American Journal of Life Sciences

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The United Equation of Animal Growth

Received: 09 August 2015    Accepted: 13 August 2015    Published: 21 August 2015
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Abstract

The equation that can describe all known types of animal growth is proposed. The equation contains two basic coefficients, one of which determines the initial rate of growth; the other determines the change of the growth rate. In separate cases two correction coefficients should be taken into account, one of which is connected with morphogenetic processes and the other is connected with spontaneous decrease of the body weight. Biorhythms that accompany growth process can be described by the equation as well. Linear recursive form of the equation allows to use regression analysis and, therefore, comparative intrapopulation, interpopulation and interspecies analysis of growth. Examples of approximation by the equation of own and literature experimental data are shown. Values of the coefficients of the equation for different types of growth in different stages of ontogenesis of the various animal systematic groups are calculated. The equation is suitable to describe change of any biological parameter which is associated with body weight by allometric (power) dependence

DOI 10.11648/j.ajls.20150305.12
Published in American Journal of Life Sciences (Volume 3, Issue 5, October 2015)
Page(s) 345-351
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Body Weight Changes, Developmental Biology, Growth, Mathematical Model

References
[1] I. I. Shmalgauzen, "Growth and differentiation," in Rost zhivotnykh, S. Ya. Kaplansky, M. S. Mitzkevich, B. T. Tokin and I. I. Shmalgauzen, Eds. Moscow and Leningrad: Gosudarstvennoe izdatelstvo biologicheskoj i meditsinskoj literatury, 1935, pp. 74–84 (in Russian).
[2] G. G. Vinberg, "Interrelation of growth and energy metabolism in poikilothermal animals," in Kolichestvennye aspekty rosta organizmov, A. I. Zotin, Ed., Moscow: Nauka, 1975, pp. 7–25 (in Russian).
[3] L. von Bertalanffy, 1965. "On the von Bertalanffy growth curve," Growth, vol. 30, pp. 123–124.
[4] M. V. Mina and G. A. Klevezal, "Animal Growth," Moscow: Nauka, 1976, 291 p. (in Russian).
[5] A. I. Zotin, "Thermodynamic aspects of developmental biology," Monographs in Developmental Biology, vol. 5. Basel et al.: S.Karger, 1972, 159 p.
[6] A. I. Zotin, "Quantitative growth theories (history, current state and prospects)," in Kolichestvennye aspekty rosta organizmov, A. I. Zotin, Ed., Moscow: Nauka, 1975, pp. 230–233 (in Russian).
[7] A. I. Zotin and R. S. Zotina, "The phenomenological theory of development, growth, and aging," Moscow: Nauka, 1993, 364 p. (in Russian).
[8] D. E. Gerrard and A. L. Grant, "Principles of animal growth and development," Dubuque, IA: Kendall/Hunt Publ. Co, 2003, 284 p.
[9] K. L. Hossner, "Hormonal regulation of farm animal growth," Wallingford, Oxfordshire, UK; Cambridge, MA: CABI Publ., 2005, 223 p.
[10] R. S. Zotina and A. I. Zotin, "Towards a phenomenological theory of growth," J. Theor. Biol., vol. 35, 1972, pp. 213–225.
[11] R. S. Zotina and A. I. Zotin, "Integrated equations of growth," Zh. Obshch. Biol., vol. 34, 1973, pp. 606–616 (in Russian).
[12] A. A. Zotin, "Patterns of growth and energy metabolism in the ontogeny of mollusks," Extended Abstract of Doctor of Sciences Dissertation, Moscow: IBR RAN, 2009, 30 p. (in Russian).
[13] A. A. Zotin and S. Yu. Kleimenov, "Endogenous biorhythms of the specific growth rate in individual development of Lymnaea stagnalis (Lymnaeidae, Gastropoda)," Biology Bull., vol. 40, 2013, pp. 1–10.
[14] A. I. Zotin, "Thermodynamics and growth of organisms in ecosystems," Can. Bull. Fish. Aquat. Sci., vol. 213, 1985, pp. 27–37.
