Growth model of the reared sea urchin Paracentrotus ... - SciViews

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Set L describes the largest size reached by sea urchins at maximum growth speed with time. P. lividus having a determinate or asymptotic growth (see Fig. 28A), final increase of size ∆D∞ = D∞ – D0 is finite for t' → ∞. However, maximum size cannot be reached instantaneously. If the largest individuals in the actual dataset are not inhibited at all, they can be used as a reference for the whole cohort to define this maximum growth curve. Supposing that a von Bertalanffy 1 curve best fit the largest fraction of the size distributions (see next section), it is an appropriate model for set L. Because we use the t' time-scale here, we choose a parameterization of the model such as D'(t' = 0) = D0: Part IV: A growth model with intraspecific competition −k1⋅t' Dt' ( ) = D +∆D⋅(1− e ) (25) 0 ∞ Membership to the L set with time, ML(t'), is modelled with a logistic function (a classical model for a transition in fuzzy sets, Cox, 1999) (Fig. 30): 1 M ( t') = 1+ l ⋅e L −k2⋅t' (26) Membership to the S set with time, MS(t'), is complementary so that MS and ML add up to one: 1 M ( t') = 1 − M ( t') = 1− 1+ l ⋅e S L −k2⋅t' (27) Thus, full-growing individuals belong to the L set from the beginning. The stronger the growth inhibition, the longer other individuals remain in the S set before gradually shifting to the L set. The fuzzy model integrates the effect of intraspecific competition (or any other inhibition mechanism having a similar effect on growth) as a delayed transition from S to L sets, as explicitly quantified by parameter l (the lag or position of the inflexion point in the membership curves, see Fig. 30). If l = 0, there is no inflexion point and ML(t') = 1; growth occurs at maximum speed from start and follows set L, that is, a von Bertalanffy curve. While parameter k1 151
quantifies maximum speed growth, k2 represents the speed at which inhibition is released with time. All parameters in this model carry a clear biological meaning, considering hypotheses that were formulated to build it. Usually, a fuzzy model is treated with fuzzy arithmetic. The output is then "defuzzified" by one of several methods (Cox, 1999) to provide a crisp number (the most probable size of an individual at a determined age). Being simple enough, the current model can also be transformed into a classical analytic equation: D( t') = M ( t') ⋅ S( t') + M ( t') ⋅ L( t') (28) S L which gives, after combination of eqs 24-28 and simplification: Dt' ( ) = D +∆D Part IV: A growth model with intraspecific competition 0 1−e 1+ l ⋅e −k1⋅t' ∞ −k2⋅t' (29) This way the model can be treated with classical (crisp) arithmetic that offers a larger panel of statistical tools than fuzzy arithmetic. Fitting the dataset Since echinoids are not tagged individually, it is not possible to track animals across measurement sets. Consequently, one will consider virtual individuals according to their relative position in the entire size distribution at each sampled time, that is, virtual individuals corresponding to fixed quantiles (or percentiles) in each size distribution. It should be noted also that, if mortality is not randomly distributed among individuals, actual growth speed could be different from the one calculated on virtual individuals. This means that if mortality preferably affects small individuals, growth speed is overestimated; conversely, if mortality affects rather larger animals, growth speed is underevaluated. In absence of individual tagging, we will thus consider the apparent growth speed of the virtual individuals as defined here above. 152
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U L B bio mar UNIVERSITE LIBRE DE B
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Acknowledgements ACKNOWLEDGEMENTS W
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Abstract ABSTRACT A rearing protoco
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Résumé RESUME Un protocole d'éle
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Table of contents TABLE OF CONTENTS
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ANNEXES............................
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List of figures LIST OF FIGURES Fig
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List of figures Figure 28. A. Histo
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List of tables LIST OF TABLES Table
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List of equations LIST OF EQUATIONS
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List of equations Equation 33. Para
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List of symbols LIST OF SYMBOLS Var
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List of symbols IW Immersed weight:
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Introduction 27
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Foreword 30
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General introduction this study. Se
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General introduction intense fishin
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General introduction habitats: inte
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General introduction substrate to s
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General introduction mm (Spirlet et
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Growth models General introduction
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. The logistic function for asympto
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d. The von Bertalanffy curves Gener
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Y Y 1 Y• 0.8 0.6 0.4 0.2 General
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Y 1 Y• 0.8 0.6 Y•êH1+bL 0.4 0.
