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Annexe A _____________________________________________ ⎛ 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. 4
Annexe A _____________________________________________ Maximum-likelihood is highly sensitive to outliers (Hilborn et Mangel 1997). To take into account that all observations are experimental measures, we implemented the Tukey’s biweight with the standard deviation between two models being multiply by a factor 3 (Hilborn et Mangel 1997). This procedure limits the influence of outliers in the maximum likelihood search. We searched for the standard error on each parameter that is necessary to render the fitted value of SD i . For this purpose, all the combinations of parameters are varied ±2 SE_p (SE_p indicates the standard error of parameter p). Using each combination, a y i vs. x i curve is calculated. The minimum (Min_y i ) and maximum (Max_y i ) values over all the parameter combinations are retained for each x i . The fit criteria is the weighted sum of squares over all n observations that permit to model the best as possible the fitted standard deviation around each point: (( y −2 SD ) −( Min_ y )) ( y −2 SD ) −( Max_ y i i i i i i ) 2 2 ( ) n SSQ = ∑ i= 1 + y −2SD y −2SD i i i i 5
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N° d’ordre : UNIVERSITE PARIS-SU
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Remerciements Je remercie tout d’
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Sommaire __________________________
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Introduction ______________________
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I - La tortue à tempes rouges, un
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II - Les tortues à tempes rouges,
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III - Etudes expérimentales des pr
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ANNEXE IV THE RIGHTING RESPONSE AS
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TURTLE, AN EXOTIC AND INTRODUCED SP
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