[15] E. Ford, "An account of the herring investigations conducted at Plymouth during the years from 1924-1933," J. Marine Biol. Assoc. U.K., vol. 19, 1933, pp. 305–381.
[16] L. A. Walford, "A new graphic method of description the growth of animals," Biol. Bull., vol. 90, 1946, pp. 141–147.
[17] A. A. Zotin, "Statistical estimation of allometric coefficients," Biology Bull., vol. 27, 2000, pp. 431–437.
[18] A. A. Zotin and E. F. Kirik, "Growth of Planorbarius corneus (Gastropoda, Planorbidae)," unpublished.
[19] T. I. Dobrynina, R. Ya. Bratchik, F. V. Monakov and E. B. Paveljeva, "Pecularities of growth, metabolism, and feeding of the clam shrimp (Conchostraca)," in Osnovy izuchenija presnovodnych ecosysytem, G. G. Vinberg, Ed ., Leningrad: ZIN AN SSSR, 1981, pp. 138–144 (in Russian).
[20] S. G. Vassetzky, "The Spanish newt Pleurodeles waltlii," in Animal species for developmental studies, D. A. Dettlaff and S. G. Vassetzky, Eds., New York and London: Plenum Press, 1991. pp. 167–201.
[21] J. W. Forsythe and R. T. Hanlon, "Effect of temperature on laboratory growth, reproduction and life span of Octopus bimaculoides," Mar. Biol., vol. 98, 1988, pp. 369–379.
[22] P. S. Lake, "The effect of temperature on growth, longevity and egg production in Chirocephalus diaphanus Prevost (Crustacea: Anostraca)," Hydrobiologia, vol. 33, 1969, pp. 342–351.
[23] H. H. Taylor and N. Leelapiyanart, "Oxygen uptake by embryos and oligerous females of two intertidal crabs, Heterozius rotundifrons (Belliidae) and Cyclograpsus lavauxi (Grapsidae): scaling and the metabolic costs of reproduction," J. Exp. Biol., vol. 204, 2001, pp. 1083–1097.
[24] T. A. Alekseeva and N. D. Ozernyuk, "Dynamics of energy metabolism in ontogenesis of striped shield bug (Graphosoma lineatum L.) and cabbage moth (Mamestra brassicae L.)," Russ. J. Dev. Biol., vol. 42, 2011, pp. 73–78.
[25] N. P. Bordzilovskaya and T. A. Dettlaff, "The axolotl Ambystoma mexicanum," in Animal species for developmental studies, D. A. Dettlaff and S. G. Vassetzky, Eds., New York and London: Plenum Press, 1991, pp. 203–230.
[26] S. Yu. Kleimenov, "The intensity of energy metabolism in the early ontogeny of animals according to direct and indirect calorimetry data," Extended Abstract of Candidate of Sciences Dissertation, Moscow: IBR RAN, 1996, 21 p. (in Russian).
[27] H. A. Murray, "Physiological ontogeny. A. Chicken embryos. 3. Weight and growth rate as function of age," J. Gen. Physiol., vol. 9, 1925. pp. 39–48.
[28] A. A. Zotin, "Individual growth of Lymnaea stagnalis (Lymnaeidae, Gastropoda): II. Late postlarval ontogeny," Biology Bul., vol. 36, 2009, pp. 591–597.
[29] A. A. Zotin and I. G. Vladimirova, "Respiration rate and species-specific lifespan in freshwater bivalves of Margaritiferidae and Unionidae families," Biology Bul., vol. 28, 2001, pp. 273–279.
[30] A. A. Zotin and N. D. Ozernyuk, "Growth characteristics of the common mussel Mytilus edulis from the White Sea," Biology Bul., vol. 31, 2004, pp. 377–381.
[31] G. E. Insarov, "Alternation of growth and reproduction in ontogenesis," in Energeticheskie aspekty rosta i razmnozheniya vodnykh bespozvonochnykh, L. M. Suschenya, Ed. Minsk: AN BSSR, 1975, pp. 23–31 (in Russian).
[32] K. Anger, "Growth and elemental composition (C, N, H) in Inachus dorsettensis (Decapoda: Majidae) larvae reared in the laboratory," Mar. Biol., vol. 99, 1988, pp. 255–260.
[33] L. I. Radzinskaya, I. S. Nikolskaya, T. A. Alekseeva, I. G. Vladimirova, P. I. Kovalenko and N. D. Ozernyuk, "Changes in the intensity of respiration during ontogenesis of some invertebrates," Ontogenez, vol. 34, 2003, pp. 317–320 (in Russian).
