Exploiting hysteresis in coordination incentives for cost-effective biodiversity conservation

Abstract

Conservation payment schemes, typically spatially homogenous, are widely used to induce biodiversity-friendly land use. They can also address habitat fragmentation if a bonus is added to the homogenous base payment when conservation measures are implemented next to other conserved lands. However, if conservation costs differ spatially, the spatial aggregation of habitat can be costly, and the cost-effective generation of contiguous habitats is an issue. Here, we use a stylised agent-based simulation model to demonstrate that land use induced by agglomeration bonus schemes can exhibit hysteresis, meaning that the amount and aggregation of conservation is to some extent resilient to changes in payment levels. This suggests that staggered payment schemes in which a relative large bonus is used to establish a habitat network and lowered afterwards to a level sufficient to sustain the habitat network, may be more cost-effective than a scheme with a constant bonus. We show that low base payments and relatively high bonuses can create hysteresis, and staggered payments based on this design principle can—especially at high spatial variation of conservation costs and long-term time preference in the decision maker—generate cost-effectiveness gains.

1. Introduction

Coordination incentives are conservation payment schemes that reward the spatial coordination of conservation efforts, addressing not only the loss of species habitat but also its fragmentation (Nguyen et al. 2023). The first and probably most popular example is the agglomeration bonus (AB) proposed by Parkhurst et al. (2002), which includes, on top of the standard spatially homogenous base payment, a bonus for each adjacent conserved land parcel. By this, landowners are incentivised to carry out conservation activities next to other conserved land, which leads to a higher connectivity of species habitat.

Since 2002, an increasing amount of research papers have been published about the AB. These comprise modelling studies (Bell et al. 2016; Delacote et al. 2016; Iftekhar and Tisdell 2016; Dijk et al. 2017), empirical analyses (Bell et al. 2018; Krämer and Wätzold 2018; Huber et al. 2021), and lab experiments (Parkhurst et al. 2002; Parkhurst and Shogren 2007; Banerjee et al. 2012, 2014, 2016; Parkhurst et al. 2016; Kuhfuss et al. 2016, 2022); for a comprehensive review, see Nguyen et al. (2023).

A major focus of this research is whether and how landowners are able to identify and establish the coordinated land-use pattern envisaged by the conservation agency. The underlying problems here are on the one hand that the (marginal) private benefits of conversation (the conservation payments) depend on the land-use decisions of neighbouring landowners (Albers et al. 2008; Lewis et al. 2009); and on the other hand that the spatial aggregation of conservation efforts can be costly due to the ‘patch selection effect’ coined by Drechsler et al. (2010): that spatial aggregation may require the inclusion of more costly land parcels, constraining the landowners’ options to select the least costly land parcels for conservation.

This leads to a coordination problem in which landowners have to decide between payoff-dominant strategies in which they conserve connected but more costly land parcels, expecting a higher economic benefit due to the bonus but facing a higher risk of economic loss if the neighbouring landowners do not conserve, too; opposed to the risk-dominant strategies in which landowners conserve isolated land parcels that promise a lower expected economic benefit, which, however, is certain.

If the number of land parcels is very large and all landowners are assumed identical except for different but randomly distributed conservation costs, a mean-field approximation, as it is used in the statistical physics of complex systems, reveals bi-stability in the land-use system with two equilibria: one with a high level and one with a low level of conservation, where the former represents the payoff-dominant and the latter the risk-dominant Nash equilibrium (Drechsler 2023a).

Each of these two equilibria is surrounded by a certain domain of attraction so that land-use patterns located in a particular domain will converge to their corresponding equilibrium. For instance, if land-use dynamics under the AB commence with all land parcels in economic use they will converge into the risk-dominant equilibrium, while if they commence with all land parcels conserved they converge into the payoff-dominant equilibrium (Drechsler 2023b).

Such bi-stability and path dependence is also known as hysteresis (Setterfield 2009), a phenomenon first observed in ferromagnetic materials like iron in which the level of magnetisation depends on whether an external magnetic field had been increased from a low value or decreased from a high value. Similar collective phenomena can occur in economic systems, too. An example are financial markets in which each agent can make a binary choice (such as being long or short on an asset), which is influenced by a collective variable, the ‘sentiment’, which is the average of the binary choices over all agents (Grinfield et al. 2009). Each agent's choice is influenced by that sentiment.

Hysteresis has been observed in various natural and social systems, which all have in common that individuals interact within some network and are affected by external drivers, such as the growth rate of a renewable natural resource (Sugiarto et al. 2015), the salary paid by an employer (Rios 2017), the reproduction number (modifiable, e.g., through a vaccination program) of spreading contagious diseases (Chen 2018), environmental conditions experienced by species populations (Cai et al. 2020), and the predisposition to adopt a particular social behaviour (Wiedermann et al. 2020).

