Premiers - Outil de Suivi des Contrats

Annexe A
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⎛
r = r ⎜1+
e
g m
⎜
⎝
⎛P
g r ⎞
⎜
− a ⎟
⎜
S g ⎟
⎝ ⎠
⎞
⎟
⎟
⎠
−1
The inhibition effect of estrogens on gonad’s growth includes the growth rate of the
aromatase activity in the gonad r a and two parameters, P g and S g that controlled respectively
the inflexion point of the function r g and the shape at this point.
General parameters fitting procedure
Log-transformed observations (mass of embryo m i , aromatase activity a i or gonad mass g i )
have been fitted to exponential growth function using maximum-likelihood criteria:
ln y = ln C+
rx
i
i
where x i is the time of development (i.e. t i ) for the embryo and gonadal mass model and the
mass of the embryo (i.e. m i ) for aromatase activity model. C is the initial value of m i, a i and g i
in respective models. As the gonad appears at stage 12 of embryogenesis (i.e. embryo mass of
170 mg), an origin shift is performed for the aromatase and gonadal model.
[For convenience in our mechanistic model, we have initially transformed data of gonad’s
protein content dependent on mass of the embryo to obtain gonad’s protein content function
of time of development from fitted embryo’s mass model m i ]
The error around each point is supposed to be Gaussian and is modeled as being:
SD = a + b y
i
i
c
This formula renders homoskedasticity (b=0) and heteroskedasticity (b≠0) within the same
formula. If c=0, the standard deviation is directly proportional to the observed output whereas
c≠0 permits to model complex shape of heteroskedasticity.
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