[34] R. Walter and I. Lamprecht, "Modern theories concerning the growth equations," in Thermodynamics of Biological Processes, I. Lamprecht and A. I. Zotin, Eds, Berlin and New York: Walter de Gruyter, 1978, pp. 143–162.
[35] Yu. E. Bregman, "The growth of sea cucumber (Stichopus japonicus) in Peter the Great Bay," Zool. Zhurnal., vol. 50, 1971, pp. 839–845 (in Russian).
[36] A. Pütter, "Studien über physiologische Ähnlichkeit. VI. Wachstumsähnlichkeiten," Pflüger's Arch. ges. Physiol., vol. 180, 1920, pp. 298–304.
[37] I. G. Vladimirova, S. Yu. Kleimenov and T. A. Alekseeva, "Dynamics of body mass and oxygen consumption in the ontogeny of the Spanish ribbed newt (Pleurodeles waltl): 2. Larval Stage," Biology Bul., vol. 39, 2012, pp. 10–14.
[38] R. K. Danilov and T. G. Borovaya, "General and medical embryology," Sankt-Peterburg: SpetzLit, 2003, 231 p. (in Russian).
[39] A. A. Zotin, "Equations describing changes in weight and mass-specific rate of oxygen consumption in animals during postembryonic development," Biology Bul., vol. 33, 2006, pp. 323–331.
[40] I. G. Vladimirova, S. Yu. Kleimenov, T. A. Alekseeva and L. I. Radzinskaya, "Specific growth rate and the level of energy metabolism in the ontogeny of axolotl, Ambystoma mexicanum (Amphibia: Ambystomatidae)," Biology Bul., vol. 30, 2003, pp. 591–596.
[41] A. A. Zotin, "Patterns of individual growth of gray garden slug Deroceras reticulatum," Biology Bul., vol. 34, 1978, pp. 457–462.
[42] I. S. Nikolskaya, L. I. Radzinskaya and E. A. Prokofjev, "Change of respiration and wtight of cricket Acheta domesticus L. during growth and aging," Izvestiya Akademii Nauk SSSR, Seriya Biologicheskaya, No 4, 1986, pp. 628–633 (in Russian).
[43] W. Thompson D'Arcy, "On growth and form," Cambridge: Univ. Press, 1942, 1116 p.
[44] I. V. Ivleva, "Growth and reproduction of potworm (Enchytraeus albidus Heule)," Zool. Zhurnal, vol. 32, 1953, pp. 394–404 (in Russian).
[45] A. A. Zotin, "Patterns of individual growth in the field slug Deroceras agreste (Gastropoda, Agriolimacidae)," Biology Bul., vol. 36, 2009, pp. 28–36.
[46] L. R. Arrington, T. C. Beaty and K. C. Kelley, "Growth, longevity, and reproductive life of the Mongolian gerbil," Lab. Anim. Sci. vol. 23, 1973, pp. 262–265.
[47] E. A. Prokofjev, "Quantitative analysis of growth and life span prediction," Extended Abstract of Candidate of Sciences Dissertation, Moscow: IBR RAN, 1983, 21 p. (in Russian).
[48] C. C. White and L. I. Brisbin, "Estimation and comparison of parameters in stochastic growth models for barn owls," Growth, vol. 44, 1980, pp. 77–111.
[49] A. I. Zotin and T. N. Vorobjeva, "Oscillatory processes in a steady state of nonlinear thermodynamic systems," in Kolebatelnye protsessy v biologicheskikh i khimicheskikh sistemakh. Vol. 2, E. E. Selkov, Ed., Pushchino-on-Oka: Institute of Biophysics, USSR Acad. Sci., 1971, pp. 120–124 (in Russian).
[50] G. Nicolis and I. Prigogine, "Self-organization in nonequilibrium systems: from dissipative structures to order through fluctuations," New York: Wiley Interscience, 1977, 512 p.
[51] A. B. Rubin, "Thermodynamics of biological processes," Moscow: Izdatelstvo MGU, 1984, 240 p. (in Russian).
[52] A. I. Zotin, "Thermodynamic bases of biological processes: physiological reactions and adaptations," Berlin and New York: Walter de Gruyter, 1990, 293 p.
[53] K. Schmidt-Nielson, "Scaling: why is animal size so important?" Cambridge: Univ. Press, 1984, 241 p.
[54] A. I. Zotin and A. A. Zotin, "Direction, rates, and mechanisms of progressive evolution: thermodynamic and experimental bases)," Moscow: Nauka, 1999, 319 p. (in Russian).
Author Information
  • Laboratory of Evolutional Developmental Biology, Kol’tsov Institute of Developmental Biology of The Russian Academy of Sciences, Moscow, Russia

