Download Biological conservation in dynamic agricultural landscapes

Ecological Economics 70 (2011) 910–920
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Ecological Economics
j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e c o l e c o n
Methods
Biological conservation in dynamic agricultural landscapes: Effectiveness of public
policies and trade-offs with agricultural production
F. Barraquand a, V. Martinet b,⁎
a
b
Centre d'Etudes Biologiques de Chizé, CNRS, 79360 Villiers-en-bois, France
Economie Publique, UMR INRA—AgroParisTech, 78850 Thiverval-Grignon, France
a r t i c l e
i n f o
Article history:
Received 3 March 2009
Received in revised form 28 December 2010
Accepted 28 December 2010
Keywords:
Agriculture
Conservation
Dynamic landscape
Ecological–economic model
Land-use change
Price volatility
a b s t r a c t
Land use change and land management intensification are major drivers of biodiversity loss, especially in
agricultural landscapes, that cover a large and increasing share of the world's surface. Incentive-based agrienvironmental policies are designed to influence farmers' land-use decisions in order to mitigate
environmental degradation. This paper evaluates the effectiveness of agri-environmental schemes for
biological conservation in a dynamic agricultural landscape under economic uncertainty. We develop a
dynamic ecological economic model of agricultural land-use and spatially explicit population dynamics. We
then relate policies (subsidies to grassland, taxation of agricultural intensity) to the ecological outcome
(probability of persistence of a species of interest). We also analyze the associated trade-offs between
agricultural production (in value) and biological conservation (in probability of persistence) at the landscape
scale.
© 2011 Elsevier B.V. All rights reserved.
1. Introduction
Land-use change has been identified as a major driver of changes
in the abundance and geographic distribution of organisms at both
local and global scales (Vitousek et al., 1997). In Western Europe,
agriculture is the most important land use (42% of the surface area)
and – contrary to widespread perception – agricultural areas are
home to a significant share of European biodiversity: up to 20% of the
British, French and German flora (Marshall et al., 2003) and 50% of
bird species (Pain and Pienkowski, 1997). A shift from extensive
agricultural land uses, such as grassland, to intensive cropland has led
to the decline of numerous species of European flora and fauna over
the last 40 years (Benton et al., 2002; Donald, 2001; Krebs et al., 1999;
Robinson and Sutherland, 2002; Siriwardena et al., 1998). Such
declines are worthy of more research on developing efficient
conservation strategies in agricultural landscapes that take into
account land-use change and intensification.
The most commonly used strategy to conserve biodiversity and
habitats worldwide has been the creation of publicly-owned natural
reserves, where optimal spatial design (see Williams et al., 2005, for a
survey), and cost-effectiveness in site acquisition and management
(Naidoo et al., 2006) are the major concerns addressed. However, this
approach is less useful for agroecosystems since land ownership and
land-use decisions are usually private. In these cases, individual landuse decisions can be influenced by incentive-based policies (Lewis
⁎ Corresponding author. Tel.: +33 130815357; fax: +33 130815368.
E-mail addresses: [email protected] (F. Barraquand),
[email protected] (V. Martinet).
0921-8009/$ – see front matter © 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.ecolecon.2010.12.019
and Plantinga, 2007), aiming at modifying practices on working lands
(Feng et al., 2005, 2006; Polasky et al., 2005). In practice, such
incentives are mainly subsidies to favor wildlife friendly agricultural
practices. While an important part of the budget of the European
Common Agricultural Policy has been allocated to schemes that aim at
mitigating the environmental effects of agricultural intensification
(Otte et al., 2007), their effectiveness in reducing biodiversity loss in
agro-ecosystems has been moderate at best (Kleijn et al., 2001; Kleijn
et al., 2006). Many of these agri-environmental schemes have
involved small spatial-scale actions undertaken by private owners
on a voluntary basis (Ohl et al., 2008). Do the benefits of such policies
outweigh their cost? To be consistent with the biological scale of
population dynamics, the effectiveness of such conservation schemes
should be evaluated at the landscape scale (Wu et al., 2004).
Agricultural landscapes are dynamic, as agricultural land-use may
evolve over time. For instance, land-use in a field can alternate
between extensive use (e.g., low-input alfalfa or grassland) and
intensive crops (e.g., high input wheat), depending on the evolution
of the associated profits of land uses. Low-input grasslands are often
favorable habitats for wildlife, while populations decline in intensive
croplands (Donald, 2001); dynamic landscapes represent for most
species a shifting habitat mosaic. The landscape is all the more
dynamic as crop prices are variable over time, and approximating
dynamic landscapes using static ones can lead to overestimation of
species persistence (Hodgson et al., 2010). Accounting for this
dynamic dimension is therefore very important when attempting to
assess the effectiveness of conservation incentives. Including a
dynamic dimension in models evaluating incentive-based policies is
pertinent for environmental agencies, as the cost of reaching a given
F. Barraquand, V. Martinet / Ecological Economics 70 (2011) 910–920
ecological target may be higher in a dynamic landscape, and may
jeopardize the feasibility of subsidy-based programs. It is also relevant
for society as a whole, as conservation incentives modify the
agricultural production performance of the landscape, and therefore
the trade-off between production of agricultural goods and benefits
for wildlife.
In this paper, we aimed to assess the effect of agri-environmental
schemes on species conservation in dynamic agricultural landscapes.
We describe the economic costs of the incentives, and their ecological
benefits in terms of the probability of persistence of the species. We
consider the viewpoint of an environmental agency interested in
weighting the costs and benefits of a given policy, without taking into
consideration what the agricultural landscape actually produces. We
also consider, in a broader perspective, the trade-offs between
agricultural and ecological outcomes at the landscape scale. We
primarily consider positive incentives for favorable habitat in the form
of subsidies to grassland, but also examine an alternative policy of
negative incentives related to unfavorable practices in the form of a
taxation on agricultural input (pesticides or nitrogen for instance).
