1. InVEST Crop Pollination
Stacie Wolny

2. Crop Pollination /
75% of important crop plants benefit from animal pollination
Fruits and vegetables, not staple grains or beans
Service valued at billions of dollars per year globally
Bees are the most important pollinators for most crops. It is said that on average one out of every 3 bites of food we eat comes from plants pollinated by insects. Pollination can increase the yield, quality, and stability of fruit and seed crops like almonds, apples, blueberries, melon, cacao, vanilla. Wild pollinators help insure food production, quality and security (especially with the decline of honeybees recently.) Valued at tens to hundreds of billions of dollars worldwide per year. Scientists at UC Berkeley did a study that found that wild pollinators are responsible for $1-$2 billion worth of crops in California alone – that’s more than 1/3. The other 2/3 is probably pollinated by commercial bees. For almonds, more than one million hives are hauled here from around the country every year.

3. / Crop Pollination Wild bees need: Food – pollen, nectar
Nesting sites - trees, ground
Wild bees provide:
Increased crop yield and quality
Food security
Our model focuses on wild bees, native bees and feral honeybees. Besides European honeybees, 20,000 other kinds of bees pollinate plants.
Bees need food, in the form of pollen and nectar, which they get from flowering plants, and places to build nests, like tree cavities and holes in the ground. Nectar: energy source and honey; pollen: protein and other nutrients, also for larvae
Pollination can increase the yield, quality, and stability of fruit and seed crops. Wild pollinators help insure food production, quality and security, especially with the recent decline of honeybees worldwide.

4. / Existing models No other generic pollination models
Mostly location- or crop-specific
Since wild bees are so important for agriculture, we need to better understand how land management can affect their numbers and the services they provide. Of the work that has been done to model crop pollination, almost all of it is location-specific or crop-specific. For example, there is a model specifically for almond pollination and fruit set. Some researchers use a combination of separate plant and pollinator models. But no generic bee pollination models exist that can be applied to any crop in any place in the world. That’s why we made the InVEST pollination model.

5. InVEST Pollination Model
Focus on wild bees
Source abundance of pollinators across landscape
Farm abundance in agricultural areas
Pollination value in agricultural areas
Survey of 23 case studies, general trend of decline in pollination services with increasing isolation from natural habitat
Native bees + feral honey bees, not managed, captive hives. Wild bees because their pollination is an ecosystem service from natural systems. Utilizes availability of nesting sites, flower supply and flight ranges to give a relative abundance of pollinators across the whole landscape, the abundance visiting farms and the value of their farm visitation.
Pictured: Sweat bee, mason bee, carpenter bee, honey bee, bumble bee

6. Big picture Floral resources Nesting resources Floral resources
Crop response
For bees to persist in an area, they need nesting sites and food (nectar and pollen from flowers.) They will travel within a certain foraging distance from nesting sites to nearby crops and flowers and pollinate them as they collect food. As crops get pollinated, they respond by yielding more fruit. The overall level of pollinator service for a farm depends on the crops grown, how they respond to pollination, the ability of the local species to pollinate those crops and their abundance.
Flower availability (food) will change with the seasons. The bee population can change as food and/or nesting sites become more or less available. Crops produce more or less fruit as pollinator populations wax and wane.
Foraging
+ Population dynamics
of pollinators / plants

7. InVEST Pollination Model
Floral resources
Nesting resources
Floral resources
Crop response
The InVEST pollination model is fairly simple, and does not take population dynamics or crop response into account. It considers the nesting availability on each cell of the landscape, the food (floral) resources nearby and the flight ranges of bees. Uses this information to map an index of bee abundance across the landscape, an index of the number of bees visiting farms and an index of the value of these farm visitations to crop yield. This is important to remember: our model does not predict absolute numbers of bees, or pollination deposition, it only creates a relative index of where bees are likely to be found and how well agricultural sites are likely to be visited.
Foraging
+ Population dynamics
of pollinators / plants

8. Approach to Abundance 1. Calculate the abundance of bees
in each cell of the landscape
- Nesting sites in that cell
- Floral resources in surrounding cells
2. Calculate the abundance of bees
visiting each farm cell
- Pollinator supply in surrounding cells
- Foraging distance
100m
300m
1/ The model first calculates the abundance index of each bee species on each cell in the landscape, based on the nesting resources available in that cell and flower resources available in surrounding cells, using the Euclidian distance between target cell and surrounding cells. Assumption that foraging frequency declines exponentially with distance. Flowers that are nearby are given more weight than those farther away, according to the species’ foraging distance. Abundance score is the product of foraging and nesting scores. This is the “supply” map.
2/ Using the results from (1), the model calculates the abundance of bees visiting each agricultural cell, based on each species’ foraging distance. Sums pollinator abundance in surrounding cells, giving more weight to nearest. Done separately for each species. This is the “service” map because it shows how the potential pollinators in the supply map benefit people.
Foraging distance = 400m

