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Dynamic energy budget theory

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460:, aiming to provide a ready-to-use tool for users with less mathematical and programing background. Number of parameters, also pointed as relatively sparse for a bioenergetic model, vary depending on the main application and, because the whole life cycle of an organism is defined, the overall number of parameters per data-set ratio is relatively low. Linking the DEB (abstract) and measured properties is done by simple mathematical operations which include auxiliary parameters (also defined by the DEB theory and included in the 39:(energy and mass budgets) of all living organisms at the individual level, based on assumptions about energy uptake, storage, and utilization of various substances. The DEB theory adheres to stringent thermodynamic principles, is motivated by universally observed patterns, is non-species specific, and links different levels of biological organization ( 508:, which prompted side-by-side analysis of the two approaches. Though the two theories can be regarded as complementary to an extent, they were built on different assumptions and have different scope of applicability. In addition to a more general applicability, the DEB theory does not suffer from consistency issues pointed out for the WBE theory. 221:. Under constant environmental conditions (constant food and temperature) the standard DEB model can be simplified to the von Bertalanffy (or better, Putter's ) growth model, but its mechanistic process-based setup enables incorporating fluctuating environmental conditions, as well as studying reproduction and maturation in parallel to growth. 135:. Assimilation of energy is proportional to surface area of the structure, and maintenance is proportional to its volume. Reserve does not require maintenance. Energy mobilization will depend on the relative amount of the energy reserve, and on the interface between reserve and structure. Once mobilized, the energy is split into two branches: 595:
of the organism. Rules for the co-variation of parameter values across species are implied by model assumptions, and the parameter values can be directly compared without dimensional inconsistencies which might be linked to allometric parameters. Any eco-physiological quantity that can be written as
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The explicitness of the assumptions and the resulting predictions enable testing against a wide variety of experimental results at the various levels of biological organization. The theory explains many general observations, such as the body size scaling relationships of certain physiological traits,
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The main criticism is directed to the formal presentation of the theory (heavy mathematical jargon), number of listed parameters, the symbol heavy notation, and the fact that modeled (state) variables and parameters are abstract quantities which cannot be directly measured, all making it less likely
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applies, i.e. the chemical composition of the body is constant). The state variables of the individual are 1 reserve, 1 structure, maturity, and (in the adult stage) the reproduction buffer. Parameter values are constant throughout life. The reserve density at birth equals that of the mother at egg
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Generality of the approach and applicability of the same mathematical framework to organisms of different species and life stages enables inter- and intra-species comparisons on the basis of parameter values, and theoretical/empirical exploration of patterns in parameter values in the evolutionary
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However, more recent publications aim to present the DEB theory in an "easier to digest" content to "bridge the ecology-mathematics gap". List of parameters is a direct result of list of processes which are of interest—if only growth under constant food and temperature is of interest, the standard
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The theory presents simple mechanistic rules that describe the uptake and allocation of energy (and nutrients) and the consequences for physiological organization throughout an organism's life cycle, including the relationships of energetics with aging and effects of toxicants. Assumptions of the
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shows which particular compound parameters can be estimated from a few simple observations at a single food density and how an increasing number of parameters can be estimated if more quantities are observed at several food densities. A natural sequence exists in which parameters can be known in
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Lika, Konstadia; Kearney, Michael R.; Freitas, Vânia; Veer, Henk W. van der; Meer, Jaap van der; Wijsman, Johannes W.M.; Pecquerie, Laure; Kooijman, Sebastiaan A.L.M. (2011). "The "covariation method" for estimating the parameters of the standard Dynamic Energy Budget model I: Philosophy and
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A fixed fraction (kappa) of mobilized reserve is allocated to somatic maintenance plus growth (soma), the rest on maturity maintenance plus maturation or reproduction. Maintenance has priority over other processes. Somatic maintenance is proportional to structural body volume, and maturity
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Dynamic energy budget theory presents a quantitative framework of metabolic organization common to all life forms, which could help to understand evolution of metabolic organization since the origin of life. As such, it has a common aim with the other widely used metabolic theory: the
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DEB theory are delineated in an explicit way, the approach clearly distinguishes mechanisms associated with intra‐ and interspecific variation in metabolic rates, and equations for energy flows are mathematically derived following the principles of physics and simplicity.
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DEB model can be simplified to the von Bertalanffy growth curve. Adding more processes into focus (such as reproduction and/or maturation), and forcing the model with fluctuating (dynamic) environmental conditions, needless to say, will result in more parameters.
