[R-sig-eco] help with a suitable code to fit a complicated non-linear model in R

[Chandrasekhar Rudrappa]

Dear All,


I have to fit the following model to growth data of Hevea (rubber) trees:

*a=a-(a-b)exp(-(2/p)(F(t)-F(t0))).*  Where *F(t)=t+(A/2pi)(sin 2pi(t-t1))*,

*F(t0)=t0+(A/2pi)(sin 2pi(t0-t1)), t1* signifies the maximum point of
*f(t)*. Thus the equation becomes:

*a=a-(a-b)exp(-(2/p)(t+(A/2pi)(sin 2pi(t-t1)))- (t0+(A/2pi)(sin
2pi(t0-t1))))*

Up to this step, I have succeeded very well.



*My problem is with the following model for which I need help. *



The same equation is further developed into a seasonal cessation model by
deriving equivalent equations to replace *F(t)*. For the purpose of
seasonal cessation model *F(t)* is derived as:



*            n(1-T)+S(t-n)               (n<=t<n+t2),  *

*F(t) =  n(1-T)+S(t2)                 (n+t2<=t<n+t3),         *

*            n(1-T)+S(t-n-T)           (n+t3<=t<n+1),*



where *S(t)=t+((1-T)/(2pi))(sin 2pi((t-t1)/(1-T))),* n=integral part of t,



*t2=t1+(1-T)/2,  t3=t1+(1+T)/2  , T=no growth period. *Similarly the above
equations have to be modified *for F(to).* These have to be integrated in
to:



*a=a-(a-b)exp(-(2/p)(F(t)-F(t0))).*



Kindly help with a suitable code to fit the above model to my data.



References: 1. Akamine, T (1993). A New Standard Formula for Seasonal
Growth of Fish in Population Dynamics. Nippon Suisan Gakkaishi
59(11):1857-1863.

2.  Akamine, T (2009). Non-linear and graphical methods for fish stock
analysis with statistical modelling. Aqua-BioScience Monographs VOL. 2 NO. 3
:1-45.


-- 
Dr. TR Chandrasekhar, M.Sc., M. Tech., Ph. D.,
Sr. Scientist
Rubber Research Institute of India
Hevea Breeding Sub Station
Kadaba - 574 221
DK Dt., Karnataka
Phone-Land: 08251-214336
Mobile: 9448780118

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