The dynamic energy budget (DEB) theory is a formal
metabolic theory which provides a single quantitative framework to dynamically describe the aspects of
metabolism
Metabolism (, from el, μεταβολή ''metabolē'', "change") is the set of life-sustaining chemical reactions in organisms. The three main functions of metabolism are: the conversion of the energy in food to energy available to run cell ...
(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 (
cell
Cell most often refers to:
* Cell (biology), the functional basic unit of life
Cell may also refer to:
Locations
* Monastic cell, a small room, hut, or cave in which a religious recluse lives, alternatively the small precursor of a monastery ...
s,
organism
In biology, an organism () is any living system that functions as an individual entity. All organisms are composed of cells (cell theory). Organisms are classified by taxonomy into groups such as multicellular animals, plants, and ...
s, and
population
Population typically refers to the number of people in a single area, whether it be a city or town, region, country, continent, or the world. Governments typically quantify the size of the resident population within their jurisdiction using a ...
s) as prescribed by the implications of energetics.
Models based on the DEB theory have been successfully applied to over a 1000 species with real-life applications ranging from conservation, aquaculture, general ecology, and
ecotoxicology
Ecotoxicology is the study of the effects of toxic chemicals on biological organisms, especially at the population, community, ecosystem, and biosphere levels. Ecotoxicology is a multidisciplinary field, which integrates toxicology and ecology.
...
(see also th
Add-my-pet collection. The theory is contributing to the theoretical underpinning of the emerging field of
metabolic ecology Metabolic ecology is a field of ecology aiming to understand constraints on metabolic organization as important for understanding almost all life processes. Main focus is on the metabolism of individuals, emerging intra- and inter-specific patterns ...
.
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, 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.
Theoretical background
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 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.
Cornerstones of the theory are:
* conservation of
mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
,
energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
and
time
Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to ...
,
* relationships between surface area and volume
*
stoichiometric
Stoichiometry refers to the relationship between the quantities of reactants and products before, during, and following chemical reactions.
Stoichiometry is founded on the law of conservation of mass where the total mass of the reactants equal ...
constraints on production
* organizational uncoupling of metabolic
modules
Broadly speaking, modularity is the degree to which a system's components may be separated and recombined, often with the benefit of flexibility and variety in use. The concept of modularity is used primarily to reduce complexity by breaking a sy ...
(assimilation, dissipation, growth)
* strong and weak
homeostasis
In biology, homeostasis (British English, British also homoeostasis) Help:IPA/English, (/hɒmɪə(ʊ)ˈsteɪsɪs/) is the state of steady internal, physics, physical, and chemistry, chemical conditions maintained by organism, living systems. Thi ...
(composition of compartments is constant; composition of the organism is constant when the food is constant)
* substrate(s) from the environment is/are first converted to reserve(s) before being used for further metabolism
The theory specifies that an organism is made up two main compartments:
(energy) reserve and structure. 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:
* a fixed proportion (termed kappa, κ) is allocated to
growth
Growth may refer to:
Biology
* Auxology, the study of all aspects of human physical growth
* Bacterial growth
* Cell growth
* Growth hormone, a peptide hormone that stimulates growth
* Human development (biology)
* Plant growth
* Secondary growth ...
(increase of structural mass) and maintenance of structure, while
* 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 systems).
The κ-rule therefore states that the processes of growth and maturation do not directly compete.
Maintenance
Maintenance may refer to:
Biological science
* Maintenance of an organism
* Maintenance respiration
Non-technical maintenance
* Alimony, also called ''maintenance'' in British English
* Champerty and maintenance, two related legal doctrine ...
needs to be paid before allocating energy to other processes.
In the context of energy acquisition and allocation, the theory recognizes three main developmental stages: embryo, which does not feed or reproduce, juvenile, which feeds but does not reproduce, and adult, which both feeds and is allocating energy to reproduction. Transitions between these life stages occur at events specified as birth and puberty, which are reached when energy invested into maturation (tracked as 'level of maturity
') reaches a certain threshold. Maturity does not increase in the adult stage, and maturity maintenance is proportional to maturity.