For this purpose, we have developed a theoretical ecological–
economic model of agricultural landscapes, where land-use may switch
between intensive farming (cropland) and extensive, wildlife-friendly
farming (grassland). We use a stochastic price model to generate
realistic changes in the economic context, and determine optimal landuse decisions by farmers with rational expectations, generating dynamic
landscapes. We consider a biological metapopulation model (i.e., a
collection of local populations linked by dispersal) and assess the
probability of persistence of the species over the simulated scenarios.
First, by considering grassland subsidy as the unique incentive, we
determine the total and marginal costs of conservation (in terms of
subsidy). An accurate estimation of the total cost of a policy is
required to compare its costs and benefits. Even when the monetary
assessment of conservation benefits is difficult, the marginal and total
costs of conservation can still help making informed management
decisions. We compute the cost of the policy as a function of the
subsidy level, and associate a benefit function for the wildlife to the
marginal cost of conservation (as in, e.g., Montgomery et al., 1994).
Sensitivity analyses reveal that species persistence decreases when
either crop price variability or the temporal autocorrelation of
agricultural prices increase. Second, we determine the production
possibility frontier of the dynamic landscape in terms of agricultural
output and ecological outcome. The resulting trade-off can be related
to the wildlife-friendly farming vs. land sparing debate (Green et al.,
2005). Using land-use simulation, Polasky et al. (2005, 2008) showed,
for instance, that it is possible to find landscapes on the Paretoefficiency frontier that obtain a high biological score for only a small
reduction in the economic score. We highlight similar results in the
case of dynamic landscapes, suggesting that wildlife-friendly farming
is also possible in these dynamic landscapes. Third, we consider a tax
on agricultural intensity as an alternative to the subsidy. We show
that these incentives are almost substitutable. Combining incentives
may be of importance when subsidies cannot be increased to levels
high enough for efficient conservation of the focal species.
From a theoretical point of view, our analysis is close to Drechsler
et al. (2007a,b) and Hartig and Drechsler (2009) in that we couple a
biological metapopulation model to an economic model of landowner
behavior. Our focus is however more specifically on conservation in
agricultural landscapes, where we attempt to quantify trade-offs
between economic returns and biological conservation, as in Polasky
et al. (2005, 2008), but in a dynamic context with decentralized landuse decisions.
The remainder of the paper is organized as follows. In Section 2, we
present an overview of the model and our main assumptions. In
Section 3, we describe in more detail the ecological–economic model
linking the farmer's behavior to the biological population through the
agricultural land use. The results of our analysis are presented in
911
Section 4. We draw conclusions in Section 5 and propose future
avenues of research. The technicalities of the model are presented in
appendixes.
2. Model overview
The economic components of our dynamic model describe how
farmers, reacting each year to prices and economic incentives,
determine a dynamic land-use, while the ecological components
describe how this land-use shapes the population dynamics of a
biological species. Our assumptions concerning the economic components of the model are as follows:
• The modeled area is composed of agricultural fields (10 × 10 grid),
and each field can be used either as grassland or cropland.
• The yield of grassland is constant over space, but that of cropland
depends both on the agronomic soil quality of the field, which is
heterogeneous over space and thus between fields, as well as on
input level (fertilizers and pesticides applied for instance).
• Grassland generates a constant revenue which depends on
subsidies. In contrast, the agricultural output of cropland is sold at
market price. The market fluctuations are modeled using a dynamic
system with price auto-correlation and random shocks. Farmers
anticipate prices with rational expectations. Knowing the quality of
their field and anticipated prices, farmers define the annual land use
of their field to maximize the Expected Net Present Value (ENPV),
i.e., the discounted anticipated profit over time, including conversion costs when land use changes.
• Conversion costs represent the extra cost of changing land-use. We
consider them to be asymmetric: converting cropland to grassland
is more costly than the reverse. The conversion cost from cropland
to grassland corresponds to the initial sowing (the grassland is then
lasting), and also includes a loss of revenue the first year because
grass production is initially low with respect to the yield of
following years. The conversion cost from grassland to cropland
corresponds to the extra mechanical work to prepare cropland after
a grassland use with respect to the soil preparation after a cropland
use, and to the required use of herbicide to avoid grass retake.
The ecological components of our dynamic model describe the
evolution of the biological metapopulation (regional scale) over time,
in the dynamic landscape generated by farmers land-use decisions.
We make the following assumptions:
• The biological population is described with a spatially explicit
metapopulation model where subpopulations, whose growth rates
depend on the local land use, are connected by dispersal processes.
As such, we assume that the growth rate of a subpopulation is only
affected by the agricultural field containing it (and not by
neighboring fields), which makes the model applicable only to
small-size organisms, for which a population can be defined at
the field scale. They might be small vertebrates (e.g., very small
Passerine birds or micromammals), insects, or even weeds. We do
not wish to model a particular species.
• Grasslands are favorable to local population dynamics (positive
growth), while croplands are not (negative growth).
• The local (field scale) population dynamics model takes into account
the saturation of the habitat (fixed local carrying capacity) as well as
demographic stochasticity due to small numbers.
• The conservation objective is the persistence of the metapopulation,
and we used the probability of persistence over a fixed time horizon
(100 time units) as our “benefit function” for the ecological outcome
(Arponen et al., 2005; Montgomery et al., 1994).
The next section provides details on the ecological economic
model built on these modeling assumptions.
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F. Barraquand, V. Martinet / Ecological Economics 70 (2011) 910–920
3. Ecological–economic model
We consider an integrated model of agricultural land use and
biological population dynamics. The use of agricultural lands
generates a dynamic landscape. This landscape is the habitat of a
species whose dynamics is modeled spatially. The general model and
results are illustrated using data and parameters from the French
Plaine de Niort case-study, presented in Appendix A.
3.1. Economic model
We consider two types of land use: intensive cropland1 (hereafter C)
and extensive grassland2 (hereafter G). At the field level, land use
decision depends on both expected agricultural commodity price and
exogenous soil quality which influences yield. At the regional level, the
landscape results from the agricultural production decisions for all fields.
