By formalizing the conceptual presentation of mobile agent-based ecosystem services (Kremen et al., 2007
) and integrating the knowledge from a large body of work, the model provides an important step in evaluating the landscape contributions to pollinator populations and crop pollination. It represents the first spatially-explicit model of landscapes for their capacity to support bees and the match between empirical and modelling results strongly supports the modelling framework. The model accurately predicted the relative abundances and richness of native pollinators in two of three landscapes, capturing a minimum of 55 % of the observed variance among farms for pollinator abundance and richness on sunflowers and watermelon in California and on coffee in Costa Rica (Fig. ). While the model did not predict pollinator abundance and richness in the NJPA data set, it may be due to low variance in this system, or to the resolution of land-cover data (relative to the scale of the ecological phenomenon in this landscape; see below) rather than faulty model assumptions. The model is relatively simple and designed to be used anywhere where sufficient land-cover data exist along with the ability to code them in terms of floral and nesting resource availability. While land-cover data for most places are widely available, the knowledge necessary to code land-use types and estimate pollinator foraging ranges and seasonality may vary; therefore we have designed a model that is flexible. For example, the model of pollinator communities in California accounted for four nesting types and three seasons of floral resources, while the model of Costa Rica used only two nesting types and only one season, because the knowledge base to resolve nesting and seasonal guilds more finely was not available.
In future work, it is planned to develop further the model as a guide to landscape-level management for pollinators. First, this model will be applied to a much larger set of crop studies conducted at the landscape scale (viz. studies in Ricketts et al., 2008
). Secondly, a landscape metric has been used as a proxy for abundance, so the larger set of studies can be used to derive and parameterize a more explicit functional relationship between this landscape metric (floral and nesting resources) and abundance are warranted. If one assumes a liner relationship (Type I) between the metric and abundance, the model may underestimate abundance at the edges, while a saturating relationship (Type II or III) between the metric and abundance may be more appropriate. Thirdly, using statistical techniques, the landscape-level outputs of the model (pollinator relative abundance) will be related to the observed measure of pollination services in each study (e.g. pollen deposition, pollen limitation) to attempt to develop a direct relationship between landscape and yield effects via pollinator abundances. Finally, by manipulating modelled landscapes (e.g. by increasing floral or nesting resources in different spatial configurations), the effects on pollinator abundance, richness and service delivery can be estimated across a range of changes in resources, and generalities looked for across landscapes in the density and arrangement of resources needed to protect pollinators and/or provide adequate pollination services. This modelling exercise would inform efforts to preserve existing habitats within degraded landscapes and also guide spatial planning of priorities for habitat restoration. Similar to the sensitivity analysis of model parameters, analyses exploring the sensitivity of modelled pollination services to resource patchiness at different grain sizes or to different landscape configurations are also envisioned.
The model was unable to predict pollinator abundances in the New Jersey landscape. It is hypothesized that this may be due to the availability of fine-scale floral and nesting resources on and surrounding the farms, which was not captured in the land-cover data. In order to standardize the methods across the data sets included in this study, the same 30-m resolution for the land cover input data was used for all three study systems. In deriving 30-m resolution for Costa Rica and California, it was possible to account for proportions of habitat within each parcel, e.g. for Costa Rica the proportion of each land-cover class within the 30-m parcel was included. But finer-scale data were not available at the time of the analysis so the NJPA parcel had only one land-cover class per 30-m parcel. Furthermore, the NJPA landscapes had greater habitat heterogeneity to begin with, so the simplification to 30-m pixels probably entailed a greater loss of detail in this system than in others. The CA and Costa Rican landscapes have larger grain sizes and are characterized by large expanses of agriculture contrasted with continuous blocks of natural habitat. In contrast, in NJPA, grain sizes are smaller with the agricultural, natural and other habitat types being inter-digitated at a small spatial scale. Furthermore, habitat heterogeneity is high even within a habitat type; for example, many agricultural fields contain weedy fallow areas that would not be separately identified in the land-cover data. In sum, although bees are known to respond to resource availability at scales smaller than the 30-m parcel size (Morandin and Winston, 2006
; Albrecht et al., 2007
; Kohler et al., 2007
), the simplification to a 30-m resolution may not matter for landscapes where there is little heterogeneity at this scale, whereas the same resolution may result in inaccuracies in landscapes with greater heterogeneity at relatively smaller scales.
Two other results support this hypothesis for the model's poor fit in the NJPA landscape. First, the sensitivity analysis of the Costa Rica landscape indicates model predictions are sensitive to floral resources provided within coffee or crop habitat (Table ), i.e. to resources distributed at a small scale. Secondly, in the NJPA system and using the same land-cover data, it has not been possible to detect any relationship between land cover variables and pollinator abundance, richness or services (Winfree et al., 2007
). These results contrast with the majority of other study systems (Ricketts et al., 2008
), and again suggests that the land-cover data in this system does not capture the relevant variables at the appropriate scale.
