[R-sig-eco] Help in code for fitting a growth model in R

[Chandrasekhar Rudrappa]

Hi All,

I have to fit the following model to growth data of Hevea (rubber) trees.
[image: a = a - (a - b){e^{ - \,\,\frac{2}{T}(F(t) - F({t_0}))}}] where [image:
F(t) = t + \frac{A}{{2\pi }}\sin 2\pi (t - {t_1})], [image: F({t_0}) =
{t_0} + \frac{A}{{2\pi }}\sin 2\pi ({t_0} - {t_1})], and *t1* signifies the
maximum point of . Thus the equation becomes:
[image: a = a - (a - b){e^{ - \,\,\frac{2}{T}((t + \frac{A}{{2\pi }}\sin
2\pi (t - {t_1})) - ({t_0} + \frac{A}{{2\pi }}\sin 2\pi ({t_0} - {t_1})))}}]


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:

[image: F(t) = \left\{ \begin{array}{l} n(1 - T) + S(t - n) & & (n \le t <
n + {t_2}),\\ n(1 - T) + S({t_2}) & & & (n + {t_2} \le t < n + {t_3}),\\
n(1 - T) + S(t - n - T) & & (n + {t_3} \le t < n + 1), \end{array} \right.]

[image: F(t) =] [image: \begin{array}{l} n(1 - T) + S(t - n) & & (n \le t <
n + {t_2}),\\ n(1 - T) + S({t_2}) & & & (n + {t_2} \le t < n + {t_3}),\\
n(1 - T) + S(t - n - T) & & (n + {t_3} \le t < n + 1), \end{array}]

[image: F(t) = \left\{ \begin{array}{l} n(1 - T) + S(t - n) & & (n \le t <
n + {t_2}),\\ n(1 - T) + S({t_2}) & & & (n + {t_2} \le t < n + {t_3}),\\
n(1 - T) + S(t - n - T) & & (n + {t_3} \le t < n + 1), \end{array} \right.]
 where, [image: S(t) = t + \frac{{1 - T}}{{2\pi }}\sin 2\pi \frac{{(t -
{t_1})}}{{1 - T}}], n=integral part of t, [image: {t_2} = {t_1} + \frac{{1
- T}}{2},{t_3} = {t_1} + \frac{{1 + T}}{2},\,\,\,\,\,\int \begin{array}{l}
1\\ 0 \end{array} \,\,f(t)dt = 1 - T,\,\,\,T = no\,growth\,period] Similarly
the above equations have to be modified for [image: F({t_0})] . These have
to be integrated in to:  [image: a = a - (a - b){e^{ - \,\,\frac{2}{T}(F(t)
- F({t_0}))}}]
 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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