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

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transformation leads to linear regressions with homoscedasticity of variance and random distribution of the residuals. However, caution is the rule as model I is not verified (the independent variable should be measured without error which is not the case here). A non-biased model II would be more adequate (Ebert, 1981, 1994; Laws & Archie, 1981; Tessier, 1948) but only biased model II are available for such data sets (Sokal & Rohlf, 1981, p. 549). Since the explained variance is higher than 98%, the bias remains negligible, whatever the model chosen. Thus, in this case, a model I is to be preferred for prediction purposes with independent regressions for reciprocal relationships (Sokal & Rohlf, 1981). Table 5. Allometric relations (model I linear regressions on double log transformed data) between parameters for Paracentrotus lividus from Morgat, n = 224. Verifications are needed when applying on other strains, or out of the announced validity range. Measured (x) Estimated (y) Allometry R 2 Std err log(y) Validity Diameter (mm) Fresh weight (g) y = 5.50·10 -4 x 2.94 0.997 0.037 10 < x < 60 Diameter (mm) SIW (g) y = 2.40·10 -4 x 2.70 0.986 0.053 10 < x < 60 Fresh weight (g) Diameter (mm) y = 12.7 x 0.35 0.995 0.011 0.5 < x < 90 Fresh weight (g) SIW (g) y = 0.22 x 0.95 0.994 0.034 0.5 < x < 90 SIW (g) Diameter (mm) y = 22.1 x 0.37 0.984 0.019 0.1 < x < 15 SIW (g) Fresh weight (g) y = 4.95 x 1.05 0.994 0.036 0.1 < x < 15 SIW (g) Skeleton(dry w. g) (a) y = 1.56 x 0.998 0.021 0.1 < x < 15 SIW (g) Soma (dry w. g) y = 1.74 x 0.98 0.999 0.010 0.1 < x < 15 (a) Measured after digestion of the organic matter with sodium hypochloride 10% under gentle agitation and drying for 48h at 70°C. The SIW being a direct in vivo measurement of the skeleton weight of the sea urchin, the latter can be calculated by the formula in Table 5. As the soma is composed of ca. 90% of skeleton (in dry weight, Grosjean, unpubl.), it is also a reasonably good in vivo estimation of the somatic dry weight, after applying possibly a correction calculated after the SIW-soma allometric relationship (Table 5). As such, it allows to follow most accurately the somatic growth of the sea urchins. In some experiments (Grosjean et al, in prep.), we were able to quantify somatic growth of sea urchins within a 7-days period using the SIW, while it would require at least a 1 or 2 months period to get the same accuracy with test diameter or Part II: Measurement for size in the sea urchin 103
e. Conclusions fresh weight! Caution must be taken, of course, when applying conversions on echinoids in particular physiological state that lead to variations in allometric relationships, such with starved individuals (Ebert, 1968; Kaneko et al, 1981). The SIW should be used whenever possible both as a reference measurement for indices (gonadal index, repletion index…) and for studies involving somatic growth. Test diameter remains the fastest measure, and thus preferred for measuring large number of individuals when accuracy is not of prime importance, or for measures in the field. Fresh weight use should be restricted to the determination of the biomass. f. Acknowledgements This work was supported by an EC research grand attributed to Ch. Spirlet (ref. ERB 4001 GT92 0223), in the framework of the contract No. AQ2.530 BFE ("Sea urchin cultivation"). We thank D. Bucaille, P. Gosselin, F. Benard & F. Louise for help in measurements. This paper is a contribution to the Centre Interuniversitaire de Biologie Marine (CIBIM). Part II: Measurement for size in the sea urchin 104
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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.
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
Page 74 and 75: earing cycle into seven stages is e
Page 76 and 77: (Grosjean et al, 1996, see Part III
Page 78 and 79: output. The quality of gametes is o
Page 80 and 81: average value of 19.5 days, a minim
Page 82 and 83: individuals were still alive 3 mont
Page 84 and 85: e. Discussion show similar GI and M
Page 86 and 87: The success of the present method l
Page 88 and 89: Fenaux (1990) for the same species
Page 90 and 91: encountered with food is its stabil
Page 92 and 93: to Christine Spirlet (ref. ERB 4001
Page 94: PART II Measurement for size in the
Page 97 and 98: Part II: Measurement for size in th
Page 99 and 100: Few studies have compared and discu
Page 101 and 102: d. Results and discussion The ambit
Page 103: Reproducibility of measurements The
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 and 152: value just after metamorphosis (D0,
Page 153 and 154: 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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