An alternative explanation for the poor fit is that among NJPA farms there simply may not be enough variation to explain in their pollinator communities, in their surrounding landscapes or both. If this were the case, comparisons of among-farm variation in the model prediction and observed data would reveal higher variation in Costa Rica and California compared with NJPA. A post hoc
comparison of the abundance, richness and pollen deposition, as well as the landscape model's prediction, was performed using the variation in these observed variables divided by the mean squared. This is a unitless quantity, often called the opportunity for selection (Arnold and Wade, 1984
), and removes the expected scaling that occurs between the mean and variance of a distribution, thus allowing comparisons among quantities that may differ in their units or mean values.
The post hoc comparison reveals that indeed Costa Rica and California have much higher standardized variances in both the observed and predicted values and that limited variation in the landscape surrounding NJPA farms may explain the model's poor fit (Fig. ). The NJPA farms show much lower variation for all three observed pollination measures and the pollinator service scores provided by the landscape analysis is consistent with the observation of little variation (Fig. A). Furthermore, the variance in the observed variables explained by the model tends to increase with increasing variability in the landscape (Fig. B) lending support to the idea there is too little variation in the NJPA landscape to pick a strong effect of the landscape. We suggest using the variance-to-mean2 ratio in other studies for future comparisons.
Fig. 4. A post hoc cross-site comparison of variation in model prediction and observed pollinator abundance, richness and pollen deposition. There is much greater variation across farms with the studies in California and Costa Rica compared with NJPA (A). This (more ...)
Despite the promising results in matching data to predictions in two of three landscapes, there are structural limitations of the model. First, it is limited to predicting relative pollinator abundance as a function of resources related to land cover, which is only one of many potential contributors to pollinator population and pollination services, e.g. pesticides. Also, while quantitative, it cannot project pollinator abundance over time, but rather assumes population stasis given a particular landscape configuration. In other words, the model does not provide an estimate of pollinator population viability or predict pollinator temporal dynamics or interaction of time and space through metapopulation dynamics. As such, it does not incorporate stochastic events, which may influence both long-term pollinator population dynamics and, ultimately, crop yield. With more information, one could expand the model to include these factors, in which case, the model presented here would simply be one input to account for resource availability while other inputs would account for other factors, e.g. weather, pesticides, etc.
Predicting crop yield from the landscape pattern is a final goal, and more research is clearly needed in this area (Kremen, 2005
; Morandin and Winston, 2006
; Kremen et al., 2007
). Translating from pollinator abundance to pollinator influence on crop yield will be limited in many cases by four major gaps in our understanding of pollinator-yield effects. The first three of these are related to the plant breeding system and only the last relates to the plant–pollinator interaction. First, the functional form of the relationship between increased number or quality of pollen grains deposited and yield is often not known. Secondly, this functional form is likely to vary significantly among crop varieties and species as some species may rely more or less on outcross pollen. Thirdly, this functional form may vary under different conditions of resource limitation (e.g. water, nutrients). Finally, the relationship between pollinator abundance and the amount and quality of pollen delivered is influenced by pollinator foraging behaviour, across scales from within the flower, to across flower patches and to foraging decisions over the entire landscape (Klein et al., 2007
; Kremen et al., 2007
; Ricketts et al., 2008
Once the relationship between pollinator abundance and crop yield is parameterized (i.e. the input–output relationships are understood), it can be used to predict the economic value of pollination or any other input, based on their relative contributions to crop yield. Using production functions in this way will result in an estimate of the economic value of pollinators at each farm
. It is most likely of interest, however, to estimate the value of the habitats in the landscape that support these pollinators. For this, the ecological models described here can be used to attribute economic value realized on farms back to the pollinator-supporting habitats. Once this is done, spatially-explicit, optimization techniques and heuristics already exist (Polasky et al., 2005
) and provide a decision structure with which to evaluate land-use plans. When combined with decision analysis, the model can be used to evaluate alternate land-use plans designed to promote pollinator services and maximize economic return from the crop.
While the economic value of pollinators for agricultural production is important to determine, we recognize that the motivation to estimate each bee species' monetary value is simply a strategy to ensure their conservation. The quantitative model presented here fills an important gap in conservation planning. Incorporating landscape models into land-use planning for multi-species conservation is an ongoing area of research but most of these models exclude pollinators focus solely on vertebrates (birds, mammals and herps) and those that have included pollinators do not incorporate much biological detail (Chan et al., 2006
). Estimating the social value of pollinators (financial or otherwise) is not a scientific exercise (Gregory et al., 2006
), but the scientific modelling framework developed here can be applied to inform management of landscapes where pollinator conservation is a fundamental objective, rather than the means to an economic end.