3.1.1. Regional soil-quality map
The modeled area is represented by a map of I = 100 identically
shaped, contiguous cells (hereafter fields), set in a 10 × 10 regular
lattice. Each field i = 1, …, I, whose position is defined by its center,
has an area 1 and some inherent fertility or quality Q i reflecting the
local variability of soil quality. For example, Q might represent the soil
depth, or its water supply properties. This quality parameter is
normalized in the range [0, 1]. It is assumed to influence crop yield but
not grassland production.
Soil quality is heterogeneous at the regional level, and this
heterogeneity is taken into account by assuming that Q follows a
Beta distribution, B(α, β). Fig. 1(a) represents a given spatial
distribution of soil qualities at the regional level.
3.1.2. Agricultural yield
At the regional level, minimum yield (Yinf) and maximum yield (Ysup)
are assumed to be known, and the relationship between soil quality and
crop yield is defined by the following Mitscherlich–Baule yield function,
which depends on the exogenous soil quality Q and on the agricultural
intensity f (level of input, e.g., fertilizers or herbicides)3:
−c f
Y ðQ; f Þ = Yinf + Q Ysup −Yinf
1−c2 e 1 :
ð1Þ
Parameters c1 and c2 describe the yield response to inputs: c2
represents the loss fraction of yield when no inputs are used; c1
represents the marginal effect of input on yield. We assume that
farmers know the quality of their field.
3.1.3. Land use rent
The land-use and land-use change decisions depend on the relative
gross return 4 of the alternative land uses: grassland G or cropland C.
If a field is used as grassland (G), the annual gross return on that
field is
πG ðsG Þ = pG + sG ;
1
ð2Þ
Consider for example the rotation wheat/rapeseed/sunflower.
Or perennial alfalfa crop with low input intensity and ecological-friendly practices.
3
See Frank et al. (1990), Llewelyn and Featherstone (1997) and Kastens et al.
(2003). In our approach, soil quality is represented by a single parameter Q, as in
Lichtenberg (1989). The agricultural production function Y(Q) depends on this
parameter in a linear way, which means that Q represents a normalized index of the
potential yield of the field (i.e., the maximal yield that could be obtained when no
other input is limiting). In practice, our methodology could be applied by directly
computing this potential yield for all fields, with respect to fertilizer use and other
agricultural practices, using crop growth simulation tools, like the agronomics models
EPIC (Williams et al., 1989), STICS (Brisson et al., 2002) or CROPSYST (Stöckle et al.,
2003) among others.
4
The gross return is defined as the difference between the product of a hectare per
period, in monetary units, and the specific costs of this production. This does not
include global costs at the farm level.
2
Fig. 1. A soil-quality map and possible resulting land use. (a) Soil quality map generated
with Beta distribution B(1.15, 2.05) (darker colors mean better quality). (b) Landscape
resulting from agricultural land use. Grasslands G are white and croplands C are black.
where pG is the revenue of grassland, which is assumed to be constant,
and sG is the subsidy per unit area of extensive grassland ([euros/ha]).
We assume here that the revenue obtained from extensive grassland
does not depend on the soil quality; costs are included in the revenue.
If a field of quality Q is used as cropland (C), the annual gross
return on that field is
πC ðpC ; Q; f ; τÞ = pC Y ðQ; f Þ−ðω + τÞf −CC ;
ð3Þ
where Y(Q, f) is the crop yield on that field in [t/ha] given by Eq. (1); pC
is the crop selling price per unit produced ([euros/t]) which evolves
over time according to a stochastic process presented below (Eq. (5));
CC represents the fixed costs of cropland (not including inputs)
([euros/ha]), and ω is the per unit input cost ([euros/unit]). The
parameter τ is a tax on the input level, which will be considered nil
except in Section 4.3.
Assuming that farmers maximize their crop profit with respect to
the input level (see Appendix B for the details), using a derivative to
find the optimal input use f⋆(pC, Q, τ), we find the annual crop profit
⋆
⋆
πC pC ; Q; f ; τ = pC Yinf + Q Ysup −Yinf
2
0
ω + τ4
−
1−ln@
c1
p c c Y
C 1 2
inf
13
ω+τ
A5:
+ Q Ysup −Yinf
ð4Þ
F. Barraquand, V. Martinet / Ecological Economics 70 (2011) 910–920
Eq. (4) defines the per area unit profit of cropland on a soil of
quality Q with respect to a given economic price of output pC. It is
interesting to note that this relationship increases with respect to Q,
i.e., the higher the soil quality, the higher the cropland profit.
3.1.4. Price variability and price anticipations
We assume that the market price for the agricultural commodity is
represented by the following stochastic process, accounting for serial
correlation (Deaton and Laroque, 1992). The price level equation is
pt = A + Bpt−1 + ut ;
ð5Þ
where pt − 1 is the agricultural price for previous year; A is the
coefficient of a constant exogenous variable; B is the coefficient term
of autocorrelation; ut is a normally distributed random variable, with
E(ut) = 0. By rescaling Eq. (5) to the average price p, we have
pt −p = Bðpt−1 −pÞ + ut :
Along with the simulated prices, we calculate the corresponding
conditional expectations, which we use to endow farmers with
rational expectations of the next period price:
Et−1 ½pt = ð1−BÞp + Bpt−1 :
More generally, expectations at period t–1 of price in n + 1 periods
are given by
n+1
n+1
p+B
pt−1 :
Et−1 pt + n = 1−B
ð6Þ
913
growth process at the field scale occurs first, and the dispersal
process connecting local populations afterwards. For each time unit,
all economic decisions are made before the population growth and
dispersal processes (which is consistent with agricultural decisions
being taken before the reproductive period of most animals and plants
in spring, if the time unit is one year).
