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The covariation method for estimating the parameters of the standard Dynamic Energy Budget (DEB) model provides a single-step method of accessing all the core DEB parameters from commonly available empirical data. In this study, we assess the robustness of this parameter estimation procedure and analyse the role of pseudo-data using elasticity coefficients. In particular, we compare the performance of Maximum Likelihood (ML) vs. Weighted Least Squares (WLS) approaches and find that the two approaches tend to converge in performance as the number of uni-variate data sets increases, but that WLS is more robust when data sets comprise single points (zero-variate data). The efficiency of the approach is shown to be high, and the prior parameter estimates (pseudo-data) have very little influence if the real data contain information about the parameter values. For instance, the effects of the pseudo-value for the allocation fraction κ is reduced when there is information for both growth and reproduction, that for the energy conductance is reduced when information on age at birth and puberty is given, and the effects of the pseudo-value for the maturity maintenance rate coefficient are insignificant. The estimation of some parameters (e.g., the zoom factor and the shape coefficient) requires little information, while that of others (e.g., maturity maintenance rate, puberty threshold and reproduction efficiency) require data at several food levels. The generality of the standard DEB model, in combination with the estimation of all of its parameters, allows comparison of species on the basis of parameter values. We discuss a number of preliminary patterns emerging from the present collection of parameter estimates across a wide variety of taxa. We make the observation that the estimated value of the fraction κ of mobilised reserve that is allocated to soma is far away from the value that maximises reproduction. We recognise this as the reason why two very different parameter sets must exist that fit most data set reasonably well, and give arguments why, in most cases, the set with the large value of κ should be preferred. The continued development of a parameter database through the estimation procedures described here will provide a strong basis for understanding evolutionary patterns in metabolic organisation across the diversity of life. © 2011 Elsevier B.V.

Several epibenthic species aggregate in large numbers in shallow waters during summer, feeding on the available benthic meio- and macrofauna. Whether this concentration leads to periods of food limitation affecting habitat quality for some of these species is not clear at present. In this study we applied the Dynamic Energy Budget (DEB) theory as a framework to analyze growth, in order to investigate the food conditions of the sand goby Pomatoschistus minutus in estuarine and coastal Atlantic waters. Average food conditions over the entire lifespan were determined based on maximum sizes of sand gobies reported in various areas. in addition, seasonal growth trajectories in the field were compared to model simulations with unlimited food conditions. Results showed that growth of sand gobies in the field is at the same level or even above model simulations. Our findings suggest that sand gobies' growth is not food-limited across their distributional range and that growth variability between areas is mainly related to environmental temperature conditions. Limitations of the present approach are discussed.

The Dynamic Energy Budget (DEB) theory for metabolic organisation captures the processes of development, growth, maintenance, reproduction and ageing for any kind of organism throughout its life-cycle. However, the application of DEB theory is challenging because the state variables and parameters are abstract quantities that are not directly observable. We here present a new approach of parameter estimation, the covariation method, that permits all parameters of the standard Dynamic Energy Budget (DEB) model to be estimated from standard empirical datasets. Parameter estimates are based on the simultaneous minimization of a weighted sum of squared deviations between a number of data sets and model predictions or the minimisation of the negative log likelihood function, both in a single-step procedure. The structure of DEB theory permits the unusual situation of using single data-points (such as the maximum reproduction rate), which we call "zero-variate" data, for estimating parameters. We also introduce the concept of "pseudo-data", exploiting the rules for the covariation of parameter values among species that are implied by the standard DEB model. This allows us to introduce the concept of a generalised animal, which has specified parameter values. We here outline the philosophy behind the approach and its technical implementation. In a companion paper, we assess the behaviour of the estimation procedure and present preliminary findings of emerging patterns in parameter values across diverse taxa. © 2011 Elsevier B.V.

An integrated cell-based dynamic mathematical model that take into account the role of the photon absorbing process, the partition of excitation energy, and the photoinactivation and repair of photosynthetic units, under variable light and dissolved inorganic carbon (DIC) availability is proposed. The modeling of the photon energy absorption and the energy dissipation is based on the photoadaptive changes of the underlying mechanisms. The partition of the excitation energy is based on the relative availability of light and DIC to the cell. The modeling of the photoinactivation process is based on the common aspect that it occurs under any light intensity and the modeling of the repair process is based on the evidence that it is controlled by chloroplast and nuclear-encoded enzymes. The present model links the absorption of photons and the partitioning of excitation energy to the linear electron flow and other quenchers with chlorophyll fluorescence emission parameters, and the number of the functional photosynthetic units with the photosynthetic oxygen production rate. The energy allocation to the LEF increases as DIC availability increases and/or light intensity decreases. The rate of rejected energy increases with light intensity and with DIC availability. The resulting rate coefficient of photoinactivation increases as light intensity and/or as DIC concentration increases. We test the model against chlorophyll fluorescence induction and photosynthetic oxygen production rate measurements, obtained from cultures of the unicellular green alga Scenedesmus obliquus, and find a very close quantitative and qualitative correspondence between predictions and data.

