Ecological Economics 52 (2005) 219 – 228
www.elsevier.com/locate/ecolecon
ANALYSIS
Economic considerations in the optimal size and number
of reserve sites
Rolf Groeneveld*
Wageningen University, Environmental Economics and Natural Resources Group, PO Box 8130, 6700 EW Wageningen, The Netherlands
Received 28 July 2003; received in revised form 27 May 2004; accepted 18 June 2004
Available online 7 January 2005
Abstract
The debate among ecologists on the optimal number of reserve sites under a fixed maximum total reserve area—the single
large or several small (SLOSS) problem—has so far neglected the economic aspects of the problem. This paper argues that
economic considerations can affect the optimal number and size of reserve sites and should therefore be taken into consideration
in the SLOSS discussion. The paper presents a tractable analytical model to determine the socially optimal number of reserve
sites to be allocated in a farming area under a fixed total reserve area, taking the opportunity costs of nature conservation (in this
case, agricultural profits) into consideration. Furthermore, the effect of land trade and related transaction costs on the socially
optimal number of reserve sites is analyzed. The analysis suggests that in the presence of diminishing returns to farming area,
the socially optimal number of reserve sites (which maximizes social welfare) is generally larger than the ecologically optimal
number (which maximizes an ecological objective such as population viability). When the opportunity costs of conservation can
be offset by land transactions, however, the socially optimal number of reserve sites might be closer to the ecological optimum.
D 2004 Elsevier B.V. All rights reserved.
Keywords: Nature conservation; SLOSS; Reserve design; Transaction costs
1. Introduction
Ecologists have long debated the optimal size and
number of reserve sites under a fixed area budget; this
is known in the ecological literature as the single large
or several small (SLOSS) problem. Diamond (1975)
stated that a single large reserve was preferred over
* Tel.: +31 317 477721; fax: +31 317 424988.
E-mail address: [email protected].
0921-8009/$ - see front matter D 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.ecolecon.2004.06.023
several small reserves (keeping total area equal) for
multispecies conservation, as a large reserve (i) can
hold more species and (ii) will have lower extinction
rates. Subsequent theoretical (Higgs and Usher, 1980)
and empirical (Gilpin and Diamond, 1980) work,
however, suggested that assuming a standard concave
species–area curve, a large number of sites covers
more species than a single large one, given that total
reserve area is constant.
Currently, the debate can roughly be divided into
two parts according to the objective of conservation:
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R. Groeneveld / Ecological Economics 52 (2005) 219–228
(i) the species richness SLOSS problem, which
focuses on the optimal number and, hence, size of
reserve sites that maximizes the number of species
protected, given that the total reserve area remains
constant and (ii) the metapopulation SLOSS problem,
which focuses on the number and size of reserve sites
(given constant total reserve area) that maximizes the
time to extinction or the size of a single species
metapopulation. The work done on the species richness SLOSS problem (see Ovaskainen (2002) for an
overview of these studies) is dominated by empirical
analyses, most of which favor a conservation strategy
with several small reserve sites. Generally, these
analyses suggest that the solution to the species
richness SLOSS problem depends largely on whether
the species found in species-poor biota can also be
found in species-rich biota. If this is so, small habitat
patches typically contain species that can also be
found in large habitat patches, and a single large
reserve site is preferred over several small reserve
sites (Wright and Reeves, 1992; Ovaskainen, 2002).
The metapopulation SLOSS problem (e.g., see
Zavala and Burkey, 1997; Burkey, 1999; Pelletier,
2000; Etienne and Heesterbeek, 20001; Ovaskainen,
2002) has received more attention from theoretical
ecologists than has the species richness SLOSS, as
metapopulation dynamics play a major role in this
problem. Metapopulation theory identifies several
mechanisms in metapopulation dynamics that can
make species more or less vulnerable to fragmentation, suggesting different solutions to the SLOSS
problem. Zavala and Burkey (1997) provide an
overview of these mechanisms. A single large reserve
site might be preferred, for instance, because small
patches have lower carrying capacity and because
small populations will have more inbreeding. Another
important reason why a single large reserve site might
be preferred to several small sites is possible density
dependence of the population growth rate also called
the Allee effect (Allee, 1938). At low population
density, individuals have, for instance, more difficulty
in finding mates. On the other hand, many reserves
and hence many local populations spread the risks of
1
To be precise, Etienne and Heesterbeek (2000) use the term
few large or many small (FLOMS) but indicate that their analysis is
related to the SLOSS debate.
extinction over several locations. After all, if a local
population goes extinct, the site can be recolonized by
individuals from other local populations. Furthermore,
local habitat patches can provide the target species
with refugia from predators and competitors.