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of the model) tracks how much energy has been invested into maturation, and therefore determines the life stage of the organism relative to maturity levels at which life stage transitions (birth and puberty) occur. Dynamics of the state variables are given by
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exceeds threshold values. Life stages typically are: embryo, juvenile, and adult. Reserve that is allocated to reproduction is first accumulated in a buffer. The rules for converting the buffer to gametes are species-specific (e.g. spawning can be once per
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the remaining proportion (1- κ) is allocated to processes of maturation (increase in complexity, installation of regulation systems, preparation for reproduction) and maintaining the level of attained maturity (including, e.g., maintenance of defense
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inclusion of more reserves (which is necessary for organisms that do not feed on other organisms) and more structures (which is necessary to deal with plants), or a simplified version of the model (DEBkiss) applicable in ecotoxicology
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Food is transformed into reserve, which fuels all other metabolic processes. The feeding rate is proportional to the surface area; food handling time and the transformation efficiency from food to reserve are independent of food
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Lika, Konstadia; Kearney, Michael R.; Kooijman, Sebastiaan A.L.M. (2011). "The "covariation method" for estimating the parameters of the standard Dynamic Energy Budget model II: Properties and preliminary patterns".
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Sarà, Gianluca; Rinaldi, Alessandro; Montalto, Valeria (2014-12-01). "Thinking beyond organism energy use: a trait-based bioenergetic mechanistic approach for predictions of life history traits in marine organisms".
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Kooijman, S. A. L. M.; Sousa, T.; Pecquerie, L.; Meer, J. Van Der; Jager, T. (2008-11-01). "From food-dependent statistics to metabolic parameters, a practical guide to the use of dynamic energy budget theory".
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Llandres, Ana L.; Marques, Gonçalo M.; Maino, James L.; Kooijman, S. A. L. M.; Kearney, Michael R.; Casas, Jérôme (2015-08-01). "A dynamic energy budget for the whole life-cycle of holometabolous insects".
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Mueller, Casey A.; Augustine, Starrlight; Kooijman, Sebastiaan A.L.M.; Kearney, Michael R.; Seymour, Roger S. (2012). "The trade-off between maturation and growth during accelerated development in frogs".
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and provides a theoretical underpinning to the widely used method of indirect calorimetry. Several popular empirical models are special cases of the DEB model, or very close numerical approximations.
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Models based on DEB theory can be linked to more traditional bioenergetic models without deviating from the underlying assumptions. This allows comparison and testing of model performance .
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All dynamic energy budget models follow the energy budget of an individual organism throughout its life cycle; by contrast,"static" energy budget models describe a specific life stage or
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and reproduction overheads (inefficiencies in transformation from reserve to reproductive material), all contribute to the consumption of oxygen and production of carbon dioxide, i.e.
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Marquet, Pablo A.; Allen, Andrew P.; Brown, James H.; Dunne, Jennifer A.; Enquist, Brian J.; Gillooly, James F.; Gowaty, Patricia A.; Green, Jessica L.; Harte, John (2014-08-01).
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Jager, Tjalling; Heugens, Evelyn H. W.; Kooijman, Sebastiaan A. L. M. (2006-04-01). "Making Sense of Ecotoxicological Test Results: Towards Application of Process-based Models".
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A DEB-module (physiological model based on DEB theory) was successfully applied to reconstruct and predict physiological responses of individuals under environmental constraints
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project is a collection of DEB models for over 1000 species, and explores patterns in parameter values across taxa. Routines for parameter exploration are available in
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maintenance to maturity. Heating costs for endotherms and osmotic work (for fresh water organisms) are somatic maintenance costs that are proportional to surface area.
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of the model are individual specific, but similarities between individuals of the same species yield species-specific parameter estimations. DEB parameters are
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DEB theory provides constraints on the metabolic organisation of sub-cellular processes. Together with rules for interaction between individuals (competition,
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that contribute to physical volume, and (in combination with reproduction buffer of adults) fully define the size of an individual. Maturity (also a
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Kooijman, S.A.L.M.; Pecquerie, L.; Augustine, S.; Jusup, M. (2011). "Scenarios for acceleration in fish development and the role of metamorphosis".
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Kearney, Michael; Porter, Warren (2009-04-01). "Mechanistic niche modelling: combining physiological and spatial data to predict species' ranges".
