• The land-use dynamics under an agglomeration bonus are simulated.

To halt the ongoing loss and fragmentation of species habitats, coordination incentives have been proposed that induce private landowners to carry out conservation measures on their land in a spatially coordinated manner (Nguyen et al., 2022). The best-known and most popular variant of coordination incentive is the agglomeration bonus (AB), which consists of a base payment for the conservation of land, irrespective of its location, plus a bonus for each neighbouring land parcel that is conserved (Parkhurst et al., 2002). The bonus offsets costs that arise if a more costly but connected land parcel is conserved rather than an isolated but less costly one (Drechsler et al., 2010). Both base payment and bonus have an impact on the total amount of conserved land, while the bonus particularly induces the spatial aggregation of conserved land parcels.

Since its first formulation, many research papers have been published about the AB. These comprise modelling studies (Albers et al., 2008; Bell et al., 2016; Delacote et al., 2016; Iftekhar and Tisdell, 2016; Dijk et al., 2017; Arora et al., 2021; Bareille et al., 2023), 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; Banerjee et al., 2014; Krawczyk et al., 2016; Parkhurst et al., 2016; Banerjee et al., 2017; Panchalingam et al., 2019; Kuhfuss et al., 2022).

A central topic of most studies is the degree of spatial coordination that emerges under the AB. An important assumption that is likely to drive their results but has so far received no attention is the spatial extent and distribution of the landowners’ (or players’ or model agents’) properties. One large group of experimental and modelling studies (e.g., Albers et al., 2008; Banerjee et al., 2012; Banerjee et al., 2014; Bell et al., 2016; Delacote et al., 2016; Iftekhar and Tisdell, 2016; Banerjee et al., 2017; Dijk et al., 2017; Arora et al., 2021) assumes that each agent or player, respectively, owns a single land parcel that is neighboured to a number of land parcels owned by other agents or players.

Somewhat more realistic are the landscapes considered in the second group of studies in which agents own several land parcels, each of which can either be enrolled in the conservation payment scheme or not. The land parcels are generally arranged in cohesive blocks (Parkhurst and Shogren, 2007; Krawczyk et al., 2016; Panchalingam et al., 2019; Bareille et al., 2023); an example is shown in Figure 1A. This spatial property structure, however, contrasts with real landscapes in which landowners not only own several land parcels but the landholdings are fragmented (LaTruffe and Piet, 2014). This fragmentation implies that the land parcels of different landowners are more or less intermingled.

Some farmland models consider the spatial structure of landholdings in a more realistic manner. An example is the AgriPoliS model by Happe et al. (2008), which, since its development, has been used in numerous applied modelling studies throughout Europe (e.g., Happe et al., 2008; Brady et al., 2012; Hristov et al., 2020). A typical agricultural model landscape, as considered in AgriPoliS, was presented by Brady et al. (2012) and is reproduced in Figure 1B. It mimics typical farm structures, such as those shown in Figure 3 of Marie et al. (2009) and in Figure 3 of Pauchard et al. (2018).

Why is the spatial structure of the landholdings relevant? Agents under an AB are situated in a coordination game (van Huyck et al., 1990; Heinemann et al., 2004; Parkhurst and Shogren, 2007) in which a player’s reward is maximised if all players coordinate by spatially agglomerating their conservation efforts. Compared to that, the reward is somewhat reduced if the player does not coordinate (by conserving isolated low-cost land parcels); but it is minimised if they coordinate but the others do not. Both the coordinated and the uncoordinated states are Nash equilibria, and the establishment of the coordinated one is greatly enhanced if the agents can communicate (Parkhurst and Shogren, 2007; Banerjee et al., 2014; Banerjee et al., 2017). Thus, and quite obviously, the coordination problem would disappear if there were only a single agent who chooses the land-use pattern that maximises the total reward. On the opposite end, one can expect that the coordinated state is most difficult to establish if there are many agents, each of them owning only a single land parcel, as assumed in those studies mentioned above.

It is not clear how the spatial structure of landholdings affects the performance of the AB (and that of coordination in general) and whether and by how much the existing studies over- or underestimate the ability of landowners to coordinate their conservation efforts. To shed some light on these issues, this study considers a range of randomly created, stylised spatial landholding structures and evaluates them using a simple spatial land-use simulation model. The sampled model landscapes range from the case in which each landowner owns only a single land parcel, via landscapes similar to that shown in Figure 1B, to landscapes similar to that in Figure 1A.