Despite Soulé and Simberloff’s (1986) critique that
reality is too complex to make general reserve design
rules applicable, the SLOSS debate has provided
important insights into the effect of habitat fragmentation on metapopulations and continues to do so in
recent publications (e.g., see Etienne and Heesterbeek,
2000; Ovaskainen, 2002). As a straightforward frame
of analysis, the SLOSS setting can serve as a model
for more realistic situations and provide a first step
toward a better understanding of these situations.
So far, however, the SLOSS discussion has
focused on the question what number and size of
reserve sites maximizes ecological benefits without
taking economic aspects into consideration. The
neglect of economic aspects in the SLOSS debate
contrasts sharply with other issues of reserve design,
where ecological and economic aspects are increasingly integrated into a single analysis. A good
example of such integrated analysis is the literature
on how to select a subset of reserve sites from a
larger set of candidate sites to protect as many
species as possible under a fixed area budget.
Generally referred to as the reserve site selection
problem (RSSP), the problem was introduced in the
ecological literature and focused mainly on the
choice of selection algorithm (e.g., see Margules
and Nicholls, 1988; Vane-Wright et al., 1991).
Recently, economists have contributed to this debate,
adding such aspects as land prices (Polasky et al.,
2001), incomplete information (Polasky and Solow,
2001), and uncertainty (Arthur et al., 2002). Recent
cost effectiveness analyses of timber production and
nature conservation (e.g., see Rohweder et al., 2000;
Calkin et al., 2002; Lichtenstein and Montgomery,
2003), where ecological models are integrated into
timber production models, are another example of
integrated ecological–economic analysis of optimal
reserve design. To my knowledge, so far, only
Drechsler and Wätzold (2001) touch upon the
SLOSS issue in their ecological–economic analysis
of the optimal allocation of reserve area under a
fixed area budget. Their analysis focuses on the
allocation of reserve area among two regions under
R. Groeneveld / Ecological Economics 52 (2005) 219–228
several assumptions with respect to the functional
properties of the cost and benefit functions. Their
analysis comes close to an economic analysis of the
SLOSS problem because it analyzes whether one
large reserve site, two equally sized reserve sites, or
an intermediate distribution of reserve area maximizes social welfare.
This paper adds to the existing literature by
presenting an integrated analytical framework of the
SLOSS problem that includes economic, as well as
ecological aspects. The aim of this paper is twofold.
First, it aims to show that economic considerations
should be included along with ecological considerations in the analysis of the optimal number and size
of reserve sites. What matters for decision making is
the number of reserve sites that maximizes social
welfare, considering both the ecological benefits and
the opportunity costs of nature conservation. If the
costs of conservation vary with the number of reserve
sites—which will be the case in a large number of
settings—the social optimum will, in most situations,
differ from the ecological optimum. In demonstrating
these effects, this paper presents a general framework
to analyze the SLOSS problem that includes economic
as well as ecological considerations. The second aim
of this paper is to demonstrate the effect of partly
offsetting nature conservation costs by land trade and
the role of transaction costs in this process. Trade in
land among farmers may affect the opportunity costs
of conservation. As land is taken out of production,
some reallocation of land might occur to offset losses
in agricultural profits. This mechanism might also
have an important impact on the optimal number of
reserve sites under a fixed area budget. The novelty of
this paper is that it focuses on the optimal number and
size of reserve sites in an agricultural area, and that it
allows farms to offset part of the costs of nature
conservation by land transactions that reduce the
production losses in agriculture. It does so in a general
framework of analysis that includes the basic mechanisms at stake and provides scope for more detailed
analysis.
The paper is organized as follows. Section 2
introduces the basic model that includes the main
economic and ecological principles. Section 3 deals
with nature conservation costs that can be partly or
fully offset by land transactions under positive transaction costs. Section 4 concludes the paper.