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of an organism. The main advantage of the DEB-theory based model over most other models is its description of energy assimilation and utilization (
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Brown, James H.; Gillooly, James F.; Allen, Andrew P.; Savage, Van M.; West, Geoffrey B. (2004-07-01). "Toward a Metabolic Theory of Ecology".
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project portal - collection of species for which DEB model parameter values were estimated and implications, inter-species parameter patterns
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Kooijman, S. A. L. M. (2013-03-01). "Waste to hurry: dynamic energy budgets explain the need of wasting to fully exploit blooming resources".
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project explores parameter pattern values across taxa. The DEB notation is a result of combining the symbols from the main fields of science (
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principle. In addition, routines for data entry and scripts for parameter estimation are available as a free and documented software package
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Kooijman, Sebastiaan A.L.M.; Lika, Konstadia (2014). "Comparative energetics of the 5 fish classes on the basis of dynamic energy budgets".
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Jager, Tjalling; Martin, Benjamin T.; Zimmer, Elke I. (2013). "DEBkiss or the quest for the simplest generic model of animal life history".
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van der Meer, Jaap; Klok, Chris; Kearney, Michael R.; Wijsman, Jeroen W.M.; Kooijman, Sebastiaan A.L.M. (2014). "35years of DEB research".
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which include the major processes of energy uptake and use: assimilation, mobilization, maintenance, growth, maturation, and reproduction.
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Huey, Raymond B.; Kearney, Michael R.; Krockenberger, Andrew; Holtum, Joseph A. M.; Jess, Mellissa; Williams, Stephen E. (2012-06-19).
491:) used in the theory, while trying to keep the symbols consistent. As the symbols themselves contain a fair bit of information (see 417: 182:') reaches a certain threshold. Maturity does not increase in the adult stage, and maturity maintenance is proportional to maturity. 269:
from several types of data simultaneously. Routines for data entry and parameter estimation are available as free software package
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van der Meer, Jaap (2006). "An introduction to Dynamic Energy Budget (DEB) models with special emphasis on parameter estimation".
3271: 170:, which both feeds and is allocating energy to reproduction. Transitions between these life stages occur at events specified as 3127:
Baas, Jan; Kooijman, Sebastiaan A. L. M. (2015-04-01). "Sensitivity of animals to chemical compounds links to metabolic rate".
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White, Craig R.; Kearney, Michael R.; Matthews, Philip G. D.; Kooijman, Sebastiaan A. L. M.; Marshall, Dustin J. (2011-12-01).
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function of DEB parameters which co-vary with size can, for this reason, also be written as function of the maximum body size.
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Kooijman, S. a. L. M. (1986-02-01). "What the hen can tell about her eggs: egg development on the basis of energy budgets".
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Lika, Konstadia; Nisbet, Roger M. (2000-10-01). "A Dynamic Energy Budget model based on partitioning of net production".
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Lika, Konstadia; Kooijman, Sebastiaan A.L.M. (2011). "The comparative topology of energy allocation in budget models".
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Mathematical Ecology - Proceedings Of The Autumn Course Research Seminars International Ctr For Theoretical Physics
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Jager, Tjalling; Zimmer, Elke I. (2012). "Simplified Dynamic Energy Budget model for analysing ecotoxicity data".
939:"Quantitative steps in the evolution of metabolic organisation as specified by the Dynamic Energy Budget theory" 3324: 3006:
Kooijman, Sebastiaan A. L. M.; Lika, Konstadia (2014-11-01). "Resource allocation to reproduction in animals".
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substrate(s) from the environment is/are first converted to reserve(s) before being used for further metabolism
2919:"The bijection from data to parameter space with the standard DEB model quantifies the supply–demand spectrum" 759:
Jusup, Marko; Sousa, Tânia; Domingos, Tiago; Labinac, Velimir; Marn, Nina; Wang, Zhen; Klanjšček, Tin (2017).
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Jager, Tjalling; Vandenbrouck, Tine; Baas, Jan; Coen, Wim M. De; Kooijman, Sebastiaan A. L. M. (2010-02-01).
1831:"What is the status of metabolic theory one century after Pütter invented the von Bertalanffy growth curve?" 158:
In the context of energy acquisition and allocation, the theory recognizes three main developmental stages:
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relationships: The assumptions of the model quantify all energy and mass fluxes in an organism (including
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Marques, G. M., Lika, K., Augustine, S., Pecquerie, L., Domingos, T. and Kooijman, S. A. L. M (2018).
