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

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General introduction Russell, 1987; Rowley, 1990; Kenner, 1992; Ebert & Russell, 1992, 1993; Russell et al, 1998; Lamare & Mladenov, 2000). This way, seasonal variation in growth is also partly eliminated. For sea urchins, it is the skeleton that is tagged using tetracycline (Kobayashi & Taki, 1969; Taki, 1972). Size increase of the ossicles can then be determined because a band of tetracycline-labeled skeleton, visible under ultraviolet light, indicates its size at tagging time. An allometric relationship between the size of the given ossicles and the body size allow estimating the latter. To fit such data, growth models need to be reworked, using a so-called Ford-Walford representation, or Walford plot (Ford, 1933; Walford, 1946; Ebert, 1999) where size at time t + 1 year (at recapture) is expressed as a function of size at time t (at capture). Ebert (1999) reviewed such transformations for von Bertalanffy, Gompertz, logistic, Richards and Tanaka models. Sainsbury (1980) demonstrated the strong biases that could occur with such a method when there is individual variation in growth in a population. In fact, relative growth does not take the age into account, by definition. Hence, due to individual variations in growth rate, some fast-growing but young individuals have same size as slower-growing but older ones at a given time. The method mixes all animals having the same size, no matter their age, and calculates a mean growth rate at that size. This mixing of age-cohorts is troublesome when growth variation is high in the population. Rejection of a particular growth model could result from these biases as Sainsbury evidenced, using a theoretical analysis with the von Bertalanffy 1 model. As individual variation in growth pattern is probable, one should be very careful using this method. Among all authors using tagged sea urchins, Gage (1992) was the only one that cited Sainsbury's work and care about a possible bias due to individual variation in growth rate. Clearly, there is no fool-proof method for modelling individual growth of sea urchins in the field. In such a context, one can rely on experiments conducted in aquaria, although it is evident that growth patterns observed in artificial conditions could be very different to what happens in the field. 59
General introduction Experiments in cages in the sea are closer to conditions of wild populations, but in the case of P. lividus populations living in tidal pools, they are impossible to perform in practice. 60
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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
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 and 56: Table 1. Models used to fit sea urc
Page 57 and 58: General introduction model 1 for Ec
Page 59: General introduction method used. I
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
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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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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