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.

We compare the implications of determinate vs. indeterminate growth of a parthenogenetic iteroparous ectotherm at constant food density in the context of the dynamic energy budget theory, which specifies the tight links between life history traits, such as feeding, aging, growth and reproduction. We do a comparative analysis using, as measure of fitness, the life span reproduction, the population growth rate, and the conversion efficiency of food to biomass. When extrinsic mortality is constant, indeterminate growth cannot maximize fitness if measured by the population growth rate or the conversion efficiency, except when mortality is low, in which case both types of animals are similar. If the fitness measure is life span reproduction, indeterminate growth maximizes fitness even with constant mortality, provided it is not very high. When mortality decreases with size, indeterminate growth maximizes fitness for almost all measures of fitness. Finally, we suggest an evolutionary link between allocation strategies and expected life span. In populations of long living species, each type of animal can establish in the population of the other. In populations of short living species, determinate growers can invade, and displace, a population of indeterminate ones. However, when the mortality risk of organisms with small size is much higher than those of large size, indeterminate growers can be superior. © 2003 Society for Mathematical Biology. Published by Elsevier Ltd. All rights reserved.

The importance of linear models in the study of the dynamics of structured populations is great. Yet, probably only a few population phenomena can be assumed to be linear. Nonlinearity arises whenever interaction is incorporated into mathematical models, as for density dependence, predator-prey relationships, competition, external forcing, and spatial effects.

The framework provided by the Dynamic Energy Budget (DEB) theory allows the quantification of metabolic processes and the associated biological rates that are of interest for aquaculture, such as growth and feeding. The DEB parameters were estimated for farmed European sea bass (Dicentrarchus labrax), a species of major importance for the Mediterranean aquaculture, using zero- and uni-variate literature data and achieving an overall good fit. The obtained parameter set was used to validate the model on sites representatively covering the geographic distribution of the aquaculture activity in Greece via comparison of model predictions to observations. Inter-individual variability of farmed fish was introduced through: 1) an individual initial weight and 2) a factor that acts as an individual-specific multiplier for some of the model parameters and produces scatter in maximum size, and age and size at puberty. Growth of E. sea bass was adequately predicted by the model while feeding tended to be underestimated, particularly during the period following the summer months when warmer temperatures promote high growth rates. The results suggest robustness of the model since it is able to simulate growth and food intake in several independent aquaculture production units, using a common parameter set. The accuracy of growth predictions supports the applicability of the model in variable environmental conditions in the context of climate change. Reconstruction of the feeding history from growth data revealed variations in the scaled functional response (f), i.e., the feeding rate as fraction of maximum possible one of an individual of a given size, throughout the production cycle. However, model simulations with constant f result in reasonably good predictions for growth and feeding in variable environmental conditions. Tendency of the model to underestimate the feeding process revealed both model weaknesses associated with higher temperatures as well as irregularities in the feeding protocols applied at the farm level. Our work demonstrates the capacity and potential of DEB theory for further development of tools that contribute to the assessment and improvement of feeding practices in aquaculture.

We have developed a mathematical model based on the underlying mechanisms concerning the responses of the photosynthetic apparatus of a microalga cell which grows under constant incident light intensity and ambient CO 2 concentration. Photosynthesis involves light and carbon-fixation reactions which are mutually dependent and affect each other, but existing models for photosynthesis don't account for both reactions at once. Our modeling approach allows us to derive distinct equations for the rates of oxygen production, NADPH production, carbon dioxide fixation, carbohydrate production, and rejected energy, which are generally different. The production rates of the photosynthesis products are hyperbolic functions of light and CO 2 concentration. The model predicts that in the absence of photoinhibition, CO 2 -inhibition, photorespiration, and chlororespiration, a cell acclimated to high light and/or CO 2 concentration has higher photosynthetic capacity and lower photosynthetic efficiency than does a cell acclimated to low conditions. This results in crossing between the two curves which represent the oxygen production rates and carbon fixation rates in low and high conditions. Finally, in the absence of photoinhibition and CO 2 -inhibition, the model predicts the carbohydrate production rate in terms of both light intensity and CO 2 concentration.

Climate change constitutes an increasing concern for aquaculture. The uncertainty surrounding the future implications of this phenomenon coupled with the financial importance of the sector necessitate the development of appropriate frameworks and tools that can support management decisions and ensure the sustainability of future aquaculture production. Facilitated by emerging information technologies, decision support systems (DSSs) are becoming increasingly popular in sectors of primary production and deal with various aspects of decision-making from the operational to the strategic level. In this paper we present ongoing work, in the frame of the EU-ClimeFish Project, towards the development of a computer-based DSS that simulates and visualises the impacts of different climate change scenarios on Greek aquaculture, including economic impacts. The description contains details on the structure, constituent models, and current status of implementation of the DSS. The applicability of the generated tool in decision-making is discussed and planning for further development is outlined.