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the production of free radicals (linked to size and nutritional status) and their effect on survival (
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Kooijman, S.A.L.M. (2014). "Metabolic acceleration in animal ontogeny: An evolutionary perspective".
579:. In addition, same parameters describe same processes across species: for example, heating costs of 2618: 2590: 1271:
Maino, James L.; Kearney, Michael R.; Nisbet, Roger M.; Kooijman, Sebastiaan A. L. M. (2014-01-01).
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develop similarly, but receive unrestricted amount of reserve from the mother during development.
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The κ-rule therefore states that the processes of growth and maturation do not directly compete.
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Lika, Konstadia; Augustine, Starrlight; Pecquerie, Laure; Kooijman, Sebastiaan A.L.M. (2014).
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non-standard embryo->juvenile->adult transitions, for example in holometabolic insects
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Dynamic energy budgets in biological systems : theory and applications in ecotoxicology
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Scientific articles including a general (aimed at ecologists) overview of the DEB theory:
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processes of adaptation (gene expression) to the availability of substrates (important in
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Kearney, Michael; Simpson, Stephen J.; Raubenheimer, David; Helmuth, Brian (2010-11-12).
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Marn, Nina; Jusup, Marko; Legović, Tarzan; Kooijman, S.A.L.M.; Klanjšček, Tin (2017).
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Comparative Biochemistry and Physiology Part A: Molecular & Integrative Physiology
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which provides a single quantitative framework to dynamically describe the aspects of
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Kooijman, S.A.L.M. (1986-08-07). "Energy budgets can explain body size relations".
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routines), and include also switching between energy-time and mass-time contexts.
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The general methodology of estimation of DEB parameters from data is described in
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Many more examples of applications have been published in scientific literature.
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Philosophical Transactions of the Royal Society of London B: Biological Sciences
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Zonneveld, C; Kooijman, S (1993). "Comparative kinetics of embryo development".
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Philosophical Transactions of the Royal Society of London B: Biological Sciences
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Philosophical Transactions of the Royal Society of London B: Biological Sciences
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Philosophical Transactions of the Royal Society of London B: Biological Sciences
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Nisbet, Roger M.; Jusup, Marko; Klanjscek, Tin; Pecquerie, Laure (2012-03-15).
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Summary of concepts of Dynamic Energy Budget theory for metabolic organisation
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Sousa, Tânia; Domingos, Tiago; Poggiale, J.-C.; Kooijman, S. A. L. M. (2010).
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Biochemical composition of reserve and structure is considered to be that of
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Compatibility (and applicability) of DEB theory/models with other approaches
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A DEB-module is also featured in the eco-toxicological mechanistic models (
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to reach its intended audience (ecologists) and be an "efficient" theory.
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the formation and excretion of metabolic products (which is a basis for
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The theory specifies that an organism is made up two main compartments:
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Nisbet, R. M.; Muller, E. B.; Lika, K.; Kooijman, S. A. L. M. (2008).
685:"From empirical patterns to theory: a formal metabolic theory of life" 295:. Estimated parameters are collected in the online library called the 3254:
An introduction to modelling and statistics is given in the document
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A list and description of most common typified models can be found
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environment, with the process of model construction explained in a
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Kearney, Michael R.; Domingos, Tiago; Nisbet, Roger (2015-04-01).
2502: 2312:"A Manipulative Test of Competing Theories for Metabolic Scaling" 572: 484: 476: 143:(increase of structural mass) and maintenance of structure, while 2760: 1783: 399: 380: 321: 281: 2916: 2445: 1336: 155:
needs to be paid before allocating energy to other processes.
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Sousa, Tânia; Domingos, Tiago; Kooijman, S. A. L. M. (2008).
373: 2309: 2063: 1163:"Dynamic energy budget theory restores coherence in biology" 817:
van der Meer, Jaap (2006). "Metabolic theories in ecology".
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inclusion of more types of food (substrate), which requires
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DEB theory has been extended into many directions, such as
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A 16-page introduction to the DEB theory is presented in
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Stage transitions occur if the cumulated investment into
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document), they are kept in most of the DEB literature.
