InVEST +VERSION+ documentation

# Pollinator Abundance: Crop Pollination¶

## Summary¶

The InVEST pollination model focuses on wild bees as a key animal pollinator. It uses estimates of the availability of nest sites and floral resources and bee flight ranges to derive an index of bee abundance nesting on each cell on a landscape (i.e., pollinator supply). It then uses flight range information to estimate an index of bee abundance visiting each agricultural cell. If desired, the model then calculates a simple index of the value of these bees to agricultural production, and attributes this value back to source cells. The results can be used to optimize agriculture and conservation investments. Required inputs include a current land use and land cover map, land cover attributes, species of pollinators present, and their flight ranges. The model’s limitations include exclusion of non-farm habitats that may determine pollinator abundance and of the effects of land parcel size. The model also does not account for managed pollinators and pollinator persistence over time.

## Introduction¶

Crop pollination by bees and other animals is a potentially valuable ecosystem service in many landscapes of mixed agricultural and natural habitats (Allen-Wardell et al. 1998, Free 1993). Pollination can increase the yield, quality, and stability of fruit and seed crops as diverse as tomato, canola, watermelon, coffee, sunflower, almond, and cacao. Indeed, Klein et al. (2007) found that 87 of 115 globally important crops benefit from animal pollination, a service valued variously in the billions to tens of billions per year globally (Costanza et al. 1997, Losey and Vaughan 2006, Nabhan and Buchmann 1997, Southwick and Southwick 1992).

Despite these numbers, it is important to realize that not all crops need animal pollination. Some crop plants are wind (e.g., staple grains such as rice, corn, wheat) or self pollinated (e.g., lentils and other beans), needing no animal pollinators to successfully produce fruits or seeds. Klein et al. (2007) provides a list of crops and their pollination requirements that can help identify whether crops in a region of interest may benefit from wild animal pollinators.

Decision-makers can use information on crop pollinators, their abundance across a landscape, and the pollination services they provide to crops in several ways. First, with maps of pollinator abundance and crops that need them, land use planners could predict consequences of different policies on pollination services and income to farmers (for an example, see Priess et al. 2007). Second, farmers could use these maps to locate crops intelligently, given their pollination requirements and predictions of pollinator availability. Third, conservation organizations or land trusts could use the tool to optimize conservation investments that benefit both biodiversity and farmers. Finally, governments or others proposing payment schemes for ecosystem services could use the results to estimate who should pay whom, and how much.

## The Model¶

A wide range of animals can be important pollinators (e.g., birds, bats, moths and flies), but bees are the most important group for most crops (Free 1993). As a result, the InVEST Pollination model focuses on the resource needs and flight behaviors of wild bees. Many people think of honeybees, managed in artificial hives, when they think of pollinators, but wild bees also contribute to crop pollination. In fact, for several important crops (e.g., blueberries), native species are more efficient and effective pollinators than honeybees (Cane 1997). These native bees, in addition to feral honeybees living in the wild, can benefit crops without active management of captive hives. This is the pollination service associated with habitat conservation.

For bees to persist on a landscape, they need two things: suitable places to nest, and sufficient food (provided by flowers) near their nesting sites. If provided these resources, pollinators are available to fly to nearby crops and pollinate them as they collect nectar and pollen. The model therefore uses information on the availability of nesting sites and flower resources, as well as flight ranges of bees, to map an index of bee abundance across the landscape. In a second step, the model uses this map and bee flight ranges again to predict an index of the number of pollinators likely visiting crops in each agricultural cell on the landscape. If you opt to also estimate value indices, the model then takes a third and fourth step. In the third step, it uses a simplified yield function to translate bee abundance into crop value on each agricultural cell. And in the fourth step, it attributes these cell values back to cells “supplying” these bees. These steps are laid out in more detail below, and the full model description can be found in Lonsdorf et al. (in press).

### How it Works¶

The model is based on a small set of biophysical data:

• land use and land cover (LULC) map;
• a biophysical table paired with the LULC raster to map LULC types to nesting suitability and floral resources;
• a pollinator guild table with properties about active seasons, nesting preferences, mean flight distances, and relative abundances;
• a farm shapefile indicating the geospatial location of farms, crop type, dependence on pollinators, proportion of managed pollinators, as well as overrides for nesting sites and floral resources.

Because bees are proficient fliers, they integrate over several elements of a landscape, moving between nesting habitats and foraging habitats (Ricketts et al. 2006). The distances they typically fly affect both their persistence and the level of service they deliver to farms. The model therefore requires a typical foraging distance for each pollinator species. These data can be supplied from quantitative field estimates (e.g., Roubik and Aluja 1983), proxies such as body size (Greenleaf et al. 2007), or from expert opinion.

