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

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(Table 1, next part) Species (1) Growth model (2) Family Echinometridae Reference Evechinus chloroticus (Valenciennes) von Bertalanffy1, Richards, Tanaka, Jolicoeur Lamare & Mladenov, 2000 Anthocidaris crassispina (A. Agassiz) von Bertalanffy1 Chiu, 1990 Heliocidaris erythrogamma (Valenciennes) Richards Ebert, 1982 Echinometra mathaei (de Blainville) von Bertalanffy1 Ebert, 1975 Richards Ebert, 1982 Echinometra oblonga (de Blainville) von Bertalanffy1 Ebert, 1975 Richards Ebert, 1982 Heterocentrotus mammillatus (Klein) Heterocentrotus trigonarius (Lamarck) Richards Richards Ebert, 1982 Ebert, 1982 Colobocentrotus atratus (L.) von Bertalanffy1 Ebert, 1975 Richards Ebert, 1982 Family Mellitidae Mellita quinquiesperforata (Leske) von Bertalanffy1 Lane & Lawrence, 1980 Mellita grantii Mortensen von Bertalanffy1 Ebert & Dexter, 1975 Encope grantis L. Agassiz von Bertalanffy1 Ebert & Dexter, 1975 Family Pourtalesiidae Echinosigra phiale (Thompson) von Bertalanffy1, Gompertz, logistic Gage, 1987 Family Hemiasteridae Hemiaster expergitus Loven von Bertalanffy1, Gompertz, logistic Gage, 1987 Family Spatangidae Spatangus purpureus Müller von Bertalanffy1, Gompertz, logistic Gage, 1987 Family Loveniidae Echinocardium cordatum (Pennant) von Bertalanffy1 Duineveld & Jenness, 1984 Echinocardium pennatifidum Norman von Bertalanffy1, Gompertz, logistic Gage, 1987 (1) Classification according to Mortensen (1950) and Durham (1955). (2) von Bertalanffy1: D = a·(1 - e -b·(t – c) ), von Bertalanffy2: D = a·(1 - e -b·(t – c) ) 3 , Richards: D = a·(1 - e -b·(t – c) ) d , Gompertz: t c = ⋅ , logistic: D = a/(1 + e -b·(t - c) ), 4p-logistic: D = (a – d)/(1 + e -b·(t - c) ) + d, Johnson: D = a·e -1/b·(t – c) , Preece-Baines 1: D a b D = a – 2·(a – d)/(e b·(t – c) + e e·(t – c) c −bt ⋅ ), linear: D = a·t + b, Weibull: D= a−d⋅ e , original model: D = e + a·(1 - e -b·t )/(1 + d·e -c·t ) (see Part IV), Tanaka: D = (1/b 1/2 )·ln(|2b·(t – c) + 2·(b 2 ·(t – c) 2 + a·b) 1/2 | + d), Jolicoeur: D = a/(1 - c·t -b ). General introduction Questioning asymptotic growth in the largest regular sea urchin, Strongylocentrotus franciscanus, Ebert & Russell (1993) introduced the indeterminate growth model of Tanaka as a better representation of the continuous growth of large individuals. However, this species seems to be a special case, even inside the Strongilocentrotidae family (Lawrence et al, 1995). The Tanaka model was not used much for other species. Lamare & Mladenov (2000) tested it on Evechinus chloroticus (Valenciennes), but concluded it is not the more appropriate one in this particular case. In an attempt to find a better model to fit echinoid growth data, various "exotic" curves were also tested. They were sometimes successful, such as in the works by Gage & Tyler (1985) that introduced the Preece & Baines 55
General introduction model 1 for Echinus affinis Mortensen or by Dafni (1992) that proposed the Johnson model to fit rapid growth with a very small initial lag phase of the Toxopneustidae Tripneustes gratilla at Elat. Based on this review (Table 1), it seems there is no ideal model to fit growth data in sea urchins and, consequently, the use of one particular model is more a question of personal preference. For instance, Ebert uses the Richards model most of the time (Ebert, 1973, 1980a, 1982, 1999), while Gage favors the Gompertz model (Gage & Tyler, 1985; Gage et al, 1986; Gage, 1987). This situation is problematic since parameters derived from these models –and others– are not comparables. Using a single model to fit all growth data would be preferable for comparison purposes (Turon et al, 1995). b. Fitting of growth models on real data for echinoids In selecting a growth model, several conditions should be met when fitting real data. First, animals sampled from a single homogeneous population should be measured at various ages. Second, one particular individual should be measured only once to ensure independence of the errors (since authors consider individual variation as part of the error term: they look for growth of a virtual "mean individual" among the population). Third, as most regression methods assume no error on the dependent variable –that is, time– (Sokal & Rohlf, 1981; Sen & Srivastava, 1990; Draper & Smith, 1998; Zar, 1999), the age of each measured individual should be known. Fourth, no interaction should exist between individuals in the population. Such ideal conditions are so restrictive that they are never met. When the age of individuals can be determined precisely, such as for sea urchins reared from the egg, it is common to measure the same specimens several times (Bull, 1938; Michel, 1984; Cellario & Fenaux, 1990; Basuyaux & Blin, 1998; Lamare & Mladenov, 2000). Errors are individual-dependent in such cases and this interaction is often ignored. 56
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U L B bio mar UNIVERSITE LIBRE DE B
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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 and 54: YY 3 2.5 2 1.5 1 0.5 General introd
Page 55: Table 1. Models used to fit sea urc
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
Page 105 and 106: 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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