9. Approach to Valuation
Assumption: Crop yields increase as pollinator visitation increases, with diminishing returns
Calculate crop yield (value)
Farm abundance
Half-saturation constant
Wild pollinator proportion
Distribute value back to supply cells
Fraction for each bee species
Distribute fraction among source cells
Relative index, not dollar value
$$$ $$ $$ $
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The model uses a simple yield function to translate bee abundance into crop value on each agricultural cell in the landscape, and attributes this value back to the cells that are “supplying” the bees (= habitat).
A half-saturation constant converts the pollinator supply into yield and represents the abundance of pollinators required to reach 50% of pollinator-dependent yield.
Wild pollinator proportion: the proportion of total crop c’s yield attributed only to wild pollination.
Since crop response is not modeled, this is not a production function, but a simple crop yield function, assuming that yield increases as pollinator visitation increases, with diminishing returns. First calculates value; then assigns fractions of that value to each bee species, according to its abundance at that farm cell; then each species’ value is distributed back to their source cells, weighted by distance. Habitats close by provide more service value than those far away. This represents the “value” map.
This model outputs relative values only, not absolute dollar values. So the resulting map will give a relative ranking of which cells on the landscape are likely to increase crop yield in nearby farm cells.

10. Validation
Coffee in Costa Rica, watermelon in California. Model parameters were derived independent of field validation data (foraging range was based on body size, floral availability based on other studies etc.)
Costa Rica – Valle del General, dominated by coffee, sugarcane, pasture; hundreds of remnants of tropical moist forests. Study conducted on 12 sites in a large coffee farm. 1m aerial photos classified by LULC, assigned nesting/floral resource values based on expert opinion and informed by other work in the area. Most common 11 types of native stingless bees and feral honeybee. No info on seasonality, assumed one season. Measured bee activity, pollen deposition, between 10m and 1600m from nearest major forest patch. Models predict 80% of abundance, not strong predictor of pollen deposition, which is a closer correlate to actual pollination service. Variation in pollen deposition also depends on the efficiency of each bee species, resource limitation of the coffee plant and other factors that our model doesn’t capture.
California: Central Valley, across farms that were located along a strong gradient from natural areas (oak woodland/chaparral/riparian.) LULC data from 30m Landsat image, plus hand-drawn areas for resources from road edges, residential, irrigation ditches etc.) Nesting/floral values from expert opinion from studies done in the same landscape. Bee visits were recorded at 12 sites, median species-specific pollen deposition was estimated. Does not include the honeybee, which is managed here. Ok fit for total abundance, better for pollen deposition from native bees.
We don’t know why these results are so different: perhaps because the bees that were present in Costa Rica weren’t interested in or good at pollinating coffee, where in CA they were more so? Don’t know. Takeaway: this model is pretty good at predicting overall abundance, but not the actual service.

11. Sensitivity For Costa Rica study:
Most sensitive to foraging resources in
coffee (t-value = , p < .05)
and forest (t-value = 3.493, p < .05)
Also species foraging distance 77 – 214m
Huge black bee (t-value 2.376, p < .05)
Trigona fulviventris (t-value 3.158, p < .05)
Goal: calculate how variation in each parameter affects estimates of a parcel’s pollinator abundance, independent of all other parameters. Selected parameter values randomly from a uniform distribution within min/max.
This indicates that estimating floral resources is the highest priority for understanding pollinator response to landscape change.

12. Input Data Land use / land cover map Land use attributes
A land use map is a grid of cells, where each cell is assigned a land use class. In this example, all of the green cells have been assigned the land use class of ‘forest’, the yellow cells the class ‘agriculture’ and the grey cells ‘urban’. The model requires this map, and optionally a list of the land use classes that represent agricultural cells.
For each land cover type, information on nesting sites and flower availability are required, which can be gotten from field estimates or expert opinion.
N = Relative index (0-1) of the availability of that nesting type in that LU class.
Give a 1 to the LULC with greatest abundance of that cover, and make all others relative to that.
F = Relative index (0-1) of the abundance of flowers in that LU class for that season.

13. Input Data Species / guild attributes Half-saturation constant
Wild pollinator proportion
Future landcover map (optional)
For each bee species or guild, the following information is needed:
NS = Nesting types (guilds) that are used by each pollinator – 1 it is used, 0 it isn’t.
FS = Pollinator activity by season. 0-1, with 1 indicating time of greatest activity, 0 no activity.
Activity level by a given species over all seasons should sum to 1.
Alpha = foraging distance for that species. Can get from field studies or a proxy such as body size.
Half-saturation constant: abundance of pollinators required to achieve 50% of pollinator-dependent yield. Used to translate abundance into yield.
Wild pollinator proportion: proportion of crop c’s yield that is attributable only to wild pollination. 1 if it requires pollination, 0 if the crop doesn’t use it at all, like a wind-pollinated grain.
Guilds are groups of species in a community that exploit the same set of resources in a similar manner
Optional: future land use map

