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

Recommendations

Info

f. Conclusions The new growth model with intraspecific competition is a very flexible one. It can accommodate different situations and has meaningful parameters that allow exploring and quantifying various aspects of growth. Using a quantile regression method, modified for envelope modelling, and constraining parameters ensures the meaning of the latter is saved into the fitted model. It takes also individual variability into account. This is particularly useful to model growth of P. lividus and probably of many other sea urchins species and other animals or plants. It is original in many aspects, including the way it was designed, by defuzzifying a fuzzy model where most of the other growth models were built from their differential equations. It is a general 'transitional' growth model. By distinguishing 'dimensional' and 'transitional' growth models, a duality in sigmoidal growth curves comes to light. A preferred dimension for modelling growth seems to exist. It is linear in the case of P. lividus but it should be most interesting to check it for other species. A generalized von Bertalanffy growth model, which is both 'dimensional' and 'transitional' and includes varying environmental effects on growth, thanks to the use of metabolic time, was proposed (eq. 42). It is, however, the visible tip of the iceberg. Fuzzy sets and transitions (membership functions) can be combined in countless ways to create many other similar models. In the present work, we studied models deriving from von Bertalanffy 1 curve, because the latter seemed to be a good basis for describing growth of P. lividus. Other models incorporating an inhibition component or any other 'transitional' feature can be derived from other growth models, including non-asymptotic ones, and would perhaps be more adapted for other species. We propose to call this family of functions 'fuzzy-remanent' models. From their fuzzy origin, they keep nothing in appearance, but the biological meaning of their parameters is still there. Recalling the fuzzy model they come from, one has a much clearer idea of how various components –sets and membership functions– interact to produce the final result. Fuzzy logic is closer to the way human Part IV: A growth model with intraspecific competition 177
ain conceptualizes complex objects. Statistical tools handle defuzzified analytic functions more conveniently. By their bivalence, fuzzy-remanent functions promise to be powerful tools for modelling complex nonlinear phenomena, like growth, in a functional way. g. Acknowledgments We thank the CREC and the University of Caen for their contribution in building a specific sea urchin rearing facility. We are grateful to Didier Bucaille who performed the laboratory measurements. We thank also the Prof. Michael Russell for constructive criticisms and Prof. Jean-Pierre Van Noppen for proofreading the manuscript. This study was conducted in the framework of the European Contracts AQ2.530, "Sea urchins cultivation" and FAIR-CT96-1623, "Biology of sea urchins under intensive cultivation (closed cycle echiniculture)". This is a contribution of the "Centre Interuniversitaire de Biologie Marine". Part IV: A growth model with intraspecific competition 178
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 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 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
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
Page 111 and 112:
110
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
Page 135 and 136: 134
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
Page 155 and 156: Table 12. Results of quantile regre
Page 157 and 158: This way, one obtains a 4-parameter
Page 159 and 160: individuals related to the presence
Page 161 and 162: Finally, ∆D∞ should follow a no
Page 163 and 164: 60 Diameter increase D' in mm 40 20
Page 165 and 166: e. Discussion Fig. 34B shows three
Page 167 and 168: Constraining parameters as we did i
Page 169 and 170: It does not consider respiration as
Page 171 and 172: this species. For other species, wh
Page 173 and 174: ecapture, McDonald & Pitcher, 1979;
Page 175 and 176: ∆D∞ D0 +∆D∞ − D0 +∆D∞
Page 177: evaluated on basis of biological kn
Page 181 and 182: 180
Page 183 and 184: General conclusions individuals, wh
Page 185 and 186: Root models: y’ = ay m -by n (exp
Page 187 and 188: General conclusions - The diauxic g
Page 189 and 190: General conclusions model not on a
Page 191 and 192: References Baker, T.T., R. Lafferty
Page 193 and 194: References Dafni, J. & R. Tobol, 19
Page 195 and 196: References Ebert, T.A., 1999. Plant
Page 197 and 198: References intermedius on a rocky s
Page 199 and 200: References Guillou, M. & Ch. Michel
Page 201 and 202: References Kobayashi, S. & J. Taki,
Page 203 and 204: References McDonald, P.D. & T.J. Pi
Page 205 and 206: References Pouvreau, S., C. Bacher
Page 207 and 208: References Sellem, F., H. Langar &
Page 209 and 210: References Stumm, W. & J.J. Morgan,
Page 211 and 212: References Webster, S.K. & A.C. Gie
Page 213 and 214: 212
Page 215 and 216: Annexes 214
Page 217 and 218: # If no graphic device currently op
Page 219 and 220: lines(edatq[, 1], predict(edat.025,
Page 221 and 222: SimRes
Page 223 and 224: Annexes Code of functions required
Page 225 and 226: plot(cumsum(dat[,columns[1]])/sum(d
Page 227 and 228: for the CI!!! Annexes SEMean
Page 229 and 230:
} Annexes # - y, a vector of classe
Page 231 and 232:
plot(x, y, type="l", col=col, lty=l
Page 233 and 234:
} Annexes } results[i, 1:5]
Page 235 and 236:
} .value Annexes dimnames(.grad)
Page 237 and 238:
#{ # # This is adapted from SSasymp
Page 239 and 240:
Exp.ival
Page 241 and 242:
SSallo
Page 243 and 244:
.expr4
Page 245 and 246:
.expr9
Page 247 and 248:
. The 'nlrq' package for nonlinear
Page 249 and 250:
nlrq.control package:nlrq R Documen
Page 251 and 252:
gradSetArgs[[2]]), call("[", gradSe
Page 253 and 254:
model.step
Page 255 and 256:
Annexes 254
Page 257 and 258:
Annexes 256
Page 259 and 260:
Annexes metamorphosis. Acquisition
Page 261 and 262:
Annexes ABSTRACT: The general allom
Page 263 and 264:
Annexes libitum for 8, 16, 24, 32,
Page 265 and 266:
Annexes EXECUTIVE SUMMARY: The aim
Page 267 and 268:
Annexes KEYWORDS: Somatic growth, d
Page 269 and 270:
Annexes amount of waste produced at
Page 271 and 272:
Annexes ABSTRACT: Multimodal distri
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?