Correspondence Berry J. Brosi, Center for Conservation Biology, Department of Biological Sciences, Stanford University, 385 Serra Mall, Stanford, CA 94107, USA. Tel: +1-650-450-3715; fax: +1-650-723-5920.E-mail: email@example.com
Developing landscape design principles for the provision of ecosystem services is crucial to efficient and widespread implementation of environmental service-based projects. We investigate optimal farm design for agricultural pollination services from bees nesting in native habitat, integrating ecological and economic approaches in a spatial modeling framework. We evaluate the simplest case, and then add consideration of bee metapopulation dynamics and heterogeneity in farmland productivity. We find that the need for spatially even pollination coverage across farms means that bee habitat is often denser at the edges, rather than the centers, of optimally designed farms, and also highly constrains the ability of farmers to site bee habitat in less-productive areas of farms with spatial gradients in agricultural fertility. Optimal farm configuration is not purely a matter of uniform size and spacing of bee habitat: in some circumstances, farms combine large parcels—to ensure bee population persistence—with smaller, dispersed patches to provide spatially continuous pollination services. The highest-yield farm designs are those with a relatively small (but non-zero) area of pollination reservoirs, suggesting a conservation strategy of small parcels of service-providing habitat interspersed throughout working landscapes. The design principles outlined here are likely general and applicable to other ecosystem services supplied at local scales, such as agricultural pest control.
Nature provides life-sustaining benefits to people in many forms, including water purification, flood control, carbon sequestration, and insect pollination of crops (Daily 1997). In many places, these ecosystem services are becoming scarce relative to demand (Millennium Ecosystem Assessment 2005), motivating investment in new mechanisms for their conservation (Chichilnisky & Heal 1998). For example, China is conserving forests for flood control, New York City is investing in sustainable farming and forestry for water purification, and Costa Rica pays landowners for biodiversity, scenic beauty, carbon storage, and water purification (Daily & Ellison 2002).
To realize the conservation potential of ecosystem services, we must better understand how to align conservation with economic incentives while replicating and scaling up such model projects. At present, however, there is little understanding of how to design ecosystem service projects in a spatially explicit and economically efficient manner (Kareiva & Marvier 2003; Kremen 2005; Kremen & Ostfeld 2005).
Here we develop a modeling framework for optimizing landscape design for the provision of pollination services that integrates basic economic trade-offs. Previous works have applied spatial models to the mapping of ecosystem services in extant landscapes, including changes in service delivery under different land-use change scenarios (e.g., Bodin et al. 2006; Chan et al. 2006; Olschewski et al. 2006). Morandin and Winston (2006) optimized the quantity of native habitat for pollination services to canola, without considering spatial configuration. By contrast, the work presented here is, to our knowledge, the first effort to develop spatially explicit landscape design principles for any one ecosystem service.
These findings point to a strategy of managing what we call pollination reservoirs, parcels of pollinator habitat integrated into agricultural production systems in order to provide crop pollination services. To implement such a strategy, we need to understand when pollination reservoirs will be an economically attractive option; how big they need to be to support pollinators; and their optimum spatial configuration on a farm. Here we develop a spatial model to configure pollination reservoirs for maximizing crop yield at the scale of a single farm.
We developed a simple, general modeling framework to understand essential trade-offs and design principles for a range of pollinators and farming systems, while allowing future modeling efforts that add more detail to understand and isolate better the sources of results. Our focus on generality and simplicity, however, comes at the necessary expense of some realism and immediate applicability.
We considered linear farms divided into cells of either agriculture or native habitat, where bees nest only in native habitat cells and forage in both native and agricultural cells. We initially assumed constant bee population density in native habitat cells (e.g., Bodin et al. 2006; Cane et al. 2006; Brosi et al. in press) and homogeneity in underlying agricultural fertility; we later relaxed these assumptions. Ultimately, we optimized the configuration of agricultural and pollination reservoir cells within the farm to maximize crop yields.