Biochemical composition of reserve and structure is considered to be that of
generalised compound
A generalized compound is a mixture of chemical compounds of constant composition, despite possible changes in the total amount. The concept is used in the Dynamic Energy Budget theory, where biomass is partitioned into a limited set of generalised ...
s, and is constant (the assumption of strong homeostasis) but not necessarily identical. Biochemical transformation from food to reserve (assimilation), and from reserve to structure (growth) include overhead costs. These overheads, together with processes of somatic and maturity
maintenance
Maintenance may refer to:
Biological science
* Maintenance of an organism
* Maintenance respiration
Non-technical maintenance
* Alimony, also called ''maintenance'' in British English
* Champerty and maintenance, two related legal doctrine ...
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.
metabolism
Metabolism (, from el, μεταβολή ''metabolē'', "change") is the set of life-sustaining chemical reactions in organisms. The three main functions of metabolism are: the conversion of the energy in food to energy available to run cell ...
.
DEB models
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
size
Size in general is the Magnitude (mathematics), magnitude or dimensions of a thing. More specifically, ''geometrical size'' (or ''spatial size'') can refer to linear dimensions (length, width, height, diameter, perimeter), area, or volume ...
of an organism.
The main advantage of the DEB-theory based model over most other models is its description of energy assimilation and utilization (
reserve dynamics) simultaneously with decoupled processes of growth,
development/ maturation, and
maintenance
Maintenance may refer to:
Biological science
* Maintenance of an organism
* Maintenance respiration
Non-technical maintenance
* Alimony, also called ''maintenance'' in British English
* Champerty and maintenance, two related legal doctrine ...
.
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.
DEB theory specifies
reserve
Reserve or reserves may refer to:
Places
* Reserve, Kansas, a US city
* Reserve, Louisiana, a census-designated place in St. John the Baptist Parish
* Reserve, Montana, a census-designated place in Sheridan County
* Reserve, New Mexico, a US vi ...
s as separate from structure: these are the two
state variable
A state variable is one of the set of variables that are used to describe the mathematical "state" of a dynamical system. Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of a ...
s that contribute to physical volume, and (in combination with reproduction buffer of adults) fully define the size of an individual. Maturity (also a
state variable
A state variable is one of the set of variables that are used to describe the mathematical "state" of a dynamical system. Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of a ...
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
ordinary differential equation
In mathematics, an ordinary differential equation (ODE) is a differential equation whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contrast w ...
s which include the major processes of energy uptake and use: assimilation, mobilization, maintenance, growth, maturation, and reproduction.
* 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 density.
* 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 maintenance to maturity. Heating costs for endotherms and osmotic work (for fresh water organisms) are somatic maintenance costs that are proportional to surface area.
* Stage transitions occur if the cumulated investment into
maturation 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 season).
Parameter
A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when ...
s of the model are individual specific, but similarities between individuals of the same species yield species-specific parameter estimations.
DEB parameters are
estimated
Estimation (or estimating) is the process of finding an estimate or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable. The value is nonetheless usable because it is der ...
from several types of data simultaneously.
Routines for data entry and parameter estimation are available as free software packag
DEBtoolimplemented in the
MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation ...
environment, with the process of model construction explained in
Wiki-style manual Estimated parameters are collected in the online library called th
The standard DEB model
The standard model quantifies the metabolism of an
isomorph
An isomorph is an organism that does not change in shape during growth. The implication is that its volume is proportional to its cubed length, and its surface area to its squared length. This holds for any shape it might have; the actual shape de ...
(organism that does not change in shape during
ontogeny
Ontogeny (also ontogenesis) is the origination and development of an organism (both physical and psychological, e.g., moral development), usually from the time of fertilization of the egg to adult. The term can also be used to refer to the stu ...
) that feeds on one type of food with a constant composition (therefore the weak
homeostasis
In biology, homeostasis (British English, British also homoeostasis) Help:IPA/English, (/hɒmɪə(ʊ)ˈsteɪsɪs/) is the state of steady internal, physics, physical, and chemistry, chemical conditions maintained by organism, living systems. Thi ...
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 formation.
Foetus
A fetus or foetus (; plural fetuses, feti, foetuses, or foeti) is the unborn offspring that develops from an animal embryo. Following embryonic development the fetal stage of development takes place. In human prenatal development, fetal develo ...
es develop similarly, but receive unrestricted amount of reserve from the mother during development.
Extensions of the standard model
DEB theory has been extended into many directions, such as
*effects of changes in shape during growth (e.g.
V1-morph
An V1-morph is an organism that changes in shape during growth such that its surface area is proportional to its volume. In most cases both volume and surface area are proportional to length
The reason the concept is important in the context of th ...
s and
V0-morph A V0-morph is an organism whose surface area remains constant as the organism grows.
