efforts. Particularly when
combined with Balmford's analysis of different methods for
prioritization, this project stage will produce a very useful set of
methods and tools for managing the risks of protected area failure. We
anticipate that park managers will use these tools to improve management
of the PNCA, but also that the methods will be replicable products that
CI and other conservation agencies could adapt to their reserves by
collecting similar information (spatial and otherwise) to that which we
used.

Finally, in Section 3, we described the GIS/RS database we have
established. As management activities proceed in PNCA, we intend to
update the GIS with reports from workers in the field and to reassess
the risks and values of various sections of the park. Once the framework
is in place and the metrics are developed, adding new information will
be very rapid and simple. This will provide a tight feedback between
management activities and their effectiveness, which should allow
standard practices to evolve and improve. A similar, though less
frequent, dynamic is expected when we update the database with annual
remote sensing imagery.

# Section 6: Site Selection Optimization Study

Though this project phase was the focus of the original proposal, it
became clear when detailed work plans were being developed that this
larger set of research goals would be met more thoroughly and
efficiently by reversing the order of research. We initially planned to
develop a model for optimizing the site-selection of protected areas
first, and tools for improving the management strategies after that, but
the initial case study areas had already been established and site
selection improvements would only be of use to future sites. Further,
our research partners expressed a more immediate interest in tools to
improve their nascent management plans. Finally, many of the subprojects
discussed already in this report develop useful components of this
larger optimization model.

The effort to date on the site-selection optimization models has been to
adapt the Western Geographic Science Center's Land Use Portfolio Model
(LUPM) to this project (Bernknopf and others, 2001). Since PNCA already
exists, we plan to use the LUPM in a hypothetical site-selection
exercise. We will posit, for example, that the entire area that is now
PNCA was available to a conservation organization like CI for inclusion
into a protected area, but that, because of budgetary or other
constraints, the organization had to choose some subportion of the
region for protection. Since we have large amounts of data on the park,
we will develop the decision framework using the LUPM to investigate the
environmental and economic tradeoffs involved in choosing subsections of
the area for protection. Below is a description of how the LUPM can be
applied to site selection in the PNCA. On the basis of this
demonstration, the decision framework will then be exported to other
areas as adequate input information becomes available.

In fact, this demonstration, or *what-if* scenario, is likely to be
close to actual situations that will occur in the future. PNCA is an
extremely large protected area, and normally CI would not be able to
procure such a large stretch of land to include in a conservation
concession. However, the Peruvian Government was eager to demonstrate
its commitment to conservation and made it available at a reduced cost
in exchange for the area being made a national park, rather than a
conservation concession (J. Hardner, 2001, oral communication).
Typically, in setting up concession-based areas, CI will be faced with
higher prices, smaller protected areas, and the prospect of weighing
tradeoffs between competing values and risks. Thus, the model from this
case study area will be useful.

# Section 7: The Land Use Portfolio Model

A goal of any decision support system (DSS) is to use the best science
and apply it in a context for decisionmakers. The LUPM integrates
available scientific information by placing it in a decision framework
that has relevance to decisionmakers (Bernknopf and others, 2001). The
LUPM is a portfolio-based approach to investment decisions in land uses
at regional (or landscape) scale, such as maximizing biodiversity
preservation. The LUPM allows the decisionmaker to compare the spatial
and temporal allocation of lands within a geographic boundary. Within
the LUPM, current land uses are termed assets and have both a stock
value (value of natural or anthropogenic capital) and a flow value
(derived from the dividend or services provided by the stock).

Investments in protection, mitigation, and/or enforcement are modeled as
different risky assets. A particular management plan represents a
portfolio. The results of decisions and actions associated with
preserving a protected area benefit local communities, visitors,
landowners, governments, conservation managers, and donors. These
stakeholders become the "investors." The investment outcome is losses
avoided to ecosystem function, services, and integrity (or attributes).
The stakeholders are assumed to desire the greatest possible return on
investment, but they are uncertain whether a loss of ecosystem
attributes will occur during a fixed time period.

The LUPM approach can be used to provide a suite of portfolios that are
hypothetical land use allocations and protection strategies that
stakeholders can consider and then use to help make land use choices
according to their own preferences. For example, one solution of the
LUPM can prioritize land for acquisition on the basis of human
recreational services and biodiversity, while another solution can
prioritize land for multiple-use development. The two policies are
displayed and analyzed in detail using a GIS.