We assumed that bees fly in a straight line either left or right from a reservoir cell R of native habitat with a fixed probability qf of stopping to forage in each cell encountered; we refer to (1 –qf) as foraging dispersal. The probability Φ of a bee from cell R foraging in cell i is:
where (|i−R|) is the distance traveled. Summations yield the total number of bees from a given reservoir cell foraging in cell i and from all reservoir cells. This movement model fits the trends compiled in a global meta-analysis of studies of bee movement from native habitat in agricultural lands (Ricketts et al. in press).
Bee density does not translate linearly into seed set because once a sufficient number of pollen grains have been deposited onto a plant's stigma, adding more does not benefit plant reproduction (e.g., Free 1993; Morandin and Winston 2006). Following these works, we related bee density to crop pollination (Ψ) assuming:
where d is the density of bees, z controls the maximum level of insect-mediated pollination, and c controls the slope of the saturation curve. The baseline level of self-pollination in the absence of bees is b, which is zero for obligately outcrossing crops such as almonds, and positive for a range of crops including coffee (Free 1993). We call the proportion of crop yield from pollinators [i.e., (Ψ−b)/Ψ]“pollinator dependence” and the saturating relationship we modeled allows for assessment of a range of hypothetical crops or cultivars with different pollinator dependencies. Default values for all parameters are given in Appendix S1.
To focus on farm design for pollination services, we assumed that yield was a function solely of crop pollination (including baseline self-pollination); we later relaxed this assumption to assess the effects of heterogeneity in underlying agricultural fertility. We optimized farm configuration to maximize crop yield using the MATLAB Genetic Algorithm from the GADS toolbox version 2.0 (The Mathworks, Inc., Natick, MA, USA); see Appendix S2 for more information.
Basic model results, trade-offs and intuition
The results from the basic model demonstrate an inherent trade-off: efficient farm plans must balance the foregone cost of not farming areas of bee habitat with the benefit of higher yields from enhanced crop pollination. Pollination reservoirs occur as single cells within larger areas devoted to agricultural production (Figure 1) because croplands adjacent to native habitat cells receive the greatest pollination benefit, and because bee density within a reservoir cell is independent of habitat area under the assumption of constant bee population size.
The quantity and spacing of pollination reservoir cells in a farm depends on bee foraging (Figure 1). When foraging dispersal (1 −qf) is zero, bees never leave their home cell, rendering them useless to farmers. At some minimum bee foraging distance (Figure 1, farm 1), it becomes profitable to forgo agricultural harvests in some cells and instead manage them as bee habitat. At such a point, bees forage over short distances and a relatively large proportion of the farm must be allocated to bee habitat to provide pollination services to the remaining croplands.
As foraging dispersal increases, bees are able to pollinate crops over a greater area, and there are fewer, more widely spaced native habitat cells (Figure 1, farms 2–4). Only at large bee foraging distances does the farmer concentrate bee habitat in the center of the farm (Figure 1, farms 4–5) to prevent excessive “spillover” of bees foraging off-farm, and because bees from the center of the farm forage far enough to pollinate croplands near the edges. With even greater foraging distances, the farmer must allocate more land to pollination reservoirs to keep enough bees foraging on the farm (Figure 1, farm 5). When bees forage over more extreme distances, most bees are foraging off-farm and it is no longer profitable to manage any bee habitat. These situations produce contrasting farm yields (Figure 1, dashed line). Yield is maximized when bees forage widely enough to provide pollination services to all of the cropland with the smallest area of native habitat on the farm (Figure 1, farm 3).
As pollinator dependence decreases (as for different crops), the optimal proportion of bee habitat in a farm declines (Figure 2), in a manner dependent on foraging dispersal. Bees with short foraging distances require farms with larger proportions of native habitat, making the trade-off of forgoing cropland for bee habitat less attractive as pollinator dependence declines (Figure 2, dotted line). In converse, with wide-ranging bees, each cell of native habitat can provide pollination services to a larger area of crops, so the total area of pollination reservoirs is initially smaller but its loss is slower as pollinator dependence decreases (Figure 2, dashed line).
