# Half-saturation rate

Dear community

The half-saturation coefficient for the crop grown in this area is the wild pollinator abundance needed to reach half of the total potential pollinator-dependent yield.

I have problems to understand the ecological meaning as this value is relative between 0-1. Especially the link to PA and PAT (pollination abundance index on cell or farm), which is described in equation 64: FP, contribution of on-farm pollinator abundance to pollinator-dependent crop yield.

Half saturation of what? relative pollinator abundance needed from PA/PAT? So e.g. if PA is 0.5, 0.05 of 0.5? For me it makes no sense, as this means from the 100% species pool S the percentage from that this pool is needed for half-saturation.

Furthermore I do not understand why relative values. 0.5 of 10 bees is not the same as 0.5 of 10’000 bees in the context of yield?

Kind regards
Sibylle

Hi @sibylles ,

In the InVEST crop pollination model, “wild pollinator abundance” is the proportion of all pollinators (of the crop of interest in this area) that are wild. So “half saturation” is in reference to the total population of pollinators. My interpretation is that this is the proportion of the pollinating community’s composition of wild individuals relative to the total number of individual pollinating organisms, not the number of species, needed to reach half of the total potential pollinator-dependent yield.

What led you to conclude that the relative values do not carry the same meaning depending on the total population size? My understanding is that a half saturation coefficient of `0.5` for 10 bees is the same as `0.5` for 10,000 or 1,000,000 bees in the context of yield.

@elonsdorf might you have any corrections or additions to this response of mine?

-Jesse

Dear Jesse

Many many thanks. Quite helpful. I see now the challenge is deeper.

1. First the guild_table with relative abundance. Intuitively I assumed the total to be 1 = 100%. It is not true and this finding makes it hard to understand all the further equations using species abundance. 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?
2. Equation 62, PA. Pollinator abundance index. Yes I now it is relative. The proportion of all pollinators that are wild to what (relative to what)? Relative to the relative abundance from the guild_table or relative to the other pixel (so in total over all pixels 1=100%?
3. To understand the half_sat rate and equation 64 we need to clearly define 1. & 2. What parameter is the total population of pollinators (see 1 total is not 100%). What parameter is the proportion of the pollinating community’s composition? What parameter is the total number of individual pollinating organisms? In my own words (please correct): half_sat is just a comparison between what is on your farm and the total relative abundance (see 1.). this is a matter of the distribution of bees around the landscape, but not directly related to yield. It is a fact that yield is based on the species diversity and species abundance (absolute values).

For sure I understand if FP (equation 64) is 0 then 0% of pollinator-dpeendent yield is achieved and 1 indicates 100% is achieved, but I need much more info to understand the ecological concept.

Kind regards

Sibylle

Hi @sibylles ,

Thanks for your reply with more questions. To streamline the discussion, I suggest we consolidate the conversation and build off @elonsdorf’s answers in your other post.

Thank you,
Jesse