The LUPM uses regional datasets with minimal field study and thus avoids
the need for site-specific evaluations. Land use threat zones are
developed at a reasonable level of resolution for the characterization
of risk. The approach divides the region into locations *k**K*, each
belonging to one of several land use threat zones *h**H,* where
locations belonging to the same zone each have the same probability of
damage to ecosystem attributes. The variable *h* represents an ordinal
ranking of the characteristics that define the susceptibility of
ecosystem disturbance. The word location refers to the smallest
geographic unit of analysis, which may be grid cells, parcels, or
watershed units.

The variation in threats to biodiversity or other environmental
resources can be represented by landscape features and functions that
have an impact on the existing land use, such as impermeable coverage,
roads, logging, and agriculture. The probability of damage or loss of
attributes must reflect the probability that a specific location in a
particular land use threat zone will experience a specified loss. Let
$q_{h}$be defined as the joint probability of experiencing a disturbance
*p*(*HAZ*) and the probability *p~h~*(*FAIL*) of the disturbance
resulting in loss of environmental values at any location in landuse
threat zone *h*:

$q_{h} = p_{h}(\text{FAIL}) \cdot p(\text{HAZ})\text{.}$ (1)

The LUPM approach to regional risk assessment begins by defining a
protected area as a set of *K* contiguous geographic locations*.* Each
location *k* is assigned to a land use category *j**J* and a land use
threat zone *h*. In general, the term *security* refers to any possible
investment vehicle where expenditure is made and a future receipt or
dividend is expected. Here, a security type *i**I* refers to an
investment in protection in a location belonging to a unique combination
of a land use type *j* and a threat zone *h*. By definition, all
locations of the same security type are in the same hazard zone, meaning
that all locations of the same security type have the same probability
of loss. Therefore, *p~i~*  *p~h\ ~*and *q~i~*  *q~h~*.

The land use portfolio, like an investment portfolio, can contain assets
with a wide range of values and risks. Locations of the same land use
type within the same threat zone can have a wide range of biological
values. Let *V~k\ ~*represent the value of location *k* or an average
value that can be used for all locations. The average value of a
location of security type *i* is defined as$\overline{V_{i}}$, the sum
of all the values of locations of type *i* divided by *K~i~*, the number
of locations of that type. For each location, only one of two possible
future states of nature *s* can occur; *s~k\ ~* = 1 if the ecosystem is
violated and causes loss of value to a location, and *s~k\ ~*= 0 if it
does not.

The return from protection in a particular location is defined as the
value of the environmental attributes that would have been lost if the
protection had not taken place. The probability of damage therefore
determines the distribution of possible returns from investment in
protection. The benefits of protection come with a cost. The cost of
protection comes from land price plus management and enforcement costs
and is assumed to vary by security type. Define *C~i~* as the cost of
protecting a cell of security type *i*. The returns from investment for
all locations of type *i* in each state of nature are an outcome for a
location *O~k~*:

$O_{k} = \begin{array}{r}
\left\{ \frac{0 - C_{i}}{C_{i}} = - 1\text{       if }s_{k} = \text{ 0}\text{.} \middle| \right.\ 
\end{array}$ (2)

The outcome associated with *s =* 0 occurs with a probability of
$1 - q_{i}$*,* and the outcome associated with *s =* 1 occurs with a
probability of $q_{i}$~.~.

The possible outcomes under different states of nature and their
associated probabilities form a probability distribution of the return
from investing in a particular security type. The expected rate of
return of a security *i* is the sum of the rates of returns for the
outcomes weighted by their probabilities:

$E_{i} = \left( \frac{{\overline{V}}_{i} - C_{i}}{C_{i}} \right)q_{i} + ( - 1)(1 - q_{i}) = \frac{{\overline{V}}_{i}q_{i}}{C_{i}} - 1\text{.}$
(3)

The variance is equivalent to the sum of the squared differences between
the outcomes in each state and the expected returns, weighted by their
probabilities:

$\sigma_{i^{2}} = \left( \frac{{\overline{V}}_{i} - C_{i}}{C_{i}} - E_{i} \right)^{2}q_{i} + ( - 1 - E_{i})^{2}(1 - q_{i})\text{.}\text{  }$

> \(4\)

Define the total amount of money invested in a portfolio as budget *B*.
A portfolio can be described by the proportion $\alpha_{i}$ of the
budget invested in each security type *i*:

$\sum_{i = 0}^{I}{\alpha_{i}\text{ = 1}}$ (5)

