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Follow Up - Corn population rate equation
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badger@uw
Posted 5/13/2014 11:15 (#3867915)
Subject: Follow Up - Corn population rate equation



East Troy, WI

I finally got around to plot the dose/response curve (Boltzmann)  for the recommended corn population versus expected (historic) yield.  See this thread: 

http://talk.newagtalk.com/forums/thread-view.asp?tid=455088&mid=3697440#M3697440 

I have not yet seen how well SMS (which I am fairly certain is a modified ArcGIS core) likes these types of exponentials. Recall the Boltzmann for a dose response takes the form:

y = A2 + (A1-A2)/(1 + exp((x-x0)/dx)), where x is your historic yield 

 A1 A2 x0 dx   

 19000  35500  123.6673 18.58726   

Unforced A2 fit : 

A1 A2 x0 dx

19000 34957.54782 121.18642 16.71197

Info on Boltzmann "one site competition" or "sigmoidal dose-response":
http://www.originlab.com/doc/Origin-Help/Boltzmann-FitFunc

I have attached a summary sheet as well as my Origins file for the forced fit (A1 and A2 force through  parameters of min and max populations).  The EC50 is the most critical I think; mid-point slope also important.     Please comment and provide more source data.  I will continue to post my parametric prescription generators.  I am already not completely satisfied with ranges 150-200,   75-110 could also use some more data.  There is interpolation inherent in this model - do not take it as gospel.  It needs a primary data source (prospective trials). 

"Multi-site cooperative binding" fits might be better, but more data is needed.   Biologically, this might make more sense. 





Attachments
----------------
Attachments Corn_pop_Boltzman.opj (229KB - 139 downloads)
Attachments Boltzman Fit Corn Population Prescription.doc (359KB - 147 downloads)
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