In all these examples, each individual can assume one of out of a few (often: two) different states. Transition from one state to another depends on the states of the other individuals. Applying an external driver like those mentioned above induces all or most of the individuals into the same state or individual behaviour, implying some macroscopic, collective behaviour of the system as a whole. Due to the interactions between the individuals, the collective behaviour (largely) prevails even if the external driver is reduced or removed.

Here, we use a stylised agent-based simulation model to study hysteresis in a land-use system subject to an AB. The external driver is the bonus that is varied over time. We explore how the magnitude of hysteresis depends on the spatial distribution of the conservation costs, and how it can be controlled by the choice of the sizes of base payment and bonus. We measure hysteresis with respect to the proportion and the spatial aggregation of species habitat (conserved land), both of which are key determinants of biodiversity.

While the value of exploring hysteresis in an AB may be regarded as somewhat academic, a practical implication emerges if one wonders whether this phenomenon can be exploited to make the AB more cost-effective. The basic idea here is to design a staggered payment scheme in which the bonus is initially set at a rather large level, in order to induce a land-use pattern with a high level of conservation. After that the bonus is reduced, with the hysteresis preventing the conservation level dropping overly. The question is whether such a scheme that initially incurs high expenses to the conservation agency in the beginning but lower expenses in the long run, achieves a given level of conservation over time at lower overall expenses than a static scheme with a constant bonus. Similar to the above ‘academic’ analysis, we explore the potential cost-effectiveness gains (with respect to the proportion and the spatial aggregation of conserved land) of the staggered scheme as a function of the distribution of the conservation costs and the conservation agency's time preference.

The simulation model is grid-based, where each grid cell represents a land parcel that can be conserved or used for economic use. Related to the experiment by Parkhurst and Shogren (2007) and similar to simulation studies such as Bell et al. (2016), the simulation starts with all land parcels in economic use. With perfectly rational but myopic landowners responding to the payment scheme, land parcels switch to conservation and time step by time step a more or less connected pattern of conserved land parcels establishes.

The paper is structured as follows. Section 2 introduces hysteresis in the AB by a numerical and a simulation example. Section 3 presents the simulation model and the systematic analysis of hysteresis, which leads in Section 4 into the introduction of the staggered payment scheme and the analysis of its cost-effectiveness. The results of Sections 3 and 4 are discussed in Section 5 before the paper concludes with some policy implications in Section 6.

2. Hysteresis in the AB

2.1 A simple analytical model

To demonstrate how hysteresis can emerge in the AB, consider three land parcels, i = 1, 2, 3, arranged on the corners of a triangle, so that each land parcel has the two respective others as its direct neighbours. Each land parcel can be conserved (x_i = 1) or used for economic purposes (x_i = 0), where conservation incurs a cost (e.g., forgone economic revenues) c_i. Without loss of generality, c₁ < c₂ < c₃.

Initially, all three land parcels were used economically. To induce conservation, a conservation agency offers for each conserved land parcel a base payment p, plus a bonus b for each neighbouring land parcel that is conserved, too. Assuming rational profit-maximising landowners, a land parcel is conserved if and only if the sum of base payment and bonus(es) exceeds the cost c_i.

Consider all land parcels in economic use, and a base payment and a bonus that obey the following constraints:

Assume that the only information available to the landowners is their neighbours’ land use, and that the landowners act myopically, not communicating with their neighbours (about intended land-use choices) nor showing strategic behaviour. Under this assumption, landowner 1 will conserve but the others do not because their costs exceed the base payment p [eq. (1a)].

Now assume a second round of play (or period of conservation contract) in which landowners can adapt their land use. Since neither costs nor payments change, landowner 1 will stay with conservation, and (assuming perfect rationality in all landowners) landowner 2 can be sure about that. So, landowner 2 now has one conserving neighbour and conservation would earn a total payment of p + b—which exceeds the cost c₂ of landowner 2 [eq. (1b)]; while the cost c₃ of landowner 3 exceeds p + b [eq. (1b)], so landowner 3 will stay with economic use.

Only in a third, and last, round will landowner 3 observe two conserving neighbours (and can, with the above argument, be sure that this will remain so), raising the payment for conservation to p + 2b, which exceeds c₃, so landowner 3 conserves, too—representing a stable Nash equilibrium. Combining eqs. (1b and 1c), the necessary and sufficient condition of this equilibrium emerging is

with

Now disregard the path into this Nash equilibrium, and just assume that all three land parcels are conserved. What conditions must the bonus b fulfil for this state being a stable Nash equilibrium? For this, consider the payoff matrix of landowners 2 and 3 in Table 1 [landowner 1 always conserves due to eq. (1)].