14. Output Maps Pollinator abundance over whole landscape
Pollinator abundance on farms
Pollinator service value
For both current and future scenario, if provided
The model can produce 3 types of output.
Pollinator abundance over landscape: An index (0-1) of the likely abundance of pollinator species nesting on each cell in the landscape, given the availability of nesting sites in that cell and of flower (food) resources nearby. Summed over all species. Represents potential sources of pollinators, but if there is no demand then there is no service being provided.
Pollinator abundance on farms: Pollinator abundance on each agricultural cell in the landscape, based on the average of all bee species or guilds. It represents the likely average abundance of pollinators visiting each farm site, based on their foraging distance. Represents the relative amount of service provided to the demand points, which are agriculture cells.
Pollinator service value: This is a map of where pollination services are coming from, and their
(relative) values. The relative value of the pollinator “supply” in each agricultural cell to crop production in the surrounding neighborhood. Units are not dollars, but the index is a relative measure of economic value.

15. Application Land use planners: Consequences of policies on farmers
Farmers: Locate crops
Land trust: Invest in places that benefit both biodiversity and farmers
Payments for ecosystem services
PES: Can combine with other InVEST tool results to rank the landscape for areas that are likely to provide multiple ES, giving the biggest bang for the buck.

16. Run the model

17. Install GDAL 1/ Download GDAL from:
2/ Open User Guide:
<InVEST install>/InVEST_2.2.1_Documentation.pdf
ArcGIS 9.3.x users need to install, Arc10 users don’t.

18. Post-analysis Colony Collapse!! Prioritize conservation efforts
Input to crop production function
Effects of field buffers
Bombus
Apis
Show a quick analysis comparing default sample data results with the results from removing Apis from the Guilds table. Big difference in outputs: for default, farms provide a lot of Apis, but hardly any Bombus, so the supply and value plummet, and nearby forest becomes more valuable.
Normalize results from Pollination and other ES outputs, add together to get rank map used to prioritize efforts.
Production function: takes into account climate, management practices, as well as pollination. Gives a more accurate crop yield than our simple function. Try using abundance maps as input.
Field buffers around farms: Good for soil, water cleaning, potentially pollination. Might help convince farmers to plant them if multiple ES (including better pollination for their crops) were improved.

19. Limitations No population dynamics over time
Relative indices of abundance and value only
No population dynamics over time
Fine-scale resources not captured
No effects of land parcel size
No managed pollinators
Strengths: it is simple, and provides both biophysical and economic output. But because the model is simple, it has significant limitations.
It only provides relative indices of abundance and value – absolute values of nest sites and floral resources are rarely available and yield functions for many crops are poorly defined. So the results cannot be applied to, say, a cost-benefit analysis of farm management or habitat restoration.
With no population dynamics, the model does not evaluate whether the pollinator populations are sustainable.
Land parcel size: for many species there is a minimum patch size necessary for their viability. But we assume that any size cell with a landuse assigned a high nesting value can support that species. Maybe the species actually needs a patch size much larger than the cell size.
Pollinators are sensitive to fine-scale features, like small patches of flowers or a single hollowed-out log for nesting that won’t be picked up by land cover maps.

20. Outlook
Specify half-saturation and wild pollinator constants per land use
Currently, the model takes the half-saturation and wild pollinator constants as single values that are applied uniformly to all agricultural land use classes. But really each crop responds differently, so in future versions these values will be specified per land use.
Otherwise, we haven’t gotten enough feedback on the model to know how well it works or what needs to be improved, so if you use it, please tell us what you think.
Poster from the US Fish and Wildlife Service

21. Equations Pollinator abundance on cell x:
Nj = suitability of nesting on LULC j
Fj = floral resources on LULC j
Dmx = Euclidian distance
a = foraging distance
D = distance between target cell x and source cells m = 1 -> M
Since pollinator abundance is limited by both nesting and floral resources, the pollinator abundance index on cell x, Px, is simply the product of foraging and nesting, weighted by distance. The denominator is the maximum amount of foraging available in the landscape, used to normalize the result.

22. Equations Farm abundance from source cell x to ag cell o:
The numerator of this equation represents the distance-weighted proportion of the pollinators supplied by cell x that forage within cell o and the denominator is a scalar that normalizes this contribution by the total area within foraging distance. The total pollinator abundance on agricultural cell o, Po, is simply the sum over all M cells.
Px = supply of pollinators on cell x
Dox = Euclidian distance
a = foraging distance

23. Equations - Valuation Expected yield of crop c on farm o:
nc = proportion of crop c’s yield attributed to wild pollination
kc = Half-saturation constant
vc would be equal to 1 if a crop is an obligately outcrossing species and equal to 0 if the crop species were wind-pollinated
kc = abundance of pollinators required to reach 50% of pollinator-dependent yield
Service value at supply cell m: Sum of values from all agricultural cells o; Po is Pollinator abundance on ag cell o; Pom is the farm abundance supplied by cell m on ag cell o
Pollinator service
value for cell m:
Vo = crop value in farm cell o