3.2.1. Population growth
The local growth in each field i is modeled according to a Poisson–
Ricker growth model with average:
Et Ni;tþ = Ni;t exp ri;t 1−αi;t Ni;t = K ;
ð8Þ
where the maximum growth rate ri, t depends on the land use of field i
at time t (with only two possible values: rG N 0, or rC b 0) and αi, t is a
correction term with value of zero whenever the growth rate is
negative and one otherwise.7 The Ricker model can generate complex
dynamics (Kot, 2001) but only for large values of r which will not be
considered here, so that it only exhibits saturating population growth.
t+ is a time N t after population growth, but before dispersal occurs.
The demographic stochasticity embedded in the Poissonian variation
around the mean allows for local extinction, we have here
Ni;tþ ∼ Poisson Et Ni;tþ .
3.2.2. Dispersal
The local dynamics within the I fields are linked by dispersal
processes according to
Etþ Ni;t + 1 = Ni;tþ + ∑ Dji Nj;tþ −Ni;tþ ;
j≠i
ð9Þ
Farmers reevaluate their long-run expectations each year.
3.1.5. Dynamic optimization of land use and land-use change
We assume that, at the beginning of each year, farmers opt for a
specific land-use by maximizing their discounted expected profit over
time, accounting for price expectations and all possible land-use
changes. We consider asymmetric land-use change costs (C), i.e.,
CC→G N CG→C N 0.
As land use decisions are made before knowing the actual selling
price, farmers base their decisions upon anticipated prices p̃, defined
by Eq. (6).5 The farmer's optimization problem therefore consists in
maximizing the Expected Net Present Value (ENPV) accounting for
conversion costs,6 and according to the following pseudo formula
which is developed further in Appendix B:
0
max
∞
∑
all land−use sequences t = t0
1
1
B
C
× @πt − Ct A;
|{z}
ð1 + δÞt−t0
ð7Þ
if any
where δ is the discount rate, πt is the anticipated profit for the chosen
land-use and Ct is the conversion cost, if land use changes at time t
along the sequence.
3.2. Ecological model
Population dynamics results from a local, field-scale growth
process with population regulation, and a dispersal process connecting the various sub-populations by exchanging individuals. The
5
The producers are price-takers and local production does not influence prices.
In our model, conversion costs are sunk costs. Land change frictions are
represented by conversion costs. As these costs are asymmetric, our model captures
land use hysteresis: “Land use hysteresis occurs when land converted as a result of
shift in relative returns does not convert back when relative returns revert to original
values” (Schatzki, 2003, p.88). In particular, a conversion from grassland to cropland,
when the price of agricultural output increases from a given low level to a higher one,
may not be converted back when the price decreases to its initial value.
6
where Dji is the proportion of individuals that disperses from field j to
field i as a function of the distance between fields dji (calculated with
respect to their centroids) and that is determined by
Dji = β
f dji
∑k≠i f ðdki Þ
:
ð10Þ
The parameter β is the percentage of disperser individuals in a
field and f is a 2D Gaussian dispersal kernel (integrating to 1)
reflecting the declining
! strength of dispersal with distance;
1
d2
exp − 2 . To prevent edge effects, margins are
f ðdÞ =
2σN
2πσN2
wrapped around so that dispersal happens between fields located at
opposite edges of the lattice (periodic boundary conditions).
Parameters of the biological model are detailed in Appendix A.
4. Results and discussion
Each stochastic simulation of the model yields a prediction of the
numbers of organisms (i.e., the abundance) at both field and
landscape spatial scales. Fig. 2 depicts a typical output of the main
variables of interest over time (evolution of the price and percentage
of grassland, land-use, local and global abundance).
Monte Carlo simulations then allow us to estimate the probability
of persistence with respect to various policy instruments.8 We first
consider the effect of a grassland subsidy, in a cost-effectiveness
analysis. We then describe the resulting trade-off between agricultural production and biological preservation, and compute the
production possibility frontier of the landscape. Lastly, we analyze
7
Such a correction is necessary to ensure that the population always decreases
when local abundance is above the carrying capacity.
8
The probability of persistence is approximated by the ratio of the number of
simulations for which landscape abundance is greater than zero to the total number of
simulation runs.
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F. Barraquand, V. Martinet / Ecological Economics 70 (2011) 910–920
Fig. 2. Dynamics of the system for a given random price scenario. Parameters are presented in Appendix A. Panel (a) presents a specific price evolution over time (blue dashed line),
and the associated proportion of grassland in the landscape (green plain line). Panel (b) shows the associated land use for all fields, with respect to time (black is for cropland and
white for grassland). Some fields (of either very good or very bad quality) have constant land use, while others exhibit land-use change. Panel (c) presents local abundance in five
fields. Time fluctuations are partly due to demographic stochasticity. One can observe local extinction as well as recolonization. Panel (d) presents global population abundance,
which is smoother.
the combined effects of two incentive schemes: subsidies to favorable
habitat and taxes on agricultural intensity.
4.1. Costs and benefits of grassland subsidies
In this section, we examine the effect of a grassland subsidy on the
probability of persistence of the species while also considering the
cost of the subsidy. We use the subsidy level as a parameter and
compute the probability of persistence of the species for a range of
subsidy levels. We then obtain a relationship describing the
probability of persistence as a function of the grassland subsidy.
The curve of probability of persistence vs. subsidy level has a
sigmoid shape (Fig. 3(a)). This convex–concave curve can be
interpreted as an ecological benefit function of the subsidy (Arponen
et al., 2005; Wu and Boggess, 1999): it relates the subsidy to its
ecological outcome, which is the probability of persistence of the
metapopulation. The costs of the conservation measure increase more
than proportionally with the subsidy level, having an almost quadratic
shape (Fig. 3(b)).9
Combining the information in panels (a) and (b) of Fig. 3, we
compute the total conservation cost, and the marginal conservation
cost, defined as the increase in conservation cost per additional unit of
probability of persistence. Fig. 4 gives the total and marginal cost
curves as a function of the probability of persistence.