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    Alexey A. Zotin. (2015). The United Equation of Animal Growth. American Journal of Life Sciences, 3(5), 345-351. https://doi.org/10.11648/j.ajls.20150305.12

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  • @article{10.11648/j.ajls.20150305.12,
      author = {Alexey A. Zotin},
      title = {The United Equation of Animal Growth},
      journal = {American Journal of Life Sciences},
      volume = {3},
      number = {5},
      pages = {345-351},
      doi = {10.11648/j.ajls.20150305.12},
      url = {https://doi.org/10.11648/j.ajls.20150305.12},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajls.20150305.12},
      abstract = {The equation that can describe all known types of animal growth is proposed. The equation contains two basic coefficients, one of which determines the initial rate of growth; the other determines the change of the growth rate. In separate cases two correction coefficients should be taken into account, one of which is connected with morphogenetic processes and the other is connected with spontaneous decrease of the body weight. Biorhythms that accompany growth process can be described by the equation as well. Linear recursive form of the equation allows to use regression analysis and, therefore, comparative intrapopulation, interpopulation and interspecies analysis of growth. Examples of approximation by the equation of own and literature experimental data are shown. Values of the coefficients of the equation for different types of growth in different stages of ontogenesis of the various animal systematic groups are calculated. The equation is suitable to describe change of any biological parameter which is associated with body weight by allometric (power) dependence},
     year = {2015}
    }
    

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    AU  - Alexey A. Zotin
    Y1  - 2015/08/21
    PY  - 2015
    N1  - https://doi.org/10.11648/j.ajls.20150305.12
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    T2  - American Journal of Life Sciences
    JF  - American Journal of Life Sciences
    JO  - American Journal of Life Sciences
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    AB  - The equation that can describe all known types of animal growth is proposed. The equation contains two basic coefficients, one of which determines the initial rate of growth; the other determines the change of the growth rate. In separate cases two correction coefficients should be taken into account, one of which is connected with morphogenetic processes and the other is connected with spontaneous decrease of the body weight. Biorhythms that accompany growth process can be described by the equation as well. Linear recursive form of the equation allows to use regression analysis and, therefore, comparative intrapopulation, interpopulation and interspecies analysis of growth. Examples of approximation by the equation of own and literature experimental data are shown. Values of the coefficients of the equation for different types of growth in different stages of ontogenesis of the various animal systematic groups are calculated. The equation is suitable to describe change of any biological parameter which is associated with body weight by allometric (power) dependence
    VL  - 3
    IS  - 5
    ER  - 

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