We present the state of the art of the development of DEB theory, and the expected developments in the near future within the molecular, biological and ecological domains. The degree of formalisation in the setup of the theory, with its roots in chemistry, physics, thermodynamics, evolution and the consistent application of Occams razor, is discussed. We will place the various contributions in the theme issue in this theoretical setting, and sketch the scope of actual and potential applications.
The dynamic modelling of metabolic networks aims at describing the temporal evolution of metabolite concentrations in cells. This area has attracted increasing attention in recent years due to the availability of high-throughput data and the general development of systems biology as a promising approach to study living organisms. Biochemical Systems Theory (BST) provides an accurate formalism to describe biological dynamic phenomena. However, knowledge about the molecular organization level, used in these models, is not enough to explain phenomena such as the driving forces of these metabolic networks. Dynamic Energy Budget (DEB) theory captures the quantitative aspects of the organization of metabolism at the organism level in a way that is non-species specific. This imposes constraints on the sub-organismal organization that are not present in the bottom-up approach of systems biology. We use in vivo data of lactic acid bacteria under various conditions to compare some aspects of BST and DEB approaches. Due to the large number of parameters to be estimated in the BST model, we applied powerful parameter identification techniques. Both models fitted equally well, but the BST model employs more parameters. The DEB model uses similarities of processes under growth and no-growth conditions and under aerobic and anaerobic conditions, which reduce the number of parameters. This paper discusses some future directions for the integration of knowledge from these two rich and promising areas, working top-down and bottom-up simultaneously. This middle-out approach is expected to bring new ideas and insights to both areas in terms of describing how living organisms operate.
Ageing is a complex multi-factorial process leading to a progressive physiological decline that, ultimately, leads to the death of an organism. It involves multiple changes in many components that play fundamental roles under healthy and pathological conditions. Simultaneously, every organism undergoes accumulative wear and tear during its lifespan, which confounds the effects of the ageing process. The scenario is complicated even further by the presence of both age-dependent and ageindependent competing causes of death. Various manipulations have been shown to interfere with the ageing process. Calorie restriction, for example, has been reported to increase the lifespan of a wide range of organisms, which suggests a strong relation between energy metabolism and ageing. Such a link is also supported within the main theories for ageing: the free radical hypothesis, for instance, links oxidative damage production directly to energy metabolism. The Dynamic Energy Budgets (DEB) theory, which characterises the uptake and use of energy by living organisms, therefore constitutes a useful tool for gaining insight into the ageing process. Here we compare the existing DEB-based modelling approaches and, then, discuss how new biological evidence could be incorporated within a DEB framework.
Stable Isotope Analysis (SIA) is a powerful tool used for reconstructing individual life histories, identifying food-web structures and tracking flow of elemental matter through ecosystems. The mechanisms determining isotopic incorporation rates and discrimination factors are, however, poorly understood which hinders a reliable interpretation of field data when no experimental data are available. Here, we extend Dynamic Energy Budget (DEB) theory with a limited set of new assumptions and rules in order to study the impact of metabolism on stable isotope dynamics in a mechanistic way. We calculate fluxes of stable isotopes within an organism by following fluxes of molecules involved in a limited number of macrochemical reactions: assimilation, growth but also structure turnover that is here explicitly treated. Two mechanisms are involved in the discrimination of isotopes: (i) Selection of molecules occurs at the partitioning of assimilation, growth and turnover into anabolic and catabolic sub-fluxes and (ii) Reshuffling of atoms occurs during transformations. Such a framework allows for isotopic routing which is known as a key, but poorly studied, mechanism. As DEB theory specifies the impact of environmental conditions and individual state on molecule fluxes, we discuss how scenario analysis within this framework could help reveal common mechanisms across taxa.
Accepted version, Electronic Appendix
The niche concept is central to ecology but is often depicted descriptively through observing associations between organisms and habitats. Here we argue for the importance of mechanistically modelling niches based on functional traits of organisms and explore the possibilities for achieving this through the integration of three theoretical frameworks: Biophysical Ecology, the Geometric Framework for Nutrition, and Dynamic Energy Budget Models. These three frameworks are fundamentally based on the conservation laws of thermodynamics, describing energy and mass balance at the level of the individual and capturing the prodigious predictive power of the concepts of "homeostasis" and "evolutionary fitness". Biophysical Ecology and the Geometric Framework of Nutrition provide mechanistic multidimensional depictions of climatic and nutritional niches, respectively, providing a foundation for linking organismal traits (morphology, physiology, behaviour) with habitat characteristics. In turn they provide driving inputs and cost functions for mass/energy allocation within the individual as determined by Dynamic Energy Budget models. We show how integration of the three frameworks permits calculation of activity constraints, vital rates (survival, development, growth, reproduction), and ultimately population growth rates and species distributions. When integrated with contemporary niche theory, functional trait niche models hold great promise for tackling major questions in ecology and evolutionary biology.