Population dynamics and sustainability of pollination services
In the simple case outlined above, we assumed constant bee population densities in native habitat cells. We relaxed this assumption to evaluate how bee population dynamics affect optimal farm design, which is of particular importance when considering the persistence of pollinator populations in a landscape and thus the sustainability of pollination services. We modeled simple metapopulation dynamics using a discrete approximation of logistic growth of bee colonies, assuming colony dispersal as for bee foraging but controlled by a separate reproductive dispersal parameter (qr). We iterated growth and dispersal dynamics for 500 generations, which consistently yielded equilibrium population numbers. At each time step, colonies first reproduced and then the newly produced propagules dispersed; propagules that stopped to nest in pollination reservoirs survived, while those that settled in agricultural cells did not. We used a seeded version of the genetic algorithm for optimization routines with population dynamics (see Appendix S2 for more detail); optimization routines were run after population equilibrium was reached. We assessed 10,000 combinations of reproductive (qr) by foraging (qf) dispersal parameters (Figure 3).
When reproductive dispersal is zero, new colonies do not leave their natal landscape cell, so each cell reaches its carrying capacity—behaving exactly as for the simple case without population dynamics (Figure 3, bottom edge of graph). For long-distance bee reproductive dispersal, all newly formed colonies disperse out of the farm boundaries, making pollination reservoirs worthless to farmers (Figure 3, top edge). Similarly, when bees forage over extremely small or large distances, farmers have no economic incentive to manage for pollination reservoirs, as for the simple case (Figure 3, left and right edges).
Both the size and isolation of native habitat patches affect bee populations. For a pollination reservoir to sustain a bee population, it must be situated close enough to other reservoirs to recruit new colonies from them (Figure 3, farms 1 and 2) or else of sufficient size to retain enough of its own newly produced colonies (e.g., Figure 3, farms 3–7). Thus, in many cases farmers will maintain larger pollination reservoirs, in contrast to the simple case where all optimal farms have single-cell reservoirs.
Farm design with bee population dynamics is largely determined by interactions between bee dispersal for foraging and reproduction (Figure 3), and a wide range of these parameters occurs in natural bee populations. For bees with low foraging dispersal, farmers must closely space pollination reservoirs to ensure effective pollination across their farm. This enforced reservoir proximity reduces the minimum reservoir size needed to sustain bee population, leading to small, closely spaced reservoirs (e.g., Figure 3, farm 1). In contrast, as reproductive dispersal increases (y-axis in Figure 3), patch size requirements become larger (Figure 3 and Appendix S3 Figure A, farms 5, 7, 9) and thus must be balanced by increased foraging dispersal. Intermediate levels of foraging and reproductive dispersal generate intermediate patch size and spacing (Figure 3, farms 3–4).
Under some parameter combinations, the conflicting demands of reservoir size and spacing lead to a hybrid farm plan design, consisting of one or more relatively large reservoirs to ensure a sustainable population of bees and smaller satellite parcels sited between them to provide spatially even crop pollination (Figure 3, farms 4–6). The conditions with the highest crop yields (Appendix S3, Figure B) occur with short bee reproductive dispersal and large foraging dispersal, leading to small, widely spaced reservoirs (Figure 3 and Appendix S3 Figure B, farm 10).
A wide range of these foraging and reproductive dispersal parameters is reasonable for natural bee populations. For many organisms (not just pollinators), reproductive dispersal occurs over longer distances than foraging dispersal (i.e., Figure 3, above and left of the x=y diagonal). The majority of bee species, including Apis mellifera (Apidae), the European honey bee (Gould & Gould 1988) likely fit this pattern. Other bee species, however, have different reproductive and foraging movement patterns. The meliponines, social stingless bees of the tropics (Apidae: Meliponini), are instrumental in pollinating coffee in both Asia and Latin America (Klein et al. 2003; Ricketts 2004). In meliponine colony reproduction, workers make multiple trips between the old and new nest sites, meaning that new colonies cannot disperse much further than normal foraging distances (Roubik 1988; Figure 3, areas near the x=y diagonal). Some ground-nesting solitary bees nest mere centimeters away from their natal nest, as part of a nesting aggregation. Such bees, including some species of Perdita (Andrenidae; e.g., Danforth 1999) and the Alkali Bee (Nomia melanderi, with nesting beds managed for alfalfa pollination, Bohart 1972), forage over larger distances than they typically disperse reproductively (Figure 3, below and right of the x=y diagonal).