9
The subsidy level has an almost linear effect on the share of grassland in the
landscape. As total costs are the product of subsidy level and number of grasslands,
one gets an almost quadratic cost function.
Note that the marginal cost is U-shaped. The cost of increasing
persistence is minimal at some intermediate persistence level.
These relationships could form the basis of a cost-benefit analysis
(Montgomery et al., 1994). If the social benefits of the probability of
persistence (in monetary units) were known, the optimal level of
subsidy to grassland would correspond to a level for which the
difference between the total benefit and the total cost is maximum.10
However, as the ecological benefits are not in monetary terms, it may
be difficult to estimate the value of the probability of persistence of the
species. In this case, knowing the marginal cost of a policy provides
relevant additional information as these marginal costs can be
compared to some marginal willingness to pay for conservation
(which is easier to assess than existence value), and used at the margin
of a given policy level to modify it. On its own, the marginal cost curve
gives policy-makers an idea of the opportunity cost of conservation.
We performed a sensitivity analysis of the previous results with
respect to the uncertainty level (price fluctuation magnitude). We
present this sensitivity analysis in Appendix C. It reveals that the
higher the price fluctuation, the lower the probability of persistence
for a given subsidy level. Moreover, the average composition of
landscape (in terms of the average grassland/cropland ratio) does not
change when price uncertainty changes. Since the probability of
persistence is lower when agricultural output price is uncertain over
time, price fluctuation must be accounted for to assess conservation
10
Given the S-shape form of the total cost, the equalization of the marginal cost and
marginal benefit is not a sufficient condition. This would also be the case if the benefit
function (in monetary terms) is a non monotonic function of the probability of
persistence. There may be several local optima (some being minima).
F. Barraquand, V. Martinet / Ecological Economics 70 (2011) 910–920
Fig. 3. Effect of grassland subsidy on the conservation objective, and associated costs.
(a) Probability of persistence as a function of the grassland subsidy level, (b) Total cost
of the conservation policy as a function of the per hectare grassland subsidy level. These
results have been obtained by averaging over 200 repeats for each subsidy level.
policies. The higher the price fluctuation, the less stable the landscape,
and thus the more useful a dynamic ecological–economic analysis
becomes. This result is consistent with general results on metapopulations in dynamic landscapes (Hodgson et al., 2010; Keymer et al.,
2000).
Additional simulations (data not shown) show that increasing crop
price time series autocorrelation has a detrimental effect on the
probability of persistence of the species through increased land-use
change. Such a result could be useful if one considers farmers with
biased estimations of future prices (for example, if they overestimate
the weight of the current price in their anticipation of the future prices).
915
Fig. 4. Cost of conservation as a function of probability of persistence. (a) Data points
are obtained by combining information in both panels of Fig. 3, while the curve is an
order 3 polynomial fitted by the least squares method. (b) The marginal cost of the
measure with respect to probability of persistence has been obtained by differentiating
the fitted curve of panel (a).
levels considered in the previous analysis, we compute the
corresponding agricultural output, which is linked to the previously
computed probability of persistence of the given subsidy level. The
data generated are plotted in Fig. 5, which represents the stochastic
production possibility frontier of the dynamic landscape, and thus the
expected trade-off between agricultural and ecological outcomes.
4.2. Trade-off between agricultural production and biological
conservation
We now consider a more general issue than the direct cost of
population conservation, and adopt a broader economic perspective.
The agricultural landscape may produce two outcomes, agricultural
and ecological. In this section, we describe the trade-offs between
agricultural production and biological conservation, in the spirit of
Polasky et al. (2008). We define the agricultural output (in value) at
the regional level as the sum over all fields of discounted actual profits
(see Eq. (13) in Appendix B), i.e., grassland revenue plus cropland net
profit; subsidies and taxes are not accounted for as they are neutral
from a macroeconomic point of view.11 For all the grassland subsidy
11
We assume that the tax revenues and subsidy costs are shared between farmers
(lump-sum transfers).
Fig. 5. Production Possibility Frontier of the dynamic landscape. Data points have been
obtained with the same simulations as Fig. 3. A polynomial of order 3 is fitted by the
least square method.
916
F. Barraquand, V. Martinet / Ecological Economics 70 (2011) 910–920
The shape of this frontier seems to indicate a limited trade-off
between biological conservation and agricultural output: ecological
outcome may be improved without significantly reducing economic
outcomes. We thus find in another context a result close to that of
Polasky et al. (2008).12 Their approach differs significantly from ours
as we consider landscapes resulting from private agents' decisions,
while they search for the spatial patterns of land-use maximizing one
outcome subject to the level of the other to build the production
possibility frontier. However, they do not examine what would be the
incentives required to obtain these landscapes from private owners
decisions. Our model thus allows us to describe this trade-off, but also
gives us the level of the incentive required to achieve any given
outcome on the Pareto frontier, and have it achieved by the individual
agents thanks to the adequate incentive.
4.3. Increasing grassland subsidies or reducing intensification?
The conservation of biodiversity in agricultural landscapes is the
subject of an on-going debate about whether policy makers should
favor ‘land-sparing’ vs. ‘wildlife-friendly’ farming (Green et al., 2005).
Should agricultural production be intensified in croplands, which
would make it possible to maintain larger protected areas for
biodiversity, or should less intensive agriculture be implemented?
Our model is not specifically designed to tackle this issue. However,
we examine the relative effect of taxation on agricultural intensity
(i.e., use of inputs) vs. subsidies for grasslands, on the economic and
ecological outputs of the agricultural area. Subsidies modify grassland's profit (closer to land-sparing solutions in our model where
grassland is the favorable habitat) while taxes affect input costs
(closer to wildlife-friendly farming solutions).
In this section, we therefore add a tax on agricultural inputs, and
study how it modifies the results of the two previous sections (first
the probability of persistence as a function of the grassland subsidy
level, and then the production possibility frontier between agricultural production in value and the probability of persistence of the
population). We simultaneously consider two policy instruments:
grassland subsidies and input taxation.
