Pollination half-saturating constant and scalar

Dear community

The model that translates pollination services to agricltural production is described here using an example:
Ricketts and Lonsdorf (2013) Mapping the maring: comparing marginal values of tropical forest remnants for pollination services. Ecological Applications 23: 113-1123.
Ricketts_2013-Mapping the margin.pdf (5.7 MB)

Question: I am wondering how the half-saturating constant and the scalar was calculated? In the method description I just found “was set to”.

We use field results from Ricketts et al. (2004) to
estimate yield parameters. The maximum yield of coffee
is approximately 21.5 fanegas per hectare (1 fanega ¼
200 liters of berries). Ricketts et al. (2004) observed that
yield declined 18% between areas with abundant bee
visits and areas with fewest bee visits, so we set mc to
0.18. To fit the saturating function to the maximum
abundance observed in the field (i.e., 108 total visiting
bees) we set jc to 30 and multiplied the saturating
function by a scalar equal to 1.27.

In a previous section it was mentioned that the half-saturating constant is 0.153 (yielding a predicted abundance of 54, however this seems to be another half-saturating constant than the one above with 30) and the shape of the saturating function is 3.298, respectively. How are these two values translated to the value of 30 and 1.27?

we used Monte Carlo parameterization to determine the
values of half-saturation constant j and c that
maximized the fit (0.153 and 3.298, respectively; Fig.
2A).

Many thanks
Sibylle

@elonsdorf
@lons0011