I am wondering how I should validate the half_sat rate for the pollination model.
User guide: tunable paramter that may be most useful to adjust following an initial run of the model and an examination of the results.
→ Examination with what? yield data: however, yield data is highly multifactorial)
→ Is there any expert knowledge or literature to find the half_sat for my crops in Switzerland?

Absent empirical yield data for your crop and region, I would run the model with a default half saturation coefficient value of 0.5 and see how the pattern of spatial yield results aligns with what you might expect. Then, vary this value slightly (up or down) to see how the results change from your baseline value of 0.5. This will give you a sense of the sensitivity of results to the half saturation coefficient parameter and how close to reality the model may or may not be representing pollinator-attributable yield.

Comparison with observations is surely the best way to validate model results. If you do not have such data, yes, you ought to perform a literature review for your crops and region. Also, Klein et al. 2007 provides a list of globally important crops and their dependence on animal pollinators (see Table 2 and the Supplemental Material).

Hmm is there really a link between Klein et al. 2007 (pollination dependency of crops) and InVEST half_sat? Half_sat has no relationship to pollination dependency, because it is already related to “total potential pollinator-dependent yield. What are the half_sat values for the five categories in Klein et al. 2007: 1. Increase, 2. Increase-seed production, 3. Increasing-breeing, 4. No-increase, 5. Mixed increase? We will work with apple, cherry, rapeseed (canola), opt sunflower, soja, berries.

Comparison with observation. We have yield data for the most important pollination-dependent crops. The challenge is more that yield data has no direct relationship to InVEST pollination ESS model. First. Yield data is multifactorial, not only dependent on pollination. Second. Y_tot: total yield index: I see to chance to relate this value to absolute yield values in kg (m2, per tree?), because the definition is completely different. In the InVest training dataset y_tot for almonds is 0.95 and for blueberries it is 0.39. So if these two farms have an absolute yield of 100 kg almonds and 10 kg blueberries, what is the relationship to Y_tot? There is no literature reference how to relate Y_tot to absolute yield: the tutorial relates e.g. observed pollination limitation (open-hand treatment) to predicted yield. However we have not pollination limitation data. An Idea would be if I have several farms / or grid points. Farms /grids with higher absolute yield should also have higher y_tot.

I can chime in a bit here. the half saturation constant can be used in two different ways - either to predict the abundance of bees visiting a crop (and then having a separate relationship between abundance and yield) or to use the yield equation directly with the pollinator visitation score itself.

In work I’ve collaborated on where bees have been sampled, we estimate the relationship bee between observed bee abundance and the pollination index. The half-saturation value indicates the pollinator index score that would lead to an estimate of half the maximum number of bees. In our past assessments, we’ve found that a value from 0.1 to 0.2 is a good estimate.

you could also look at the relationship between bee-contributed yield and the index directly. In this case, we’ve used the value of 0.1 again as an estimate.

with respect to Klein et al’s estimates: yes, this is separate. so if one were to connect pollinator-dependence, and the half saturation constant. A simpler way to see the function without subscripts used in the user guide is this:
Y = ( (1-v) + v * PA / (PA + hs) ) ; Y = relative yield; v = pollinator dependence (Klein); PA is pollinator abundance index; hs is the half-saturation constant. So for something like almonds with a 90% or more dependent on bees - an abundance index score of 0.1 would lead to an estimated relative yield of 0.55; while something more like coffee where only 20% of yield depends on external pollination, an abundance index of 0.1 would lead to yield of 0.90. the 2013 paper by ricketts and lonsdorf is perhaps a good example of this - Coffee in costa Rica. Hope this helps! - eric

In your example. Can we say that Y=0.55, so 55% of the potential (maximum) yield is reached 05 90%?

Ok I see the link half_sat and pollinator dependency. However a technical question. Equation 64 which is implemented in the model differs from your suggestion. In this equation we just consider half_sat. If I had understood correctly the present model does not consider pollination dependency? Is there a way to include your idea in the present model? I am still not sure if the present model uses a combined factor?

A question about the guild_table with relative abundance that is related to the understanding of half_sat. Intuitively I assumed the total to be 1 = 100%. It is not true Is it right that this means a species with 0.5 has half the abundance of a species with 1. How is 1 calibrated. Is it just the most abundant species?