in

A new framework for growth curve fitting based on the von Bertalanffy Growth Function

  • 1.

    Holm, S. et al. A comparative perspective on longevity: the effect of body size dominates over ecology in moths. J. Evol. Biol. 29(12), 2422–2435 (2006).

    • Article
    • Google Scholar
  • 2.

    Woodward, G. et al. Body size in ecological networks. Trends Ecol. Evol. 20(7), 402–409 (2005).

  • 3.

    Kwapich, C.L. Valentini, G. & Hölldobler, B. The non-additive effects of body size on nest architecture in a polymorphic ant. Philos. Trans. R. Soc. Lon., B, Biol Sci, 373(1753), 20170235 (2018).

  • 4.

    Mayer, M., Shine, R. & Brown, G. P. Bigger babies are bolder: effects of body size on personality of hatchling snakes. Behaviour 153(3), 313–323 (2016).

  • 5.

    Mirth, C. K., Frankino, W. A. & Shingleton, A. W. Allometry and size control: what can studies of body size regulation teach us about the evolution of morphological scaling relationships? Curr. Opin. Insect. 13, 93–98 (2016).

    • Article
    • Google Scholar
  • 6.

    Gutowsky et al. Interactive effects of sex and body size on the movement ecology of adfluvial bull trout (Salvelinus confluentus). Can. J. Zool. 94(1), 31–40 (2015).

    • Article
    • Google Scholar
  • 7.

    Green, D. M. Implications of female body-size variation for the reproductive ecology of an anuran amphibian. Ethol. Ecol. Evol. 27(2), 173–184 (2015).

    • Article
    • Google Scholar
  • 8.

    Davies, P. S. Physiological ecology of Patella. I. The effect of body size and temperature on metabolic rate. J. Mar. Biol. Assoc. UK 46(3), 647–658 (1966).

    • Article
    • Google Scholar
  • 9.

    Illius, A. W. & Gordon, I. J. Modelling the nutritional ecology of ungulate herbivores: evolution of body size and competitive interactions. Oecologia 89(3), 428–434 (1992).

  • 10.

    González-Wangüemert, M., Valente, S. & Aydin, M. Effects of fishery protection on biometry and genetic structure of two target sea cucumber species from the Mediterranean Sea. Hydrobiologia 743(1), 65–74 (2015).

    • Article
    • Google Scholar
  • 11.

    Jackson, C. J. & Wang, Y. G. Modelling growth rate of Penaeus monodon Fabricius in intensively managed ponds: effects of temperature, pond age and stocking density. Aquac. Res 29(1), 27–36 (1998).

    • Article
    • Google Scholar
  • 12.

    Ansah, Y. B. & Frimpong, E. A. Using model-based inference to select a predictive growth curve for farmed tilapia. N. Am. J. Aquac. 77(3), 281–288 (2015).

    • Article
    • Google Scholar
  • 13.

    Sulardiono, B., Prayitno, S. B. & Hendrarto, I. B. The growth analysis of Stichopus vastus (Echinodermata: Stichopodidae) in Karimunjawa waters. J. Coast. Dev 15, 315–323 (2012).

    • Google Scholar
  • 14.

    Petersen, J. K. et al. Mussels as a tool for mitigation of nutrients in the marine environment. Mar. Pollut. Bull. 82(1–2), 137–143 (2014).

  • 15.

    Bridges, T. C., Turner, L. W., Smith, E. M., Stahly, T. S. & Loewer, O. J. A mathematical procedure for estimating animal growth and body composition. Trans. ASAE 29(5), 1342–1347 (1986).

    • Article
    • Google Scholar
  • 16.

    Kirkwood, G. P. Estimation of von Bertalanffy growth curve parameters using both length increment and age–length data. Can. J. Fish. Aquat. Sci. 40(9), 1405–1411 (1983).

    • Article
    • Google Scholar
  • 17.

    Panik, M. J. Growth Curve Modelling: Theory and Applications (John Wiley & Sons, 2014).

  • 18.

    Potthoff, R. F. & Roy, S. N. A generalized multivariate analysis of variance model usefulespecially for growth curve problems. Biometrika, 51(3-4), 313-326 (1964).

  • 19.

    Richards, F. J. A flexible growth function for empirical use. J. Exp. Bot. 10(2), 290–301 (1959).

    • Article
    • Google Scholar
  • 20.

    Strenio, J. F., Weisberg, H. I. & Bryk, A. S. Empirical Bayes estimation of individual growth curve parameters and their relationship to covariates. Biometrics 39(1), 71–86 (1983).

  • 21.

