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

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a. Choice of the growth model for sea urchins General introduction Von Bertalanffy 1 is the model most often used. Among 69 studies of sea urchins (regardless of species), this model was used 32 times, the Richards model 17 times, the Gompertz model 9 times and other models 11 times (Table 1). However, in 13 studies where several models were tested in addition to von Bertalanffy 1, the latter was considered as being the best one only twice. The reason invoked to reject the von Bertalanffy model was the initial lag phase in growth that is correctly represented solely by a sigmoid like in the Richards, Gompertz or logistic models (Yamagushi, 1975). In many studies where no other model was tested, it seems that the von Bertalanffy 1 curve was just a default choice: it represents the model "usually" fitted on such kind of data. The Richards model was first proposed by Ebert (1973) as a better alternative to the von Bertalanffy 1 curve to fit echinoid growth data. It was intensively used by the same author (Ebert, 1973, 1980a, 1982, 1999; Ebert & Russell, 1992, 1993) as well as by some others (Gage & Tyler, 1985; Russell, 1987; Kenner, 1992; Turon et al, 1995; Lamare & Mladenov, 2000). The Gompertz model is also a favorite when there seems to be a lag phase in growth and it has been used in various studies (Gage et al, 1986; Gage, 1987; Cellario & Fenaux, 1990; Dafni, 1992; Turon et al, 1995; Ebert, 1999). Each of these models (i.e., Richards or Gompertz) was preferred in 50% of the multi-model studies which considered them. The logistic curve, although also sigmoidal, was systematically rejected in multi-models studies of sea urchins, except for the irregular echinoid Echinocardium pennatifidum Norman (Gage, 1987). 53
Table 1. Models used to fit sea urchins growth data (the one preferred by authors in multimodels studies is in bold). Species (1) Growth model (2) Family Cidaridae Reference Eucidaris tribuloides (Lamarck) von Bertalanffy1 McPherson, 1968 Family Diadematidae Diadema setosum (Leske) Richards Ebert, 1980a von Bertalanffy1, Richards, Gompertz, logistic Ebert, 1999 Diadema antillarum Philippi von Bertalanffy1 Ebert, 1975 Echinotrix diadema (L.) von Bertalanffy1 Ebert, 1975 Richards Ebert, 1982 Centrostephanus rodgersii (A. Agassiz) Richards Ebert, 1982 Family Stomopneustidae Stomopneustes variolaris (Lamarck) Richards Ebert, 1982 Family Temnopleuridae Salmacis belli Döderlein Richards Ebert, 1982 Family Toxopneustidae Lytechinus variegatus (Lamarck) von Bertalanffy1 Ebert, 1975 Tripneustes gratilla (L.) von Bertalanffy1, Gompertz, logistic, Johnson Dafni, 1992 Tripneustes ventricosus (Lamarck) von Bertalanffy1 McPherson, 1965 Sphaerechinus granularis (Lamarck) von Bertalanffy1 Lumingas & Guillou, 1994 von Bertalanffy1 Jordana et al, 1997 Family Echinidae Echinus esculentus L. Richards Ebert, 1973 logistic Nichols et al, 1985 logistic Sime & Cranmer, 1985 Gompertz Gage et al, 1986 von Bertalanffy1 Gage, 1992 Echinus acutus Lamarck logistic Sime & Cranmer, 1985 von Bertalanffy1, Gompertz, logistic Gage et al, 1986 Echinus elegans Düben & Koren von Bertalanffy1, Gompertz, logistic Gage et al, 1986 Echinus affinis Mortensen von Bertalanffy1, Richards, Gompertz, logistic, Preece-Baines 1 Gage & Tyler, 1985 Gompertz Gage et al, 1986 linear Middleton et al, 1998 Psammechinus miliaris (Gmelin) von Bertalanffy1 Jensen, 1969a von Bertalanffy1 Allain, 1978 von Bertalanffy1 Gage, 1991 Paracentrotus lividus (Lamarck) von Bertalanffy1 Allain, 1978 (von Bertalanffy1), Gompertz Cellario & Fenaux, 1990 Gompertz, logistic, Richards Turon et al, 1995 von Bertalanffy1 Sellem et al, 2000 von Bertalanffy1, von Bertalanffy2, Gompertz, Grosjean et al (submitted), logistic, 4p-logistic, Weibull, original model see Part. IV Loxechinus albus Molina von Bertalanffy1 Gebauer & Moreno, 1995 Family Strongylocentrotidae Strongylocentrotus droebachiensis (Müller) von Bertalanffy1 Munk, 1992 von Bertalanffy1 Hagen, 1996b logistic Meidel & Scheibling, 1998 Tanaka Russell et al, 1998 Strongylocentrotus intermedius (A. Agassiz) von Bertalanffy1, Gompertz Fuji, 1967 Strongylocentrotus nudus (A. Agassiz) von Bertalanffy1 Ebert, 1975 Strongylocentrotus purpuratus (Stimpson) von Bertalanffy1 Ebert, 1977 Richards Russell, 1987 Richards Kenner, 1992 Strongylocentrotus franciscanus (A. Agassiz) von Bertalanffy1 Ebert, 1977 Richards Ebert & Russell, 1992 Richards, Tanaka, Jolicoeur Ebert & Russell, 1993 Tanaka Ebert, 1998 Richards, Tanaka Ebert, 1999 Hemicentrotus pulcherrimus (A. Agassiz) von Bertalanffy1 Fuji, 1963 Allocentrotus fragilis (Jackson) von Bertalanffy1 Sumich & McCauley, 1973 General introduction 54
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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 24 and 25: List of symbols LIST OF SYMBOLS Var
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: YY 3 2.5 2 1.5 1 0.5 General introd
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 and 104: 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
Page 257 and 258:
Annexes 256
Page 259 and 260:
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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