[R-sig-eco] Simultaneous estimation of nonlinear models

[Fred Takahashi]

Hello

I work with plant ecophysiology and use R for about 5 years. Now I
need to fit nonlinear data of response of photosynthetic rate to CO2
concentration  according well know mechanistic models. Basically,
there are one equation for the first part of the curve, and in the
second part, another equation (different factors limiting
photosynthesis). But some recent research pointed out that is better
to fit the data simultaneously to that two equations, than arbitrarily
cut the data in the half (simultaneous estimation, also know as
segmented regression). That is possible if the algorithm, like
Levenberg-Marquardt, minimizes some function of two equations,
informed in the conditional syntax (ex. If (eq1>eq2) then eq1 else
eq2).

Dubois et al. (2007) showed the procedure using SAS. The key point of
that is to inform the equations in the conditional syntax like:
“
 if rubisco <  RuBP then A =  rubisco;
 else A =  RuBP;
 ...
or the equivalent:
 ...
A =  min(rubisco, RuBP);
 ...
“
when “rubisco” and “RuBP” are objects representing the two equations.

Also in Dubois et al. (2007), there are the entire syntax in SAS:
“
proc sort data=ACI;
by factor1 factor2 days;
run;
ods output ParameterEstimates=estimates;
proc NLIN data=ACI method=Marquardt outest=status noitprint;
by factor1 factor2 days;
rubisco= ((Vcmax*(Ci-Gstar))/(Ci+(Kc*(1+(O/Ko)))));
RuBP= ((J*(Ci-Gstar))/((4*Ci)+(8*Gstar)));
control O=210; *fixes the value of O;
bounds -3<Rd<50;
parameters Vcmax= 5 to 330 by 25
J= 15 to 505 by 35
Rd= 1E-8 to 10.1 by .5;
model A=min(rubisco,RuBP)-Rd;
output out=ACiOUT parms=Vcmax J Rd predicted=Ahat student=student;
run;
ods listing;
data temporary;
set status;
where(_TYPE_ ne'GRID' and _TYPE_ ne'COVB');
run;
data estimates;
merge estimates temporary(keep=factor1 factor2 days _status_ _iter_);
by factor1 factor2 days;
run;
”

I try to do that in R in several ways, using the function nls, without
success. Does someone have a clue?

Thank you for your help!

Regards
Fred Takahashi

PhD student
Universidade de Brasilia – Brazil




Reference:
Dubois, Fiscus, Booker, Flowers and Reid (2007) Optimizing the
statistical estimation of the parameters of the Farquhar–von
Caemmerer–Berry model of photosynthesis. New Phytologist 176: 402–414