3290:- collection of scientific literature on the DEB theory 2505:"Modelling the ecological niche from functional traits" 1132:
Dynamic Energy Budget Theory for Metabolic Organisation
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a fixed proportion (termed kappa, κ) is allocated to
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The Dynamics of Physiologically Structured Populations
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Dynamic energy and mass budgets in biological systems
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West-Brown-Enquist (WBE) metabolic theory of ecology
2724: 1622: 1447:Kearney, Michael R.; White, Craig R. (2012-11-01). 937:Kooijman, S. A. L. M.; Troost, T. A. (2007-02-01). 327: 307:The standard model quantifies the metabolism of an 2132: 1745: 3301: 336:effects of changes in shape during growth (e.g. 311:(organism that does not change in shape during 936: 228:as separate from structure: these are the two 2402: 1324:"Zotero DEB library of scientific literature" 98:relationships between surface area and volume 3126: 3091: 3056: 3005: 1961:: CS1 maint: multiple names: authors list ( 1446: 1386: 1273:"Reconciling theories for metabolic scaling" 1083:: CS1 maint: multiple names: authors list ( 1031:: CS1 maint: multiple names: authors list ( 816: 3182:. In Metz, Johan A.; Diekmann, Odo (eds.). 2102: 16:Ecological mathematical model of metabolism 1687: 166:, which feeds but does not reproduce, and 3180:"Population dynamics on basis of budgets" 2698: 2617: 2536: 2479: 2278: 2234: 2193: 1932: 1922: 1854: 1653: 1602: 1288: 1244: 1194: 1003:. Cambridge: Cambridge University Press. 954: 908: 784: 716: 302: 70: 3177: 2881: 2830: 2795: 1536: 1507: 1128: 874: 1828: 107:organizational uncoupling of metabolic 3302: 2720: 2718: 2256: 2254: 2128: 2126: 2098: 2096: 1892: 1890: 1824: 1822: 1820: 1818: 1816: 1779: 1777: 1741: 1739: 1737: 1735: 1683: 1681: 1618: 1616: 1614: 1584: 1580: 1578: 1576: 1503: 1501: 1442: 1440: 1438: 1436: 1434: 1318: 1316: 1266: 1264: 1262: 1260: 1258: 1256: 3256:Basic methods for Theoretical Biology 2559: 1382: 1380: 1378: 1376: 1374: 1372: 1370: 1368: 1222: 1220: 1218: 1216: 1214: 1124: 1122: 1120: 1118: 1116: 1114: 678: 676: 674: 672: 670: 668: 666: 664: 662: 660: 3315:Mathematical and theoretical biology 1156: 1154: 1152: 1112: 1110: 1108: 1106: 1104: 1102: 1100: 1098: 1096: 1094: 1046: 1044: 1042: 994: 992: 990: 932: 930: 928: 870: 868: 866: 864: 862: 860: 858: 856: 812: 810: 808: 806: 804: 754: 752: 750: 748: 746: 744: 742: 740: 738: 736: 379:the growth of body parts (including 162:, which does not feed or reproduce, 3171: 2824: 2715: 2251: 2123: 2093: 1887: 1813: 1774: 1732: 1678: 1611: 1573: 1530: 1498: 1431: 1313: 1253: 761:"Physics of metabolic organization" 111:(assimilation, dissipation, growth) 13: 3204: 1365: 1211: 1050: 998: 657: 14: 3346: 3262: 3178:Kooijman, S.A.L.M. (2014-03-11). 1149: 1091: 1039: 987: 925: 853: 819:Trends in Ecology & Evolution 801: 733: 548:context, focusing for example on 2896:10.1111/j.1600-0706.2012.00098.x 2417:10.1111/j.1461-0248.2008.01277.x 2027:10.1111/j.1469-185x.2008.00053.x 1748:Bulletin of Mathematical Biology 1246:10.1111/j.1365-2656.2000.00448.x 956:10.1111/j.1469-185x.2006.00006.x 328:Extensions of the standard model 79:Cornerstones of the theory are: 3120: 3085: 3050: 2999: 2985:10.1016/j.ecolmodel.2017.07.001 2957: 2910: 2875: 2833:Journal of Mathematical Biology 2789: 2754: 2658: 2597: 2563:Making sense of chemical stress 2553: 2496: 2439: 2396: 2361: 2303: 2267:Journal of Experimental Biology 2210: 2169: 2117:10.1016/j.ecolmodel.2011.11.012 2057: 2005: 1969: 1690:Journal of Mathematical Biology 1330: 1051:M., Kooijman, S. A. L. (2000). 