Accepted version, Appendix
Pesticide use leads to complex exposure and response patterns in non-target aquatic species, so that the analysis of data from standard toxicity tests may result in unrealistic risk forecasts. Developing models that are able to capture such complexity from toxicity test data is thus a crucial issue for pesticide risk assessment. In this study, freshwater snails from two genetically differentiated populations of Lymnaea stagnalis were exposed to repeated acute applications of environmentally realistic concentrations of the herbicide diquat, from the embryo to the adult stage. Hatching rate, embryonic development duration, juvenile mortality, feeding rate, and age at first spawning were investigated during both exposure and recovery periods. Effects of diquat on mortality were analyzed using a threshold hazard model accounting for time-varying herbicide concentrations. All endpoints were significantly impaired at diquat environmental concentrations in both populations. Snail evolutionary history had no significant impact on their sensitivity and responsiveness to diquat, whereas food acted as a modulating factor of toxicant-induced mortality. The time-course of effects were adequately described by the model, which thus appears suitable to analyze long-term effects of complex exposure patterns based upon full life-cycle experiment data. Obtained model outputs (e.g. No Effect Concentrations) could be directly used for chemical risk assessment.
Accepted version, Figures & tables
In this work, we compare multi-limiting nutrients formulations obtained from DEB theory with empirical ones. Data are fitted with these formulations, which validate the DEB one. Then we study the effects of the DEB-based mechanistic approach on population and community dynamics by comparing population models based on different colimited uptake formulations (mechanistic and empirical) fitting the same set of data. By introducing physiological details for the mechanistic description of uptake, we obtain more complex models and we use quasi-steady state assumptions for the enzymatic processes in order to keep a reduced complexity.
A Dynamic Energy Budget (DEB) model for microalgae is proposed. This model deviates from the standard DEB model as it needs more reserves to cope with the variation of assimilation pathways, requiring a different approach to growth based on the synthesizing unit (SU) theory for multiple substrates. It is shown that the model is able to accurately predict experimental data in constant and light-varying conditions with most of the parameter values taken directly from the literature. Also, model simulations are shown to be consistent with stylized facts (SFs) concerning N:C ratio. These SFs are reinterpreted and the general conclusion is that all forcing variables (dilution rate, temperature and irradiance) impose changes in the nitrogen or carbon limitation status of the population, and consequently on reserves densities. Model predictions are also evaluated in comparison with SFs on chlorophyll concentration. It is proposed that an extra structure, more dependent on the nitrogen reserve, is required to accurately model chlorophyll dynamics. Finally, SFs concerning extracellular polymer substances (EPS) production by benthic diatoms are collected and interpreted and a formulation based in product synthesis and rejection flux is proposed for the EPS production rate.
The quick answer to the title question is: by bookkeeping, introduce as p(opulation)-state a measure telling how the individuals are distributed over their common i(ndividual)-state space, and track how the various i-processes change this measure. Unfortunately, this answer leads to a mathematical theory that is technically complicated as well as immature. Alternatively, one may describe a population in terms of the history of the population birth rate together with the history of any environmental variables affecting istate changes, reproduction and survival. Thus a population model leads to delay equations. This delay formulation corresponds to a restriction of the p-dynamics to a forward invariant attracting set, so that no information is lost that is relevant for longterm dynamics. For such equations there exists a well-developed theory. In particular, numerical bifurcation tools work essentially the same as for ordinary differential equations. However, the available tools still need considerable adaptation before they can be practically applied to the DEB model. For the time being we recommend simplifying the i-dynamics before embarking on a systematic mathematical exploration of the associated p-behaviour. The long term aim is to extend the tools, with the DEB model as a relevant goal post.
The interest of environmental management is in long-term health of populations and ecosystems. However, toxicity is usually assessed in short-term experiments with individuals. Modelling based on Dynamic Energy Budget (DEB) theory aids the extraction of mechanistic information from the data, which in turn supports educated extrapolation to the population level. To illustrate the use of DEB models in this extrapolation, we analyse a data set for life-cycle toxicity of copper in the earthworm Dendrobaena octaedra. We compare four approaches for the analysis of the toxicity data: no model, a simple DEB model without reserves and maturation (the Kooijman-Metz formulation), a more complex one with static reserves and simplified maturation (as used in the DEBtox software), and a full-scale DEB model (DEB3) with explicit calculation of reserves and maturation. For the population prediction, we compare two simple demographic approaches (discrete-time matrix model and continuous-time Euler-Lotka equation). In our case, the difference between DEB approaches and population models turned out to be small. However, the differences between DEB models increased when extrapolating to more field-relevant conditions. The DEB3 model allows for a completely consistent assessment of toxic effects, and therefore greater confidence in extrapolating, but poses greater demands on the available data.