221
2. The basic model
The problem of the optimal number of reserve sites
under a fixed area budget constraint can be specified
as follows. We seek to maximize social welfare W that
depends on agricultural profits P, as well as some
ecological indicator E. E can be interpreted as the
species richness or population viability of a given
species or a combination of several criteria. The
control variable in this problem is the number N,
which has direct implications for the size H i of an
individual reserve site i=1,. . ., N given that the total
reserve area remains constant2. If we assume that all
reserve sites are of equal size (hence, H i =H̄/N 8i) and
all farms are identical, the mathematical specification
of the problem is as follows:
max W ðP; EÞ
ð1Þ
s:t: P ¼ Pð N Þ
ð2Þ
E ¼ E ð N Þ:
ð3Þ
N
Sections 2.1 and 2.2 discuss the functional form of P
and E.
2.1. The relation between the number of reserve sites
and agricultural profits
Assume a homogeneous area with M̄ farmers,
with each farm initially holding a farm area Ā. Land
can be used for either agricultural production or
nature conservation. Assume all farms have profit
function:
pj ¼ p Aj ;
ð4Þ
where A j denotes the area of farm j. Assuming a
farm can include only one reserve site, we can
distinguish two types of farms: those whose farming
area has been reduced by the placement of a reserve
site and those whose farming area remains unaf2
Many different arrangements have been developed to conserve biodiversity in agricultural landscapes, ranging from imposing
mild restrictions on agricultural land in exchange for annual
payments to purchasing land from farmers and converting it to
reserve land. To preserve tractability, as well as to focus on the
methodological issues at stake, the analysis in this paper assumes a
social planner seizes farm land to convert it to reserve land.
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R. Groeneveld / Ecological Economics 52 (2005) 219–228
fected. The farming area of affected farms is
reduced to:
Aa ¼ A H
N
ð5Þ
where A a denotes the area of an affected farm.
Furthermore, assume for now that affected farmers
cannot buy land to compensate for the loss of
agricultural land (this assumption is relaxed in
Section 3). A specific choice of the number of
reserve sites N then reduces total agricultural profits
to:
P ¼ N p A H þ ðM N ÞpðAÞ:
ð6Þ
N
The first term on the RHS denotes the agricultural
profits generated by affected farms (farms reduced in
farming area by the conservation strategy), and the
second term denotes the profits generated by
unaffected farms. Taking the first derivative with
respect to N and rearranging, we get the following
result:
dP
H
H
H:
¼ p A
pðAÞ þ pV A dN
N
N
N
ð7Þ
The term between square brackets in Eq. (7)
denotes the change in total profits as more farms
contribute land to nature conservation, which is a
negative effect that I will call the number effect. On
the other hand, the second term shows a positive size
effect; as more sites are established, the size of each
site and, therefore, the contribution to nature conservation of each affected farm is smaller. Hence, total
agricultural profits are higher under a large number of
reserve sites (i.e., high N) compared to a small
number of reserve sites (low N) if the size effect
dominates the number effect:
H:
pðAÞ p A H bpV A H
ð8Þ
N
N
N
Fig. 1. If farms have diminishing returns to farm area, the size effect
dominates the number effect.
The size effect can be found by multiplying the
marginal profits of farm area of affected farms by the
size of a single reserve site. Fig. 1 shows that
condition (8) holds if the farms have diminishing
returns to farm area.
Farms can have diminishing returns to farm area
due to differences in environmental quality and
location. It is reasonable to assume a farmer will
devote the least productive patches to nature conservation. I will therefore focus on diminishing returns
to farm area in this paper, but alternative assumptions
regarding the profit function can be analyzed in the
same framework of analysis3. Fig. 2 depicts P as a
function of N under diminishing returns to farm area.
Note that this analysis only considers the case
where there are less reserve sites than farms (NVM̄),
and the total reserve area is smaller than a single farm
(H̄VĀ). If the number of reserve sites (N) exceeds the
number of farms M̄, some farms will include more
than one reserve site. In that case, there are more than
two groups of farms: unaffected farmers, affected
farmers with one reserve site, affected farmers with
two reserve sites, etc. If the total reserve area H̄
exceeds the size of a single farm Ā, we should include
3
Whether this is the case depends on the profit
function of the farms. Fig. 1 depicts the size and
number effect under diminishing returns to farm area.