#### Pollinator Supply¶

Using these data, the model first estimates the abundance index of each pollinator species in every cell in the landscape, based on the available nesting sites in that cell and the flowers (i.e., food) in surrounding cells. Flowers in nearby cells are given more weight than distant cells, according to the species’ average foraging range. Since pollinator abundance is limited by both nesting and floral resources, the pollinator abundance for species $$s$$ index on cell x, $$PA(x,s)$$, is the product of available floral resources and weighted exponential distance of pollinator supply such that:

$PA(x,s)=FR(x,s)\frac{\sum_{x'\in X}PS(x',s) \exp(-D(x,x')/\alpha_s)}{\exp(-D(x,x')/\alpha_s)}$

where $$D(x,x')$$ is the Euclidean distance between cells $$x$$ and $$x'$$ and $$\alpha_s$$ is the expected foraging distance for the pollinator $$s$$ (Greenleaf et al. 2007).

$$PS(x,s)$$ is the pollinator supply index at pixel $$x$$: for species $$s$$ defined as

$PS(x,s)=FR(x,s) HN(x,s) SA(s)$

where $$FR(x,s)$$: is the floral resources index at pixel $$x$$: for species $$s$$ defined as

$FR(x,s)=\frac{\sum_{x'\in X}\sum_{j\in J}RA(l(x),j) FA'(s,j) \exp(-D(x,x')/\alpha_s)}{\sum_{x'\in X}\exp(-D(x,x')/s)}$

$$HN(x,s)$$ is the habitat nesting suitability at pixel $$x$$ for species $$s$$

$HN(x,s)=\max_{n\in N}\left[N(l(x),n) ns(s,n)\right]$

where

• math:SA(s) is the relative species abundance for species s in the range $$[0.0, 1.0]$$, and $$\sum_{s\in S} SA(s) = 1$$
• $$N(l,s)$$ is the nesting suitability for landcover type $$l$$ for species $$s$$ in the range $$[0.0, 1.0]$$.
• $$l(x)$$ is the landcover type at pixel $$x$$

see the Table of Variables Appendix for all variable definitions and properties.

#### Farm Supply and Yield¶

Given pollinator supply, the model can calculate an index of potential yield in agricultural cells. Assuming index of 0 yields 0% of pollinated yield, and 1.0 is a 100% pollinator dependent yield, we use a tunable “half saturation” function for farm pixel yields:

$FP(x,j)=\max(0, \min(mp(x,j) +\sum_{s\in S}PA(x,s)\cdot FA(s,j),1))$

note the max/min notation clamps $$FP$$ to 0..1 where $$mp(x,j)$$ is the index of managed pollinators available at pixel $$x$$ during season $$j$$ due to a farm polygon overlaying that pixel. We use a tunable half-sigmoid to calculate the expected index of yield per farm due to pollinators as

$PY(x)=\frac{\sum_{j\in J}FP(x,j)(1-h(x,j))}{h(x,j)(1-2FP(x,j))+FP(x,j)}$

where $$h(x,j)$$ is the half saturation constant at pixel $$x$$ during season $$j$$ indicating what proportion of pollinators cause half the yield to be pollinated.

Using units of the model and accounting for total yield at a pixel, we can calculate the total yield on the farm as

$Y(f)=1-\nu(f)\left(1-\sum_{x\in X(f)}PY(x)/|X(f)|\right)$

where $$f$$ is a particular farm, $$X(f)$$ are the set of pixels covering farm $$f$$, and $$|X(f)|$$ is the count of pixels covered by farm $$f$$. The $$\nu(f)$$ function represents the property that crops vary in their dependence on pollinators; some crop species are self-compatible and yield is less dependent on pollination while other species obligately require pollination to generate any yield (Klein et al. 2007). In this case $$\nu(f)$$ is a scalar $$\in [0,1]$$ representing what proportion of yield is dependent on pollinators.

### Limitations and Simplifications¶

The model predicts only relative patterns of pollinator abundance and pollination value (using indices of 0-1). This is because absolute estimates of nest density, resource availability, and pollinator abundance are rarely available, and yield functions (including pollinator abundance) for many crops are poorly defined. Relying on relative indices limits our ability to estimate absolute economic values to better inform land-use planning decision-making, often based on cost-benefit analyses.

The model does not include the dynamics of bee populations over time, and therefore cannot evaluate whether these populations are sustainable given the current landscape. Instead, the model simply provides a static snapshot of the number of pollinators on each cell in the landscape, given simple estimates of nesting sites and food resources. Some of the factors that influence bee populations, like habitat disturbances and typical population fluctuations, are not captured.

