For what its worth, here are the best fit  Hill (cooperative binding assumptions).  It is a better over- all fit.

You cannot call a corn plant a single protein; these fits are just tools and my data points are themselves interpolations of aggregate data.  n= '6.27' binding sites are a meaningless interpretation currently (what 6 land factors that would make up expected yield [independent variable] would work cooperatively to dictate corn 'carrying capacity'?).  The Hill is related to typical logistical fits that are generic modelling tools.   Whether they can be leading to further insight is unknown.  I do  suggest seed corn companies use a similar parameterizations (either Hill or other logistical fits)  if altered relationships for different hybrids are suspected. 

To use the normalized Hill fit, final population rate equation takes the form   :

y=Vmax*x^n/(k^n+x^n) *(Rate_max-Rate_min) + Rate_min.   I used Rate_max of 35,500, Rate_min of 19,000 per acre for 2014. 

Vmax , k,  n

1.00933,  122.5594,  6.27842

Hill Fit Corn Population Prescription.doc (357KB - 87 downloads)

Corn_pop_Boltzmann_and_Hill.opj (1416KB - 88 downloads)