Comparing the payoffs reveals that the equilibrium is stable if and only if p + 2b > max{c₂, c₃} = c₃, implying the bonus b must exceed

Comparing with eqs. (2) and (3) reveals that b** is smaller than b* by the amount

Thus, if the base payment p is not too large and the cost c₃ is not too large compared to c₂, so that Δ > 0, the bonus b** required to maintain the coordinated Nash equilibrium is smaller (by the difference Δ/2) than the bonus b* required to establish it. This is effectively hysteresis, so that the level of an external driver (external magnetic field in the case of ferromagnetism, the salary in Rios (2017), or here: the bonus) required to establish a certain state (high level of magnetism, many employees showing a high work performance, large number of conserved land parcels) is higher than the level required to maintain it.

2.2 Simulation model

The following demonstration and the further analyses in this paper are based on a stylised spatially explicit simulation model. We consider a model landscape with 30 ×30 land parcels i, arranged on a square grid with periodic boundary conditions, each of which may be conserved (x_i = 1) or in economic use (x_i = 0). Conservation incurs a cost c_i, for example, in terms of additional equipment or labour required or reduced agricultural productivity that may in addition be influenced by non-pecuniary motives such as personal attitudes towards biodiversity. These costs are randomly sampled from a normal distribution with mean 1 and standard deviation σ. To account for this randomness, the analyses in Sections 3 and 4 are based on a large number of replicates, each considering a randomly sampled cost landscape. To offset the conservation costs, a payment

is offered for each conserved land parcel i, where p is a spatially homogenous base payment and b an additional bonus that is paid for each conserved land parcel in the Moore neighbourhood M_i, that is, within the eight adjacent land parcels around parcel i. Landowners change use of a land parcel from economic to conservation if and only if the payment p_i exceeds the conservation cost c_i.

After such a change, some of the economically used land parcels will have more conserved neighbours, increasing their p_i, so some of them will change to conservation, as well. These land-use dynamics continue until a final, static state is reached, which mimics observations from corresponding real-world experiments (Parkhurst and Shogren 2007).

For the hysteresis experiments, the simulation starts from an economically used landscape (x_i = 0 for all i), and a payment p and a bonus b₁ offered to conserving landowners. The proportion q(b₁) and spatial aggregation γ(b₁) of conserved land parcel are determined in the steady state, where

is the average proportion of conserved land parcels in the (8-cell) Moore neighbourhood of conserved land parcels.

From the steady state, the simulation is continued with a reduced bonus b₂ < b₁ until again a steady state is reached and the proportion and aggregation of conserved land parcels, q^↓(b₂) and γ^↓(b₂) recorded.

Instead of the ‘detour’ via the bonus b₁ and conservation levels q(b₁) and γ(b₁), one could apply the bonus b₂ right-away to the economically used landscape. The proportion and aggregation of conserved land parcels in the steady state may be denoted as q^↑(b₂) and γ^↑(b₂), where the up-arrow indicates that q^↑(b₂) and γ^↑(b₂) have been reached from q = γ = 0, while the down-arrow indicates that q^↓(b₂) and γ^↓(b₂) have been reached from the larger q(b₁) and γ(b₁), respectively. We are interested in the spreads

between the two levels of q(b₂) and γ(b₂) (the notation q^↓(b₂|b₁) indicates that q^↓(b₂) actually depends on the level of b₁ that had been applied before reduction to b₂; analogous for γ^↓(b₂|b₁)). A numerical example is shown in Fig. 1. A high bonus b₁ = 0.7σ is applied during the first twelve time steps. Clusters of conserved land parcels emerge gradually. In time step t = 13, the bonus is reduced to a level b₂ = 0.45σ, implying that the payment p_i is reduced and for some land parcels falls below the cost c_i—which reconvert to economic use. Conserved land parcels in the neighbourhood of these reconverted land parcels lose conserved neighbours, and for some of these the p_i drops below c_i, too, so in t = 14 these land parcels reconvert to economic use, too. This process of reconversion proceeds until a steady state is reached in which no other conserving landowner has an incentive to reconvert.