Effect of cropland heterogeneity
In the simple case and with population dynamics, we assumed equivalence of farm cells in potential agricultural yield (analogous to soil fertility). While such an assumption holds in industrial, large-scale agriculture, heterogeneity in fertility is present in many smaller-scale operations, particularly in the developing world. To address this issue, we relaxed the assumption of homogeneity in fertility by considering farms with a linear gradient in cropland fertility, capturing a simple type of variation found on hill slopes and along distance gradients to rivers.
We established a fertility gradient by multiplying the self-pollination of each agricultural cell (variable b, Equation (2)) by a linear fertility factor. We set up paired farms of equal average fertility in farms with and without fertility gradients by adjusting the baseline level of self-pollination, allowing us to focus on the differences in spatial configuration. For crop yields with fertility gradients, see Appendix S5.
Fertility gradients create an incentive for farmers to shift bee habitat toward the less-fertile side of the farm (Figure 4). Most such shifts are relatively modest (Figure 4, farms 3–6), though they vary with the strength of the fertility gradient and with bee foraging dispersal. The subtlety of farm plan response to fertility gradients is driven by the fact that the most fertile agricultural cells are the most costly to trade off, but they also have the most to gain from nearby bee habitat.
Surprisingly, the greatest changes in farm plans occur with short bee foraging dispersal (Figure 4, dotted line) in crops with low to intermediate pollinator reliance. With a relatively strong fertility gradient, farmers do not trade off any cropland for bee habitat on the higher-fertility side of the farm (Figure 4, farms 1–2), but do on the less fertile end of the farm where there is a lower cost to maintaining bee habitat. For crops with high pollinator reliance, this pattern reverses because pollination services are necessary across the breadth of the farm.
Our model demonstrates three novel and nonintuitive insights into the design of agricultural landscapes for maximizing pollination services: (1) Rather than concentrating pollination reservoir cells in the center of farms to minimize bee loss, most optimal farm designs have reservoirs spread across their breadth. Counter-intuitively, some farm plans have a greater density of reservoir cells at their edges as compared to the center; (2) Optimal farm configuration is not a simple matter of uniform size and spacing of pollination reservoirs. Instead, many optimal designs include large patches to ensure bee population persistence, with smaller, dispersed patches to provide spatially even pollination services; and (3) The need for spatially continuous pollination services constrains the ability of farmers to site pollination reservoir cells in less-fertile areas of heterogeneous farms. Surprisingly, the largest shifts in reservoir placement occur when bees forage over small scales.
To achieve satisfactory crop yields, pollination must be provided across the breadth of a farm. Croplands on farm edges often need a greater density of nearby pollination reservoirs than those in farm centers (e.g., Figure 1, farms 1–3, Figure 2, farms 1–6) due to the lack of bee input from adjacent land and the “leakage” of bees foraging off-farm, which is greater at farm edges. This is surprising because we had anticipated that farm designs with bee habitat concentrated in their centers would minimize bee loss—a configuration that only occurs at large foraging distances (e.g., Figure 1, farm 5). For most parameter combinations, the increased concentration of pollination reservoirs is near, rather than directly on, the edges of farms, and the differences in concentration are relatively subtle.
Small pollination reservoirs spaced evenly across a farm are not necessarily sufficient to ensure bee population persistence. Our initial intuition was that inclusion of population dynamics would uniformly increase reservoir patch sizes. Instead, it sometimes leads to a hybrid design with one or more large reservoir patches (“sources”) mixed with smaller, dispersed “sink” patches that allow for spatially continuous pollination services. Thus, farm design is not necessarily a simple matter of a uniform size and spacing of bee habitat.