The reason why the concept is important in the context of the Dynamic Energy Budget theory is that food (substrate) uptake is proportional to surface area, and mai ...
s)
*non-standard embryo->juvenile->adult transitions, for example in holometabolic insects
*inclusion of more types of food (substrate), which requires
synthesizing units to model
*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
*the formation and excretion of metabolic products (which is a basis for
syntrophic relationships, and useful in
biotechnology
Biotechnology is the integration of natural sciences and engineering sciences in order to achieve the application of organisms, cells, parts thereof and molecular analogues for products and services. The term ''biotechnology'' was first used b ...
)
*the production of free radicals (linked to size and nutritional status) and their effect on survival (
aging
Ageing ( BE) or aging ( AE) is the process of becoming older. The term refers mainly to humans, many other animals, and fungi, whereas for example, bacteria, perennial plants and some simple animals are potentially biologically immortal. In ...
)
*the growth of body parts (including
tumour
A neoplasm () is a type of abnormal and excessive growth of tissue. The process that occurs to form or produce a neoplasm is called neoplasia. The growth of a neoplasm is uncoordinated with that of the normal surrounding tissue, and persists ...
s)
*effects of chemical compounds (
toxicant
A toxicant is any toxic substance, whether man-made or naturally occurring. By contrast, a toxin is a poison produced naturally by an organism (e.g. plant, animal, insect). The different types of toxicants can be found in the air, soil, water, or ...
s) on parameter values and the hazard rate (which is useful to establish
no effect concentrations for environmental
risk assessment
Broadly speaking, a risk assessment is the combined effort of:
# identifying and analyzing potential (future) events that may negatively impact individuals, assets, and/or the environment (i.e. hazard analysis); and
# making judgments "on the to ...
): the
DEBtox
The DEBtox method for the evaluation of effects of toxicants makes use of the Dynamic Energy Budget (DEB) theory to quantify the effect. See the Organisation for Economic Co-operation and Development (OECD) report, below, for a description of the ...
method
*processes of adaptation (gene expression) to the availability of substrates (important in
biodegradation
Biodegradation is the breakdown of organic matter by microorganisms, such as bacteria and fungi. It is generally assumed to be a natural process, which differentiates it from composting. Composting is a human-driven process in which biodegrada ...
)
A list and description of most common typified models can be foun
here
Criticism
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 to reach its intended audience (ecologists) and be an "efficient" theory.
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 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.
The general methodology of estimation of DEB parameters from data is described i
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 principle. In addition, routines for data entry and scripts for parameter estimation are available as a free and documented software packag
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 th
routines), and include also switching between energy-time and mass-time contexts.
project explores parameter pattern values across taxa. The DEB notation is a result of combining the symbols from the main fields of science (
biology
Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary i ...
,
chemistry
Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...
,
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
,
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
) used in the theory, while trying to keep the symbols consistent.
As the symbols themselves contain a fair bit of information
(se
DEB notationdocument), they are kept in most of the DEB literature.
Compatibility (and applicability) of DEB theory/models with other approaches
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
West-Brown-Enquist (WBE) metabolic theory of ecology, 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.
Applications
Add my pet (AmP)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 i
* 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 .
* A DEB-module (physiological model based on DEB theory) was successfully applied to reconstruct and predict physiological responses of individuals under environmental constraints
* A DEB-module is also featured in the eco-toxicological mechanistic models
for modeling the sublethal effects of toxicants (e.g., change in reproduction or growth rate)
* 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 context,
focusing for example on
development
Development or developing may refer to:
Arts
*Development hell, when a project is stuck in development
*Filmmaking, development phase, including finance and budgeting
*Development (music), the process thematic material is reshaped
* Photograph ...
,
energy utilization in a specific environment, reproduction, comparative energetics, and toxicological sensitivity linked to metabolic rates.
* Studying patterns in
body size scaling relationships: The assumptions of the model quantify all energy and mass fluxes in an organism (including
heat
In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is al ...
,
dioxygen
There are several known allotropes of oxygen. The most familiar is molecular oxygen (O2), present at significant levels in Earth's atmosphere and also known as dioxygen or triplet oxygen. Another is the highly reactive ozone (O3). Others are:
*A ...
,
carbon dioxide
Carbon dioxide (chemical formula ) is a chemical compound made up of molecules that each have one carbon atom covalently double bonded to two oxygen atoms. It is found in the gas state at room temperature. In the air, carbon dioxide is transpar ...