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YY 3 2.5 2 1.5 1 0.5 General introd
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Table 1. Models used to fit sea urc
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General introduction model 1 for Ec
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General introduction method used. I
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General introduction Experiments in
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Aim of the thesis 62
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PART I: SET UP OF AN EXPERIMENTAL R
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Land-based closed-cycle echinicultu
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Aquaculture of echinoderms, includi
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6b. exploitation KCl water renewal
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earing cycle into seven stages is e
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(Grosjean et al, 1996, see Part III
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output. The quality of gametes is o
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average value of 19.5 days, a minim
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individuals were still alive 3 mont
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e. Discussion show similar GI and M
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The success of the present method l
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Fenaux (1990) for the same species
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encountered with food is its stabil
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to Christine Spirlet (ref. ERB 4001
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PART II Measurement for size in the
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Part II: Measurement for size in th
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Few studies have compared and discu
Page 101 and 102: d. Results and discussion The ambit
Page 103 and 104: Reproducibility of measurements The
Page 105 and 106: e. Conclusions fresh weight! Cautio
Page 107 and 108: principal axis 3 1 0.8 0.6 0.4 0.2
Page 109 and 110: a relative homogeneous growth of al
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Page 113 and 114: Part III: Experimental studies of t
Page 115 and 116: assumption of normality can be test
Page 117 and 118: occurred. From this moment on, and
Page 119 and 120: d. Results Size distribution among
Page 121 and 122: Nber of ind. 120 100 80 60 40 20 0
Page 123 and 124: Table 9. Statistics on the six batc
Page 125 and 126: Table 10. Size distribution of Fe e
Page 127 and 128: purpuratus; Dafni & Tobol, 1987: Tr
Page 129 and 130: Nbr. of ind. Nbr. of ind. A. Size d
Page 131 and 132: Nbr. of ind. Nbr. of ind. Nbr. d'in
Page 133 and 134: Part III: Experimental studies of t
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Page 137 and 138: Part IV: A growth model with intras
Page 139 and 140: . Introduction fuzzy-remanent funct
Page 141 and 142: considered factor on the curve's sh
Page 143 and 144: Diameter D 20 in mm Diameter D in m
Page 145 and 146: d. Results Theoretical consideratio
Page 147 and 148: some two-dimensional processes like
Page 149 and 150: implements this method ('nlrq' pack
Page 151: value just after metamorphosis (D0,
Page 155 and 156: Table 12. Results of quantile regre
Page 157 and 158: This way, one obtains a 4-parameter
Page 159 and 160: individuals related to the presence
Page 161 and 162: Finally, ∆D∞ should follow a no
Page 163 and 164: 60 Diameter increase D' in mm 40 20
Page 165 and 166: e. Discussion Fig. 34B shows three
Page 167 and 168: Constraining parameters as we did i
Page 169 and 170: It does not consider respiration as
Page 171 and 172: this species. For other species, wh
Page 173 and 174: ecapture, McDonald & Pitcher, 1979;
Page 175 and 176: ∆D∞ D0 +∆D∞ − D0 +∆D∞
Page 177 and 178: evaluated on basis of biological kn
Page 179 and 180: ain conceptualizes complex objects.
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Page 183 and 184: General conclusions individuals, wh
Page 185 and 186: Root models: y’ = ay m -by n (exp
Page 187 and 188: General conclusions - The diauxic g
Page 189 and 190: General conclusions model not on a
Page 191 and 192: References Baker, T.T., R. Lafferty
Page 193 and 194: References Dafni, J. & R. Tobol, 19
Page 195 and 196: References Ebert, T.A., 1999. Plant
Page 197 and 198: References intermedius on a rocky s
Page 199 and 200: References Guillou, M. & Ch. Michel
Page 201 and 202: References Kobayashi, S. & J. Taki,
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References McDonald, P.D. & T.J. Pi
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References Pouvreau, S., C. Bacher
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References Sellem, F., H. Langar &
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References Stumm, W. & J.J. Morgan,
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References Webster, S.K. & A.C. Gie
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212
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Annexes 214
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# If no graphic device currently op
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lines(edatq[, 1], predict(edat.025,
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SimRes
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Annexes Code of functions required
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plot(cumsum(dat[,columns[1]])/sum(d
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for the CI!!! Annexes SEMean
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} Annexes # - y, a vector of classe
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plot(x, y, type="l", col=col, lty=l
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} Annexes } results[i, 1:5]
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} .value Annexes dimnames(.grad)
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#{ # # This is adapted from SSasymp
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Exp.ival
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SSallo
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.expr4
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.expr9
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. The 'nlrq' package for nonlinear
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nlrq.control package:nlrq R Documen
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gradSetArgs[[2]]), call("[", gradSe
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model.step
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Annexes 254
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Annexes 256
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Annexes metamorphosis. Acquisition
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Annexes ABSTRACT: The general allom
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Annexes libitum for 8, 16, 24, 32,
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Annexes EXECUTIVE SUMMARY: The aim
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Annexes KEYWORDS: Somatic growth, d
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Annexes amount of waste produced at
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Annexes ABSTRACT: Multimodal distri
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Growth model of the reared sea urchin Paracentrotus ... - SciViews

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