Dynamic energy budget theory
The dynamic energy budget theory is a formal metabolic theory which provides a single quantitative framework to dynamically describe the aspects of metabolism 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 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 . The theory is contributing to the theoretical underpinning of the emerging field of metabolic ecology.
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 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, energy and time,
- relationships between surface area and volume
- stoichiometric constraints on production
- organizational uncoupling of metabolic modules
- strong and weak homeostasis
- substrate from the environment is/are first converted to reserve before being used for further metabolism
- a fixed proportion is allocated to growth and maintenance of structure, while
- the remaining proportion is allocated to processes of maturation and maintaining the level of attained maturity.
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 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 compounds, and is constant but not necessarily identical. Biochemical transformation from food to reserve, and from reserve to structure include overhead costs. These overheads, together with processes of somatic and maturity maintenance and reproduction overheads, all contribute to the consumption of oxygen and production of carbon dioxide, i.e. metabolism.
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 of an organism. The main advantage of the DEB-theory based model over most other models is its description of energy assimilation and utilization simultaneously with decoupled processes of growth, development/ maturation, and maintenance. DEB theory specifies reserves as separate from structure: these are the two state variables that contribute to physical volume, and fully define the size of an individual. Maturity 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 occur. Dynamics of the state variables are given by ordinary differential equations 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 of mobilized reserve is allocated to somatic maintenance plus growth, 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 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.
The standard DEB model
The standard model quantifies the metabolism of an isomorph that feeds on one type of food with a constant composition. The state variables of the individual are 1 reserve, 1 structure, maturity, and the reproduction buffer. Parameter values are constant throughout life. The reserve density at birth equals that of the mother at egg formation. Foetuses 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
- non-standard embryo->juvenile->adult transitions, for example in holometabolic insects
- inclusion of more types of food, which requires synthesizing units to model
- inclusion of more reserves and more structures, or a simplified version of the model applicable in ecotoxicology
- the formation and excretion of metabolic products
- the production of free radicals and their effect on survival
- the growth of body parts
- effects of chemical compounds on parameter values and the hazard rate : the DEBtox method
- processes of adaptation to the availability of substrates
Criticism
The main criticism is directed to the formal presentation of the theory, number of listed parameters, the symbol heavy notation, and the fact that modeled variables and parameters are abstract quantities which cannot be directly measured, all making it less likely to reach its intended audience 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". The general methodology of estimation of DEB parameters from data is described in ; 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 package , 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 and measured properties is done by simple mathematical operations which include auxiliary parameters, 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 used in the theory, while trying to keep the symbols consistent. As the symbols themselves contain a fair bit of information , 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 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
- 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 .
- 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 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
- 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, 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 while avoiding using the allometric relationships. In addition, same parameters describe same processes across species: for example, heating costs of endotherms are regarded separate to volume-linked metabolic costs of both ectotherms and endotherms, and cost of growth, even though they all contribute to metabolism 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, it also provides a basis to understand population and ecosystem dynamics.