The model does not account for the sizes of habitat patches in estimating abundance. For many species, there is a minimum patch size, under which a patch cannot support that species over the long term. There is some evidence that small patches support fewer species of bees (Kremen et al. 2004), but bees can also survive in surprisingly small areas of suitable habitat (Ricketts 2004).

Pollinators are likely to be influenced by fine-scale features in the landscape, which are difficult to capture in typical land-cover data with typical resolutions of 1km or even 30m. For example, small patches of flower resources in an otherwise hostile habitat for bees can provide important food resources, but will not be detected by typical land cover maps. Some bees are also able to nest in small but suitable areas (a single suitable roadside or tree hollow). Using average values of nesting site or flower availability for each land cover type, along with 30m pixels or larger, will therefore not capture these fine scale but important areas of resources.

## Data Needs¶

1. Land cover map (required). A GIS raster, with a land use and land cover (LULC) code for each cell. The raster should be projected in meters and the projection should be defined. This coverage must be of fine enough resolution (i.e., sufficiently small cell-size) to capture the movements of bees on a landscape. If bees fly 800 meters on average and cells are 1000 meters across, the model will not fully capture the movement of bees from their nesting sites to neighboring farms.
2. Table of pollinator species or guilds (required). A table containing information on each species or guild of pollinator to be modeled. Guild refers to a group of bee species that show the same nesting behavior, whether preferring to build nests in the ground, in tree cavities, or other habitat features. If multiple species are known to be important pollinators, and if they differ in terms of flight season, nesting requirements, or flight distance, provide data on each separately. If little or no data are available, create a single ‘proto-pollinator,’ with data taken from average values or expert opinion about the whole pollinator community.

File Type: Comma separated CSV.

Rows: each row is a unique species or guild of pollinator.

Columns: columns contain data on each species or guild. Column order doesn’t matter, but columns must be named as follows (italicized portions of names can be customized for meaning, but must be consistent with names in other tables):

1. species: Name of species or guild (Note: species names can be numerical codes or names.
2. Any number of nesting_suitability_[SUBSTRATE]_index for each substrate modeled: Values should be entered as a number between 0 or 1, with 1 indicating a nesting substrate that is fully utilized and 0 indicating a non-utilized nest substrate. Substrates can be user defined, but might include ground nests, tree cavities, etc.
3. foraging_activity_[SEASON]_index: Pollinator activity by floral season (i.e., flight season). Values should be entered as a number between 0 to 1, with 1 indicating the time of highest activity for the guild or species, and 0 indicating no activity. Seasons are user defined but might include spring, summer, fall; wet, dry, etc.
4. Alpha: average distance each species or guild travels to forage on flowers, specified in meters. The model uses this estimated distance to define the neighborhood of available flowers around a given cell, and to weight the sums of floral resources and pollinator abundances on farms. Value can be determined by typical foraging distance of a bee species based on an allometric relationship (see Greenleaf et al. 2007).

Example: A hypothetical study with four species. There are two main nesting types, “cavity” and “ground.” Species A is exclusively a cavity nester, species B and D are exclusively ground nesters, and species C uses both nest types. There is only a single flowering season, “Allyear,” in which all species are active. Typical flight distances, specified in meters (Alpha), vary widely among species.

Example Guilds Table
SPECIES nesting_suitability_cavity_index nesting_suitability_ground_index foraging_activity_spring_index foraging_activity_summer_index alpha relative_abundance
Apis 1 1 1 1 500 0.75
Bombus 1 0 0.8 1 1500 1
1. Table of biophysical land cover attributes (required). A table containing data on each class in the LULC map (as described above in #1). Data needed are relative indices (0-1). Data can be summarized from field surveys, or obtained by expert assessment if field data is unavailable.

File type: comma separated CSV.

Rows: each row is a different LULC class.

Columns: each column contains a different attribute of each LULC class, and must be named as follows:

1. LULC: Land use and land cover class code. LULC codes match the ‘values’ column in the LULC raster and must be numeric, in consecutive order, and unique.
1. nesting_[SUBSTRATE]_availability_index: Relative index of the availability of the given nesting type within each LULC type, on a scale of 0-1. The substrate must match one-for-one the substrates given in the guild table.
2. floral_resources_[SEASON]_index: Relative abundance (0-1) of flowers in each LULC class for the given season. There are two aspects to consider when estimate relative floral abundance of each LULC class: % floral abundance or % floral coverage as well as the duration of flowering during each season. For example, a land cover type that comprises 100% of a mass flowering crop that flowers the entire season with an abundance cover of 80% would be given a suitability value of 0.80. A land cover type that flowers only half of the season at 80% floral coverage would be given a floral suitability value of 0.40. The season must match one-for-one the seasons given in the guild table.