,
ammonia
Ammonia is an inorganic compound of nitrogen and hydrogen with the formula . A stable binary hydride, and the simplest pnictogen hydride, ammonia is a colourless gas with a distinct pungent smell. Biologically, it is a common nitrogenous was ...
) while avoiding using the
allometric relationships.
In addition, same parameters describe same processes across species: for example, heating costs of
endotherm
An endotherm (from Greek ἔνδον ''endon'' "within" and θέρμη ''thermē'' "heat") is an organism that maintains its body at a metabolically favorable temperature, largely by the use of heat released by its internal bodily functions inste ...
s (proportional to surface area) are regarded separate to volume-linked metabolic costs of both
ectotherm
An ectotherm (from the Greek () "outside" and () "heat") is an organism in which internal physiological sources of heat are of relatively small or of quite negligible importance in controlling body temperature.Davenport, John. Animal Life a ...
s and
endotherm
An endotherm (from Greek ἔνδον ''endon'' "within" and θέρμη ''thermē'' "heat") is an organism that maintains its body at a metabolically favorable temperature, largely by the use of heat released by its internal bodily functions inste ...
s, and cost of growth, even though they all contribute to
metabolism
Metabolism (, from el, μεταβολή ''metabolē'', "change") is the set of life-sustaining chemical reactions in organisms. The three main functions of metabolism are: the conversion of the energy in food to energy available to run cell ...
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 function of DEB parameters which co-vary with size can, for this reason, also be written as function of the maximum body size.
* DEB theory provides constraints on the metabolic organisation of sub-cellular processes.
Together with rules for interaction between individuals (competition,
syntrophy In biology, syntrophy, synthrophy, or cross-feeding (from Greek ''syn'' meaning together, ''trophe'' meaning nourishment) is the phenomenon of one species feeding on the metabolic products of another species to cope up with the energy limitations b ...
, prey-predator relationships), it also provides a basis to understand population and ecosystem dynamics.
Many more examples of applications have been published in scientific literature.
See also
*
Metabolic ecology Metabolic ecology is a field of ecology aiming to understand constraints on metabolic organization as important for understanding almost all life processes. Main focus is on the metabolism of individuals, emerging intra- and inter-specific patterns ...
*
Comparative physiology
Comparative physiology is a List of academic disciplines, subdiscipline of physiology that studies and exploits the diversity of functional characteristics of various kinds of organisms. It is closely related to evolutionary physiology and environ ...
*
Evolutionary physiology
Evolutionary physiology is the study of the biological evolution of physiological structures and processes; that is, the manner in which the functional characteristics of individuals in a population of organisms have responded to natural selectio ...
*
Metabolic theory of ecology
The metabolic theory of ecology (MTE) is the ecological component of the more general Metabolic Scaling Theory and Kleiber's law. It posits that the metabolic rate of organisms is the fundamental biological rate that governs most observed patterns ...
*
Power law
In statistics, a power law is a Function (mathematics), functional relationship between two quantities, where a Relative change and difference, relative change in one quantity results in a proportional relative change in the other quantity, inde ...
(also known as a
scaling law
In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one qua ...
),
Allometry
Allometry is the study of the relationship of body size to shape, anatomy, physiology and finally behaviour, first outlined by Otto Snell in 1892, by D'Arcy Thompson in 1917 in ''On Growth and Form'' and by Julian Huxley in 1932.
Overview
Allom ...
References
Further reading
Summary of concepts of Dynamic Energy Budget theory for metabolic organisation (Kooijman 2010)
* A 16-page introduction to the DEB theory is presented i
* Scientific articles including a general (aimed at ecologists) overview of the DEB theory
Jusup et al 2017 derivation and concepts b
Ledder 2014 and
Sara et al 2014
formalisation b
* An introduction to modelling and statistics is given in the documen
Basic methods for Theoretical Biology
External links
DEBwiki- main page with links to events, software tools, collections, research groups etc. linked to DEB theory
project portal - collection of species for which DEB model parameter values were estimated and implications, inter-species parameter patterns
Zotero DEB library- collection of scientific literature on the DEB theory
page
{{DEFAULTSORT:Dynamic energy budget theory
Ecological theories
Mathematical and theoretical biology
Metabolism
Developmental biology
Systems biology
Theoretical ecology