Fig. 6 presents the effect of the input tax. Panel (a) exhibits the
effect of the input tax on the probability of persistence. This effect is
similar to that of the grassland subsidy. It is thus possible to combine
the two instruments to address our conservation issue. As shown in
Fig. 6(b), adding a tax on inputs level (fertilizer/pesticide) increases
species persistence for a given grassland subsidy, especially when the
grassland subsidy is low. Note that here, such an effect is conveyed
through an increase in the relative profitability of grassland over
cropland, which results in an increase in the average grassland
percentage (Fig. 6(c)). More direct effects of inputs on the biological
population could have been implemented here, such as a negative
growth in croplands proportional to the input quantity, hastening
local population extinction; we explored that possibility in additional
simulations. For the parameter values we used, these effects were
negligible compared to the effect of the variation in grassland
percentage, and this is the reason why they were not included in
the analysis. However, this might be worthy of further exploration, in
order to deepen our understanding of the relative advantages of landsparing vs. friendly-farming.
The production possibility frontier for various tax levels (Fig. 7)
shows the effect of intensification taxation on the global agricultural
profit, and thus on the trade-off between ecological and economic
outcomes. The tax makes a given subsidy level more efficient, but
lowers the associated economic outcome. However, taxation does not
seem to substantially modify the set of achievable outcomes (the
12
Polasky et al. (2008) considered species richness in a static framework, while we
consider probability of persistence of one species in a dynamic framework.
Fig. 6. Effect of input taxation on probability of persistence (panel a), and modified
effect of subsidy on probability of persistence (panel b) and grassland percentage
(panel c), for various levels of fertilizer tax. (200 repeats).
shape of the production possibility frontier).13 This is a surprising
result for the following reason. Taxes on intensity have a double effect
on agricultural production. First, such taxes reduce the profitability of
croplands and increase the proportion of grassland. Second, such
taxes reduce intensity, and thus the production levels for all
croplands, including those with high soil quality. In comparison, the
grassland subsidy only reduces the proportion of land devoted to
13
Increasing tax however reduces possibility of obtaining high economic outcomes
and increases that of ecological outcome. Note however that taxation does not offer
new achievable outcomes (except that of lower economic outcome associated to a
binding probability of persistence of one, which are not Pareto efficient).
F. Barraquand, V. Martinet / Ecological Economics 70 (2011) 910–920
Fig. 7. Production possibility frontier for several levels of fertilizer tax. Dots are average
over 200 repeats corresponding to one fixed grassland subsidy level.
cropland, without reducing the economic output of croplands. One
could expect that the tax reduce the agricultural outcome. In fact, it
would appear that the effect of the tax is important from a
microeconomic point of view (i.e., at farm level), but not from a
macroeconomic point of view.14
Altogether, the tax acts almost like a substitute for the subsidy
policy.
5. Conclusion
As agricultural land use results from private, and not public,
decision-making processes, incentive policies may be used to
efficiently protect biodiversity in agricultural landscapes. However,
conservation measures have to balance economic and conservation
objectives to gain wider acceptance among both farmers and policymakers. Moreover, the economic context in the agricultural sector is
strongly influenced by market price volatility, and leads to land-use
conversion, which means a more dynamic landscape. This dynamic
aspect makes it harder to assess conservation incentives effectiveness
using only landscape indicators and static biological models.
In this paper, we have developed a dynamic economic model of
agricultural land-use coupled with a meta-population model. We
considered two land uses: grassland which has a positive effect on
local (species) population dynamics, and cropland which has a
negative effect on population growth. Land-use change occurs in
response to fluctuating crop prices. We examined the effect of
incentives for conservation on the probability of persistence of the
species.
First, a cost-benefit analysis of grassland subsidies revealed that
the conservation cost curve is concave–convex, corresponding to a Ushaped marginal cost of conservation. This differs from the usual
economic assumptions of increasing marginal costs and decreasing
marginal returns, but is in line with the ecological theory on habitat
14
We can compare the magnitude of these two effects. At the farm level, the tax
reduces the profit from cropland by some percentage points (about 8% for instance for
a farmer with a field of medium quality, for the mean price of output and a medium
tax). This micro-economic effect induces change in land-use (grasslands are favored).
However, a large part of this loss is related to the cost of the tax, which is neutral from
a macro-economic point of view. The loss in terms of agricultural value (agricultural
production) is small (between one and two percent only, per cropland field). The
global effect on agricultural output, aggregated at the landscape scale, is thus
approximately one percent. This does not significantly modify the (stochastic)
production possibility frontier.
917
amount thresholds for species persistence (Keymer et al., 2000). The
total cost function can be used in a cost-benefit analysis to determine
the optimal conservation level when the social benefit of conservation
is known. The marginal cost function can be used to tune the subsidy
level when marginal willingness to pay is the only information
available. Moreover, the probability of persistence is sensitive to price
fluctuation magnitude, and decreases with landscape instability. This
means that, when assessing the costs and benefits of a policy, one
should account for the dynamics of the system, to avoid underestimation of the risk of meta-population extinction, or overestimation of
the ecological outcomes of conservation policies.
Second, we defined the production possibility frontier (PPF) of the
dynamic landscape in terms of economic and ecological outcomes,
revealing the trade-off between agricultural production (in expected
net present value) and biological conservation (expressed as the
probability of persistence of the species). We find once more in a
dynamic framework the conclusion of Polasky et al. (2008), i.e., that it
is possible to increase the ecological outcome significantly without
heavily impacting the economic outcome. Describing this trade-off is
helpful for decision makers, and will probably be of practical
importance when using models similar to the one presented here,
but with parameters tuned to real-world species. Our framework also
provides the incentive level corresponding to any given ecological–
economic outcome, and thus the way to achieve it.
