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

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Nbr of individuals 0 20 40 60 80 100 A Diameter increase D' in mm 60 50 40 30 20 10 1 0 10 20 30 40 50 60 Diameter increase D' in mm Figure 34. Diagnostic of the envelope model (eq. 35) fitted in Fig. 33. A. Contour plot of the residuals as [observed D' - predicted D'] (shades according to the scale at right, in mm). Quantiles 0.025, 0.5 and 0.975, obtained from the initial dataset (points) and corresponding curves extracted from the envelope model by fixing τ (lines) are superimposed. Three "slices" are cut in the 3D-surfaces of Fig. 33 at t' = 300 (1), 600 (2) and 1800 (3) days (vertical dotted lines in Fig. 34A) and represented as size distributions in B. For each pair of distributions, the smoothest one is the model. Differences are clearly visible and correspond to positive or negatives patches in the residuals in A. Part IV: A growth model with intraspecific competition 500 1000 1500 2000 2500 Time t' in days 2 3 quantile 0.975 quantile 0.5 quantile 0.025 B 163 4 2 0 -2 -4
e. Discussion Fig. 34B shows three sections across the surfaces of Fig. 33 at three given times t' = 300, 600 and 1800 days. Overall size spreading and asymmetries in the original dataset are quite well respected by the model. The higher peak in the first section of the model at 300 days is partly a consequence of considering D0 as strictly equivalent for all individuals while, in reality, it is normally distributed. With the simple relation between l and τ, as established in eq. 32, multiples modes are just approximated by a unimodal, skewed distribution. This is most visible in the second section, at 600 days. A more complex model would be required to fit multimodal distributions. Fitting methods We have argued in favor of quantile regression instead of least-square regression in modelling growth. Distribution of the "error", that is, mainly individual variation in the present case, can be either asymmetrical or multimodal and this is a violation of basic assumptions of the least-square model. In the same circumstance, a mean effect obtained by least-square is less representative of the tendency. Quantile regression fits any part of the distribution, including extremes, and accommodates any kind of size distribution. It is also robust against any power transformation and it is a guarantee that the regression remains independent from the dimension of measurements for size (linear versus surface versus volume/weight). Leastsquare regression is very sensitive to any power transformation, and thus to the dimension of the variables. For purely descriptive fittings, we introduced the triple τ = 0.975 / 0.5 / 0.025 quantile regression representation as an informative summary of the data. 5% is a commonly used critical level in statistics. The curves for τ = 0.975 and t = 0.025 materialize a kind of two-tailed 5% nonparametric conditional confidence interval of the dataset: 95% of data Part IV: A growth model with intraspecific competition 164
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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
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d. Results and discussion The ambit
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Reproducibility of measurements The
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e. Conclusions fresh weight! Cautio
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principal axis 3 1 0.8 0.6 0.4 0.2
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a relative homogeneous growth of al
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110
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 and 152: value just after metamorphosis (D0,
Page 153 and 154: quantifies maximum speed growth, k2
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: 60 Diameter increase D' in mm 40 20
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,
Page 203 and 204: References McDonald, P.D. & T.J. Pi
Page 205 and 206: References Pouvreau, S., C. Bacher
Page 207 and 208: References Sellem, F., H. Langar &
Page 209 and 210: References Stumm, W. & J.J. Morgan,
Page 211 and 212: References Webster, S.K. & A.C. Gie
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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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