The expected return for a given portfolio *A* is the weighted average of
the returns for each security multiplied by their proportions:

$E_{A} = \sum_{i = 0}^{I}{\alpha_{i}E_{i}} = \sum_{i = 0}^{I}{\alpha_{i}\left( \frac{{\overline{V}}_{i}q_{i}}{C_{i}} - 1 \right)}$.
(6)

The variance of returns from a portfolio depends on the standard
deviations of its component securities, the proportions invested in each
security type, and the correlation of returns from mitigation in one
location to another. Variance in the return is attributable to sources
such as the susceptibility of the ecosystem to disruption, whether or
not the land threat event occurs, and the variation in the value of
properties of the same security type.

$\begin{array}{r}
\sigma_{A}^{2} = \left( \sum_{i = 0}^{I}\frac{\alpha_{i}{\overline{V}}_{i}p_{i}}{C_{i}} \right)^{2}p(\text{HAZ})\left( 1 - p(\text{HAZ}) \right) + \frac{1}{B}\left( \sum_{i = 0}^{I}\frac{\alpha_{i}{\overline{V}}_{i^{2}}p_{i}(1 - p_{i})}{C_{i}} \right)p(\text{HAZ}) \\
 + \frac{1}{B}\left( \sum_{i = 0}^{I}\frac{\alpha_{i}\sigma_{{V_{i}}^{2}}p_{i}}{C_{i}} \right)p(\text{HAZ})\text{.}
\end{array}$(7)

Choices are modeled as portfolios that can be described and compared by
the distributions of their rates of return.

A stakeholder coalition is assumed to have an existing level of wealth,
*W~0~*, which is equal to a protection budget *B* plus the sum of the
biological values in the geographic area:

$W_{0} = B + \sum_{i = 0}^{I}{\overline{V}}_{i}K_{i}\text{.}$ (8)

Budget funds come from external grants that are contingent on their use
for protection. The stakeholders then choose how to allocate the budget
among the available security types. Each allocation results in a unique
conservation scenario expressed as a portfolio. Each portfolio's
expected return and standard deviation can be calculated and different
portfolios can be compared. Because the region has a geographic
boundary, there are a limited number of "shares" of each security type
available. A portfolio can be described by the fraction of locations in
each security type, *f~i~*, that would be protected under that strategy:

$f_{i} = \frac{\alpha_{i}B}{C_{i}K_{i}}\text{.}$ (9)

A forest health and wealth outcome is dependent on how many locations
experience each state of nature. A protection policy positively affects
this value by reducing risk of loss of ecosystem resources from
specified locations. The expected wealth outcome *EW* for a given
portfolio *A* involves subtracting from *W~0~* both the budget and the
expected losses that remain for all the locations that were not
protected under a specific scenario. The possible wealth outcomes from a
particular portfolio choice for each of the two possible states of
nature are calculated as follows:

$\text{EW}_{A} = W_{0} - B - \left( \sum_{i = 0}^{I}{{\overline{V}}_{i}K_{i}q_{i}\left( 1 - f_{i} \right)} \right)\text{.}\text{     }$

> \(10\)

Expected wealth also has a variance:

![](media/image2.wmf){width="5.0625in" height="0.9923611111111111in"}

\(11\)

For a given budget, the expected wealth outcomes that result from
different conservation scenarios can be compared. The goal is to aid the
investor (that is, a donor and a conservation organization) in deciding
upon a set of land purchases and spatially specific management
investments that maximize expected biological benefits while minimizing
the uncertainty of the projected outcome. The LUPM could be constructed
to solve the constrained optimization problem:

$\underset{k}{\text{min}}\lbrack\text{EW}_{A} - \underset{A}{\sigma}\rbrack$
(12)

subject to: $k > 0$

> $B \geq 0$

The next step in this part of the project is to complete the adaptation
of the LUPM and to conduct a proof-of-concept demonstration in the PNCA.

# Section 8: Selected References

Alverson, W.S., Moskovits, D.K., and Shopland, J.M., eds., 2000,
Bolivia-Pando, Rio Tahuamanu---rapid biological inventories report 1:
Chicago, Ill., The Field Museum.

Alverson, W.S., Rodriguez, L.O., and Moskovits, D.K., 2001, Perú-Biabo
Cordillera Azul---rapid biological inventories report 2: Chicago, Ill.,
The Field Museum.

Aspinall, Richard, and Pearson, Diane, 2000, Integrated geographic
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