Third, we examined the joint effect of an incentive for habitat
preservation (grassland subsidy) and an incentive for reducing
agricultural intensity by taxing inputs (e.g., fertilizers or pesticides).
We showed that even in the absence of any direct effect of input
reduction on population growth rates, such a tax could be a substitute
for grassland subsidies.
Our paper is a contribution to the increasing number of studies
that show that ecological–economic modeling is a useful way to
integrate social and natural sciences in order to tackle biological
conservation issues (Cooke et al., 2010). We view theoretical models
as useful tools to help efficient conservation, but however think that a
next stage in model development would be to tune the model to a
particular species and a more realistic landscape in order to estimate
in practice the costs of conservation and the feasibility of the various
policies.
Accounting for ecological dynamics, land-use change, and variability of the economic context has been highlighted as an important issue
by Polasky et al. (2008, p.1521–1522) when defining the trade-offs
between economic and ecological landscape outcomes in the analysis
of conservation measures. Our model is a step in this direction, but a lot
remains to be done. A first limitation, that we do not address in this
paper but is of major importance, is the definition of spatially
differentiated incentives. In our model, a key element in land use
decision is soil quality. Further studies are needed to understand the
relationship between spatial correlation of soil quality and land-use
patterns, and their influence on biological dynamics (e.g., how they
interact with dispersal processes). This should strongly influence
optimal policy design, and should be part of future research on the
matter. A second and more theoretical challenge would be to define
efficient dynamic incentives (“smart temporal incentives”, to rephrase
Hartig and Drechsler (2009)), in response to changes in the economic
context, in order to optimize the intertemporal cost of conservation
policies, e.g., the discounted sum of conservation cost over time.
Acknowledgments
This work has been supported by the French National Research
Agency (Project BiodivAgriM, ANR-07-BDIV-002). We thank Pablo
Inchausti for its involvement in the early stages of the project, Vincent
Bretagnolle for comments on an earlier draft, and the participants of
EAERE 2009 Conference (Amsterdam), BIOECON 2009 Workshop
(Venise), especially Olli Tahvonen and Steve Polasky, for interesting
918
F. Barraquand, V. Martinet / Ecological Economics 70 (2011) 910–920
suggestions. We are grateful to Florian Hartig for insightful comments
on the manuscript, and we are also much indebted to the editor and
two reviewers who provided excellent feedback on how to improve
both the model and the manuscript.
Appendix A. Case-study, data and parameters
Illustrating results have been obtained using data and parameters
from the French Plaine de Niort case study.
Land quality heterogeneity
Each soil quality map is generated using a Beta function distribution
calibrated on French regional soil quality data (see Figs. 1 and 8).
Economic parameters
Parameters are inspired by the Plaine de Niort (Deux-Sèvres,
France) case-study. For agronomic and economic data, we refer to
Girard (2006) and Desbois and Legris (2007). The mean wheat price
in the area is p = 113:42 euros/t (average between 1993 and 2007). In
= 220 euros/t. The
the initial context (2008 data), the price is p2008
C
costs of production (excluding fertilization cost) are cc = 222 euros/
ha. Nitrogen costs are ω = 1.15 euros/kg. We assume that the benefits
for grassland are equal to the opportunity cost of alfalfa, i.e.,
pG = 191 euros/ha (including costs). For the estimation of price
fluctuation parameters, we use the Grilli and Yang (1988) commodity
prices, updated by Pfaffenzeller et al. (2007). Prices are annual and
extend from 1900 to 2003. We use price information on wheat.
Agricultural prices have a positive first order correlation, and this
behavior can be related to the effect of storage that tends to smooth
shocks over several periods (Deaton and Laroque, 1992). This implies
that a period of low (high) prices is most likely to be followed by low
(high) prices. Auto-correlation of wheat price with previous year is
highly significant (at the 1% level), and the coefficient value is
B = 0.559, with a variance residual of 0.058. Fig. 9 exhibits an example
of random price time series.
The Mitscherlich nitrogen response function for wheat is calibrated with the following parameters (Monod et al., 2002): c1 = 0.015 and
c2 = 0.61. In order to adjust the nitrogen response function to the
actual yield level in the considered area, the minimum expected
potential yield of wheat in the area is set at Yinf = 4.8 t/ha (tons per
hectare) and the maximum potential yield is Ymax = 10.8 t/ha.
Land-use conversion costs are estimated at CC → G = 200 euros and
CG → C = 50 euros.
Fig. 9. Random price time series, and the expected price from the initial year.
Biological parameters
The ecological model is adequate for small terrestrial organisms
living in agricultural fields, e.g., small Passerine birds, micromammals
such as voles, insects, or weeds, although in the latter case dispersal
would occur over time (seed bank) rather than space. Of course, no
actual species or environment can be adequately described using such
a crude model; the model aims at generality given the large number of
species inhabiting agricultural habitats. However, we tried to have
meaningful parameter values matching the orders of magnitude
involved in real-world population dynamics. Parameters used to
produce the figures and results have thus been chosen as approximately close to those of Passerine birds (e.g., Arlt et al., 2008;
Siriwardena et al., 1998). The local carrying capacity K is set to 30, the
local growth rate in grassland rG to 0.1 (+ 10.5% increase in
abundance) and in cropland rC to − 0.1 (10.5% decrease in abundance).
Modeling insects would probably require higher growth and decline
rates (e.g., rG = − rC = 1.0); this has been done in additional simulations and does not change qualitatively the results. The percentage of
dispersers β is set to 0.25 (varied in additional simulations, no
qualitative change) and the dispersal range σ to 0.05, so that the
average dispersal range is 1 interpatch distance. A quarter of the
individuals thus disperse; most of them close by. N0, the abundance at
the start of the simulation in each field, was set to K/3.
Appendix B. Economic optimization problem
Computing crop profit
The gross return from cropland depends both on the field soil
quality, which is an exogenous parameter, and on the agricultural
intensity, which is a decision variable. There is a unique optimal
fertilizer use for cropland on a field, which depends on its soil quality
Q and on the price of output (and, when relevant, on the input tax τ).