With heterogeneity in agricultural fertility, farmers could ideally site pollination reservoirs in less fertile areas, freeing more fertile zones for crop production. With linear gradients in fertility, however, pollination reservoirs cannot be too far from the most valuable croplands or they would suffer reduced pollination services and smaller harvests. Therefore, shifts in the placement of pollination reservoir cells toward the less fertile end of the farm are typically small, constrained by the need for spatially continuous pollination services. Farm designs can change strongly with fertility gradients, but surprisingly, this is not with long-range bee foraging dispersal. Instead, with low pollinator dependence and short-foraging bees, farm plans place all pollination reservoirs on the less fertile end of the farm and manage the more fertile side purely for agricultural production.
A more general result is that the conditions leading to the greatest crop yields have relatively small amounts of native habitat (e.g., Figure 1, farm 3; Figure 3 and Appendix S3 Figure B, farm 10). This result may underpin management recommendations where some land is removed from production to provide ecosystem services. In many such cases, investing in environmental services will be most profitable and commonplace when landowners can set aside the smallest area needed to realize ecosystem service benefits, suggesting that environmental service-based projects may favor widespread implementation of small-scale measures interwoven throughout working lands.
The results of our model link to previous works in a number of ways. In some respects, the crop pollination system is most analogous to marine reserve models, some of which have attempted to optimize the size and configuration of no-take reserves interspersed with fishable areas (e.g., Neubert 2003). Such models, however, typically attempt to maximize the number of fish produced across a seascape, without regard to where they are produced. By contrast, in a crop pollination system the goal is not maximizing bee populations; it is producing enough pollinators to provide sufficient crop pollination (subject to the diminishing-returns relationship captured in our Equation (2)). In addition, an optimal landscape is also subject to the inherently spatial constraint of ensuring that the pollinators are spread across the breadth of the farm so that they can reach as much of the crop as possible.
Compared with other works on pollination, our findings are consistent with those of Bodin et al. (2006), who showed that small forest reserves scattered across a landscape could provide substantial pollination services. They are also in accord with findings from Morandin and Winston (2006) who found that landscapes with about 30% native habitat generated optimal farmer profit in a canola agroecosystem. Our default parameters generated similar estimates of about 25% native habitat, though for a crop with about 40% of yield due to self-pollination (which is likely higher than the percentage for canola [Free 1993]).
Extensions of our model would contribute additional insights to the design principles presented here. One possibility would consider multispecies bee communities with stochastic extinction–colonization dynamics, linking pollination reservoir size with population persistence and bee species richness. The availability of season-long foraging resources may be a limiting factor for bees in some landscapes, and could change optimal landscape configurations. Considering several adjacent farms rather than an isolated one with no bee input from surrounding areas could also change the design of optimal farms, especially at their edges. It would also be valuable to parameterize the models for a specific crop system, considering economic variables like crop prices, farm inputs, and the availability and price of managed honeybee pollination services.
Given the increasing investment in ecosystem service-based conservation projects, it is imperative to develop spatially explicit strategies for provisioning such services in an economically efficient manner. The models presented here lay a conceptual foundation for strategies to provide agricultural pollination services, which could easily be extended to other services that native habitats provision over small spatial scales, like agricultural pest control. We hope that this framework will assist in moving ecosystem services toward becoming a mainstream, commonplace strategy for improving both biological conservation and human welfare.
Editor : Dr. Corey Bradshaw
We thank M. Boni, M. MacPherson, S. Ramachandran, and J. Van Cleve for programming assistance and advice. W. Murray gave helpful suggestions and advice on optimization methods. K. Al-Kafaji, M. Boni, S. Jackson, and J. Van Cleve gave insightful and constructive comments on the article. B. Brosi was supported during this work by the Anne and Robert Bass Stanford Graduate Fellowship in Science and Engineering and by a Teresa Heinz Scholarship for Environmental Research. We gratefully acknowledge further support from the Winslow Foundation and Peter and Helen Bing.