The number effect in this graph is the difference in
profits between an affected and an unaffected farm.
Assuming homogeneous land quality and ignoring transport
costs, constant returns to scale might also occur. In that case, the
number of reserve sites given a fixed total area would have no effect
on total agricultural profits. Under increasing returns to farm area,
the number effect would dominate the size effect, so that a single
large reserve site might be preferred over several small sites as far as
agricultural profits are concerned.
R. Groeneveld / Ecological Economics 52 (2005) 219–228
Fig. 2. Total agricultural profits P as a function of the number of
reserve sites N for a given size H̄of total reserve area in the absence
of trade and assuming diminishing returns to scale in the profit
function p(A).
the possibility that at least for small values of N a
reserve site can be partially located on one farm and
for the other part on one or more other farms.
However, in both cases, the general intuition still
holds that, under diminishing returns to farm area,
reserve area should be distributed over farms as
equally as possible.
2.2. The relation between the number of reserve sites
and the ecological objective
Although metapopulation theory provides different
possible solutions to the SLOSS problem, the SLOSS
debate suggests at least that there is some number of
reserve sites N E for which the ecological objective E
is at its maximum. For illustrative purposes, I assume
that E is a continuous differentiable function with the
following properties4:
N0 if N bN E
;
ð9Þ
EN ð N Þ
b0 if N NN E
223
single large (SL); (ii) several small (SS), and (iii)
intermediate (IN). The SL strategy implies that N E =1,
and the IN strategy implies N E N1, but it is less clear
what the real-world interpretation of SS should be.
Mathematically, it implies N E approaches infinity,
whereas the size of each individual site approaches
zero. Therefore, in the context of this paper, I assume
that, in the SS strategy, all farms are affected by the
E
establishment of reserve sites (hence, N SS
=M̄). The
marginal ecological effect E N could still be positive at
N=M̄, but a larger number of reserve sites would not
be possible under the assumptions given. Fig. 3
depicts possible curves of E N as a function of N that
satisfy condition (9) for the three possible solutions to
the SLOSS problem.
2.3. Finding the socially optimal number of reserve
sites
Now that the relation has been specified between
the number of reserve sites, on one hand, and
agricultural profits and the ecological indicator, on
the other hand, we can further analyze the optimization problem stated in Eq. (1). To do this, I assume an
additive social welfare function such that the basic
properties of P and E are maintained:
W ¼ U ð E ð N ÞÞ þ V ðPð N ÞÞ;
ð10Þ
where U denotes the social benefits of the ecological
objective E (such as recreational amenities and
existence values) with U E N0 and U EE V0, and V
where E N denotes the first derivative of E with respect
to N. The value of N E is still the subject of the SLOSS
debate and depends on the magnitude of the mechanisms in metapopulation dynamics, which in their turn
depend on the species, the characteristics of the
reserve sites, and the ecological objective (Zavala
and Burkey, 1997; Burkey, 1999; Etienne and
Heesterbeek, 2000; Ovaskainen, 2002). Ovaskainen
(2002) distinguishes three possible outcomes: (i)
4
I use the following notation throughout the paper to indicate
partial derivatives: F x =dF/dx and F xx =d2F/dx 2.
Fig. 3. Marginal ecological indicator E N as a function of the number
of reserve sites N for three possible solutions to the SLOSS
problem: single large (SL); several small (SS), and intermediate
(IN).
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R. Groeneveld / Ecological Economics 52 (2005) 219–228
denotes the social benefits of P with V P N0 and
V PP V0. The first-order condition for the maximum of
W is:
UE EN ¼ VP PN
ð11Þ
Let us call the solution to condition (11) N W.
Because U E , V P, and P N are positive for all values of
N, condition (11) holds only if E N b0, which is true
only for NNN E . Therefore, the number of reserve sites
that maximizes social welfare (N W ) is higher than the
number of reserve sites that maximizes the ecological
objective (N E ), as shown in Fig. 4.