    Higgins, R. M., Diogo, H. & Isidro, E. J. Modelling growth in fish with complex life histories. Rev. Fish Biol. Fish. 25(3), 449–462 (2015).

    • Article
    • Google Scholar
  • 22.

    Chang, Y. J., Sun, C. L., Chen, Y. & Yeh, S. Z. Modelling the growth of crustacean species. Rev. Fish Biol. Fish. 22(1), 157–187 (2012).

    • Article
    • Google Scholar
  • 23.

    Fuentes-Santos, I., Labarta, U., Arranz, K. & Fernández-Reiriz, M. J. From classical to nonparametric growth models: Towards comprehensive modelling of mussel growth patterns. Mar. Environ. Res. 127, 41–48 (2017).

  • 24.

    Huchard, E. et al. Additive genetic variance and developmental plasticity in growth trajectories in a wild cooperative mammal. J. Evol. Biol. 27(9), 1893–1904 (2014).

  • 25.

    Jager, T. & Ravagnan, E. Modelling growth of northern krill (Meganyctiphanes norvegica) using an energy-budget approach. Ecol. Model. 325, 28–34 (2016).

    • Article
    • Google Scholar
  • 26.

    Marshall, D. J. & White, C. R. Have we outgrown the existing models of growth? Trends Ecol. Evol. 34(2), 102–111 (2018).

  • 27.

    Quince, C. Abrams, P.A. Shuter, B.J. & Lester, N.P. Biphasic growth in fish I: theoretical foundations. J. Theor. Biol., 254(2), 197–206 (2008).

  • 28.

    Derocher, A. E. & Wiig, Ø. Postnatal growth in body length and mass of polar bears (Ursus maritimus) at Svalbard. J. Zool. (Lond.) 256(3), 343–349 (2002).

    • Article
    • Google Scholar
  • 29.

    Tjørve, K. M. C. & Tjørve, E. Shapes and functions of bird-growth models: how to characterise chick postnatal growth. Zoology 113(6), 326–333 (2010).

  • 30.

    Ernsting, G., Zonneveld, C., Isaaks, J. A. & Kroon, A. Size at maturity and patterns of growth and reproduction in an insect with indeterminate growth. Oikos 66, 17–26 (1993).

    • Article
    • Google Scholar
  • 31.

    Siegel, V. Age and growth of Antarctic Euphausiacea (Crustacea) under natural conditions. Mar. Biol. 96(4), 483–495 (1987).

    • Article
    • Google Scholar
  • 32.

    Lehman, T. M. & Woodward, H. N. Modeling growth rates for sauropod dinosaurs. Paleobiology 34(2), 264–281 (2008).

    • Article
    • Google Scholar
  • 33.

    Pütter, A. Studies on the physiological similarity. VI. Similarities in growth. Eur. J. Physiol. 180, 280 (1920).

    • Google Scholar
  • 34.

    Bertalanffy, Lvon Problems of organic growth. Nature 163(4135), 156–158 (1949).

  • 35.

    Bertalanffy, Lvon A quantitative theory of organic growth (inquiries on growth laws. II). Hum. Biol. 10(2), 181–213 (1938).

    • Google Scholar
  • 36.

    Schnute, J. A versatile growth model with statistically stable parameters. Can. J. Fish. Aquat. Sci. 38(9), 1128–1140 (1981).

    • Article
    • Google Scholar
  • 37.

    Góngora-Gómez, A. M., Leal-Sepúlveda, A. L., García-Ulloa, M., Aragón-Noriega, E. A. & Valenzuela-Quiñónez, W. Morphometric relationships and growth models for the oyster Crassostrea corteziensis cultivated at the southeastern coast of the Gulf of California Mexico. Lat. Am. J. Aquat. 46(4), 735–743 (2018).

    • Article
    • Google Scholar
  • 38.

    Reynaga-Franco, F. J. et al. Multi-model inference as criterion to determine differences in growth patterns of distinct Crassostrea gigas stocks. Aquacul. Int. 27, 1–16 (2019).

    • Article
    • Google Scholar
  • 39.

    Castillo-Vargasmachuca, S. G. Ponce-Palafox, J.T. Arámbul-Muñoz, E. Rodríguez-Domínguez, G. & Aragón-Noriega, E.A. The spotted rose snapper (Lutjanus guttatus Steindachner 1869) farmed in marine cages: review of growth models. Rev. Aquacult., 10(2), (2018).

  • 40.

    Lugert, V., Tetens, J., Thaller, G., Schulz, C. & Krieter, J. Finding suitable growth models for turbot (Scophthalmus maximus L.) in aquaculture 1 (length application). Aquac. Res. 48(1), 24–36 (2017).

