{"title":"Universal ontogenetic growth without fitted parameters: implications for life history invariants and population growth","authors":"Andrés Escala","doi":"10.1007/s12080-023-00565-1","DOIUrl":null,"url":null,"abstract":"Abstract Since the work of von Bertalanffy (Q Rev Boil 32:217–231, 1957), several models have been proposed that relate the ontogenetic scaling of energy assimilation and metabolism to growth, which are able to describe ontogenetic growth trajectories for living organisms and collapse them onto a single universal curve (West et al. in Nature 413:628–631, 2001; Barnavar et al. in Nature 420:626, 2002). Nevertheless, all these ontogenetic growth models critically depend on fitting parameters and on the allometric scaling of the metabolic rate. Using a new metabolic rate relation (Escala in Theor Ecol 12(4):415–425, 2019) applied to a Bertalanffy-type ontogenetic growth equation, we find that ontogenetic growth can also be described by a universal growth curve for all studied species, but without the aid of any fitting parameters (i.e., no fitting procedure is performed on individual growth curves). We find that the inverse of the heart frequency $$\\mathrm f_H$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>H</mml:mi> </mml:msub> </mml:math> , rescaled by the ratio of the specific energies for biomass creation and metabolism, defines the characteristic timescale for ontogenetic growth. Moreover, our model also predicts a generation time and lifespan that explain the origin of several “Life History Invariants’ (Charnov in Oxford University Press, Oxford, 1993) and predict that the Malthusian parameter should be inversely proportional to both the generation time and lifespan, in agreement with the data in the literature (Duncan et al. in Ecology 88:324–333 2007; Dillingham et al. in Paper 535, 2016; Hatton et al. in PNAS 116(43):21616–21622 2019). In our formalism, several critical timescales and rates (lifespan, generation time, and intrinsic population growth rate) are all proportional to the heart frequency $$\\mathrm f_H$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>H</mml:mi> </mml:msub> </mml:math> , and thus, their allometric scaling relations come directly from the allometry of the heart frequency, which is typically $$\\mathrm f_H \\propto M^{-0.25}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>H</mml:mi> </mml:msub> <mml:mo>∝</mml:mo> <mml:msup> <mml:mi>M</mml:mi> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>0.25</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> under basal conditions.","PeriodicalId":51198,"journal":{"name":"Theoretical Ecology","volume":"104 1","pages":"0"},"PeriodicalIF":1.2000,"publicationDate":"2023-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical Ecology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s12080-023-00565-1","RegionNum":4,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ECOLOGY","Score":null,"Total":0}
引用次数: 1
Abstract
Abstract Since the work of von Bertalanffy (Q Rev Boil 32:217–231, 1957), several models have been proposed that relate the ontogenetic scaling of energy assimilation and metabolism to growth, which are able to describe ontogenetic growth trajectories for living organisms and collapse them onto a single universal curve (West et al. in Nature 413:628–631, 2001; Barnavar et al. in Nature 420:626, 2002). Nevertheless, all these ontogenetic growth models critically depend on fitting parameters and on the allometric scaling of the metabolic rate. Using a new metabolic rate relation (Escala in Theor Ecol 12(4):415–425, 2019) applied to a Bertalanffy-type ontogenetic growth equation, we find that ontogenetic growth can also be described by a universal growth curve for all studied species, but without the aid of any fitting parameters (i.e., no fitting procedure is performed on individual growth curves). We find that the inverse of the heart frequency $$\mathrm f_H$$ fH , rescaled by the ratio of the specific energies for biomass creation and metabolism, defines the characteristic timescale for ontogenetic growth. Moreover, our model also predicts a generation time and lifespan that explain the origin of several “Life History Invariants’ (Charnov in Oxford University Press, Oxford, 1993) and predict that the Malthusian parameter should be inversely proportional to both the generation time and lifespan, in agreement with the data in the literature (Duncan et al. in Ecology 88:324–333 2007; Dillingham et al. in Paper 535, 2016; Hatton et al. in PNAS 116(43):21616–21622 2019). In our formalism, several critical timescales and rates (lifespan, generation time, and intrinsic population growth rate) are all proportional to the heart frequency $$\mathrm f_H$$ fH , and thus, their allometric scaling relations come directly from the allometry of the heart frequency, which is typically $$\mathrm f_H \propto M^{-0.25}$$ fH∝M-0.25 under basal conditions.
自von Bertalanffy (Q Rev Boil 32:17 - 231,1957)的工作以来,已经提出了几个将能量同化和代谢的个体发生尺度与生长联系起来的模型,这些模型能够描述生物体的个体发生生长轨迹,并将它们分解为单一的通用曲线(West et al. in Nature 413:628-631, 2001;Barnavar et al. Nature 420:626, 2002)。然而,所有这些个体生长模型都严重依赖于拟合参数和代谢率的异速缩放。将新的代谢率关系(Escala in Theor Ecol 12(4): 415-425, 2019)应用于bertalanffy型个体生长方程,我们发现个体生长也可以用所有研究物种的通用生长曲线来描述,但不需要任何拟合参数的帮助(即不需要对个别生长曲线进行拟合程序)。我们发现心脏频率$$\mathrm f_H$$ f H的倒数,通过生物质创造和代谢的比能量的比率重新缩放,定义了个体生长的特征时间标度。此外,我们的模型还预测了世代时间和寿命,解释了几个“生命史不变量”的起源(Charnov在牛津大学出版社,牛津,1993年),并预测马尔萨斯参数应该与世代时间和寿命成反比,这与文献中的数据一致(Duncan et al. in Ecology 88:324-333 2007;Dillingham et al., Paper 535, 2016;哈顿等人,PNAS 116(43): 21616-21622 2019)。在我们的形式中,几个关键的时间尺度和速率(寿命、生育时间和内在人口增长率)都与心脏频率$$\mathrm f_H$$ f H成正比,因此,它们的异速缩放关系直接来自心脏频率的异速,在基本条件下,心脏频率通常为$$\mathrm f_H \propto M^{-0.25}$$ f H∝M - 0.25。
期刊介绍:
Theoretical Ecology publishes innovative research in theoretical ecology, broadly defined. Papers should use theoretical approaches to answer questions of ecological interest and appeal to and be readable by a broad audience of ecologists. Work that uses mathematical, statistical, computational, or conceptual approaches is all welcomed, provided that the goal is to increase ecological understanding. Papers that only use existing approaches to analyze data, or are only mathematical analyses that do not further ecological understanding, are not appropriate. Work that bridges disciplinary boundaries, such as the intersection between quantitative social sciences and ecology, or physical influences on ecological processes, will also be particularly welcome.
All areas of theoretical ecology, including ecophysiology, population ecology, behavioral ecology, evolutionary ecology, ecosystem ecology, community ecology, and ecosystem and landscape ecology are all appropriate. Theoretical papers that focus on applied ecological questions are also of particular interest.