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Annexe A
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the gonad appears at stage 12 of embryogenesis (i.e. mass of the embryo of 170 mg), an origin
shift is performed to describe aromatase activity into TSP. The general equation is:
am ( ) = ae a
0
r ( m−170)
where a 0 is the aromatase activity at the beginnig of TSP, m the mass of the embryo and r a the
growth rate of aromatase activity. A sigmoid scaled logistic function is used to model the
effect of incubation temperature upon aromatase activity growth rate r a :
⎛
r = A 1+
e
a Max⎜
⎝
⎛P
a T ⎞
⎜
−
⎟
⎜ S ⎟
⎝ a ⎠
⎞
⎟
⎠
−1
The growth rate r a is dependent on incubation temperature during the TSP. At low
temperature (T=25°C), r a is null whereas it increases until a maximum to reach the threshold
A Max at very high temperature (T>35°C). The inflexion point of r a is reach at T=P a and the rate
of change at this point is dependent on parameter S a .
Model for the growth of the gonad
The growth of the gonad, estimated by protein content during incubation period, is also
related to incubation temperature and exponentially increases with time from the beginning of
TSP up to hatching (Pieau et al. 1998, Pieau et Dorizzi 2004). The general equation is:
()
g t
rg
( t t
0 )
= g e −
0
where g 0 is the protein content in the gonad at the beginning of the TSP (i.e. t 0 ) , r g the growth
rate of the gonad and t the time of development. The growth rate r g is modeled as a function
of the growth rate of the sharing embryo r m scaled by the potential inhibition of gonadal
growth by estrogens (Girondot et al. 1998):
3