    • Article
    • Google Scholar
  • 41.

    Yuancai, L., Marques, C. P. & Macedo, F. W. Comparison of Schnute’s and Bertalanffy-Richards’ growth functions. Forest Ecol. Manag. 96(3), 283–288 (1997).

    • Article
    • Google Scholar
  • 42.

    Gompertz, B. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Phil. Trans. R. Soc. Lon. 115, 513–583 (1825).

    • ADS
    • Google Scholar
  • 43.

    Tjørve, K.M. & Tjørve, E. The use of Gompertz models in growth analyses, and new Gompertz-model approach: An addition to the Unified-Richards family. PLoS ONE, 12(6), (2017).

  • 44.

    Alldredge, A. L. & Madin, L. P. Pelagic tunicates: unique herbivores in the marine plankton. Bioscience 32(8), 655–663 (1982).

    • Article
    • Google Scholar
  • 45.

    West, G. B., Brown, J. H. & Enquist, B. J. A general model for the origin of allometric scaling laws in biology. Science 276(5309), 122–126 (1997).

  • 46.

    Barneche, D. R. & Allen, A. P. The energetics of fish growth and how it constrains food-web trophic structure. Ecol. Lett., 21(6) (2018).

  • 47.

    West, G. B., Brown, J. H. & Enquist, B. J. A general model for ontogenetic growth. Nature 413(6856), 628–631 (2001).

  • 48.

    Moses, M. E. et al. Revisiting a model of ontogenetic growth: estimating model parameters from theory and data. Am. Nat. 171(5), 632–645 (2008).

  • 49.

    HirstA.G. & Forster, J. When growth models are not universal: evidence from marine invertebrates. Proc. Biol. Sci., 280(1768), (2013).

  • 50.

    Verhulst, P. F. Notice sur la loi que la population suit dans son accroissement. Corresp. Mathématique Phys 10, 113–21 (1839).

    • Google Scholar
  • 51.

    Katsanevakis, S. Modelling fish growth: model selection, multi-model inference and model selection uncertainty. Fish. Res. 81(2-3), 229–235 (2006).

    • Article
    • Google Scholar
  • 52.

    Shi, P. J. et al. On the 3/4-exponent von Bertalanffy equation for ontogenetic growth. Ecol. Model. 276, 23–28 (2014).

    • Article
    • Google Scholar
  • 53.

    Schnute, J. & Fournier, D. A new approach to length–frequency analysis: growth structure. Can. J. Fish. Aquat. Sci. 37(9), 1337–1351 (1980).

    • Article
    • Google Scholar
  • 54.

    Kvålseth, T. O. Cautionary note about R-squared. Am. Stat. 39(4), 279–285 (1985).

    • Google Scholar
  • 55.

    Willett, J. B. & Singer, J. D. Another cautionary note about R-squared: Its use in weighted least-squares regression analysis. Am. Stat., 42(3), 236-238 (1988).

  • 56.

    Maino, J. L. & Kearney, M. R. Ontogenetic and interspecific scaling of consumption in insects. Oikos, 124(12), 695-701 (2015).

  • 57.

    Maino, J. L. & Kearney, M. R. Testing mechanistic models of growth in insects. Proc. Soc. Biol. Sci., 282(1819), 20151973 (2015).

  • 58.

    Rosenfeld, J., Van Leeuwen, T., Richards, J. & Allen, D. Relationship between growth and standard metabolic rate: measurement artefacts and implications for habitat use and life‐history adaptation in salmonids. J. Anim. Ecol. 84(1), 4–20 (2015).

  • 59.

    Killen, S. S., Atkinson, D. & Glazier, D. S. The intraspecific scaling of metabolic rate with body mass in fishes depends on lifestyle and temperature. Ecol. Lett 13(2), 184–193 (2010).

  • 60.

    Ellenby, C. Body size in relation to oxygen consumption and pleopod beat in Ligia oceanica L. J. Exp. Biol. 28(4), 492–507 (1951).

    • CAS
    • Google Scholar
  • 61.

    Glazier, D.S. Hirst, A.G. & Atkinson, D. Shape shifting predicts ontogenetic changes inmetabolic scaling in diverse aquatic invertebrates. Proc. Biol. Sci., 282(1802), (2015).

  • 62.

    Hirst, A. G., Glazier, D. S. & Atkinson, D. Body shape-shifting during growth permits tests that distinguish between competing geometric theories of metabolic scaling. Ecol. Lett. 17(10), 1274–1281 (2014).

  • 63.