Fig. 4 shows the curves of U N and V N , as well as
the optima N E and N W for two different possible
curves of U N . U N can be interpreted as the marginal
ecological benefits of the number of reserve sites and
U N as the marginal ecological costs. V N can be
interpreted as the marginal agricultural benefits of the
number of reserve sites. Because this graph will be
used also in the next section, I will refer to the curves
of U N and V N as, respectively, the marginal
ecological cost curve and the marginal agricultural
benefits curve.
Fig. 4 shows that, under diminishing returns to
scale, the socially optimal number of reserve sites N W
is higher than the ecologically optimal number N E as
long as N E bM̄. If a single large reserve site maximizes
the ecological objective (i.e., if N E =1), N W might be
lower than if several small sites are preferred, but it
could still be advisable to establish more than one
reserve site as the gains in agricultural profits could
outweigh losses in ecological benefits. Note, however,
that as N is an integer variable, this is not necessarily
the case.
Fig. 4 also shows that the difference between N W
and N E depends strongly on the slope of the marginal
ecological cost and marginal agricultural benefits
curves. In Fig. 4, the curves U Nsteep and U Nflat
depict the marginal ecological costs under two different assumptions with respect to the ecological
function; U Nsteep depicts the marginal ecological
costs if the ecological objective E depends strongly on
the number of reserve sites N, whereas U Nflat depicts
the marginal ecological costs if N has a modest effect
on E. The figure shows that a weak dependence of E
on N allows for a larger number of reserve sites.
The results indicate that the opportunity costs of
conservation are important factors determining the
optimal number of reserve sites under a fixed total
reserve area. Under the given assumptions, more
specifically if farms have diminishing returns to farm
area and if the total reserve area is fixed, the number
of reserve sites that maximizes social welfare might be
larger than the number of reserve sites that maximizes
the ecological objective.
3. Land trade and transaction costs
Fig. 4. Graphical presentation of the first-order condition (11).
Under diminishing returns to farm area, the socially optimal number
of reserve sites N W is higher than the ecologically optimal number
of reserve sites N E . Note that the symbol U Nsteep depicts the
marginal ecological costs if the ecological objective depends
strongly on the number of reserve sites N, whereas U Nflat depicts
the marginal ecological costs if the effect of N on E is weaker. The
figure shows that a weaker dependence of E on N allows for a larger
number of reserve sites.
So far, I have excluded the possibility to offset
reductions in farm area by land transactions. Farmers
might, however, consider trading land to reduce the
negative impacts of the conversion of agricultural land
to reserve land. If N is low (i.e., if only a small
number of farms contribute to nature conservation),
affected farmers are likely to buy land from unaffected
farms to partially offset their production losses. Under
perfect competition, land transactions will equalize
the marginal profits among farms, and any value of N
will end up in a situation where land is distributed
equally. The social optimum N W would be equal to
the ecological optimum N E , and total agricultural
profits would be equal to:
H
P¼P A
ð12Þ
M
R. Groeneveld / Ecological Economics 52 (2005) 219–228
Under positive transaction costs, however, we can
expect that farms will not fully equalize their marginal
profits of land area so that some effect of the number
of sites will prevail. Let T denote the total area of land
traded of which each affected farm buys T/N.
Assuming transaction costs are proportional to T by
a per unit cost s, the total profit function originally
specified in Eq. (6) becomes:
H
T
P ¼ Np A N
T
þ M N p A
sT :
ð13Þ
M N
The land market equilibrium value of T can be
found by solving the first-order condition:
H T
T
pV A s ¼ pV A :
N
M N
ð14Þ
The RHS of Eq. (14) represents the marginal gains
of trade ( G). We can identify three helpful properties
of G as a function of the area of land traded (T) and
transaction costs (s). First, for s=0, the value of T is
such that G is zero. Because we assume identical
concave profit functions, farming areas should also be
equal so we can calculate T by equalizing the
arguments within the marginal profit functions. The
result shows that, in the absence of transaction costs,
T is proportional to the fraction of unaffected farms in
the total number of farms:
M
N
T ð s ¼ 0Þ ¼ H
:
ð15Þ
M
Second, there is a value for s where s becomes too
high for any trade to be profitable. Above this value,
no trade takes place so we can find it by calculating
the marginal gains from trade for T=0:
H
GðT ¼ 0Þ ¼ pV A ð16Þ
pVðAÞ:
N
Third, as G T b0, we know that G(T) is a downward
sloping curve. Fig. 5 shows these three properties of
G as a function of T. Point (A) in Fig. 5 is the point
where T becomes zero, which corresponds to Eq. (16).
