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Ecological Economics 70 (2011) 910–920 Contents lists available at ScienceDirect 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. 912 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. 914 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. 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