Altogether, the reduction of the bonus from b₁ to b₂ has reduced the proportion and aggregation of conserved land parcels to q^↓(b₂) and γ^↓(b₂). However, had the same bonus b₂ been applied to an initially economically used landscape (without the detour via the larger b₁) the proportion of conserved land parcels would have increased only to smaller values q^↑(b₂) < q^↓(b₂) and γ^↑(b₂) < γ^↓(b₂). Obviously, the spatial interaction between the landowners in the sense that their profits depend on the land use of the neighbours, introduces some inertia in the system that prevents q dropping down all the way to q^↑(b₂) and γ^↑(b₂).

3. Comprehensive simulation analysis of the hysteresis in the AB

3.1 The ‘way up’: establishment of a habitat network (bonus b₁)

The example of Fig. 1 considers two levels for the bonus, a high level of b₁ = 0.7σ that is applied in the upper row of the figure and a low level of b₂ = 0.45σ that is applied in the lower row. The bonus levels here are scaled in units of the cost variation σ because a doubling of σ, for example, has the same effect as a doubling of b₁ (see Online Appendix A). Similarly, the base payment is measured in units of σ relative to the mean cost (equal to one). The reason is that (with zero bonus) the proportion of conserving landowners is just the quantile of the cumulative distribution of the conservation costs and depends only on how many standard deviations the payment is above or below the mean cost (cf. Online Appendix A). For instance, a homogenous payment of size 1−2σ (as applied in Fig. 1) induces the conservation of about 2.5 per cent of the land parcels. These settings strongly simplify the model analysis because σ does not have to be considered explicitly.

Figure 2a shows the proportion q and aggregation γ of conserved land parcels in the Nash equilibrium as functions of the bonus b₁. One can observe, with increasing b₁, a more or less sharp transition between a landscape with few and spatially dispersed conserved land parcels to a landscape with many and spatially aggregated conserved land parcels.

Especially for b₁ below that transition, the spatial agglomeration γ exceeds the proportion q of conserved land parcels. To interpret this observation, note that in a totally random allocation of the conserved land parcels the expected proportion of conserved neighbours is γ = q. So a spatial agglomeration of γ = q is a mere ‘statistical’ effect and does not indicate any ‘bonus-induced’ agglomeration. That bonus-induced agglomeration is measured by the surplus

In Fig. 2a, one can see that Γ (i.e., the difference between solid and dashed lines) first increases with increasing b₁ and then decreases, so that it assumes a maximum Γ_max at a bonus level denoted as b₁(Γ_max) (in the example of Fig. 2a, Γ_max ≈ 0.14 and b₁(Γ_max) ≈ 0.63). As Fig. 2b shows, both Γ_max and b₁(Γ_max) decline with increasing base payment p, so high levels of bonus-induced agglomeration Γ are obtained only for small base payments; and the level b₁(Γ_max) at which that bonus-induced agglomeration is maximised declines, too, if the base payment is increased.

3.2 The ‘way down’: partial disintegration of the habitat network (bonus b₂)

Now consider the equilibrium obtained by a base payment of p = 1−2σ and a bonus of b₁ = 0.7σ (as in Fig. 1B upper row), with proportion q(b₁) = 0.78 and aggregation γ(b₁) = 0.95 (right vertical dashed lines in Figs. 3a, b) and reduce the bonus to values b₂ < b₁ (move along the red lines from upper right and lower left). For the example of b₂ = 0.45σ (left vertical lines), we obtain q = 0.58 and γ = 0.82.

In contrast, had the same bonus level of 0.45σ been offered in a landscape with all land parcels in economic use the proportion and aggregation of conserved land parcels would have been only q = 0.04 and γ = 0.17, respectively. The difference between the two values is the spread defined in eq. (8), which equals H_q = 0.58−0.04 = 0.54 (green double arrow in Fig. 3a) and H_γ = 0.82−0.17 = 0.65 (green double arrow in Fig. 3b). The fact that the red lines are always above the blue lines indicates hysteresis in the land-use system. The letter H in eq. (8) for the spread between upper and lower conservation levels as a function of b₁ and b₂ was chosen as a reference to that feature.

In this manner, H_q and H_γ can be calculated for all other levels of b₂ between 0 and b₁. Clearly, the levels of the H_q and H_γ for given b₂ depend on the level of b₁ (the upper-right ends of the red lines in Fig. 3). The full dependence of H_q and H_γ on b₁ and b₂ is shown in Fig. 4. High levels of H_q and H_γ are achieved only if b₁ had been raised to a sufficiently large value above ca. b₁^(min) ≈ 0.7σ (bluish areas right to the vertical white lines in Fig. 4), where b₁^(min) is defined as the level of b₁ that reduces H to half of its maximum value H_max.