Point (B) is the point where T is maximal, and all
farms have equal farm area after trade has taken place,
225
Fig. 5. The marginal gains from trade G as a function of the area of
land traded T. At zero, intermediate (s M ), and high (s H ) transaction
costs, the equilibrium area of land traded is B, T*, and zero,
respectively. As N increases, the curve of G shifts from AB to A1B1,
and the equilibrium area of land traded shifts from T* to T 1*.
which corresponds to Eq. (15). The curve between the
two points denotes the value of G as a function of T.
The figure also shows the equilibrium area of land
traded T*, which is the value of T where condition
(14) holds if s=s M .
Now we can evaluate the effect of a change in the
number of reserve sites N on the equilibrium area of
land traded T* and the location of the points (A and
B). Suppose the number of reserve sites N is increased
to N 1. As G N b0, the curve of G(T) shifts toward the
origin as the number of reserve sites N increases so
that the new curve of G(T) shifts from AB to A1B1.
Consequently, the new equilibrium area of land traded
shifts to T 1*.
In other words, the larger the number of reserve
sites, the lower the amount of land traded to offset
conservation costs. Furthermore, because point (A)
shifts down, a given value of s is more likely to be too
high to allow for any profitable transactions.
These observations are helpful in constructing the
relation between total agricultural profits P and the
number of reserve sites N. Fig. 6 shows the curve of
the marginal agricultural profits with respect to the
number of reserve sites N as a function of N. If
transaction costs are too high (e.g., s=s H ), no trade
takes place. In that case, the curve of total agricultural
profits P is the same as without the possibility to
trade land. If s=s M , there is some cut-off number of
reserve sites N a at which N is just too high for land
trade to be profitable. Therefore, for NbN a , the curve
of the marginal agricultural benefits P N is flatter for
s M than for s H for these values of N. For NNN a , no
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R. Groeneveld / Ecological Economics 52 (2005) 219–228
trade takes place, and the curve is the same as for s H .
If s=0, all marginal profits are equalized so that N has
no influence on P, which is then a horizontal curve at
which P satisfies Eq. (12).
The next step is to construct the social welfare
curve and to analyze how the social optimum N W
depends on transaction costs. Fig. 7 shows the curves
of the marginal social value of the ecological indicator
(U N ) and the marginal social value of agricultural
profits (V N ). The difference from Fig. 4, however, is
that agricultural profits P and, hence, V vary with s.
For prohibitively large values of s (e.g., s H ), trade
is not profitable, and the social optimum remains N W.
If transaction costs decrease to s M , the social optimum
shifts to N W,M . The figure also shows that the
possibility to offset conservation costs by land trade
only has an effect on N W if the cut-off number of
reserve sites N a is higher than the socially optimal
number of reserve sites N W in the absence of the
possibility to trade. This condition in turn implies that
s and N W satisfy the following condition:
H
ð17Þ
pV A W pVðAÞNs
N
Condition (17) can be interpreted as follows. The
LHS denotes the marginal gains from trade G at the
social optimum N W if the possibility to trade is not
taken into account. If the social optimum includes
more reserve sites than the cut-off number (N W NN a ),
G does not satisfy condition (17). In that case, G is
not high enough to make land trade profitable, and the
social optimum remains equal to N W.
Fig. 6. Marginal agricultural profits of N as a function of N for two
different values of s.
Fig. 7. For s=s H , the social optimum remains equal to N W. For
s=s M , the social optimum is N W,M .
This analysis shows that, under the assumptions
given, the possibility to offset profit losses by land
trade lowers the socially optimal number of reserve
sites. Under zero transaction costs, the socially
optimal number of reserve sites might be equal to
the number of reserve sites that maximizes the
ecological benefits. Under positive transaction costs,
however, the socially optimal number of reserve
sites might be higher as land trade cannot offset all
profit losses caused by the establishment of reserve
sites.