999:M., Kooijman, S. A. L. (1993). 511: 386:effects of chemical compounds ( 239:ordinary differential equations 3186:. 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(1988). 786:10.1016/j.plrev.2016.09.001 632:Metabolic theory of ecology 610: 575:) while avoiding using the 10: 3351: 2943:10.1016/j.jtbi.2014.03.025 2155:10.1016/j.jtbi.2013.03.011 1903:PLOS Computational Biology 1799:10.1016/j.cbpa.2012.05.190 831:10.1016/j.tree.2005.11.004 3246:concepts in Kooijman 2001 3141:10.1007/s10646-014-1413-5 2683:10.1007/s10646-009-0417-z 2628:10.1007/s10646-006-0060-x 1591:Letters in Biomathematics 1277:Journal of Animal Ecology 1233:Journal of Animal Ecology 104:constraints on production 577:allometric relationships 392:no effect concentrations 3094:Journal of Sea Research 3059:Journal of Sea Research 2798:Journal of Sea Research 2763:Journal of Sea Research 2728:Journal of Sea Research 2319:The American Naturalist 1979:Journal of Sea Research 1516:. #N/A. pp. 3–45. 1456:The American Naturalist 1389:Journal of Sea Research 1339:Journal of Sea Research 1290:10.1111/1365-2656.12085 765:Physics of Life Reviews 627:Evolutionary physiology 215:development/ maturation 2521:10.1098/rstb.2010.0034 2464:10.1098/rstb.2012.0005 2452:Phil. Trans. R. Soc. B 2178:"On Theory in Ecology" 1585:Ledder, Glenn (2014). 1179:10.1098/rstb.2010.0166 893:10.1098/rstb.2000.0771 701:10.1098/rstb.2007.2230 622:Comparative physiology 303:The standard DEB model 71:Theoretical background 3325:Developmental biology 2236:10.1093/biosci/biv013 2195:10.1093/biosci/biu098 2067:Ecological Monographs 1702:10.1007/s002850000049 555:Studying patterns in 542:DEBtox implementation 224:DEB theory specifies 187:generalised compounds 57:Add-my-pet collection 21:dynamic energy budget 3248:, formalisation by 2973:Ecological Modelling 2105:Ecological Modelling 3335:Theoretical ecology 3310:Ecological theories 3106:2014JSR....94...19K 3071:2011JSR....66..381L 2935:2014JThBi.354...35L 2810:2014JSR....94..128K 2775:2011JSR....66..419K 2740:2011JSR....66..278L 2515:(1557): 3469–3483. 2458:(1596): 1665–1679. 2147:2013JThBi.328....9J 1991:2011JSR....66..270L 1915:2018PLSCB..14E6100M 1638:2014MarEc..35..506S 1551:1986JThBi.121..269K 1401:2006JSR....56...85V 1351:2014JSR....94....1V 1173:(1557): 3413–3428. 777:2017PhLRv..20....1J 695:(1502): 2453–2464. 446:Kooijman et al 2008 280:implemented in the 3288:Zotero DEB library 3274:2019-10-22 at the 3008:Biological Reviews 2845:10.1007/BF00276955 2280:10.1242/jeb.059675 2015:Biological Reviews 1835:Biological Reviews 1760:10.1007/BF02460653 1646:10.1111/maec.12106 943:Biological Reviews 527:2018-04-09 at the 467:2017-03-18 at the 456:2017-03-18 at the 420:2019-10-25 at the 394:for environmental 352:synthesizing units 297:Add-my-pet project 291:2020-08-05 at the 276:2017-03-18 at the 3225:van der Meer 2006 3020:10.1111/brv.12082 2079:10.1890/14-0976.1 1847:10.1111/brv.12668 887:(1407): 331–349. 639:(also known as a 617:Metabolic ecology 557:body size scaling 442:van der Meer 2006 286:Wiki-style manual 61:metabolic ecology 3342: 3282:Add my pet (AmP) 3250:Sousa et al 2008 3233:Jusup et al 2017 3229:Sousa et al 2010 3198: 3197: 3175: 3169: 3168: 3124: 3118: 3117: 3089: 3083: 3082: 3054: 3048: 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Index

metabolic theory
metabolism
cells
organisms
populations
ecotoxicology
Add-my-pet collection
metabolic ecology
mass
energy
time
stoichiometric
modules
homeostasis
(energy) reserve
growth
Maintenance
generalised compounds
maintenance
metabolism
size
reserve dynamics
development/ maturation
maintenance
reserves
state variables
state variable
ordinary differential equations
maturation
Parameters

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