After that critical value has been reached, H_q and H_γ do not change much with a further increase in b₁. There is a wide range of values b₂ (vertical width of the bluish areas) that are associated with large H_q and H_γ. Maximum values of H_q and H_γ are observed about in the middle of these areas at b₂(H_max) ≈ 0.55σ and b₂(H_max) ≈ 0.48σ for q and γ, respectively (upper horizontal white lines in Fig. 4).

3.3 More comprehensiveness to the model results

As the last step towards a comprehensive model analysis, note that the results of Fig. 4 were obtained for a particular base payment of p = 1−2σ and may change if that base payment is changed. Figure 5 shows that for both, q and γ, the maximum level of H, as well as the associated b₂(H_max) and the levels of b₁^(min) and b₂^(min) decline with increasing base payment p. The reason for the decline in H_max with increasing p is that the bonus-induced aggregation Γ [eq. (9)] declines with increasing p (Fig. 2b). And it is this latter quantity that measures the overall strength of the landowners’ interaction and inertia of the habitat network. As a confirmation, note the strong quantitative similarity between the b₁(Γ_max) in Fig. 2b (green line) that leads to maximum bonus-induced aggregation and the critical bonus b₁^(min) in Fig. 5 (green lines) beyond which hysteresis is observed.

3.4 Spatially correlated conservation costs

The analyses in Section 3 indicate that the hysteresis is a product of the bonus-induced aggregation (Γ) of conserved land parcels. This is likely to depend on the spatial distribution of the conservation costs. If these are spatially correlated, aggregation of conserved land parcels is—at least—partly created through an aggregation of conservation in the ‘valleys’ of the cost landscape and to a lesser extent through the bonus. So we hypothesise that Γ and H decline with increasing cost correlation.

Figure 6a shows that for spatially correlated costs the spatial aggregation γ of conserved land parcels is 0.4 even for zero bonus b₁. If we measure γ for non-zero b₁ relative to that value (dash-dotted line) the difference Γ between that aggregation and the proportion of conserved land parcels is much smaller than that in Fig. 2a. This leads to reduced spreads H_q and H_γ (Fig. 7).

4. Exploiting hysteresis for cost-effectiveness gains

4.1 Methodology

If there is hysteresis in the land-use system so that the bonus can be reduced without overly losing conserved land parcels one might consider a staggered payment scheme in which a relatively large bonus b₁ is applied temporarily to generate a habitat network with many conserved land parcels, and once this habitat network has established the bonus is reduced to b₂ < b₁ and kept at that level once and for all. Compared to a static payment scheme in which a constant bonus b₀ is applied throughout, the first phase would incur higher and second phase would incur lower expenses to a conservation agency.

This question represents a classical inter-temporal trade-off: Should one invest now to save later, or not? Which of the two choices should be preferred depends, among other things, on the time preference of the decision maker. If the decision maker is interested only in the short term, she will prefer the static scheme. In contrast, if she is interested in the long term, she may prefer the staggered scheme.

To model the decision maker's time preference, we consider the present values of the (time t dependent) proportion of conserved land parcels q = q(t), their aggregation γ(t) and the budget B(t):

with discount rate δ. The budget covers the conservation agency's expenses for the base payment p and the bonuses b_k (where k = 0 for the static scheme, and k = 1 and k = 2 for the first and second phases of the staggered scheme, respectively):

By the factor 1/N in eq. (11) the budget is measured per land parcel. To calculate the cost-effectiveness gains G_q and G_γ of the staggered over the static payment scheme, we identify for each scheme type the combinations of base payment and bonus(es) that maximises the benefit-cost ratios

These ratios are determined for static and staggered schemes {p, b₀} and {p, b₁, b₂} with p ∈ [1−3σ, 1] and b_0,1,2 ∈ [0, σ], where for the staggered (static) scheme the scheme parameters p and b_0,1,2 are varied in 100 (40) equidistant steps. The lower bound of the base payment, p = 1−3σ, means that the base payment is three standard deviations below the mean conservation cost, which implies that, statistically, only ca. 0.1 per cent of all land parcels have costs below p (cf. Fig. A1). To encompass the randomness in the sampled cost landscapes (cf. Section 2), averages over 20,000 (static scheme) and 5,000 (staggered scheme) replicates are considered. The resolution of the scheme parameters and the number of replicates were chosen to optimise the trade-off between the minimisation of output stochasticity and computation time.

For the present value budget PV_B, a range of [0, 0.5/δ] is considered. Noting that 1/δ would be the budget required to conserve half of the land parcels through a homogenous payment scheme (with p = 1), a value of 0.5/δ is quite large compared to typical budgets in real biodiversity conservation instruments.