Example:

Example Biophysical Table
lucode nesting_cavity_availability_index nesting_ground_availability_index floral_resources_spring_index floral_resources_summer_index
1 0.3 0.2 0.7 0.5
2 0.3 0.2 0.7 0.5
3 0.3 0.2 0.7 0.5
4 0.3 0.2 0.7 0.5
6 0.3 0.2 0.7 0.5
7 0.3 0.2 0.7 0.5
8 0.3 0.2 0.7 0.5
1. Farm Polygon: In order to do yield calculations, the model uses a polygon vector layer to indicate farm areas, and the attribute table of that vector to provide farm-specific information. Specifically, the vector’s attribute table must include the following fields:
1. crop_type (string): Name of the crop grown on that polygon, ex. “blueberries”, “almonds”, etc.
2. half_sat (float in the range [0.0, 1.0]): The half saturation coefficient for the crop grown on that farm.
3. season (string): the season in which the crop is pollinated. This season must match the seasons provided in the guilds table.
4. fr_[SEASON] (float in the range [0.0, 1.0]): the floral resources available at this farm for the given season. Seasons must match one-for-one the seasons provided in the guild table.
5. n_[SUBSTRATE] (float in the range [0.0, 1.0]): the nesting substrate suitability for the farm for the given substrate. Substrates must match one-for-one the substrates provided in the guild table.
6. p_dep (float in the range [0.0, 1.0]): the proportion of crop dependant on pollinators.
7. p_managed (float in the range [0.0, 1.0]): the proportion of pollinator supply on the farm provided by managed pollinators.

## Interpreting Results¶

### Final Results¶

Final results are found in the workspace directory specified when the model is run.

• Parameter log: Each time the model is run, a text (.txt) file will appear in the Output folder. The file will list the parameter values for that run and will be named according to the service, the date and time, and the suffix.
• total_pollinator_yield.tif: per-pixel pollinator yield index for pixels that overlap farms.
• pollinator_abundance_[SPECIES].tif: Pollinator abundance per species.
• farm_yields.shp: A copy of the input farm polygon vector file with the additional fields:
1. p_av_yield: average yield index on farm due to pollinator activity.
2. t_av_yield: average yield index on farm due to pollinator and other pollination (eg. wind) activity.

#### Intermediate Results¶

You may also want to examine the intermediate results. These files can help determine the reasons for the patterns in the final results. They are found in the intermediate_outputs folder within the workspace directory defined on the model run.

## Appendix: Table of Variables¶

• $$x$$ - a pixel coordinate.
• $$X$$ - set of all pixels in the landcover map.
• $$F$$ - set of all pixels that are located in farms.
• $$s$$ - bee species.
• $$n$$ - nesting type (ground, cavity).
• $$N$$ - set of all nesting types.
• $$j$$ - season (fall, spring, etc).
• $$J$$ - set of all seasons (ex: {fall, spring}).
• $$ns(s,n)$$ - nesting suitability preference for species $$s$$ in nesting type $$n$$.
• $$HN(x,s)$$ - habitat nesting suitability at pixel $$x$$ for species $$s$$ [0.0, 1.0].
• $$N(l,s)$$ - nesting suitability for landcover type $$l$$ for species $$s$$ in the range $$[0.0, 1.0]$$.
• $$RA(l,j)$$ - relative abundance of flowers on landcover type $$l$$ during season $$j$$. $$[0.0, 1.0]$$
• $$FA(s,j)$$ - foraging activity for pollinator species species $$s$$ during season $$j$$
• $$FA’(s,j)$$ - relative foraging activity for species $$s$$ during season $$j$$ calculated by dividing $$FA(s,j)$$ by the sum of all seasons.
• $$FR(x,s)$$ - floral resources available at pixel $$x$$ for species $$s$$.
• $$D(x,x')$$ - euclidian distance between the centroid of pixel $$x$$ and $$x'$$.
• $$s$$ - mean foraging distance for species s.
• $$PS(x,s)$$ - pollinator supply index at pixel $$x$$ for species $$s$$.
• $$PA(x,s)$$ - pollinator abundance at pixel $$s$$ for species $$s$$.
• $$FP(x)$$ - pollinator abundance at a farm pixel accounting for all species, seasonal activity, and managed bee populations.
• $$p$$ - pollinator abundance; an abstraction for any particular $$PA(x,s)$$
• $$k(f)$$- half saturation coefficient of the crop grown on farm $$f$$.
• $$MP(f)$$ - index of availability of managed pollinators on farm $$f$$.
• $$fs(x)$$ - species that pollinates the crop on the farm at pixel $$x$$.
• $$h(x)$$ - half saturation coefficient for the farm located at pixel $$x$$.
• $$PY(x,j)$$ - yield at pixel x for season $$j$$.
• $$SA(s)$$ - relative species abundance for species $$s$$.
• $$Y(f)$$ - average farm yield for farm parcel $$f$$ accounting for pollinator dependency of crop.