The optimality condition on the use of input is given by the following
first order condition:
∂πC ðpC ; Q ; f ; τÞ
= 0;
∂f
which implies after some basic computation
0
1
−1 @
ω+τ
A:
ln
f ðpC ; Q ; τÞ =
c1
pC c1 c2 Yinf + Q Ysup −Yinf
⋆
Fig. 8. Soil quality distribution, following Beta probability distribution with parameters
α = 1.15 and β = 2.05.
ð11Þ
F. Barraquand, V. Martinet / Ecological Economics 70 (2011) 910–920
919
Fig. 10. Effect of grassland subsidy on conservation objective, and associated costs, for various levels of crop price variability. Blue (plain) lines are σ = 10, green (dashed) σ = 20, and
red (dotted) σ = 30.
Having characterized input choices, we will henceforth consider
them as (optimally) given, focusing instead on soil quality and its
impact on yields and land use. In particular, using Eq. (11), one can
compute the optimal production level of a given crop on soil quality Q:
Given the initial land use of field i, i.e., 1iLU(t0), the aim of the farmer
is to maximize the expected net present value15:
1
ð1 + δÞt−ðt0 + 1Þ
i
i
⋆
1LU ðt ÞπG + 1−1LU ðt Þ πC p̃t0 ðt Þ; Q ; f p̃t0 ðt Þ; Q; τ ; τ
i
i
i
−1LUC ðt Þ 1LU ðt ÞCC→G + 1−1LU ðt Þ CG→C :
∞
max ∑t = t0 + 1
1iLU ð:Þ
ω + τ
⋆
⋆
:
YC Q; f ðpC ; Q ; τÞ = Yinf + Q Ysup −Yinf −
pC c1
The optimal crop production increases linearly with respect to the
soil quality. One can now define the profit of that crop with respect to
the soil quality:
⋆
⋆
⋆
⋆
⋆
πC pC ; Q ; f ðpC ; Q ; τÞ; τ = pC YC Q ; f ðpC ; Q ; τÞ −ðω + τÞf ðpC ; Q ; τÞ
= pC Yinf + Q Ysup −Yinf
2
0
13
ω+ τ 4
ω+τ
@
A5:
1−ln
−
c1
p c c Y +Q Y −Y
C 1 2
inf
sup
inf
We introduce, for each field i, the boolean land-use indicator
1iLU(t),
(
i
1LU ðt Þ =
0 if
1 if
LU i ðt Þ = C;
LU i ðt Þ = G:
We also introduce the boolean land-use change indicator 1iLUC(t),
(
i
1LUC ðt Þ =
0 if
1 if
LU i ðt Þ = LU i ðt−1Þ;
LU i ðt Þ≠LU i ðt−1Þ:
We denote the anticipated price at year t from year s by p̃s ðt Þ, with
t N s.
ð12Þ
Computing the discounted agricultural profit
We define agricultural production at the regional level as the sum
over the whole landscape of discounted actual profit.
I
1
ð1 + δÞt−ðt0 + 1Þ
× 1iLU ðt ÞpG + 1−1iLU ðt Þ πC pðt Þ; Q i ; f ⋆ p̃t−1 ðt Þ; Q i ; τ ; 0 ð13Þ
W= ∑
i=1
∞
∑t = t0 + 1
:
−1iLUC ðt Þ 1iLU ðt ÞCC→G + 1−1iLU ðt Þ CG→C
Note that optimal input use is determined with respect to the
anticipated price, while the actual profit depends on the actual price
15
The ENPV approach may not be relevant for land use change if conversion is quasiirreversible and affects the return on long periods (e.g., forest land use, in which case
real options approach is more accurate (Schatzki, 2003)), but is a relevant approach
when land conversion is reversible, which is reasonable for grassland conversion as
conversion to grassland affects only next period profit and the cost to convert back to
cropland are not significant. To approximate the infinite time maximum discounted
expected profit, we introduce the following benchmark πC ðQ Þ = πC ðp; Q Þ, which is the
cropland profit for a field of quality Q for the mean price p. Given price expectation
defined by Eq. (6), the expected price converges toward the mean price p. There is
thus a finite time T ≥ t0 such that, for t N T, j p̃t0 ðt Þ−p jb. We compute the discounted
value of constant profits of the alternative land use, i.e., πC ðQ Þ and (pG + sG). This gives
us a terminal condition NPV(T). We then define Net Present Values of both land-use
over time, from t = t0 to T, using Bellman's principle and backward optimization.
920
F. Barraquand, V. Martinet / Ecological Economics 70 (2011) 910–920
for the given scenario. This economic outcome does not include
grassland subsidies or input taxation, as they are considered to be a
lump-sum transfer between agents at the global level. We compute
this agricultural actual Net Present Value along any given scenario. For
any level of grassland subsidy, we then take the mean value over the
scenarios to obtain expected agricultural production for the area, in
discounted monetary terms. We relate this agricultural production to
the survival probability associated with the given subsidy level. This
allows us to represent the trade-off between agricultural production
and biological conservation (Fig. 5).
Appendix C. Sensitivity of the results to the price fluctuation level
Fig. 10 describes the effect of a fixed grassland subsidy on the
probability of persistence for various crop price variabilities (σ).
Higher crop price variability induces lower probability of persistence
(panel (a)). A higher subsidy level will then be required to maintain
the population above a given extinction risk level. Panel (d) shows
that the rate of change in land use is sensitive to the intensity of price
fluctuation, indicating a higher frequency of land use conversion
when prices are more uncertain. Panel (c) shows that the mean
percentage of grassland is not significantly modified by the magnitude
of price fluctuations. The effect of price fluctuation on the probability
of persistence is thus due to land-use conversion, and not to a global
effect on mean habitat suitability. Panel (b) shows that our result on
quadratic costs is not sensitive to the magnitude of price fluctuation.
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