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

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List of symbols LIST OF SYMBOLS Variables and parameters are in italic; function names are in roman type according to standard mathematical notation. For instance, e (in italic) is the name of a variable and e (in roman) is the exponentiation function as in y = e x and thus e equals Euler constant: 2.71282. α, α, α, α, ββ ββ Parameters of the Huxley's allometric equation y = α·x β . ∆D∞ Maximum increase in diameter of the test of a sea urchin from a defined initial value (usually, at metamorphosis) D0 to the asymptotic maximum diameter D∞ (in mm). ∆Y∞ Maximum increase in size from a defined initial size (at birth, at metamorphosis…) Y0 to the asymptotic size Y∞ (same unit as Y). δδδδ1 Deviance of quantile regression, according to Koenker & Bassett (1978) (same unit as the dependent variable y in the model). δδδδ2 Deviance of quantile regression; modified version for envelope models (same unit as the dependent variable y in the model). δδδδs Apparent mean density of the skeleton of a sea urchin (in g/l). ττττ Quantile (0 < τ < 1) of a distribution or of a quantile regression (dimensionless). ˆ ττττ Estimator of the quantile τ. Value calculated after a sample of the distribution (dimensionless). ωωωω Parameter corresponding to k·Y∞ in the von Bertalanffy equation Y = Y∞·(1 – e -k·(t – t 0 ) ), as proposed by Gallucci et al (1979) to solve the problem of intercorrelation between k and Y∞ (same unit as Y·t -1 ). ξξξξ1 Value returned by a function of the form Y = f(t) at time t and for the current solution for the parameters (same unit as Y). 23
List of symbols ξξξξ2 Value returned by a function of the form Y = f(t, τ) (envelope model) at time t and quantile τ and for the current solution for the parameters (same unit as Y). a, b, c, d, e Parameters in growth models with no particular functional meaning or used in a context where the possible functional meaning has no importance (fitting for descriptive purpose only) (units are context-dependent). D Diameter of the test of a sea urchin measured at the ambitus and considered without spines (in mm). D' Relative diameter of the test of a sea urchin: increase of the diameter from a defined initial value (usually at metamorphosis) D0 to the current value D (in mm). D0 Diameter of the test of a sea urchin at time t = t0, usually at metamorphosis (in mm). D∞ Maximum asymptotic diameter of the test of a sea urchin (determinate growth) (in mm). DWs Dry weight of the skeleton of a sea urchin (in g). Fx A reared batch of sea urchins issued from a single fertilization x used in an experiment. If several batches issued from the same fertilization are used, they are further labeled with numbers (Fx1, Fx2…). fi A frequency observed in the i th class of a size distribution (dimensionless). fsi Same as fi but after applying a moving average smoothing (dimensionless). GI Gonad index: the ratio between the weight of the gonads and the total weight of a sea urchin, either in wet or in dry weight (dimensionless). 24
Page 1 and 2: U L B bio mar UNIVERSITE LIBRE DE B
Page 4 and 5: Acknowledgements ACKNOWLEDGEMENTS W
Page 6 and 7: Abstract ABSTRACT A rearing protoco
Page 8 and 9: Résumé RESUME Un protocole d'éle
Page 10 and 11: Table of contents TABLE OF CONTENTS
Page 12 and 13: ANNEXES............................
Page 14 and 15: List of figures LIST OF FIGURES Fig
Page 16 and 17: List of figures Figure 28. A. Histo
Page 18 and 19: List of tables LIST OF TABLES Table
Page 20 and 21: List of equations LIST OF EQUATIONS
Page 22 and 23: List of equations Equation 33. Para
Page 26 and 27: List of symbols IW Immersed weight:
Page 28: Introduction 27
Page 31 and 32: Foreword 30
Page 33 and 34: General introduction this study. Se
Page 35 and 36: General introduction intense fishin
Page 37 and 38: General introduction habitats: inte
Page 39 and 40: General introduction substrate to s
Page 41 and 42: General introduction mm (Spirlet et
Page 43 and 44: Growth models General introduction
Page 45 and 46: . The logistic function for asympto
Page 47 and 48: d. The von Bertalanffy curves Gener
Page 49 and 50: Y Y 1 Y• 0.8 0.6 0.4 0.2 General
Page 51 and 52: Y 1 Y• 0.8 0.6 Y•êH1+bL 0.4 0.
Page 53 and 54: YY 3 2.5 2 1.5 1 0.5 General introd
Page 55 and 56: Table 1. Models used to fit sea urc
Page 57 and 58: General introduction model 1 for Ec
Page 59 and 60: General introduction method used. I
Page 61 and 62: General introduction Experiments in
Page 63 and 64: Aim of the thesis 62
Page 66 and 67: PART I: SET UP OF AN EXPERIMENTAL R
Page 68 and 69: Land-based closed-cycle echinicultu
Page 70 and 71: Aquaculture of echinoderms, includi
Page 72 and 73: 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
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Part III: Experimental studies of t
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assumption of normality can be test
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occurred. From this moment on, and
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d. Results Size distribution among
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Nber of ind. 120 100 80 60 40 20 0
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Table 9. Statistics on the six batc
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Table 10. Size distribution of Fe e
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purpuratus; Dafni & Tobol, 1987: Tr
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Nbr. of ind. Nbr. of ind. A. Size d
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Nbr. of ind. Nbr. of ind. Nbr. d'in
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Part III: Experimental studies of t
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134
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Part IV: A growth model with intras
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. Introduction fuzzy-remanent funct
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considered factor on the curve's sh
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Diameter D 20 in mm Diameter D in m
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d. Results Theoretical consideratio
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some two-dimensional processes like
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implements this method ('nlrq' pack
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value just after metamorphosis (D0,
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quantifies maximum speed growth, k2
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Table 12. Results of quantile regre
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This way, one obtains a 4-parameter
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individuals related to the presence
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Finally, ∆D∞ should follow a no
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60 Diameter increase D' in mm 40 20
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e. Discussion Fig. 34B shows three
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Constraining parameters as we did i
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It does not consider respiration as
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this species. For other species, wh
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ecapture, McDonald & Pitcher, 1979;
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∆D∞ D0 +∆D∞ − D0 +∆D∞
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evaluated on basis of biological kn
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ain conceptualizes complex objects.
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180
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General conclusions individuals, wh
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Root models: y’ = ay m -by n (exp
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General conclusions - The diauxic g
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General conclusions model not on a
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References Baker, T.T., R. Lafferty
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References Dafni, J. & R. Tobol, 19
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References Ebert, T.A., 1999. Plant
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References intermedius on a rocky s
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References Guillou, M. & Ch. Michel
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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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