4. Discussion and conclusions
In this paper, I have explored the effects of
economic considerations—including agricultural
profit losses, diminishing returns to farm area, land
trade, and transaction costs—on the optimal size and
number of reserve sites under a fixed total reserve
area. The analysis compares three optima. The first
optimum is the ecologically optimal number of
reserve sites defined as the number that maximizes
an ecological indicator under a given total size of the
reserve area. The ecological indicator can be species
richness, time to extinction of a metapopulation, or
expected metapopulation size, depending on the
objectives of the conservation policy. The second
optimum is the socially optimal number of reserve
sites defined as the number of reserve sites that
maximizes social welfare under a given total reserve
area, taking both the ecological indicator and the
opportunity costs of nature conservation into consideration. The third optimum is the social optimum if
R. Groeneveld / Ecological Economics 52 (2005) 219–228
we also take into account that land transactions can
partly offset conservation costs.
The analysis shows that, in the presence of
diminishing returns to farming area, it is generally
recommended that conservation effort be distributed
over farms. Under the assumptions made, this implies
a larger number of reserve sites than suggested by the
ecological optimum. How much larger the socially
optimal number of reserve sites is than the ecological
optimum still depends on the shape of the ecological
and agricultural objective functions and on the
dependence of social welfare on these objectives.
The analysis also shows that land transactions could
offset some of the opportunity costs of conservation.
In the absence of transaction costs, farmers might be
able to offset their profit losses such that the number
of reserve sites under a fixed total reserve area has no
effect on total profits. In that case, the socially optimal
number of reserve sites might be equal to the
ecological optimum. Under positive transaction costs,
the socially optimal number of reserve sites might still
be larger than the ecologically optimal number of
reserve sites.
In the interpretation of the results, the reader
should be aware that the analysis focuses on a
simplified representation of reality, as does the
original SLOSS problem. As Soulé and Simberloff
(1986) point out, the answer to the problem depends
strongly on the situation considered. Local differences
in environmental quality, as well as geographic
variables, such as the distance between reserve sites
and the characteristics of the species involved, are
extremely important for the optimal number of sites.
For the sake of tractability, the analysis assumed that
the area has a homogeneous habitat quality and
excluded the spatial configuration of reserve sites, as
well as the existence of ecological corridors and
stepping stones, in the economic and ecological
relations. Furthermore, for the sake of tractability,
ecological relations are assumed to be smooth,
whereas ecological functions often have discontinuities, threshold effects, and multiple equilibria (e.g.,
see Mäler et al., 2003). Wu and Boggess (1999)
provide an analysis of the effect of threshold effects
on the optimal allocation of conservation efforts. As
regards the economic effects, the analysis assumes
homogeneous farms, whereas in reality, there is a
wide variety of sizes, management, and skills. Lastly,
227
the analysis assumes that a farm can only include one
reserve site, and a reserve site can be established on
only one farm, whereas in reality, planners can locate
large reserve sites on several adjacent patches of land
or several small landscape elements on land owned by
the same farm. This might be necessary in real
planning situations, as the ownership structure in
agricultural landscapes tends to be patchy. Farmers
seldom own a convenient spatial cluster of patches,
and the area of individual farms is often spatially
dispersed. Therefore, whether the general intuition
that conservation area should be distributed over
farms implies a bseveral small sitesQ or bintermediateQ
strategy depends strongly on the spatial configuration
of the farmland. In general, the simplifications
mentioned here can be included in the general
framework of analysis presented in this paper. The
model presented is also capable of including ecological services to farmers, such as pollination and
erosion prevention.
The analysis in this paper shows that the opportunity costs of nature conservation and land transactions are important factors determining the optimal
number of reserve sites under a fixed total reserve
area, as well as metapopulation dynamics. Therefore,
if the SLOSS problem is to provide useful guidelines
for reserve design, it should take these economic
aspects into consideration. The analytical framework
presented in this paper can provide a powerful tool to
integrate additional economic and ecological insights
into the metapopulation SLOSS debate.
Acknowledgements
This paper was written with financial support from
the Netherlands Organization for Scientific Research
(NWO). The author acknowledges useful comments
on this paper by Frank van Langevelde, Ekko van
Ierland, Hans-Peter Weikard, Erwin Bulte, and Henry
Thille. As usual, any remaining errors are the sole
responsibility of the author.
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