This chosen budget range is split into 50 equidistant intervals. For each of these budget intervals the static and staggered schemes are determined that maximise the benefit-cost ratio of eq. (12). Denoting these maximum ratios as R^(stat) and R^(dyn), respectively, the gain in cost-effectiveness (as a function of the conservation budget) of the staggered over the static scheme is determined as

For each budget level, also the cost-effective levels of p and b₀ (static scheme) and p, b₁, and b₂ (staggered scheme) are determined. The analysis is carried out for two levels of the discount rate: δ ∈ {0.01, 0.1} (which, if we consider annual time steps, encompass typical real discount rates) and three levels of cost heterogeneity: σ ∈ {0.05, 0.15, 0.3} (so that about 95 per cent of all land parcels have costs of 1 ± 0.1, 1 ± 0.3, and 1 ± 0.6, respectively). Gerling et al. (2022, Fig. 3c) report cost differences with a ratio of about 2.5, which corresponds to about σ = 0.2. The values of the discount rate encompass the range of discount rates reported by Zhuang et al. (2007) for a large number of developing and developed countries (maximum reported values of 12 and 15 per cent for Pakistan and the Philippines, respectively, and minimum reported values of 0.5–3 per cent in intergenerational discounting by the US EPA).

4.2 Results

The relative cost-effectiveness gains G_q and G_γ of the staggered payment scheme over the static scheme can be substantial (Fig. 8), so that the proportion and spatial aggregation of conserved land parcels for given conservation budget increases by up to 40 per cent. This cost-effectiveness gain is largest for small discount rates δ and high cost heterogeneity σ (red bold lines). It further depends on the conservation budget PV_B and in most of the considered parameter combinations increases with increasing PV_B.

The functioning of the staggered scheme is revealed in Fig. 9. The cost-effective base payments increase in both schemes with increasing conservation budget PV_B. However, for small discount rates δ and moderate or large cost variation σ (where the cost-effectiveness gain of the staggered scheme is large) this increase is much weaker in the staggered scheme than in the static scheme. And conversely, while in the static scheme the bonus always declines with increasing budget, in the staggered scheme it increases or has a maximum if δ is small and σ moderate or large.

Consequently, the cost-effective designs between the two schemes differ, especially when δ is small and σ moderate or large (and the cost-effectiveness gain of the staggered payment is large: Fig. 8). Here, especially for larger budgets > 0.3/δ the cost-effective base payment in the staggered scheme is much smaller than that in the static scheme and the cost-effective levels of both b₁ and b₂ are larger than that of b₀ (with the cost-effective b₁ larger than the cost-effective b₂ as suggested by the analyses in the previous sections). For the cases of δ = 0.1 and σ = 0.3, where the cost-effectiveness gain is maximal for budgets around 0.2/δ the results are similar, except that the cost-effective b₂ (which exhibits a maximum as a function of the budget) is smaller than the cost-effective b₀ in the static scheme.

The cost-effective scheme design also helps understanding why an increasing cost variation σ leads to higher cost-effectiveness gains. As noted above, the staggered scheme involves smaller base payments than the static scheme. In both schemes, a higher σ (compare the red with the blue lines) requires higher bonuses to offset the patch selection effect explained in the Introduction, so to meet the budget constraint the base payment must be smaller accordingly. Since the bonus is paid for each conserved neighbour, it affects the conservation budget 8γ times stronger than the base payment (where γ is the average proportion of conserved neighbours).

Focusing on the bonus b₂, which is the decisive quantity for small discount rates, its cost-effective level at smaller budgets (PV_B < 0.3) is smaller than the cost-effective bonus b₀ in the static scheme, explaining the cost-effectiveness gain of the staggered scheme. For larger budgets and medium σ = 0.15 (blue lines in Fig. 9), the cost-effective b₂ is moderately larger than the cost-effective b₀, but this is offset by the much smaller cost-effective base payment in the staggered scheme, explaining the moderate cost-effectiveness gain of the staggered scheme.

For the large σ = 0.3 (red lines), the cost-effective b₂ is equal or slightly larger than the cost-effective b₀, which however is again offset by the much smaller base payment, explaining the cost-effectiveness gain of the staggered scheme. Compared with the case of σ = 0.15, the (cost-effective) difference b₂−b₀ is smaller, and together with the smaller cost-effective level of b₁, this explains why σ = 0.3 leads to higher cost-effectiveness gains than σ = 0.15.

Not unexpectedly, spatial correlation in the conservation costs reduces the cost-effectiveness gains G_q and G_γ of the staggered scheme. For a cost correlation length of l = 4, especially G_θ does not significantly differ from zero (Fig. B2 in Online Appendix B).