    Hirst, A. G. Intraspecific scaling of mass to length in pelagic animals: Ontogenetic shape change and its implications. Limnol. Oceanogr. 57(5), 1579–1590 (2012).

  • 64.

    Kooijman, S. A. L. M. Dynamic Energy Budgets in Biological Systems (Cambridge University Press, 1993).

  • 65.

    Kooijman, S. A. L. M. Dynamic Energy and Mass Budgets in Biological Systems (Cambridge University Press, 2000).

  • 66.

    Ohnishi, S., Yamakawa, T. & Akamine, T. On the analytical solution for the Pütter – Bertalanffy growth equation. J. Theor. Biol. 343, 174–177 (2014).

  • 67.

    Charnov, E. L. Fish growth: Bertalanffy k is proportional to reproductive effort. Environ. Biol. Fish. 83(2), 185–187 (2008).

    • Article
    • Google Scholar
  • 68.

    Lester, N. P., Shuter, B. J. & Abrams, P. A. Interpreting the von Bertalanffy model of somatic growth in fishes: the cost of reproduction. Proc. Soc. Biol. Sci. 271(1548), 1625–1631 (2004).

  • 69.

    Armstrong, D. P., Keevil, M. G., Rollinson, N. & Brooks, R. J. Subtle individual variation in indeterminate growth leads to major variation in survival and lifetime reproductive output in a long lived reptile. Funct. Ecol. 32(3), 752–761 (2017).

    • Article
    • Google Scholar
  • 70.

    Moore, D. W. & Farrar, J. D. Effect of growth on reproduction in the freshwater amphipod, Hyalella azteca (Saussure). Hydrobiologia 328(2), 127–134 (1996).

    • Article
    • Google Scholar
  • 71.

    Bouchard, L. & Winkler, G. Life cycle, growth and reproduction of Neomysis americana in the St. Lawrence estuarine transition zone. J. Plankton Res 40(6), 693–707 (2018).

    • Google Scholar
  • 72.

    Quesnel, L., King, W. J., Coulson, G. & Festa-Bianchet, M. Tall young females get ahead: size-specific fecundity in wild kangaroos suggests a steep trade-off with growth. Oecologia 186(1), 59–71 (2018).

  • 73.

    Rollo, C. D. Growth negatively impacts the life span of mammals. Evol. Dev. 4(1), 55–61 (2002).

  • 74.

    Bruce, R. C. Relative growth rates in three species of Desmognathus (Amphibia: Plethodontidae). Herpetologica 72(3), 174–180 (2016).

  • 75.

    Pardo, S. A., Cooper, A. B. & Dulvy, N. K. Avoiding fishy growth curves. Methods Ecol. Evol. 4(4), 353–360 (2013).

    • Article
    • Google Scholar
  • 76.

    Glazier, D. S. The 3/4-power law is not universal: evolution of isometric, ontogenetic metabolic scaling in pelagic animals. BioScience 56(4), 325–332 (2006).

    • Article
    • Google Scholar
  • 77.

    Bhowmick, A. R., Chattopadhyay, G. & Bhattacharya, S. Simultaneous identification of growth law and estimation of its rate parameter for biological growth data: a new approach. J. Biol. Phys. 40(1), 71–95 (2014).

  • 78.

    L’Abée-Lund, J. H., Langeland, A., Jonsson, B. & Ugedal, O. Spatial segregation by age and size in Arctic charr: a trade-off between feeding possibility and risk of predation. J. Anim. Ecol. 62, 160–168 (1993).

    • Article
    • Google Scholar
  • 79.

    Tan, H., Hirst, A. G., Glazier, D. S. & Atkinson, D. Ecological pressures and the contrasting scaling of metabolism and body shape in coexisting taxa: cephalopods versus teleost fish. Philos. Trans. R. Soc. Lon., B, Biol. Sci. 374(1778), 20180543 (2019).

    • Article
    • Google Scholar
  • 80.

    Seibel, B. A., Thuesen, E. V., Childress, J. J. & Gorodezky, L. A. Decline in pelagic cephalopod metabolism with habitat depth reflects differences in locomotory efficiency. Biol. Bull. 192(2), 262–278 (1997).

  • 81.

    Mitchell, S. F., Trainor, F. R., Rich, P. H. & Goulden, C. E. Growth of Daphnia magna in the laboratory in relation to the nutritional state of its food species, Chlamydomonas reinhardtii. J. Plankton Res. 14(3), 379–391 (1992).

    • Article
    • Google Scholar
  • 82.

    Lilley, M. K. et al. Culture and growth of the jellyfish Pelagia noctiluca in the laboratory. Mar. Ecol. Prog. Ser. 510, 265–273 (2014).