For each sampled landscape, here, the model agents are subjected to an AB and the dynamics of their induced land use are stimulated. As functions of the regulator’s budget and the AB scheme design, this study determines the proportion and spatial agglomeration of conserved land parcels, as well as their ecological benefit (and hence, cost-effectiveness), assuming the conservation of a species with a limited dispersal range. The dependence of these scheme performance indicators on the described characteristics of the agents’ landholdings is analysed, as well as their dependence on other features, including the spatial variation and autocorrelation of the conservation costs and the species’ dispersal range.

In the next section, the rationale of the analysis is presented, as well as the structure and analysis of the model; followed by the presentation of the results and their discussion and a short concluding section.

The results are presented in three steps. First, to explore the influence of the number of agents, M, on the performance of the AB, the three performance indicators q, γ, and V (Eqs 4–6 are shown as functions of M, for the five budget levels of Table 2 in the base scenario of Table 3. Second, to understand the influences of the model parameters σ, l, α, and β (cf. Table 3), the ratio r of Eq. 8 that measures the impact of M on the scheme performance is shown for each of the five scenarios defined in Table 3. Lastly, to assess the influence of the bonus b, the scheme cost-effectiveness (V) is shown, for the base scenario, as a function of M, for the three levels of b (Table 3) and three budget levels.

Figure 3 shows that the three AB performance indicators (proportion q and agglomeration γ of conserved land parcels, and ecological benefit V (cost-effectiveness)) decrease with the increasing number of agents M (i.e., decreasing number of land parcels per landowner). As expected, they increase with increasing budget. The largest influences of M are generally observed for larger budgets, with the ratios r between the outcomes for small and large M reaching values around 0.25.

The effects of the model parameters (scenarios) on these effects of M are less clear than hypothesised (Figure 4). A low-cost variation (Figure 4, scenario 2) does reduce the effect of M on the proportion q and the benefit V (Figures 4A, C), but the effect of M on the spatial agglomeration γ seems to be quite independent of the cost variation and of all model parameters altogether (Figure 4B). A positive cost correlation length (scenario 3) slightly reduces the effect of M on q and γ and considerably reduces its effect on V.

As hypothesised, if the land parcels are not cohesive per landowner but the landholdings are strongly fragmented (α = 0), the influence of M is weakened for all three performance indicators (scenario 4). Other than hypothesised, an unlimited dispersal range (β = 0, scenario 5) increases the influence of M on the ecological benefit V. The reason is that for β = 0, we have V(β = 0) = q ², so the spatial agglomeration of conserved land parcels has no influence on the benefit function V, which instead quadratically increases with increasing q. Thus, the influence of M on q (i.e., decreasing M increases q, Figure 3A) is amplified in V.

The final issue of interest is the cost-effective level of the bonus b. Since only three levels of b were considered, it is determined which of these three levels generates, for the given budget, the highest ecological benefit V. Figure 5 delivers three insights. First, with increasing budget, smaller levels of the bonus become cost-effective. The reason is that there is a trivial correlation between the proportion q and the spatial agglomeration γ of conserved land parcels in the sense that, necessarily, γ ≥ q. So, even for a zero bonus, a high budget implies, via a high q, a high γ. Consequently, smaller bonuses are required to achieve the cost-effective level of spatial agglomeration.

Second, the effect of the landowner number M is higher for larger bonus levels. This implies that, third, the relative advantage of a given bonus level relative to other levels changes with changing M. In particular, for the smallest budget (Figure 5A), at large M, the largest bonus b = 0.5σ is only slightly more cost-effective than the other two bonus levels, while at small M, it is much more cost-effective. A similar result is observed for the medium budget (Figure 5B), where there is even a small rank reversal: while for large M, the largest bonus level appears slightly less cost-effective than the medium level (b = 0.3σ), at small M, it is clearly more cost-effective.

For the largest budget (Figure 5C), at large M, the smallest bonus level (b = 0.1σ) is clearly more cost-effective than the other two levels, while at small M, it is about as cost-effective as the medium bonus level. The results of N = 64 land parcels Figs. C1–3 of Supplementary Appendix C are very similar to those presented in Figure 5.

Coordination incentives like the agglomeration bonus of Parkhurst et al. (2002) in which conservation of a land parcel earns a base payment, plus an additional bonus if that land parcel is adjacent to other conserved land parcels, have been proposed to induce the spatial agglomeration of conservation efforts. Many of the numerical and simulation studies, as well as experimental studies, that have contributed to a better understanding of the functioning of the AB assume that each landowner owns only a single land parcel that can either be conserved or used for economic purposes like intensive agriculture. On the opposite end of the spectrum, other studies assume that landowners own several land parcels, but these land parcels are arranged in cohesive blocks, with crisp boundaries between the properties of different landowners.