5. Discussion

The AB induces the implementation of conservation measures next to areas with (the same) conservation measures to address the problem of the continuing fragmentation of species habitats. While the suitability of the AB for that very purpose has been documented in various theoretical and applied studies, the concept appears to have a number of positive side effects (Drechsler et al. 2010; Bell et al. 2016) that arise from the fact that the AB induces the interaction of landowners. Since networks of interacting entities are well-known to exhibit complex dynamics, we hypothesised another positive side effect: that the AB induces a particular feature of complexity, hysteresis, meaning that the same level of the bonus leads to different levels of conservation, depending on whether it has been reached from a smaller or from a larger level. We further show that this hysteresis can be exploited to raise the cost-effectiveness of AB—by introducing staggered schemes with a high bonus initially that is reduced after a network of conserved land parcels has established.

In the present analysis, a stylised spatial agent-based simulation model was used to explore hysteresis effects in the land-use dynamics induced by the AB. As demonstrated in Section 2, the basic concept here is that to establish a stable network of conserved land parcels (in the sense of a Nash equilibrium) a larger bonus (b₁) is required than (b₂) to maintain it. This relates to a bi-stability that can be observed in the system dynamics under certain assumptions: either by assuming a very (mathematically, infinitely) large number of land parcels—as in Donovan (2021) and Drechsler (2023a), or by averaging the model output (proportion and aggregation of conserved land parcels) over a large number of randomly drawn cost landscapes—as in Drechsler (2023b) and the present model. Each state has its own domain of attraction (i.e., set of land-use patterns that, over time, converge into the state); and the size of these domains and whether a particular land-use pattern falls into a particular domain can be affected by the scheme design (base payment and bonus).

As the present analyses reveal, an obvious prerequisite for the creation of hysteresis is a small base payment, because it allows for a steep, almost discontinuous, dependence of the proportion and aggregation of conserved land parcels as a function of the bonus (Fig. 2a). This relates to a ‘contagion effect’ where a few landowners switch to conservation who ‘infect’ neighbours to do the same, who ‘infect’ their neighbours, and so on. The reason for this is that if the base payment is at the lower end of the cost distribution (Fig. A1) and the bonus relatively large (with respect to the standard deviation σ of the cost distribution), the payment p_i, as the sum of base payment and bonuses [eq. (6)], spans the entire cost distribution as the number of conserved neighbours increases from zero to its maximum value. So at the beginning of the simulation, the payment p_i is at the lower end of the cost distribution and exceeds only the costs of the few least costly land parcels, while at the end of the simulation it is far up in the cost distribution and exceeds the costs of many or most land parcels.

The existence of this contagion effect is associated with a high exceedance (Γ) of the average proportion of conserved neighbours (here termed spatial aggregation γ) over the proportion of conserved land parcels q (Fig. 2b). This Γ can be regarded as a measure of the bonus-induced spatial aggregation of conserved land parcels, where each conserving landowner is surrounded by conserving landowners, which generates high bonus-induced profits and provides the habitat network with some sort of resilience.

This resilience creates the hysteresis observed in Fig. 3. On the one hand, the state of little or zero conservation is resilient and the bonus needs to to cross a certain threshold to establish a connected habitat network (Fig. 2 and blue line in Fig. 3). The threshold is represented by the vertical white dashed lines (b₁^(min)) in Fig. 4 and depends on the size of the base payment (cf. the green lines in Fig. 5).

The established habitat network, in turn, has some resilience, too, so when the bonus is lowered it must cross another threshold b₂^(min) (represented by the lower horizontal line in Fig. 4 and depending on the base payment: olive line in Fig. 5) before a significant loss of conserved land parcels can be initiated (red lines in Fig. 3).

These mechanisms are fundamentally different to those behind the micro- and macro-economic hysteresis discussed by Göcke (2002), where fixed (sunk) costs create barriers to transitions between individual decisions or macroscopic system states. Similarly, the resilience of the established habitat network to reductions in the bonus is fundamentally different to the ‘permanence’ discussed by Pagiola et al. (2020) that occurs where the uptake of conservation measures is associated with upfront costs only, while long-term conservation costs are low, so that conservation payments only need to offset these upfront costs and can be lowered after land-use change has occurred.

Closer related, instead, are contagion effects that are observed, for example, in the spread of diseases or in the spread of shocks through financial markets (Iwanicz-Drozdowska et al. 2021). And related to the present context of biodiversity conservation, in Chen et al. (2012), each 10 per cent of neighbouring landowners participating in a conservation scheme in China were observed to increase a landowner's probability to enrol in the scheme by 3.5 per cent.