Accepted version Figures and tables
Review Only Dynamic Energy Budget (DEB) theory offers a perspective on population ecology whose starting point is energy utilization by, and homeostasis within, individual organisms. It is natural to ask what it adds to the existing large body of individual-based ecological theory. We approach this question pragmatically - through detailed study of the individual physiology and population dynamics of the zooplankter Daphnia and its algal food. Standard DEB theory uses several state variables to characterize the state of an individual organism, thereby making the transition to population dynamics technically challenging, while ecologists demand maximally simple models that can be used in multi-scale modeling. We demonstrate that simpler representations of individual bioenergetics with a single state variable (size), and two life stages (juveniles and adults), contain sufficient detail on mass and energy budgets to yield good fits to data on growth, maturation and reproduction of individual Daphnia in response to food availability. The same simple representations of bioenergetics describe some features of Daphnia mortality, including enhanced mortality at low food that is not explicitly incorporated in the standard DEB model. Size-structured, population models incorporating this additional mortality component resolve some long-standing questions on stability and population cycles in Daphnia. We conclude that a bioenergetic model serving solely as a regression connecting organismal performance to the history of its environment can rest on simpler representations than those of standard DEB. But there are associated costs with such pragmatism, notably loss of connection to theory describing inter-specific variation in physiological rates. The latter is an important issue, as the type of detailed study reported here can only be performed for a handful of species.
Accepted version, supplementary material
Temperature tolerance and sensitivity were examined for some North Atlantic marine species and linked to their energetics in terms of species-specific parameters described by Dynamic Energy Budget (DEB) theory. There was a general lack of basic information on temperature tolerance and sensitivity for many species. Available data indicated that the ranges in tolerable temperatures were positively related to optimal growth temperatures. However, no clear relationships with temperature sensitivity were established and no clear differences between pelagic and demersal species were observed. The analysis was complicated by the fact that for pelagic species, experimental data were completely absent and even for well-studied species, information was incomplete and sometimes contradictory. Nevertheless, differences in life history strategies were clearly reflected in parameter differences between related species. Two approaches were used in the estimation of DEB parameters: one based on the assumption that reserve hardly contributes to physical volume; the other does not make this assumption, but relies on body size scaling relationships, using parameter values of a generalized animal as pseudo-data. Temperature tolerance and sensitivity seemed to be linked with the energetics of a species. In terms of growth, relatively high temperature optima, sensitivity and/or tolerance were related to lower relative assimilation rates as well as lower maintenance costs. Making the step from limited observations to underlying mechanisms is complicated and extrapolations should be carefully interpreted. Special attention should be devoted to the estimation of parameters using body-size scaling relationships predicted by the DEB theory.
Accepted version Figures Tables Appendix
Dynamic Energy Budget (DEB) models for individual growth of cockles (Cerastoderma edule) and mussels (Mytilus edulis) are developed and calibrated by formulating and parameterizing the functional responses using field observations from the Oosterschelde. The resulting model predictions satisfactorily fit the observations. Differences between sites in the calibrated saturation constant may indicate spatial differences in food quality. Though the calibrated scaled functional responses of mussels and cockles are very similar, results do show differences in the contribution of detritus to their food. Furthermore, the functional responses of mussels in the present study are clearly higher than those of mussels in other systems, which may indicate the importance of intra-specific competition.
In this paper we describe a technique to evaluate the evolutionary dynamics of the timing of spawning for iteroparous species. The life cycle of the species consists of three life-stages, embryonic, juvenile and adult whereby the transitions of life-stages (gametogenesis, birth and maturation) occur at species specific sizes. The dynamics of the population is studied in a semi-chemostat environment where the inflowing food concentration is periodic (annual). A Dynamic Energy Budget (DEB) based continuous-time model is used to describe the uptake of the food, storage in reserves and allocation of the energy to growth, maintenance, development (embryo's, juveniles) and reproduction (adults). A discrete event process is used for modelling reproduction. At a fixed spawning date of the year the reproduction buffer is emptied and a new cohort is formed by eggs with a fixed size and energy content. The population consists of cohorts: for each year one consisting of individuals with the same age which die after their last reproduction event. The resulting mathematical model is a finite dimensional set of ordinary differential equations (ode)s with fixed one-year periodic boundary conditions yielding a stroboscopic map. We will study the evolutionary development of the population using the Adaptive Dynamics (AD) approach. The trait is the timing of spawning. Pairwise and Mutual Invasibility Plots are calculated using bifurcation analysis of the stroboscopic map. The evolutionary singular strategy (ESS) value belonging to the evolutionary endpoint for the trait allows for an interpretation of the reproduction strategy of the population. In a case study, parameter values from the literature for the bivalve Macoma balthica are used.