Both assumptions are not realistic. Instead, real landholdings are fragmented (Marie et al., 2009; LaTruffe and Piet, 2014; Pauchard et al., 2018). The present simulation analysis reveals that the number of land parcels per landowner and their spatial distribution matters. A decreasing number of landowners (so that each landowner owns an increasing number of land parcels), and a declining level of fragmentation of the landholdings (so that the landholdings become spatially cohesive as, e.g., in Figure 2C; rather than fragmented as, e.g., in Figure 2A) increase the proportion and spatial agglomeration of land parcels as well as the cost-effectiveness (ecological benefit for given conservation budget) of the scheme.

The reason for this finding is that adjacent land parcels allow the landowner to transfer the economic surpluses from agglomeration from high-cost to low-cost land parcels (as outlined in Section 2.1); so, for the given base payment and bonus, they will conserve more land. While, if the land parcels of each landowner are dispersed and surrounded by the land parcels of other landowners, the situation is similar to that in which each landowner owns only a single land parcel, and where surpluses are not transferred and coordination of conservation efforts is impeded.

These observed effects are especially large if 1) the conservation costs are spatially heterogeneous and spatially uncorrelated and 2) the bonus is large. To avoid a misunderstanding about the latter result, it should be noted that all the analyses are carried out under a fixed conservation budget so that a larger bonus is accompanied by a smaller base payment in order to meet the budget constraint.

The reason for result 1) is that the AB is meant to offset the cost difference between less costly but isolated land parcels and connected but costly land parcels (e.g., Parkhurst and Shogren, 2007; Drechsler et al., 2010); so, it is most effective if there is sufficient variation in the costs of neighbouring land parcels. Result 2) is obtained because the above-described internal surplus transfer from low-cost to high-cost land parcels within each landholding is most effective and relevant if the bonus is large.

Result 2) implies that the number of land parcels per landowner affects the cost-effective level of the bonus. The analysis reveals that with an increasing number of land parcels per landowner, larger bonus levels (and accordingly smaller base payments) become more cost-effective relative to smaller ones (which, of course, does not mean larger bonus levels are always more cost-effective than smaller levels, since this depends on many other ecological and economic parameters). The reason is, again, that the described “internal surplus transfer” is most effective when the landholdings are spatially cohesive.

As the rationale of Section 2.1 reveals, the results are driven by the assumption that the landowners do not communicate with each other, which would allow for transferring agglomeration surpluses between landowners, as in Drechsler et al. (2010), and more conservation and agglomeration could be achieved for given levels of base payment and bonus. The landowners also do not decide strategically, which implies that they are locked in the uncoordinated Nash equilibrium (cf. Parkhurst and Shogren, 2007) and that they can leave only with sufficiently high levels of the bonus. With strategic behaviour (Drechsler, 2023) and communication (Parkhurst and Shogren, 2007; Banerjee et al., 2014; Banerjee et al., 2017), in contrast, the coordinated Nash equilibrium could be found more easily.

Future research may explore the role of strategic behaviour and communication between landowners in more detail. Further issues of interest would be different types of coordination incentives, like threshold payments (Nguyen et al., 2022). Like most theoretical and experimental studies of coordination incentives, the present analysis is based on a number of simplifying assumptions, e.g., about the landowner behaviour, the consideration of only two land-use types, and the structure of the model landscapes. These abstract landscapes ignore many details of real landscapes to focus on the spatial structure of the landholdings and to allow for a systematic variation between large and small landholdings and between cohesive and fragmented landholdings. An application of the model to a real agricultural landscape, therefore, would be a fruitful avenue for future research.

The analysis highlights the substantial influence of the spatial structure of landholdings on the dynamics and performance of coordination incentives, represented here by the agglomeration bonus (AB). The smaller and the more fragmented the landholdings are, the more difficult is it for landowners to coordinate their conservation efforts and the lower the cost-effectiveness of the AB, especially if the conservation costs vary strongly in space. As a consequence, the cost-effective scheme design, too, depends on the spatial structures of the landholdings. Especially when the landholdings are spatially dispersed, the facilitation of communication between landowners is an important instrument for the enhancement of coordination and scheme performance.