  • 83.

    Ross, R. M. Energetics of Euphausia pacifica. II. Complete carbon and nitrogen budgets at 8 and 12 °C throughout the life span. Mar. Biol. 68(1), 15–23 (1982).

  • 84.

    Lombard, F., Renaud, F., Sainsbury, C., Sciandra, A. & Gorsky, G. Appendicularian ecophysiology I: Food concentration dependent clearance rate, assimilation efficiency, growth and reproduction of Oikopleura dioica. J. Mar. Sys 78(4), 606–616 (2009).

    • Article
    • Google Scholar
  • 85.

    Båmstedt, U., Wild, B. & Martinussen, M. Significance of food type for growth of ephyrae Aurelia aurita (Scyphozoa). Mar. Biol. 139(4), 641–650 (2001).

    • Article
    • Google Scholar
  • 86.

    Båmstedt, U., Ishii, H. & Martlnussen, M. B. Is the scyphomedusa Cyanea capillata (l.) dependent on gelatinous prey for its early development? Sarsia 82(3), 269–273 (1997).

    • Article
    • Google Scholar
  • 87.

    Kheder, R. B., Quéré, C., Moal, J. & Robert, R. Effect of nutrition on Crassostrea gigas larval development and the evolution of physiological indices. Part A: Quantitative and qualitative diet effects. Aquaculture 305(1–4), 165–173 (2010).

  • 88.

    Thomsen, J., Casties, I., Pansch, C., Körtzinger, A. & Melzner, F. Food availability outweighs ocean acidification effects in juvenile Mytilus edulis: laboratory and field experiments. Glob. Chang. Biol. 19(4), 1017–1027 (2013).

  • 89.

    Domingues, P. M., Sykes, A. & Andrade, J. P. The effects of temperature in the life cycle of two consecutive generations of the cuttlefish Sepia officinalis (Linnaeus, 1758), cultured in the Algarve (South Portugal). Aquacult. Int 10(3), 207–220 (2002).

    • Article
    • Google Scholar
  • 90.

    Maranhão, P. & Marques, J. C. The influence of temperature and salinity on the duration of embryonic development, fecundity and growth of the amphipod Echinogammarus marinus Leach (Gammaridae). Acta Oecol. 24(1), 5–13 (2003).

  • 91.

    Stumpf, L., Tropea, C. & Greco, L. S. L. Recovery growth of Cherax quadricarinatus juveniles fed on two high-protein diets: Effect of daily feeding following a cyclic feeding period on growth, biochemical composition and activity of digestive enzymes. Aquaculture 433, 404–410 (2014).

  • 92.

    Ito, M. & Lucas, J. S. The Complete Larval Development of the Scyllarid Lobster, Scyllarus demani holthuis, 1946 (Decapoda, Scyllaridae), in the Laboratory. Crustaceana 58(2), 144–167 (1990).

    • Article
    • Google Scholar
  • 93.

    Ibánez, C. M. & Keyl, F. Cannibalism in cephalopods. Rev. Fish Biol. Fish. 20(1), 123–136 (2010).

    • Article
    • Google Scholar
  • 94.

    Pérez-Losada, M. A. R. C. O. S., Nolte, M. J., Crandall, K. A. & Shaw, P. W. Testing hypotheses of population structuring in the Northeast Atlantic Ocean and Mediterranean Sea using the common cuttlefish Sepia officinalis. Mol. Ecol. 16(13), 2667–2679 (2007).

  • 95.

    Olaya-Restrepo, J., Erzini, K. & González-Wangüemert, M. Estimation of growth parameters for the exploited sea cucumber Holothuria arguinensis from South Portugal. Fish. Bull. 116(1), 1–8 (2018).

    • Google Scholar
  • 96.

    Taylor, N. G., Walters, C. J. & Martell, S. J. A new likelihood for simultaneously estimating von Bertalanffy growth parameters, gear selectivity, and natural and fishing mortality. Can. J. Fish. Aquat. Sci. 62(1), 215–223 (2005).

    • Article
    • Google Scholar
  • 97.

    Pauly, D. On the interrelationships between natural mortality, growth parameters, and mean environmental temperature in 175 fish stocks. ICES J. Mar. Sci. 39(2), 175–192 (1980).

    • Article
    • Google Scholar

  • Source: Ecology - nature.com

    Susan Solomon earns Killian Award, MIT’s highest faculty honor

    The Role of European Starlings (Sturnus vulgaris) in the Dissemination of Multidrug-Resistant Escherichia coli among Concentrated Animal Feeding Operations