## Appendix: Data Sources¶

List of globally important crops and their dependence on animal pollinators: (Klein et al. 2007).

## References¶

Allen-Wardell, G., P. Bernhardt, R. Bitner, A. Burquez, S. Buchmann, J. Cane, PA Cox, V. Dalton, P. Feinsinger, M. Ingram, D. Inouye, CE Jones, K. Kennedy, P. Kevan, and H. Koopowitz. 1998. The potential consequences of pollinator declines on the conservation of biodiversity and stability of food crop yields. Conservation Biology 12: 8-17.

Cane, JH. 1997. Lifetime monetary value of individual pollinators: the bee habropoda laboriosa at rabbiteye blueberry (vaccinium ashei reade). Acta Horticulturae 446: 67-70.

Costanza, R., R. d’Arge, R. de Groot, S. Farber, M. Grasso, B. Hannon, K. Limburg, S. Naeem, RV O’Neill, J. Paruelo, RG Raskin, P. Sutton, and M. van den Belt. 1997. The value of the world’s ecosystem services and natural capital. Nature 387: 253-260.

Free, JB. 1993. Insect pollination of crops. Academic Press, London.

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Greenleaf, SS, and C. Kremen. 2006. Wild bee species increase tomato production and respond differently to surrounding land use in Northern California. Biological Conservation 133:81-87.

Klein, AM, BE Vaissiere, JH Cane, I. Steffan-Dewenter, SA Cunningham, C. Kremen, and T. Tscharntke. 2007. Importance of pollinators in changing landscapes for world crops. Proceedings of the Royal Society B-Biological Sciences 274: 303-313.

Kremen, C., NM Williams, RL Bugg, JP Fay, and RW Thorp. 2004. The area requirements of an ecosystem service: crop pollination by native bee communities in California. Ecology Letters 7: 1109-1119.

Lonsdorf, E., C. Kremen, T. Ricketts, R. Winfree, N. Williams, and SS Greenleaf. 2009. Modelling pollination services across agricultural landscapes. Annals of Botany 1: 12. online [http://aob.oxfordjournals.org/content/103/9/1589.abstract?sid=b0f6fc9e-bd52-4bec-8248-50e56b78344d]

Lonsdorf, E., TH Ricketts, CM Kremen, NM Williams, and S. Greenleaf. in press. Pollination services in P. Kareiva, TH Ricketts, GC Daily, H. Tallis, and S. Polasky, eds. The theory and practice of ecosystem service valuation.

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Nabhan, GP, and SL Buchmann. 1997. Services provided by pollinators. Pages 133-150 in GC Daily, ed. Nature’s services. Island Press, Washington, D.C.

Priess, JA, M. Mimler, AM Klein, S. Schwarze, T. Tscharntke, and I. Steffan-Dewenter. 2007. Linking deforestation scenarios to pollination services and economic returns in coffee agroforestry systems. Ecological Applications 17: 407-417.

Ricketts, TH. 2004. Tropical forest fragments enhance pollinator activity in nearby coffee crops. Conservation Biology 18: 1262-1271.

Ricketts, TH, NM Williams, and MM Mayfield. 2006. Connectivity and ecosystem services: crop pollination in agricultural landscapes. Pages 255-289 in M. Sanjayan and K. Crooks, eds. Connectivity for Conservation. Cambridge University Press, Cambridge, UK.

Roubik, DW, and M. Aluja. 1983. Flight ranges of Melipona and Trigona in tropical forest. Journal of the Kansas Entomological Society 56: 217-222.

Southwick, EE, and L. Southwick. 1992. Estimating the economic value of honey-bees (Hymenoptera; Apidae) as agricultural pollinators in the United States. Journal of Economic Entomology 85: 621-633.

Winfree, R., J. Dushoff, EE Crone, CB Schultz, RV Budny, NM Williams, and C. Kremen. 2005. Testing simple indices of habitat proximity. American Naturalist 165(6): 707-717.