Interestingly, the minimum level of bonus b₁^(min) to establish a resilient network (green line in Fig. 5) is quantitatively almost identical to the bonus b₁(Γ_max) at which the bonus-induced aggregation Γ is maximal (green line in Fig. 2b), which suggests a tight relationship between bonus-induced aggregation and hysteresis. This importance of the bonus-induced aggregation explains why a too strong spatial correlation in the conservation costs reduces the hysteresis (Figs. 6a and 7), because the aggregation of conserved land parcels is largely due to conservation efforts aggregating in the ‘valleys’ of the cost landscape rather than bonus-induced.

The described results are qualitatively, and to a large extent even quantitatively, independent of whether hysteresis is measured with respect to the proportion or the spatial aggregation of conserved land parcels, referring to the two key drivers of biodiversity decline: the loss and the fragmentation of species habitats.

In Section 4, we explored whether hysteresis can be translated into cost-effectiveness gains by introducing staggered payment schemes with a high bonus b₁ initially (to establish a large habitat network) that is lowered afterwards to a level b₂ (sufficient to maintain the network). These cost-effectiveness gains can be substantial, especially if the spatial variation in the conservation costs is large and the decision maker considers long-term costs and benefits (low discount rate) (Fig. 8). Not unexpectedly after the considerations above does too strong spatial correlation in the conservation costs diminish the cost-effectiveness gains of the staggered payment scheme (Fig. B2 in Online Appendix B).

The cost-effectiveness gain of the staggered scheme can be explained by the different designs of the two schemes. In particular, the staggered scheme is characterised by a much smaller base payment and a smaller (or at maximum moderately larger) second bonus (b₂) relative to the constant bonus b₀ in the static scheme (for further details, see the discussion of Fig. 9 in Section 4.2).

Associated with its stylised nature, the present model involves a number of assumptions and limitations. May be the most striking is that each land parcel is owned by a single landowner, and landowners act myopically. This implies that, for example, two landowners whose costs are slightly above the base payment will not conserve, while with strategic behaviour they would realise that if they were both conserving they would earn both the bonus, moving from the risk-dominant Nash equilibrium to the payoff-dominant Nash equilibrium (Drechsler 2023c).

Probably the most important instrument to facilitate coordination is communication and information provision (e.g., Parkhurst and Shogren 2007; Banerjee et al. 2012, 2014, 2016). An extreme case of perfect communication would be represented by a perfectly informed social planner who is able to determine the unique cost-effective land-use pattern (cf. Hartig and Drechsler 2010). This is independent of the initial land-use pattern, so no hysteresis would exist. A realistic level between myopic landowners and a perfectly informed social planner might be described by the coalition formation model of Bareille et al. (2023).

A problem with staggered payments might be that landowners may feel fooled if the payment is reduced after some time, reducing acceptance of such schemes. However, one should note that at each time step the landowners maximise their profits and are free to change their land use in each time step, so even if they knew the bonus is reduced in the second phase of the scheme it would still be profitable for them to conserve in the first phase (given the payment exceeds the cost). This freedom to change the land use could be constrained by conversion costs, which would slow down the establishment of the habitat network as well as its destruction. The inclusion of conversion costs would be an interesting extension of the present model.

Results could also change if land prices and conservation costs change over time. Panchalingam et al. (2019) consider a negative feedback, so that due to increased pollinator abundance, land next to other conserved land becomes more profitable. This enhances the tendency to habitat fragmentation and requires higher budgets on the side of the conservation agency to finance an AB scheme.

The simplicity of the present model limits direct practical applications. A possible way forward could be the integration of the proposed idea for payment design into specific or applied models (e.g., Happe et al. 2006; Brown et al. 2022; Huber et al. 2022) that consider land cover and land use in much more detail than the present model—but so far focus only on relatively simple economic drivers such as crop price or flat payments that ignore spatial and temporal aspects.

6. Policy implications and conclusion

The neglect of strategic behaviour, communication, ownership of multiple land parcels and side payments, as well as other complexities of real systems limit the practical applicability of the present results. However, the study demonstrates that the consideration of staggered policies in which payments are changed over time deliberately (to be distinguished from ‘flexible’ policies that react to observed changes in the system) is worthwhile. With respect to coordination incentives like the AB, it may pay off in the long term to offer some higher payments in the beginning to establish a desired habitat network—which then can be maintained in the long run at lower payments. Altogether, the AB, and coordination incentives in general, have quite a number of interesting facets next to their original motivation of Parkhurst et al. (2002), which makes them a worthwhile topic for future research.

Acknowledgments

We are very grateful for the thorough and helpful comments of two anonymous reviewers that greatly helped in the revision of this manuscript.

References